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On the characterization of subpixel effects for passive microwave remote sensing of snow in montane environments

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On the characterization of subpixel effects for passive microwave
remote sensing of snow in montane environments
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy
in the Graduate School of The Ohio State University
By
Benjamin John Vander Jagt, M.S.
Graduate Program in Geodetic Science
The Ohio State University
2015
Dissertation Committee:
Dr. Michael Durand, Advisor
Dr. Douglas Alsdorf
Dr. Ian Howat
ProQuest Number: 10146165
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Copyright by
Benjamin Vander Jagt
2015
Abstract
Snow and its water equivalent plays a vital role in global water and energy balances, with
particular relevance in mountainous areas with arid and semi-arid climate regimes.
Spaceborne passive microwave (PM) remote sensing measurements are attractive for
snowpack characterization due to their continuous global coverage and historical record;
over 30 years of research has been invested in the development of methods to
characterize large-scale snow water resources from PM-based measurements.
Historically, use of PM data for snowpack characterization in montane enviroments has
been obstructed by the complex subpixel variability of snow properties within the PM
measurement footprint. The main subpixel effects can be grouped as: the effect of snow
microstructure (e.g. snow grain size) and stratigraphy on snow microwave emission,
vegetation attenuation of PM measurements, and the sensitivity PM brightness
temperature (Tb) observation to the variability of different subpixel properties at
spaceborne measurement scales. This dissertation is focused on a systematic examination
of these issues, which thus far have prevented the widespread integration of snow water
equivalent (SWE) retrieval methods. It is meant to further our comprehension of the
underlying processes at work in these rugged, remote, a hydrologically important areas.
The role that snow microstructure plays in the PM retrievals of SWE is examined first.
Traditional estimates of grain size are subjective and prone to error. Objective techniques
ii
to characterize grain size are described and implemented, including near infrared (NIR),
stereology, and autocorrelation based approaches. Results from an intensive Colorado
field study in which independent estimates of grain size and their modeled brightness
temperature (Tb) emission are evaluated against PM Tb observations are included. The
coarse resolution of the passive microwave measurements provides additional challenges
when trying to resolve snow states via remote sensing observations.
The natural
heterogeneity of snowpack (e.g. depth, stratigraphy, etc) and vegetative states within the
PM footprint occurs at spatial scales smaller than PM observation scales. The sensitivity
to changes in snow depth given sub-pixel variability in snow and vegetation is explored
and quantified using the comprehensive dataset acquired during the Cold Land Processes
experiment (CLPX). Lastly, vegetation has long been an obstacle in efforts to derive
snow depth and mass estimates from passive microwave (PM) measurements of
brightness temperature (Tb). We introduce a vegetation transmissivity model that is
derived entirely from multi-scale and multi-temporal PM Tb observations and a globally
available vegetation dataset, specifically the Leaf Area Index (LAI).
This newly
constructed model characterizes the attenuation of PM Tb observations at frequencies
typically employed for snow retrieval algorithms, as a function of LAI. Additionally, the
model is used to predict how much SWE is observable within the major river basins of
Colorado and the central Rockies.
iii
Dedication
I dedicate this to my father, who despite being pessimistic from time to time, taught me to
think critically about the world and to pursue Truth.
iv
Acknowledgements
First and foremost, I want to thank my advisor, Michael Durand. Without his guidance,
support, and patience, none of this would be possible. After enrolling at OSU, I quickly
realized how fortunate I was to have a mentor that took such a strong interest in the
personal, academic, and professional development of his students. I hope that I, in some
way, met expectations.
I want to thank my support system, in particular my family and close friends, for
providing support when it was needed most. Aditi, Mom, Dad, Jennie, Maria, Joe, Gabe,
Jacob, Omar, Dongyue, Siavash, Melissa, Jinmei, Megan, et al., thank you for enduring
daily conversations and feigning interest, even if you didn’t want to hear about snow or
fishing maps.
This research was generously supported by a NASA Earth and Space Science Fellowship
(NESSF). Additionally, further financial support was provided through The Ohio State
Universities Presidential Fellowship.
v
Vita
Sep. 2005 – June 2008 ............ B.S. Surveying Engineering, Ferris State University, Big
Rapids, MI.
Nov. 2006……………….…...Pipeline Surveying Technician, Holland Engineering
June 2005 – Aug 2008 ............ Internship at Michigan Department of Transportation,
Grand Rapids, MI
Aug. 2009 – Aug 2010 ............ M.S. Geomatics Engineering, Purdue University, West
Lafayette, Indiana
Aug. 2009 – May 2010 ........... Graduate Teaching Assistant, Purdue University, West
Lafayette, Indiana
Sept. 2010 – Aug. 2015........... Graduate Research Associate, The Ohio State University,
Columbus, Ohio
Nov. 2012…………………….NASA Earth and Space Science Fellowship
May. 2013…………………… Netjets Innovation Grant
Dec. 2013…………………… AGU Student Paper Award
Nov. 2012…………………… AAGS Graduate Student Award
Nov. 2013……………………. OSU Presidential Fellowship Award
Dec. 2014…………………… ASPRS Paul Wolf Memorial Scholarship
Dec. 2014…………………… ASPRS William Fischer Memorial Scholarship
vi
Sept. 2015 – Present................ Graduate Teaching Assistant, The Ohio State University,
Columbus, Ohio
Publications
Vander Jagt, B. J., Durand, M. T., Margulis, S. A., Kim, E. J., & Molotch, N. P. (2013).
The effect of spatial variability on the sensitivity of passive microwave measurements to
snow water equivalent. Remote Sensing of Environment, 136, 163-179.
Vander Jagt, B. J., Durand, M. T., Margulis, S. A., Kim, E. J., & Molotch, N. P. (2015).
On the characterization of vegetation transmissivity using LAI for application in passive
microwave remote sensing of snowpack. Remote Sensing of Environment, 156, 310-321.
Vander Jagt, B. J., Lucieer, A., Wallace, L., Turner, D., & Durand, M. (2015). Snow
depth retrieval with UAS using photogrammetric techniques. Geosciences, 5(3), 264-285.
Ostrowski, S., Jóźków, G., Toth, C., & Vander Jagt, B. (2014). Analysis of Point Cloud
Generation from UAS Images. ISPRS Annals of Photogrammetry, Remote Sensing and
Spatial Information Sciences, 1, 45-51.
Fields of Study
Major Field: – Geodetic Science
vii
Table of Contents
Abstract ............................................................................................................................... ii Dedication .......................................................................................................................... iv Acknowledgements ............................................................................................................. v Vita..................................................................................................................................... vi Acronyms List................................................................................................................... xii List of Tables ................................................................................................................... xiv List of Figures ................................................................................................................... xv Chapter 1 Introduction ........................................................................................................ 1 1.1 Motivation ................................................................................................................. 1 1.2 Introduction to Passive Microwave Remote Sensing ................................................ 7 1.2.1 Principles of PM Tb measurements .................................................................... 7 1.2.2 Microstructural and snow emission principles (Tbss) ....................................... 12 1.2.3 Effects of Spatial Resolution (Tbsv).................................................................. 16 1.2.4 The Effect of Vegetation (Tbv and tv) ............................................................... 18 1.3 Significance and Organization of the Dissertation .................................................. 19 Chapter 2 Microstructure Characterization ....................................................................... 21 viii
2.1 Overview ................................................................................................................. 21 2.2 Microwave Emission Model for Layered Snowpack (MEMLS) ............................ 24 2.2.1 Microwave Emission Model for Layered Snowpack (MEMLS) ..................... 24 2.3 Snow Microstructure ............................................................................................... 25 2.4 Data and Methods.................................................................................................... 26 2.4.1 Radiometer Data ............................................................................................... 26 2.4.2 Snowpit Data .................................................................................................... 28 2.4.3 Stereology and Analysis of Snow Samples ...................................................... 29 2.4.4 Near Infrared Camera Data............................................................................... 31 2.5 MEMLS Model and Simulations ............................................................................ 33 2.6 Discussion and Conclusion ..................................................................................... 35 Chapter 3 The Effect of Scale and Spatial Resolution ...................................................... 37 3.1 Overview ................................................................................................................. 37 3.2 Study Area and Data ............................................................................................... 38 3.3 Methods and Models ............................................................................................... 47 3.3.1 Snow Radiative Transfer Model ....................................................................... 47 3.3.2 Vegetation Model ............................................................................................. 52 3.3.3 Measurement Scale Modeling .......................................................................... 56 3.4 Results ..................................................................................................................... 59 ix
3.4.1 Simulated Tb vs True Tb ................................................................................... 59 3.4.2 Effects of Heterogeneous Snow Properties ...................................................... 62 3.4.3 Vegetation Effects ............................................................................................ 66 3.4.4 Effects of Measurement Scale .......................................................................... 71 3.5 Discussion ............................................................................................................... 73 3.5.1 The non-unique nature of the depth and Tb relationship .................................. 75 3.5.2 Uncertainty propogation in snow depth estimates ............................................ 76 3.6 Conclusions and Future Work ................................................................................. 78 Chapter 4 Macroscale Vegetation Effects......................................................................... 81 4.1 Background ............................................................................................................. 82 4.2 Data and Methods.................................................................................................... 85 4.2.1 NASA CLPX .................................................................................................... 85 4.2.2 Remotely Sensed Vegetation Indices ............................................................... 90 4.2.3 SNODAS SWE ................................................................................................. 95 4.2.4 Transmissivity Estimation ................................................................................ 95 4.3 Results and Discussion .......................................................................................... 100 4.3.1 Estimation of transmissivity from brightness temperature variability ........... 100 4.3.2 Mapping passive microwave-retrievable SWE .............................................. 104 4.4 Discussion and Conclusion ................................................................................... 110 x
4.4.1 Discussion....................................................................................................... 110 4.4.2 Conclusion ...................................................................................................... 115 Chapter 5 Conclusion...................................................................................................... 117 5.1 Research Findings and Contribution ..................................................................... 117 5.1.1 Microstructure Characterization ..................................................................... 117 5.1.2 Scaling Issues (PM) ........................................................................................ 118 5.1.3 Vegetation Contributions................................................................................ 120 References ....................................................................................................................... 122
Appendix A: Estimating Spatially Continous Snow Properties ..................................... 139 xi
Acronyms List
LiDAR – Light Detection And Ranging
PM – Passive Microwave
NIR – Near Infrared
CLPX – Cold Land Processes Experiment
AMSR-E – Advance Microwave Scanner Radiometer Experiment
PSR – Polarametric Scanning Radiometer
RS – Remote Sensing
NASA – National Aeronautic and Space Association
RMSE – Root Mean Square Error
S– Specific Surface Area
MEMLS – Microwave Emission Model for Layered Snowpack
MODIS – Moderate Resolution Imaging Spectroradiometer
NASA – National Aeronautics and Space Administration
NSIDC – National Snow and Ice Data Center
RTM – Radiative Transfer Model
SNOTEL – Snowpack Telemetry
SWE- Snow Water Equivalent
xii
Tb – Brightness Temperature
Vis – Visible
xiii
List of Tables
Table 1: Ground resolution of Advanced Microwave Scanning Radiometer (AMSR) at
different measurement frequencies. .................................................................................. 10 Table 2: Predicted vs observed Tb using different drivers of Le for MEMLS .................. 33 Table 3: Sensitivity reduction attributable to vegetation within each of the four different
ISAs. ................................................................................................................................. 69 Table 4: Total range of signal is shown at four different intensive study areas, as a
function of snow, and as a function of a mixed pixel scene. ............................................ 70 Table 5: Major river basins of Colorado, with percentages of area accessible to PM
remote sensing techniques (according to LAI), and the associated retrievable SWE (from
SNODAS) at both airborne (AB) and spaceborne (SB) measurement scales. ............... 110 xiv
List of Figures
Figure 1: Map of snow-dominated regions of the world (Barrett et al., 2005). Blue
regions in the map represent snow (and melt runoff) dominated climate regimes. ............ 1 Figure 2: Inverse relationship between SWE accumulation and Tb over a winter season. . 3 Figure 3: Geometry of a conical scanning spaceborne passive microwave radiometer. .... 9 Figure 4: Within the IFOV of a PM observation, there is multiple contributions to the
observed Tb. The contributions can be characterized using Equation 4. ......................... 11 Figure 5: Physical basis for PM remote sensing. As the snow depth increases, the
scattering of radiance at PM wavelengths also increases, leading to lower Tb observations.
Figure used with permission from NCAR. ....................................................................... 13 Figure 6: Snow casts being utilized for stereology purposes. Intersections of the cycloids
(red) across the air/snow interface are counted and related to the specific surface area (S).
........................................................................................................................................... 15 Figure 7: Underestimation of SWE due to forest cover. The error bars denote uncertainty
of the underestimation (a). The forest factor F as a function of fractional forest cover.
Figure used with with permission from Foster et al., 2005 .............................................. 18 xv
Figure 8: Two views of the radiometer and its field of view, at Stormpeak Laboratory in
Steamboat Springs, Colorado, USA. The red oval in the photo on the left indicates the
approximate location of the radiometer footprint. ............................................................ 27 Figure 9: Photographs of snow samples from February 22 (left); top left is layer 1, top
right is layer 2, bottom left is layer 3, and bottom right is layer 4. Stratigraphy (right),
geometric grain size, and morphological classification according to Fierz et al. [2009] for
the snowpits on 22 February (left) .................................................................................... 30 Figure 10: For sample 2, image 6 of the February 22 snowpit, the cycloid test grid used to
estimate S is shown overlaid (left), and a binary representation of the photo(right). Black
in the photograph and in the classified image indicates ice, whereas gray and white
indicate pore space (see text). The arrow indicates the “up” direction, and the length of
the vertical bar is 1.0 mm. ................................................................................................. 31 Figure 11: A processed NIR image to obtain S (right). The variation in stratigraphy is
easily visible. Units are in mm. ......................................................................................... 32 Figure 12: Predicted vs observed Tb using different drivers of Le for MEMLS. Red bars
indicate Tb observations and the estimated precision. Blue corresponds to hand lens,
black to NIR, and cyan to stereology measurements. Crosses indicate β B , while triangles
represent β M . .................................................................................................................... 34 Figure 13: The three mesocell study areas: Fraser, Rabbit Ears and North Park (from
south to north), with nested intensive study areas (marked with x) within each MSA.
Study areas are shown in relation to their elevations in meters above mean sea level. All
study areas were located in North/Central Colorado (inset). ............................................ 39 xvi
Figure 14: In a) the numbered CLPX snow pit sampling protocol is shown within the
Fraser Alpine ISA. In b), the snowpit (red), depth transect (blue), and PSR microwave
data footprints (cyan) are draped over a LiDAR generated elevation model of the area. 41 Figure 15: Scatter plot of observed snow depth vs SWE for all 191 snow pit
measurements from the CLPX IOP3 observation period. ................................................ 43 Figure 16: The layering structure and the prevailing exponential correlation lengths
(pex)of each layer (function of grain size) are shown the 16 different pits in the Fraser
Alpine ISA. ....................................................................................................................... 46 Figure 17: Figures (a) and (b) show an original and augmented depth (0.5) at Fraser
Alpine ISA. The scale factor is applied to the stratigraphy only, the properties of the
snow, such as grain size, density, etc , remain the same, as shown in (c). ....................... 51 Figure 18: Fraser Alpine (ISA) orthophoto (top left). Conversion of orthoimage of Fraser
Alpine ISA to binary format for vegetation classification purposes (top middle) and
spatially continuous snowpack depth as estimated by McCreight (2010) (top right) .
Fraser Fool Creek (middle) and Rabbit Ears Buffalo Pass (bottom) ISAs are also
included. Snow depths are in meters................................................................................. 54 Figure 19: Illustration of FWHM sampling method utilized in order to study the effects of
scale on the microwave measurement at 100, 400, and 1000 meter resolution. The
dimensions of each square is 1km2. The different color (red to blue) represents the signal
power of the simulated Tb observation through Gaussian Inverse Distance Weighting. .. 57 Figure 20: Observed and estimated PSR radiance data from Fraser Alpine (a), Fraser Fool
Creek (b) , Rabbit Ears Buffalo Pass (c), and Rabbit Ears Spring Creek (d) ISAs. The red
xvii
line is the median of the dataset, whereas the whiskers extend to minimum and maximum
data points not considered outliers (no outliers were present). ......................................... 60 Figure 21: Observed(left) and estimated(right) PSR Tb data from Fraser Alpine as a
function of measured depth (top), the associated histograms of both(middle), and the
cumulative distribution function (bottom). ....................................................................... 61 Figure 22: Typical Voronoi diagram, where individual pixels are classisfied by distance
to nearest snow pit (a), where the different colors represent the different snowpits. A
multinomial distribution is used to map individual pixels to adjacent snow pits in a
probabilistic manner, where the probilities are a function of the spatial distance between
pixel and snowpit (b). The brightness temperature scene was then simulated as a function
of snow properties only (c) and vegetation contributions (d). In the figures above, the
modeled site is Fraser Alpine. Brightness temperatures are in kelvins. ........................... 63 Figure 23: The sensitivity of modeled PM observations to mean subpixel depth, in spite
of heterogeneous snow properties taken from different ISAs. Fraser Alpine and Fool
Creek ISAs are shown in (a) and (b), while Rabbit Ears Buffalo Pass and Spring Creek
are shown in (c) and (d), respectively. .............................................................................. 65 Figure 24: Spatial comparison of observed PSR Tb (a), to the spatially continous modeled
Tb field (b), in kelvins. While we can model the spatially continuous Tb from depth and
snow pit measurements, we only have discrete measurements of PSR Tb. Note the
anomolous cold PSR Tb observations over the forested component of Fraser alpine (top
left in figure 10a). This artifact decreases our confidence in the geolocation procedures
used for the PSR dataset. .................................................................................................. 67 xviii
Figure 25: Estimated radiances (a) for different snow pits taken from Fraser Fool Creek
ISA, shown in blue. Vegetation is then added to the “scene”, with a transmissivity
estimate of 0.55. Radiances with vegetation shown in green. For comparison (b), the
mean and standard deviation of observed PSR Tb over snow covered areas in all the
MSA’s was plotted against
averaged winter NDVI values obtained from MODIS
imagery. As the vegetation (NDVI) values increase, the signal attributable to snow is lost.
........................................................................................................................................... 68 Figure 26: Sensitivity of the observations at different scales as a function of mean snow
depth (assuming no vegetation) at four different ISA’s (Fraser Alpine (a), and Fraser
Fool Creek (b), Rabbit Ears Buffalo Pass (b), Rabbit Ears Spring Creek (d), respectively.
........................................................................................................................................... 72 Figure 27: Uncertainty modeling as a function of snow depth (cm) using snow properties
from six different snow pits (a). Blue corresponds to modeled snow scene, while green
corresponds to the same modeled scenes with vegetation imposed. The red “x” is the
mean of the modeled snow uncertainties. In (b), the mean uncertainties are shown with a
bar graph for better visualization. ..................................................................................... 77 Figure 28: Digital elevation model (DEM) of the study area (with inset of the continental
USA) showing flight tracks where the PSR airborne dataset was collected (black lines) as
part of CLPX. The AMSR-E data was collected over the entire study area. Elevations are
in meters. ........................................................................................................................... 86 Figure 29: Example of the characteristic sampling pattern of the PSR dataset as collected
during the CLPX (here shown over the Rabbit Ears MSA), draped over a DEM, with
xix
elevations in meters (top). The sampling density within each 500 meter pixel varied
spatially, as seen in (bottom). Plots are shown to scale. ................................................... 88 Figure 30: Monthly variability in the LAI within the CLPX LRSA (2002-2003) during
the winter months (top). LAI values over the LRSA for seven days from the month of
January (bottom). .............................................................................................................. 92 Figure 31: Visible images corresponding to the following different LAI values, 0, 2, 4,
and 6 (clockwise from top left). The locations of each image are shown in the bottom
figure. ................................................................................................................................ 94 Figure 32: The variability in observed Tb () for one grid cell is calculated based on the
temporal variation over the winter season for spaceborne AMSR-E data, whereas for
airborne PSR measurements, we use subgrid spatial variation due to the lack of temporal
sampling. ........................................................................................................................... 97 Figure 33: The green line and the blue lines correspond to the mean, minimum and
maximum observed air temperature from the 9 meteorological sites respectively, from a
subset of the Nov 2002-March 2003 dataset..................................................................... 98 Figure 34: Variance of Tb with respect to LAI (a). The spaceborne AMSR-E Tb data is
shown in blue, as compared to the airborne PSR (red).
The empirically derived
transmissivity from PSR (red) and AMSR-E (blue) were fit to an exponential curve for
model generation, using non-linear least squares (b). The X’s denote the LAI cutoff
values for the different measurement scales. .................................................................. 101 Figure 35: Scatter plot of the observed Tb variability from 2004 and 2005 as compared to
LAI (a). The transmissivity derived from the 2004 and 2005 AMSR-E data (y-axis), as
xx
compared to the predicted transmissivity from the exponential model(x-axis), with an R2
value of 0.85 (b). ............................................................................................................. 104 Figure 36: The retrievable land area for both airborne (a) and spaceborne (b) PM remote
sensing. The blue pixels correspond to optimal areas for PM SWE retrieval, whereas red
is suboptimal (due to vegetation coverage). The bottom figure has been gridded to the
approximate spatial resolution of AMSR-E measurements. The horizontal line in the top
figure corresponds to MODIS LAI tile boundaries. ....................................................... 105 Figure 37: Upper Colorado river basin delineated into optimal (blue) and suboptimal
(red) bins based on the MODIS LAI , at airborne resolution (a). The corresponding basin
SWE, as obtained from SNODAS, is shown as well (b), with units in mm. .................. 107 Figure 38: Major river basins of Colorado with elevation in meters(a), with percentages
of SWE (from SNODAS) accessible to PM remote sensing techniques at airborne (cyan)
and spaceborne (black) resolutions(b). River basins are the Yampa, upper Colorado,
upper Gunnison, Arkansas, North Platte, and Delores, respectively (from left). ........... 109 Figure 39: By varying the LAI cutoff threshold which defines adequate variability in the
PM Tb signal (a) for SWE retrieval, we can estimate the total percentage of SWE that is
retrievable over our study area(b), as a function of changing LAI. ................................ 113 xxi
Chapter 1 Introduction
1.1 Motivation
A large percentage of the total water supply in many areas of the world comes
from snowmelt, rather than rainfall (Barnett et al., 2005), as shown in Figure 1. Snow
represents an important hydrologic reservoir, storing water during winter months through
snow accumulation and releasing it in the spring and summer months via snowmelt when
water resources are often needed most. One need look no further than the 2015 drought
crisis in California(Stevens, 2015) to understand how significant the contribution of snow
is to water resource issues.
Figure 1: Map of snow-dominated regions of the world (Barrett et al., 2005). Blue regions in the
map represent snow (and melt runoff) dominated climate regimes.
1
Snowmelt runoff is used for crop irrigation, industrial and manufacturing
processes, municipal water supply, and recreational purposes. Additionally, snowmelt has
been found to impact carbon uptake from vegetated areas, thus playing a role in climate
variability (Hu et al., 2010). Being able to provide accurate and reliable estimates of
snow and its water equivalent (SWE) is attractive for hydrologic modeling, flood
prediction, and risk mitigation.
Efforts to measure snow depth and water equivalent have an extensive historical
record starting with in situ methods (e.g. Peck, 1972; Hall et al., 1991). In situ sampling
methods such as snow courses, snow pillows, and snow pits, while accurate, often only
provide point estimates of a spatially varying quantity. Spatial interpolation of in situ
measurements has been investigated; however even the most accurate methods (e.g.,
kriging) only explain 30 percent of the overall variability in snow depth (Erxleben et al.,
2002). Additionally, in situ methods are subject to logistical and safety restrictions that
limit when and where measurements can be made, especially in mountainous areas which
are often characterized by high snowfall. Because of these limitations, there exists a need
for observations of snow properties with improved spatial coverage and reduced
personnel risk as compared to existing conventional methods.
Remote sensing provides a means by which measurements can be made in a
temporal and spatially distributed manner, while at the same time minimizing the risk
associated with traditional in-situ based methods. Measurements of the Earth surface in
the microwave spectral regions can be largely insensitive to weather conditions and solar
2
illumination. Passive microwave (PM) measurements are sensitive to the presence and
quantity of snow, a fact that has long been used to monitor snowcover from space (e.g.
Chang et al.,1976; Choudhury et al., 1995; Pulliainen et al., 2006). These properties make
satellite-based microwave remote sensing attractive for providing spatially distributed
information about snow properties at a global scale. More than thirty years of research
has now been invested in the development of methods to characterize large-scale snow
water resources from spaceborne platforms utilizing passive microwave (PM)
measurements.
Evidence exists to show that PM measurements contain significant
information about snow accumulation even in mountainous areas (e.g., Rango et al.,
1989; Durand & Margulis, 2007; Li et al., 2012), as shown in Figure 2.
Figure 2: Inverse relationship between SWE accumulation and Tb over a winter season.
3
In recent years, advances have been made in understanding how the snowpack,
terrain, vegetation and other components of mountain environments contribute to passive
microwave measurements of snow-covered landscapes (Wiesmann and Mätzler, 1999;
Tsang et al., 2000; Durand et al., 2008; Durand et al., 2011; Langlois et al., 2011).
Several factors have impeded widespread use of PM measurements to accurately
characterize snow depth (SD) and SWE in heterogeneous environments, such as
mountainous areas, where there is substantial snow accumulation over the winter season.
Because microwave wavelengths (3 mm – 40 mm) are of the same order of snow grains
(generally 0.1 mm – 5 mm), microwave emission of snowpack is sensitive to grain size
(e.g., Tsang et al., 2000). Due to this, there is a many-to-one relationship between snow
depth and grain size; i.e, different vertical profiles of grain size, depth, and temperature
can yield the same observed Tb. Other sub pixel effects such as forest cover, topography,
and the liquid water are all known to affect the PM signal (Davis et al., 1987; Hall et al.,
1986; McDonald and Ulaby, 1993; Josberger et al., 1996, Kim, 1999; Rosenfeld and
Grody, 2000). Improving the accuracy of such retrievals has been a goal for decades (e.g.
Chang et al.,1976; Goodison & Walker 1994; Choudhury et al., 1995; Kelly et al., 2003;
Durand & Margulis, 2007).
Further understanding of these processes is a critical step
towards improved snow water resources monitoring and management via spaceborne PM
Tb observations.
This dissertation is motivated by three main problems that exist in the state of the
art of PM remote sensing for snow properties in mountain environments. 1) Objectively
4
characterizing a microstructural grain size using multiple measurement methods in order
to improve forward modeling practices 2) Conducting detailed analyses of the scale
dependencies between remotely sensed and ground based observations of snowpack
properties to understand observing capabilities for estimating the spatial distribution of
snow accumulation. 3) Understanding and quantifying the role of vegetation with respect
to PM remote sensing of snow properties.
The organization of the dissertation is as follows. In Chapter 1, an overview of the
history of passive microwave remote sensing techniques and the relationship between
snow properties and observed Tb is presented. A short background on the factors which
currently impede snow property characterization from passive microwave observations is
presented, including microstructural characterization of snow grain size, the impact of
measurement scale on the ability to invert PM Tb observations for accurate
characterization of SWE (and other snow properties), and the contribution of vegetation
to the passive microwave observation.
In Chapter 2, multiple microstructural characterization techniques are presented
and validated against each other using ground-based PM Tb observations. In order to
optimally utilize spaceborne passive microwave (PM) measurements for snowpack
characterization, it is requisite to model microwave emission, which is highly sensitive to
snow microstructure. Snow microstructure is often characterized by its grain size.
Utilizing in-situ measurements of snowpack properties and a forward microwave
modeling framework, predicted Tb is compared against observed Tb to determine the
efficacy of the different methods for characterizing microstructure utilizing the
5
microwave emission model of layered snowpacks (MEMLS), a commonly used RTM for
layered snowpack.
In Chapter 3, the effect of spatial resolution is examined. The purpose of the
analysis is to estimate the sensitivity of the microwave brightness to variability of in situ
measurements, as a function of the scale of the footprint. By investigating how this
sensitivity is affected by perturbing sub-pixel inputs to the radiative transfer model
(RTM) at a variety of spatial scales, we hope to gain insight about how sub-pixel
quantities affect the information about SWE as a function of scale. From this analysis, the
most important information that we hope to gather will be the way that variability
amongst subpixel snow and vegetation properties aggregate to spaceborne measurement
scales, and whether or not passive microwave Tb observations are sensitive to
perturbations in depth (and SWE). The current analysis differs from previous analyses of
in situ and PM measurements in that we focus on sub-pixel effects and how they change
across spatial scales of the PM measurements. The Cold Land Processes (CLPX) dataset
provides us with the ability to make comparison across scales, and examine how
relationships change with respect to input variables.
In Chapter 4, a systematic and applied characterization of vegetative contributions
to PM observations is made. Vegetation has long been an obstacle in efforts to derive
snow depth and mass estimates from passive microwave (PM) measurements of
brightness temperature (Tb). Though certain metrics have been derived in an effort to
characterize the effects of vegetation, some are restricted to certain vegetation types,
while others are difficult to measure over the large scales at which spaceborne PM
6
measurements are made. PM measurements at multiple observation scales in Colorado
and Wyoming were examined and it was found that spatial variations of airborne Tb data
and temporal variation of spaceborne Tb data are both highly correlated with a globally
available remotely-sensed vegetation dataset, specifically the Leaf Area Index (LAI)
derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor. The
effective vegetation transmissivity, a physical variable used in existing simple radiative
transfer models, is derived from a conservative assumption based on the variability in the
measured Tb. The transmissivity estimates are validated over multiple snow seasons, and
geographic domains.
Chapter 5 concludes with additional discussion related to the research process,
findings, and conclusion, in addition to a summary of the work performed.
1.2 Introduction to Passive Microwave Remote Sensing
1.2.1 Principles of PM Tb measurements
Passive microwave remote sensing typically involves measuring thermally
generated radiation in the microwave region of the electromagnetic spectrum (Rees,
2001). Radiation observed by the instruments antenna is converted to brightness
temperature (Tb). Tb of an object is the absolute blackbody’s temperature at which the
absolute blackbody has the same spectral radiant intensity with that object at the
wavelength under consideration. Tb is a function of the temperature of the object, and the
wavelength (or frequency) of interest. The exact mathematical form is given below
(Rees, 2001).
7
Tb =
hc
1 λhckT
λ k ln(1+ (e − 1))
εs
(1.1)
Where ε s is the emissivity, λ is the wavelength, and T is the temperature of the object.
The remaining variables are known constants that correspond to the speed of light (c =
299792458 m/s), the Planck constant (h = 6.62607004 × 10-34 m2 kg / s), and lastly
Boltzmann’s constant (k = 1.38064852 × 10-23 m2 kg s-2 K-1).
At microwave
wavelengths, the Rayleigh Jeans approximation holds, which simplifies (1) to the
following form, where
Lλ is the spectral radiance
λ4
Tb =
Lλ
2kc
(1.2)
The instrument responsible for producing measurements of Tb is a radiometer.
Passive microwave radiometers measure spectral radiance ( Lλ ) which is converted to Tb
through (2) above. In most airborne and spaceborne applications, a scanning microwave
radiometer is employed in which the mechanical rotation of a mirror focuses energy onto
the radiometer antenna. One particularly common form of mechanical scanning is the
conical scan, in which the antenna beam is rotated around the nadir direction at a fixed
angle with respect to the nadir direction (Rees, 2001). This allows for much greater
spatial coverage, as shown below in Figure 3. In all systems the size of the antenna is
constrained by the practical limitations on size and weight whilst maintaining sufficient
sensitivity (Woodhouse, 2006).
8
Figure 3: Geometry of a conical scanning spaceborne passive microwave radiometer.
The measurement footprint, also known as the instantaneous field of view (IFOV)
of the microwave antenna is governed by the effective area of the antenna and the
wavelength of the observation ( λ ), as shown below in (3).
Ω A Ae = λ 2
(1.3)
Where Ω A is the beam solid angle, Ae is the effective area of the antenna, and λ is
wavelength. An antenna with a large effective area will have a small beam solid angle,
and conversely (Rees, 2001).
According to (3) above (and assuming unit area), the difference in beam solid
angle between 37 GHz and 19 GHz would be a factor of 3.8, with the ground IFOV
equivalently scaled. 37 GHz and 19 GHz (K and Ka band) are the two most common
frequencies employed in spaceborne microwave remote sensing for SWE retrieval
(Chang et al., 1976). In Table 1 below, changes in IFOV are shown for the Advanced
9
Microwave Scanning Radiometer – Experiment (AMSR-E) spaceborne multi-frequency
radiometer instrument formerly operating on the Aqua spacecraft.
Table 1: Ground resolution of Advanced Microwave Scanning Radiometer (AMSR) at different
measurement frequencies.
The measured Tb will be a weighted average of the spectral radiance ( Lλ )
observed within the IFOV of the radiometer.
Because of relatively low levels of
naturally emitted microwave energy, passive microwave observations of Tb are
characterized by coarse spatial resolution (e.g. Table 1). As such, there are many different
terrain and land cover features integrated into a single grid-cell that can affect the overall
observed Tb , as shown below in Figure 4.
10
Figure 4: Within the IFOV of a PM observation, there is multiple contributions to the observed
Tb. The contributions can be characterized using Equation 4.
To understand what individual contributions are often present within the IFOV of
a radiometer pointed towards a heterogeneous montane environment that is both snowcovered and vegetated. it is helpful to decompose the total microwave emission within
the IFOV into it’s individual components, which can be well approximated using a
simple radiative transfer model. The Tb measured by a radiometer above a vegetated, but
snow-covered scene ( Tbsv ) can be modeled in the following manner, assuming negligible
reflectivity from vegetation and dry snow conditions.
Tbsv = Tbsst v + Tbv
11
(1.4)
where Tbss is the Tb attributable to snow only, t v is the vegetation transmissivity, Tbv is
the brightness temperature of the vegetation. Thus we are left with only two parameters
sv
ss
from (4) to characterize as a function of the observation ( Tb ), specifically Tb and
tv .
The goal of this thesis is a study of how each of the variables above contributes to
ss
the overall observed Tbsv. For Tb , better characterization of the contribution of
heterogeneous grain size is needed, for which reliable methods to measure grain size are
sv
requisite. For Tb
ss
, understanding how microstructure ( Tb ) and vegetation contributions
v
( t v , Tb ) aggregate up to higher scales is important, as well as quantifying what amount
of vegetation within the passive microwave footprint will mask the microwave signal
attributable to snow.
In the following subsections, a brief review of these topics will be provided to
familiarize the reader with the concepts and techniques that will be discussed throughout
chapters 2-4.
1.2.2 Microstructural and snow emission principles (Tbss)
Microwave emission from a snow layer over a ground medium consists of
contributions from the snow itself and from the underlying ground (Foster et al, 2005).
Both contributions are governed by the transmission and reflection properties of the air–
snow and snow–ground boundaries, and by the absorption/emission and scattering
properties of the snow layers (Chang et al., 1976 and Wiesman & Mätzler, 1999). Snow
crystals essentially scatter part of the cold sky radiation, which reduces the upwelling
12
radiation measured with a radiometer (Schmugge, 1980). The deeper or more compact
the snowpack is, the more snow crystals are available to scatter the upwelling microwave
energy (Tsang, 1987; Matzler, 1994). It is this property that is used to estimate snow
mass, as shown in Figure 5.
Figure 5: Physical basis for PM remote sensing. As the snow depth increases, the scattering of
radiance at PM wavelengths also increases, leading to lower Tb observations. Figure used with
permission from NCAR.
Additionally, stratification influences the microwave transmission through the
snowpack, and thus the observed Tb, as compared to a homogeneous medium. Matzler
(1994) found from surface-based experiments that scattering by different types of grains
and layering of dry snow can dominate the signal variation, as compared to overall snow
depth and/or water equivalent.
In order to understand the influence of snowpack properties on the microwave
signal and to explain snow signatures, theoretical investigations have been performed
13
(Chang et al., 1976; Tsang, 1987, Durand et al., 2011).
Validating the results of
modeling efforts has been difficult, mainly because the snow structure (e.g. grain size)
cannot be quantified easily or accurately. Traditional grain size measurements, i.e. those
made with hand lens and scale, do not describe the radiometric quantity that controls
microwave brightness temperature. Painter et al. (2007) found that traditional grain size
measurements do not accurately describe the optical equivalent grain radius, which
controls visible and NIR reflection by snow. However, the optical equivalent grain radius
can be physically related to snow grain correlation length, which has been shown to
control the radiometric response of snowpack for microwave frequencies (Mätzler, 2002).
Durand et al. (2008) developed a simple statistical relationship between traditional grain
measurements and the snow grain correlation length, although the limited number of
samples from which the relationship was derived led to significant uncertainty in the
relationship.
In the past five years a number of methods have been developed to estimate
specific surface area (S), and thus an effective grain size (Montpetit et al., 2013). Near
Infrared (NIR) imaging techniques (Matzl and Schneebeli, 2006; Painter et al., 2007;
Gallet et al., 2009) are based on the fact that NIR reflection of direct and diffuse radiation
can be inverted to estimate snow specific surface area (S). These methods are being
shown to produce adequate brightness temperature simulations (Toure et al., 2008).
Additionally, Matzl and Schneebeli (2010) showed that accurate measurements of S can
be made via cycloid measurements and stereology techniques. Figure 3 shows an image
of a snow cast made of alpine snow near Steamboat Springs, Colorado; S was measured
14
with cycloids and grain size correlation length was measured following Wiesmann et al.
(1998). The resulting microwave simulation shows excellent agreement with in-situ
microwave observations collected at that site.
Figure 6: Snow casts being utilized for stereology purposes. Intersections of the cycloids (red)
across the air/snow interface are counted and related to the specific surface area (S).
Each of the methods listed above have benefits and drawbacks. Traditional hand
lens measurements can be made quickly in the field with little training, however
estimates of grain size are subjective from person to person. Stereological techniques
have proven to both objectively characterize grain size and successfully reproduce Tb
observations, however they are labor intensive and require highly sensitive handling
procedures in order for samples to be sufficiently preserved. To date, no comprehensive
comparison of these different measurement techniques for characterizing grain size have
been conducted.
15
1.2.3 Effects of Spatial Resolution (Tbsv)
Operational SWE algorithms that use passive microwave data have been
extensively used in global snow mapping. Due to the low spatial resolution of passive
microwave sensors, the spatiotemporal heterogeneity of snow can and does affect the
accuracy of these conventional algorithms. The impact of the heterogeneous nature of
snow properties within microwave footprints (combined with the non-linear processes
whereby microwaves propagate through the snowpack) is one of the most important
outstanding issues in microwave remote sensing of snow, especially in complex terrain
(e.g. mountains).
Snow properties vary significantly at the scale of meters in complex terrain, but
satellite based microwave measurements have footprints on the order of tens of
kilometers (Li et al., 2012). The difference in scale between snowpack physical processes
and microwave remote sensing has important, but largely unquantified effects on the
passive microwave observation of snow. Understanding the effect of subpixel
heterogeneity on the PM measurement in a scaling context is fundamental to improving
SWE retrievals, as has been advocated in previous studies (Derksen et al., 2005, Tedesco
et el., 2005). Any work to compare in situ and remote sensing measurements of snow
must take the particle size, ice layers, and vegetation into account, either implicitly or
explicitly.
A recent study by Davenport et al. (2012) examined the effect of spatial variability
in snow properties for spatial scales larger than 5 km using a single-layer radiative
transfer model and a probabilistic model of snowpack variability. At scales of less than 1
16
km, snowpack spatial variability is controlled by factors such as terrain, wind, and
vegetation (e.g. Molotch & Bales, 2005); at scales from 1 km to 5 km it is more
controlled by orographic effects. Herein, we extend the work of Davenport et al. (2012)
to focus on variability at scales less than 1 km, using a multi-layer radiative transfer
model and explicit representation of snowpack properties.
Using measured snow stratigraphy from sampling areas of the Cold Land
Processes experiment (CLPX), which are realistic in terms of the variability of the states
that we would expect to encounter in typical alpine areas, we alter the mean variables of
the states, as well as the distributions of the mean within the footprint, and examine what
affects this has on the microwave brightness temperature. Using snow depth for example,
we will conduct synthetic analysis at different mean snow depth values, in order to study
the relationship each value has on the observed measurement.
The fundamental objective of the CLPX experiment was to provide the
comprehensive data sets necessary to develop an understanding of the relationships
between microwave measurements and snowpack characteristics, and the associated
uncertainties, across multiple scales. A goal of this thesis is to explore and examine those
datasets in an attempt to characterize and quantify the way in which information about
SWE and snowpack properties is affected by sub-pixel variations within the microwave
measurement, as a function of the scale of the measurement. It is known that that
microwave measurement contains information regarding snow. Our goal is to understand
how changes in the scale affect the snowpack information contained within the
microwave observation
17
1.2.4 The Effect of Vegetation (Tbv and tv)
Vegetation coverage (Hallikainen et al., 1992; Schmugge & Jackson, 1992; Chang
et al., 1996; Foster et al., 2005; Langlois et al., 2011) further complicates the Tb – SWE
relationship, due to the fact that in-scene vegetation masks the time-varying response of
PM Tb to snow properties (Hallikainen et al., 1984). Consequently, SWE retrievals
derived from PM Tb observations in vegetated areas are often characterized by large
errors and uncertainty (Hall et al., 1982; Chang et al., 1996; Foster et al., 2005), as shown
in the figure below.
Figure 7: Underestimation of SWE due to forest cover. The error bars denote uncertainty of the
underestimation (a). The forest factor F as a function of fractional forest cover. Figure used with
with permission from Foster et al., 2005
The recent study by Langlois et al. (2011) illustrates that stem volume and
fractional forest coverage can be used to model vegetation transmissivity at 19 and 37
18
GHz, and that vegetation transmissivities at high stem volumes asymptote to
approximately 0.6 at both frequencies. This essentially confirms prior literature
transmissivity values (Kruopis et al., 1999). These values indicate that while vegetation
does indeed mask the brightness temperature signal, and reduces signal-to-noise ratio, it
does not completely obliterate the signal. Radiance assimilation schemes including
vegetation effects showed that SWE retrieval is still feasible in vegetated areas using
synthetic measurements (Durand and Margulis, 2006; 2007).
However, even these
methods are not immune from these issues. Whether Tb is assimilated directly (Durand et
al., 2007; Andreadis et al., 2008) or indirectly through empirically fit relationships which
link snow depth and/or SWE to Tb (Pulliainen et al.,2001; De Lannoy et al., 2010; Takala
et al., 2011), vegetation must, in some way, be accounted for in the assimilation process.
However, there is no unified vegetation metric that has been used in literature to
parameterize the vegetation transmissivity, which is globally available in both the spatial
and temporal domains. The stem volume model proposed by Langlois et al. (2011) is
impractical due to the time and labor requirements required to make field measurements
of stem volume. Thus, there is a clear need to to determine what relationships exist
between PM Tb and a globally available vegetation dataset, and characterize the
vegetation transmissivity as a function of the global vegetation dataset.
1.3 Significance and Organization of the Dissertation
While each research question listed above requires its own independent
investigation, they are all intrinsically related to each other, and to the utilization and
improvement of current passive microwave retrievals algorithms for snow.
19
Each topic
will require careful analysis as it relates to the interpretation, characterization, and
modeling of remote sensing data. As it stands, we cannot accurately model microwave
brightness temperatures without having accurate inputs that from in situ data. However,
unless we are able to correctly estimate the spatial distribution and the variables that
control its distribution within our scale of interest, we cannot accurately generate data
inputs to our RTM model that are indicative of the spatial variability of snow within the
footprint without directly introducing bias.
By utilizing snowpit observations that
represent the variability of the different snow properties within montane environments
and more specifically, the passive microwave footprint, we hope to gain insight into what
sensitivities, if any, the microwave signal has to each respective variable.
This study will provide insight into the way in which the spatial scale of the
measurement leads to loss of information about the mean SWE, given the spatial
heterogeneity of the sub-footprint properties. Understanding how the information about
SWE is lost (if indeed it is), will add value and relevance to historical PM datasets, some
of which date back 30 years. While it is beyond the scope of this study, we expect that
this analysis will ultimately aid in the development of more accurate global SWE
datasets, and improved retrieval algorithms for snowpack retrieval from spaceborne
microwave remote sensing observations.
20
Chapter 2 Microstructure Characterization
In this chapter we discuss microscale snow processes and methods by which they
can be observed. Optimal utilization of spaceborne passive microwave (PM)
measurements for snowpack characterization requires the ability to model microwave
emission, which is highly sensitive to snow microstructure. Snow microstructure is often
characterized by its grain size. In this study, we evaluate the potential to force the
microwave emission model of layered snowpacks (MEMLS) with objective
measurements of snow specific surface area (S).
2.1 Overview
Passive microwave (PM) measurements are sensitive to the presence and quantity
of snow, a fact that has long been used to monitor snow cover from space (Chang et al.,
1987; Tedesco & Narkevar, 2010; Takala et al., 2011). In order to estimate total snow
water equivalent (SWE) within PM footprints (e.g., 14 km x 8 km, for the 37 GHz
AMSR-E Level 2A measurements), it is prerequisite to understand snow microwave
emission at the point scale. This is due to the fact that snow microstructure is a
fundamental control in the propagation of microwave radiation through snowpack.
21
Many studies have used the so-called grain size (Fierz et al., 2009), in which the
average or the maximum linear extent of the prevailing grain is identified using a ruled
card and a loupe-style hand lens. This approach has the advantage of rapid measurement
in the field, but such measurements are subjective and non-repeatable. Moreover it has
been argued that grain size is not an effective metric of snow microstructure for
microwave modeling (Davis et al., 1987). Thus grain size measurements are often
combined with an empirical model and related to other microstructural parameters (e.g Le)
which better characterize the snowpack radiative properties.
Weismann and others (1998) correlated scattering and absorption coefficients at
microwave frequencies to the exponential correlation length (Le) of snow particles, which
can be measured using stereological techniques. In stereology approaches (Davis &
Dozier, 1989; Matzl & Schneebli, 2010) snow samples are obtained in the field and
microstructure is preserved via a casting agent. In a laboratory, the casts are cut with a
microtome and photographed. For microwave modeling, the photographs are analyzed to
obtain the exponential correlation length (Davis et al., 1987; Davis & Dozier, 1989).
While offering an unbiased quantitative measurement method, stereology is both timeand resource-intensive.
Near Infrared (NIR) methods deliver spatial information on natural snow profiles
and stratigraphies while requiring only simple equipment. Near Infrared (NIR) imaging
techniques (Matzl and Schneebeli, 2006; Painter et al., 2007; Gallet et al., 2009) are
based on the fact that NIR reflection of direct and diffuse radiation can be inverted to
estimate Le. These methods are being shown to produce adequate brightness temperature
22
simulations (Toure et al., 2008). These show great promise for coupling with microwave
modeling (Toure et al., 2011).
Each of the methods listed above have benefits and drawbacks. For instance,
traditional hand lens measurements can be made quickly in the field, however estimates
of grain size are subjective from person to person and empirical relationships between
grain size and Le have considerable uncertainty. Stereological techniques have proven to
both objectively characterize grain size and successfully reproduce Tb observations,
however they are labor intensive and require highly sensitive handling procedures in
order for samples to be sufficiently preserved. While NIR approaches have been utilized
(Matzle & Schneebli, 2006; Toure et al., 2008), little literature exists in which they are
compared directly (Le) and indirectly (Tb) against other techniques (Montpetit et al.,
2013).
The goal of this chapter is to drive a radiative transfer model with objective
measurements of snow exponential correlation length (Le) using multiple characterization
techniques to reproduce measured brightness temperatures. Being able to relate past,
present, and future grain size measurements in a unified framework is an important
endeavor that will help to validate microwave modeling efforts and allow for greater
exploitation of legacy datasets.
23
2.2 Microwave Emission Model for Layered Snowpack (MEMLS)
2.2.1 Microwave Emission Model for Layered Snowpack (MEMLS)
A seasonal snowpack is fundamentally a layered medium (Colbeck, 1991), and in
many cases microwave emission cannot be understood apart from the layered character of
snowpacks (Hall et al., 1986; Boyarskii & Tikhonov, 2000; Durand et al., 2008; Durand
et al., 2011). This has motivated the development of multi-layer radiative transfer models
(Liang et al., 2008; Wiesmann & Mätzler, 1999; Lemmetyinen et al., 2010). In this study,
we utilize MEMLS, which is built on extensive theoretical (Mätzler, 1996; Mätzler,
1998) and experimental (Mätzler, 1996; Wiesmann et al., 1998) work.
MEMLS treats snow microstructure by assuming that the two-point
autocorrelation function of the irregular ice-air system A(x) as a function of the distance x
between any two points in the system can be modeled as an exponential, as shown in
equation 1:
A(x) = e
−
x
Le
(1.5)
Thus, MEMLS implicitly assumes that Le constitutes all of the required
information for computing the extinction coefficients and the subsequent microwave
response (assuming the remaining stratigraphic properties are provided as input).
In the following section, we will describe methods for relating the different grain
size parameterizations into a unified Le framework for comparison.
24
2.3 Snow Microstructure
Grain size estimated following Fierz et al. (2009) is referred to as Dg. While
estimates of Dg are highly uncertain and non-repeatable, a legacy of Dg data exists, for
example, in the case of the NASA Cold Lands Processes Experiments (CLPX) dataset
[26]. In order to relate Dg to Le, Durand et al. (2008)) developed an empirical relationship
from the data in Table 1 of Mätzler (2002).
(1.6)
where a0, a1 and p0 are best-fit parameters and v is the ice volume fraction (ratio
of snow density to density of ice); it was estimated that uncertainty in modeling
brightness temperatures at 37 GHz due to uncertainty in these parameters was
approximately 10 K (Durand et al., 2008).
Additional parameterizations exist to characterize Le. Specific surface area (S),
which is defined as the ratio of the total surface area of ice in a snow sample (including
grains, bonds, etc.) to the total volume of ice, can be theoretically related to Le by means
of the following equation and a relationship between S and v (Mätzler, 2002)
Le =
4(1− v)
S
(1.7)
Stereological and near infrared (NIR) methods can be utilized to objectively
measure S (Davis & Dozier, 1989; Matzl & Schneebli, 2006). While equation (2) holds
in theory, it has been determined that a constant of proportionality is required to account
for deviations of autocorrelation function from the exponential (Mätzler, 2002).
25
Combining equations 3 and 5 and applying the constant of proportionality gives an
expression for relating Le and S in the following manner:
Le* = β
4(1− v)
S
(1.8)
Using snow sections from Davos, Switzerland, Mätzler determined β to have a
value of 0.748. This value of β also led to agreement between MEMLS simulations and
radiometer observations in Antarctica (Mätzler, 2002).
By calibrating ground-based
radiometer observations with the coupled MEMLS-CROCUS predictions, Brucker et al.
(2011) found a best-fit value β value of 0.63. In this study, we used both values in hopes
of identifying if one performed more reliably than the other.
2.4 Data and Methods
2.4.1 Radiometer Data
In order to measure snow microwave radiance, we used a ground-based version of
the NASA Airborne Earth Science Imaging Radiometer (AESMIR) operating at 19 and
37 GHz (Kim, 2009). We mounted the radiometer approximately 3.5 m vertically above
the soil-snow interface, with an incidence-angle of 50° from nadir, as shown in Figure 8.
26
Figure 8: Two views of the radiometer and its field of view, at Stormpeak Laboratory in
Steamboat Springs, Colorado, USA. The red oval in the photo on the left indicates the
approximate location of the radiometer footprint.
Considering that the radiometer full-width half-max beam width is 8° and the
radiometer was 1.8 m above the snow surface, the footprint on the snow surface is
elliptical with a minor-axis radius of approximately 20 cm. We performed a calibration
once per day for each of three days, and estimated the brightness temperature (Tb) once
per day, immediately after calibration on that day. From the nearby Tower SNOTEL site,
there was no change in SWE (i.e. no precipitation) from 21 to 23 February; thus, Tb
would be expected to be fairly similar. Only vertically-polarized Tb was measured. At 19
GHz, the brightness temperatures ranged from 247.5 to 252 K, with a mean of 249.2 K.
At 37 GHz, the brightness temperatures ranged from 227 to 231 K, with a mean of 230.3
K. The range of the observations was thus 4.5 K and 6K at 19 and 37 GHz respectively.
27
2.4.2 Snowpit Data
Snowpits were excavated on 22 and 23 February close to the radiometer field of
view (FOV). The pit on 23 February was excavated directly in the center of the
radiometer FOV (after the Tb measurement was made on that day), while the pit on 22
February was approximately two meters from the center of the FOV. The pit depths were
174 cm and 165 cm on 22 and 23 February, respectively. This difference is likely due to
local variability in snow depth, as opposed to any temporal variability due to ablation or
transport by wind. Stratigraphy of each pit was identified using standard snow hardness
tests based on protocols established under the CLPX field campaign (Cline et al., 2004).
There were six layers identified on 22 February and eight layers identified on 23
February. In both pits, the bottom layer (layer 1) was identified as a melt-refreeze layer,
and the layer immediately above (layer 2) was identified as faceted crystals. This was
followed by two layers and four layers of faceted/round mix for 22 and 23 February,
respectively. The top two layers were identified as new snow for both pits.
Geometric grain (Dg) size was measured using the aid of a loupe-style hand lens;
following the CLPX grain size measurement protocol (Cline et al., 2004), the maximum
and minimum extent of large, medium and small snow grains was measured for each of
the stratigraphic layers identified in the snowpit. Figure 2 shows the profile of Dg
measurements for the February 22 snow pit. Snow temperature was measured using a
standard field thermometer to a precision of 1° C, at vertical increments of 10 cm. Snow
density was measured to a precision of 1 kg m-3 with a standard snow density cutter with
28
a volume of 1000 cm3. The density, temperature, and Dg protocols were identical to those
used in the CLPX field campaign.
Finally, we made snow casts for stereological analysis. For each of the
stratigraphic layers identified in the snowpit, we extracted a cubic sample of snow
approximately 10 cm on a side. We preserved the samples using dimethyl phthalate dyed
with Sudan black, following the procedure of Matzl and Schneebeli (2010). Successful
casts of layers 1-4 were made for 22 February, and successful casts of layers 1-5 were
made for 23 February: note, here and throughout, layers are listed in bottom-first order,
i.e., layer “1” refers to the bottom layer. Casts of the upper layers were unsuccessful, as
revealed by looking at the photographs of the snow sections. Thus, Le for these layers
were estimated in the following fashion
For 22 February, layer 5 and 6, Le was estimated to be 0.05 mm, a typical value
for fresh snow (Mätzler, 2002). For 23 February, layer 8, we estimated Le to be 0.05 mm.
Note that layers 6 and 7 on 23 February are at similar heights above the snow-soil.
interface as layer 4 on 22 February. Moreover, layers 6 and 7 on 23 February have similar
densities to layer 4 on 22 February; see Figure 3. Thus, on the basis of similarity in
density and height above snow surface, for layers 6 and 7 on 23 February, we estimated
Le to be identical to that estimated for February 22, layer 4.
2.4.3 Stereology and Analysis of Snow Samples
One photograph from each of the samples from the February 22 snowpit is shown
in Figure 9. Layer 1 shows melt-refreeze morphology, layer 2 shows faceted snow
characteristic of depth hoar, and layers 3 and 4 show rounded shapes with smaller ice
29
structures. Black pixels indicate ice, grey pixels indicate dimethyl phthalate that has filled
the snow pore space, and white pixels indicate either recrystallized dimethyl phthalate or
air bubbles (Matzl & Schneebli, 2010).
Figure 9: Photographs of snow samples from February 22 (left); top left is layer 1, top right is
layer 2, bottom left is layer 3, and bottom right is layer 4. Stratigraphy (right), geometric grain
size, and morphological classification according to Fierz et al. [2009] for the snowpits on 22
February (left)
In order to calculate S, we used the methods explained and described in Matzl and
Schneebli (2010), and overlaid a test grid of cycloids on each of the images: see Figure
10. The basic principle of the methodology is to overlay a test system of lines on each
image. The total number of intersections of the lines with the ice-air boundaries provides
an unbiased estimate of S:
S=
2I
vd
(1.9)
where I is the total number of intersections, and d is the total length of test line.
For validation purposes, the stereologic counting was done by two separate research
30
teams from Ohio State University and Swiss Federal Institute for Forest, Snow and
Landscape Research (WSL). Differences in counting ranged from 5-10% average
percentage error. The small differences in counting estimates lends credence to the
reliability of stereological methods, albeit time consuming.
Figure 10: For sample 2, image 6 of the February 22 snowpit, the cycloid test grid used to
estimate S is shown overlaid (left), and a binary representation of the photo(right). Black in the
photograph and in the classified image indicates ice, whereas gray and white indicate pore space
(see text). The arrow indicates the “up” direction, and the length of the vertical bar is 1.0 mm.
2.4.4 Near Infrared Camera Data
The camera used to record NIR data was a Canon G14. The wavelength of the
detected light ranged from 840 to 940 nm. The distance between camera and profile wall
varied between 1.4 and 2.0 m, resulting in pit wall photos varying from 0.5-1.0 m2.
The calibration targets were manufactured of Spectralon greyscale standards with
NIR reflectances of 50% and 99%. Alongside the geometrical correction, these values
corrected illumination variations by interpolation from the original image. The NIR
reflectance, r, of the snow was calibrated with regard to the pixel intensities of the targets
in the following manner:
31
r = a + bi
(1.10)
Where i is the intensity of each pixel and a and b are determined by a linear
regression on the pixel intensities of the greyscale standards. The specific surface area is
related to the measured NIR reflectance through the following relationship, where A and t
are empirical constants (Matzl & Schneebeli, 2006).
S = Aer/t
(1.11)
For comparison purposes with snow pit samples, the S estimates were averaged in
both the vertical and horizontal directions within each layer, in order to satisfy the input
constraints of MEMLS. An example processed NIR photo is shown below, illustrating
the stratigraphic variability of snow properties.
Figure 11: A processed NIR image to obtain S (right). The variation in stratigraphy is easily
visible. Units are in mm.
32
2.5 MEMLS Model and Simulations
Table 1 and Figure 12 show the predicted Tb at 19 and 37 GHz using different
drivers of Le for MEMLS simulations, including traditional hand lens, stereological, and
NIR measurements. Using hand lens measurements from February 22 and February 23 in
conjunction with (1), MEMLS predicts the observed Tb with a MAE of 10.3 K. Using
stereological methods of Le to drive MEMLS, the MAE is 5.1 K using β M and 5.3 K
using β B . Using NIR measurements of S to drive Le, the MAE is 7.9 K and 2.3 K, using
β M and β B , respectively. All MEMLS results are shown below in Table 2 and Figure 12.
At 37 GHz, which is the frequency most utilized for spaceborne SWE retrievals, we can
see that for both stereologic and NIR estimates of Le using β B , the MAE is very low at
2.8 and 1.9 K for February 22, and 2.0 and 4.0K for February 23. This is significantly
less than the MAE of 7.4 and 10.8 MAE for Tb estimates driven with hand lens
measurements and equation (1) on February 22nd and 23rd.
Table 2: Predicted vs observed Tb using different drivers of Le for MEMLS
As can be seen, modifying the Le term with β B produces the most consistent (in
terms of MAE) Tb predictions, followed by the β M . In terms of measurement techniques,
33
Le estimates derived via NIR techniques have the lowest MAE, followed by the
stereology, and finally hand lens measurements. While the overall sample size is low, it
is interesting to note that the there is less variability in the Tb predictions when using
stereological Le estimates as compared to the Tb predictions driven with Le estimates from
NIR camera measurements.
Figure 12: Predicted vs observed Tb using different drivers of Le for MEMLS. Red bars indicate
Tb observations and the estimated precision. Blue corresponds to hand lens, black to NIR, and
cyan to stereology measurements. Crosses indicate β B , while triangles represent β M .
In terms of stratigraphy, the different estimates of Le are well-correlated for both
February 22 and 23, with the exception of hand lens estimates for the bottom layer on the
22nd, and hand lens, stereologic, and NIR estimates for the bottom two layers on the 23rd.
While the disparity in Le estimates driven by hand lens measurements can be
expected for the bottom two layers on February 23rd based on the uncertainty in the
relationship between Dg and grain size (Durand et al., 2008) the large differences
between NIR and stereologic measurements is surprising.
34
As mentioned previously, the stereologic counting was done independently
among two different research groups, thus we are confident in the stereologic method.
The NIR photography was examined near the lower layers, but nothing suggested that
significant changes in reflectance would cause this large variation in the lower layers of
February 23.
2.6 Discussion and Conclusion
Utilizing in-situ measurements of snowpack properties and a forward microwave
modeling framework, predicted Tb was compared against observed Tb to determine the
efficacy of the different methods for characterizing microstructure utilizing the
microwave emission model of layered snowpacks (MEMLS), a commonly used RTM for
layered snowpack.
We confirmed that estimates of S can be utilized to drive MEMLS to estimate Tb
when the theoretical relationship between Le and S is modified with an empirical
constant. Two possible modifications to the theoretical relationship between S and Le
were tested using values published in previous literature, using both NIR and stereologic
estimates of S. Both of these fits perform adequately in the MEMLS simulations, with
MAE of approximately 5.3 K and 6.4 K, respectively.
This study illustrates that using MEMLS with measurements of S is more
attractive than using MEMLS with measurements of Dg, for several reasons. First,
measurements of S are repeatable and objective, while measurements of Dg vary from
observer to observer, and are highly subjective. Second, in this study, the MAE of the Tb
simulations using Dg is roughly four times that when using the objective measurements of
35
S. Lastly, MEMLS simulations forced with S are capable of replicating the observed Tb if
the theoretical relationship between Le and S is modified with an empirical constant. In
this study, it was found that the empirical constant suggested by Brucker et al. (2011)
provides the optimal fit between observed Tb and those predicted by MEMLS when
relating S to Le.
All of this has implications for utilization of microwave measurements in
characterizing SWE. Microwave inverse algorithms calculate estimates of SWE and grain
size (Tedesco & Narvekar, 2010), and these grain size estimates must be validated in the
course of algorithm development. Moreover, grain size prognostic models (Flanner &
Zender, 2006) are a critical component of radiance assimilation schemes (Durand et al.,
2009); as the models typically prognose S, a robust link between S and Le is required for
coupling to MEMLS. Objective characterization of snow microstructure in forward
radiative transfer modeling is critical in being able to accurately calculate SWE from
measurements of microwave radiance.
36
Chapter 3 The Effect of Scale and Spatial Resolution
This chapter analyzes how subpixel variability in snow depth, stratigraphy,
vegetation density aggregates to the PM measurement scales. The coarse resolution of the
passive microwave measurements provides challenges when trying to resolve snow states
via remote sensing observations. The natural heterogeneity of snowpack (e.g. depth,
stratigraphy, etc) and vegetative states within the PM footprint occurs at spatial scales
smaller than PM observation scales. The sensitivity to changes in snow depth given subpixel variability in snow and vegetation is explored and quantified using the
comprehensive dataset acquired during the Cold Land Processes experiment (CLPX).
3.1 Overview
Our goal is to better understand the relationship of the coarse spatial resolution
microwave measurements to the primary quantity of interest, depth, given spatial
variability of depth, vertical and horizontal variations in snowpack stratigraphy and grain
size, and the presence of vegetation. Using a physically based radiative transfer model
with inputs derived from measured in situ snow properties, we simulate spatially
continuous Tb to answer the following specific research questions:
37
1. Are coarse spatial resolution passive microwave measurements sensitive to
mean snow depth in heterogeneous environments, given the spatial
heterogeneity of snow depth and other snow properties?
2. What are the effects of vegetation on microwave sensitivity to snow depth in
the context of snow and vegetation spatial heterogeneity?
3. Does the sensitivity of Tb to snow depth change as a function of the scale of
the Tb measurement?
The NASA Cold Lands Processes Experiment (CLPX) dataset facilitates this analysis by
providing snow depth and snow pit measurements in intensive study areas throughout
Colorado, U.S.A. in 2002 and 2003 (described in section 3.2). We model the soil, snow,
and vegetation microwave radiative transfer with existing forward models (section 3.3),
and then analyze the effect of spatial variability on the sensitivity of passive microwave
measurements to snow water equivalent (section 3.4). We discuss the results of our
modeling efforts in section 3.5. Additionally, in order to ensure the fidelity of our
synthetic Tb simulations, we compare them to measured airborne Tb. We present
conclusions in section 6, and explore future opportunities related to studies of this nature.
3.2 Study Area and Data
The NASA CLPX was a multi-sensor, multi-scale field campaign conducted in
parts of Colorado in 2002-2003 designed to extend knowledge of local-scale processes to
regional and global scales (Cline et al., 2002). One important aspect of this campaign was
spatially nested study areas that varied widely in scale, from 1km2 to 160,000 km2. The
Meso-Cell Study Areas (MSA) and the Intensive Study Areas (ISA) are the focus of this
38
paper, as these are where the majority of the field data were collected. The size of each
MSA was 25 km x 25 km, while the size of each of the ISAs nested within the MSAs was
1 km x 1 km. There was a total of 3 MSAs, each containing 3 nested ISAs (see Figure
13).
Figure 13: The three mesocell study areas: Fraser, Rabbit Ears and North Park (from south to
north), with nested intensive study areas (marked with x) within each MSA. Study areas are
shown in relation to their elevations in meters above mean sea level. All study areas were located
in North/Central Colorado (inset).
The MSAs and ISAs were chosen specifically to represent the different alpine,
subalpine and prairie environments found globally. Shallow, moderate, and deep
snowpacks correspond to North Park, Fraser, and Rabbit Ears MSAs, respectively. In this
analysis, we only examined ISAs within Fraser and Rabbit Ears, due to the lack of snow
39
cover in parts of North Park during data collection.
Additionally, the vegetation
characteristics fluctuate from MSA to MSA. Rabbit Ears mainly consists of a mix of
deciduous and coniferous forest cover, whereas Fraser has relatively dense coniferous
forest cover, and North Park is composed primarily of open grasslands and shrublands.
Processing of Moderate-Resolution Imaging Spectroradiometer (MODIS) Land Cover
data revealed 14 of 16 total land cover classifications were identified within the 3 MSAs,
as defined by the International Geosphere Biosphere Programme (IGBP) global
vegetation classification (Townshend, 1992).
Airborne passive microwave Tb data were obtained using the Polarimetric Scanning
Radiometer (PSR) over all the MSAs and ISAs (e.g. Figure 14).
40
Figure 14: In a) the numbered CLPX snow pit sampling protocol is shown within the Fraser
Alpine ISA. In b), the snowpit (red), depth transect (blue), and PSR microwave data footprints
(cyan) are draped over a LiDAR generated elevation model of the area.
The microwave data was gathered at an incidence angle of 55 degrees from nadir, the
same as AMSR-E for comparison purposes. PM observations were recorded at multiple
frequencies known to be sensitive to snowpack properties (e.g. 6.9, 18.7, 37, and 89
GHz). The calibration uncertainty is typically given as +/- 1-2 Kelvin, depending on
frequency (Kim, personal communication, January 2012). The size of the microwave
footprint varied depending on the frequency, as well as the flying height and orientation
41
of the aircraft. At 37 GHz, the frequency used in this study, the spatial resolution of the
microwave footprint was typically on the order of 110-180 meters in size. For this study,
we used the raw PSR Tb measurements at their native resolution, and no resampling or
gridding was performed. As can be seen in Figure 14, the PSR observations at the ISA
scale are irregular in spatial coverage, due to the conical scanning geometry of the PSR
radiometer (Stankov et al., 2008). The irregularities can be attributed to overlapping
swaths from adjacent flight lines as well the ray tracing algorithm associated with the
geolocation of the PSR dataset. The PSR airborne microwave dataset (Cline et al., 2008)
was mainly used in this study to validate our modeling efforts (section 4.1).
Snow pit measurements were made in each ISA (e.g., Figure 14). Snow density,
temperature, wetness, and grain size were measured at each stratigraphic layer within all
snowpits. In this study we use only snowpit measurements from the third Intense
Observation Period (IOP-3) from 19-25 February, 2003. Because snow grains are known
to be a primary snowpack parameter that influences the scattering of microwave
radiation, a total of six different snow grain measurements were taken at each
stratigraphic layer following the CLPX sampling protocol (Cline et al., 2002). Snow
grain measurements were made using a loupe-style hand lens with reticule graduations of
0.1mm (Elder, 2007). Three snow grains were selected from each layer, ranked by size,
and labeled “small”, “intermediate”, and “large”. The experiment plan called for a total
of 16 snowpits in each individual ISA, but due to accessibility restraints in certain areas,
several ISAs had fewer snowpits.
42
Much of the existing literature in this field has focused on the sensitivity of
passive microwave Tb to SWE (e.g. Chang et al., 1982, Goita et al., 2003, etc). However,
because snow density measurements are very time-consuming, recent literature has
suggested characterizing SWE based on depth measurements alone, due to the fact that
SWE is more closely linked to depth than it is to density (Sturm et al., 2010). Integrated
snow pit observations taken from CLPX suggest that SWE can be directly predicted from
snow depth using a linear relationship, as shown in Figure 15.
Figure 15: Scatter plot of observed snow depth vs SWE for all 191 snow pit measurements from
the CLPX IOP3 observation period.
The fitted SWE had an R2 value of 0.99, and an RMS error of 1.78 cm SWE.
This linear relationship allows us to make use of the high density, spatially continuous
43
snow depth measurements taken with LiDAR, and simplifies our stratigraphic sampling
procedures, as described in section 3.
Spatially continuous snow depths were estimated a posteriori using a LiDAR
dataset collected during CLPX. At roughly the peak of the accumulation period (8 and 9
April, 2003), a LiDAR dataset was collected that indicates the combined terrain and snow
height. After snow ablation, another LiDAR dataset was collected to generate a bare
earth, vegetation free model (18 and 19 September, 2003). The mode of spacing between
surface elevation measurements from LiDAR was close to 1.5 m (average observation
density 376, 000/km2). Each LiDAR dataset was interpolated to a regular 1.5 m grid
using locally-fit power-law variograms in ordinary Kriging estimation by McCreight
(2010). Snow depth was then calculated as the difference in height between the gridded
height on September and April. Snow depth RMSE for all sites ranged from 6 cm to 19
cm, with an average 11.1 cm over all sites, which is comparable to standard LiDAR error
(McCreight, 2010). It is unfortunate that the LiDAR acquisition does not correspond with
IOP-3, when the snowpit measurements were made. In this study, we use a combination
of the LiDAR-derived snow depths and the IOP-3 snow pits to drive the radiative transfer
model. Because we only use the LiDAR data as a model for spatial variations in snow
depth, the time lag between the snowpit observations and the LiDAR collection is
acceptable. The main application of the LiDAR dataset was to provide a realistic highresolution estimate on the spatial variability of snow within the 1km x 1km scale of our
measurement area. In section 4.1, where we compare the true Tb measurements against
those modeled from snowpit data, we were forced to account for the time offset between
44
the IOP-3 measurements and the LiDAR collection. To do this, we found an optimum
scaling factor by minimizing the difference between the scaled LiDAR dataset and the
measured depth transects. The results were robust, with RMS errors ranging from 4.8 –
8.9 cm for the different ISAs.
While we incorporated data from multiple ISAs in this analysis, Fraser Alpine
(FA) served as a “benchmark” in different components of this sensitivity study. The FA
ISA was ideal because of the spatial variability observed in vegetation, snow depth, and
the snowpits. To the northwest, FA is densely forested, while to the southeast the area is
above timberline and there is little or no forest cover. The range of the LiDAR snow
depth in FA was in excess of 4.5 meters. The snow pit data indicate large variability was
observed in snow grain size, density, and layering in FA, all of which are known to
greatly influence the microwave signal. To illustrate this variability, we have plotted the
stratigraphy, correlation length, and depth of each snow pit from the FA ISA in Figure
16.
45
Figure 16: The layering structure and the prevailing exponential correlation lengths (pex)of each
layer (function of grain size) are shown the 16 different pits in the Fraser Alpine ISA.
The grain sizes exponential correlation lengths (Mätzler, 2002) were derived from the
measured geometric grain sizes, and range from 0.05 mm to 0.275 mm. We concede the
possibility that the CLPX snow pit data underestimates the true variability of different
snow properties such as grain size, but contend that the measured variability is sufficient
for the purposes of this research.
To our knowledge, no study has been reported in the literature which incorporates such a
heterogeneous dataset of in situ snow pit measurements in a forward modeling scheme in
46
order to examine the theoretical response of snow brightness to the total depth at various
measurement scales. Existing studies have compared CLPX microwave observations to
modeled observations by embedding a microwave emissions model into a hydrologic
prediction scheme with mixed results (e.g. Andreadis et al., 2008, Davenport et al.,
2012), but none have used the actual snowpit data for modeling purposes. The rich
datasets gathered during the CLPX provided the sole means by which this analysis was
possible. While other datasets exist that have attractive temporal sampling characteristics
(e.g. Derksen et al., 2012, Langlois et al., 2012), we chose to use the CLPX dataset
because the data is large in volume, well documented, and easily accessed by the general
public.
3.3 Methods and Models
For our analysis, it is necessary to model three main factors that control the scene
composition of a recorded PM observation: 1) modeling microwave emission of the
snowpack, 2) modeling the interaction between vegetation and snow, and 3) modeling the
aggregation of the microwave radiation to different measurements scales. We describe
statistical methods for estimating spatially-continuous distributions of snow properties
(snow depth, density, stratigraphy, grain size, and temperature) from the CLPX snow pits
and Lidar datasets in the Appendix.
3.3.1 Snow Radiative Transfer Model
In order to analyze the effects of spatial variability on passive microwave remote
sensing of snow, we utilized a forward model of the propagation of microwave radiation
47
through a snowpack. Over the past two decades, the theory of microwave interaction with
snow has developed significantly (e.g. Wiesmann & Mätzler, 1999; Mätzler &
Wiesmann, 1999; Tsang et al., 2000). The effects of stratigraphy on microwave emission
can now be modeled explicitly (Wiesmann & Mätzler, 1999; Liang et al., 2009;
Lemmetyinen et al., 2010).
The microwave model used for the simulations is the
Microwave Emission Model for Layered Snowpacks (MEMLS). MEMLS uses a
combination of empirical and physical relationships to characterize the radiative
properties of each snowpack layer (Wiesmann & Mätzler, 1999; Mätzler & Wiesmann,
1999). MEMLS predicts the scattering coefficient (γs) from physical snow parameters
and the absorption coefficient (γa ) from dielectric properties of snow and ice. The
scattering coefficient was determined via the improved Born approximation (Mätzler &
Wiesmann, 1999), and the absorption coefficient, the effective permittivity, refraction
and reflection at layer interfaces were based on physical models and empirical
approximations based on measured ice dielectric properties. The primary inputs to
MEMLS are snow density, snow grain correlation length, layer thickness, physical
ground temperature, snow temperature at each layer, liquid water content, and snowground interface reflectivity. The secondary parameters (γs, γa) in the radiative transfer
model can then be derived from the above inputs (Mätzler and Wiesmann, 1999; Langlois
et al., 2010). These inputs then lead to the parameters characterizing the radiative transfer
in and between the layers: interface reflectivity, transmissivity, and emissivity. The
transfer of radiation through the multi-layer snowpack, including the refraction, is
48
computed with a matrix method. The inputs required for MEMLS were gathered as part
of the in situ snow pit measurements taken during the CLPX campaign.
Snow grain size exponential correlation length has been shown to control the radiometric
response of snowpack for microwave frequencies (Mätzler, 2002). Hand lens grain size
measurements made in the CLPX ISA snow pits do not explicitly include exponential
correlation length. We used a simple empirical relationship between hand lens grain size
measurements, density, and the snow grain size exponential correlation length, as
described by Durand et al. (2008).
For this study, the measurement frequency at 37 GHz was used in the forward
modeling process. Studies have shown PM measurements at 37 GHz frequency exhibit
maximum sensitivity to variations in SWE (Foster et al., 1984). Furthermore, vertical
polarization was used exclusively due to the small variations between vertical and
horizontal polarizations at 37 GHz in the observed PSR data over the ISAs we examined,
which ranged from 7.6-12 K in non-vegetated areas, depending on the ISA. No
atmospheric contributions were modeled in this study. Note that passive microwave
observations, especially from spaceborne sensors, include atmospheric effects that must
be taken into account; note we use airborne observations in this study, which makes
atmospheric corrections far less critical. Additionally, following Foster et al. (2005),we
did not model the effects of terrain relief, which is known to contribute to observed
spaceborne Tb, as described in existing literature (Mätzler & Standley, 2000). Because of
the extreme variability in the snow measurements as well as the forest cover variation, we
49
assume the effects of terrain relief to be negligible, as compared to other potential error
sources listed above.
In order to answer question (1) posed in section 1, we devised an experiment to
address whether or not PM measurements are sensitive to the mean snow depth contained
within the measurement footprint, given highly heterogeneous sub pixel properties. The
spatially continuous snowpack depths in Fraser Alpine ISA (as computed in McCreight,
2010) were found to have a mean depth of 128 centimeters, at the time of LiDAR
collection. In order to explore the sensitivity to the mean depth, we generated three
additional snowpacks, where the snow depth at each original pixel value was divided by
2, 4, and 8, respectively. The corresponding means of the four snowpacks used in this
study are then 128, 64, 32, and 16 centimeters, respectively, for the Fraser Alpine ISA;
note values range from 132 to 308 cm for the other ISAs. The layering in the original
snow pit data is scaled by a depth factor, while the rest of the stratigraphic data for each
layer (grain size, density, etc.) remains the same, as shown in Figure 17.
50
Figure 17: Figures (a) and (b) show an original and augmented depth (0.5) at Fraser Alpine ISA.
The scale factor is applied to the stratigraphy only, the properties of the snow, such as grain size,
density, etc , remain the same, as shown in (c).
Other ISAs were modeled in the same way. Thus, four different spatially
heterogeneous snowpacks with four different mean depths at each site (i.e. 16 different
high resolution model runs) were created for this analysis. This allows us to isolate the
effects of depth from other snow parameters in our subsequent analysis.
In order to ensure that our stratigraphic sampling methodologies were unbiased
and reasonable, we implemented a jackknife validation procedure (Efron et al. 1983). We
estimated the radiance at each pit using its measured stratigraphic properties. We then
51
took the remaining snow pits within each ISA, scaled the depth of all other pits to match
that of the pit being estimated, and computed the difference in estimated Tb from true Tb .
This process yields a total sample size of n ×(n-1) within each ISA, where n is the total
number of pits. Our results were consistent, yielding unbiased distributions; the bias for
the four ISAs we utilized with was 0.0015, 0.17, -1.2, and 0.06, for the FS, FF, FA, and
RS. Standard deviations ranging from 7-23 K; for all four ISAs, a t-test indicated that the
means were unbiased and not different than zero K (α=0.05).
3.3.2 Vegetation Model
Vegetation has been shown to influence the observed Tb of winter landscapes
(Langlois et al. 2011). Thus, the contribution of vegetation to the observed Tb must be
understood and quantified. At the most basic level, vegetation changes two components
of the modeling process involved with the remote sensing of snow. First, vegetation
emits its own microwave signature that is observed by the radiometer, increasing the
observed Tb. Second, vegetation attenuates the radiation emitted from the underlying
earth and snowpack with a high degree of complexity due to its fractional volume, basal
area, and foliage biomass (Langlois et al. 2011); this essentially reduces the sensitivity of
the PM signal to SWE.
In the literature, the Tb of a sensor footprint is typically modeled as a function of the
fractional vegetation coverage within a scene. The microwave emission of a partiallyforested pixel can be modeled following Langlois et al. (2011) based on the forest-cover
fraction F:
(3.1)
52
(3.2)
where
Tbforest is the brightness temperature of the forested fraction of the pixel, Tbsnow is
the brightness temperature of the non-forested fraction, tveg is the vegetation
transmissivity, eveg is the vegetation emissivity, Tveg is the vegetation physical
temperature, and esnow is snow emissivity. Note there are some ambiguities in defining
what exactly forest fraction (F) is, in the context of remote sensing datasets. Some have
suggested using NDVI (Normalized Differential Vegetation Index) as a proxy for forest
fraction (Hall et al. 2002), while others have created alternative indices, such as finding
the land cover characteristics within the radiometer footprint and assigning a fraction
based on the subpixel forested component (Foster et al. 2005). In our case, we estimate
the forest cover using a binary pixel algorithm, in which the orthophotos (at 1.5 m spatial
resolution) taken during the CLPX experiment were converted to a value of 255 (white),
or 0 (black) based on a defined pixel threshold (see Figure 6).
53
Figure 18: Fraser Alpine (ISA) orthophoto (top left). Conversion of orthoimage of Fraser Alpine
ISA to binary format for vegetation classification purposes (top middle) and spatially continuous
snowpack depth as estimated by McCreight (2010) (top right) . Fraser Fool Creek (middle) and
Rabbit Ears Buffalo Pass (bottom) ISAs are also included. Snow depths are in meters.
We do note however, that this method is susceptible to bias because of “shading”
caused by the sun angle at the time of image exposure, but we did not feel it was
significant enough to compensate for in this analysis. The effect of including this shading
would overestimate the presence and role of vegetation at each ISA in the microwave
54
analysis; thus, our assumption is conservative. Using a binary approach for vegetation,
the scene Tb for each pixel then becomes:
(Vegetation)
Tbpix = Tbsnow (No Vegetation)
(3.3)
(3.4)
Extensive studies have explored tveg as a function of vegetation properties (Kurvonen et
al., 1997; Kruopis et al., 1999; Parde et al., 2005; Langlois et al., 2011). From these
studies, tveg has been modeled according to the following exponential function:
(3.5)
(3.6)
where a and b are regression coefficients, V is stem volume, and f is frequency. The main
difference between the studies listed above has been the differing values assigned to the
regression coefficients, a and b.
The vegetation transmissivity algorithms are
parameterized by estimates of stem volume, but the CLPX dataset did not contain any in
situ measurements of stem volume. Taking a conservative approach, we assumed that the
stem volume for each pixel was high enough that we could assume the vegetation
transmissivity was at the saturation value. This left us with a total of four transmissivity
values , from which we could find the best fit. The best fit was found by minimizing the
difference between the observed PM data and a replicated observation scene, where the
Tb is modeled as a combination of the snow properties (MEMLS) and the different
vegetation transmissivities. We found that the transmissivity saturation values given by
55
(Langlois et al., 2011) led to the best fit between our model simulations and the PSR Tb
measurements. We therefore assume a constant transmissivity of 0.55 for the different
ISAs within our dataset. By defining the transmissivity values for our study areas, we
were then able to quantify its effect on the PM remote sensing measurements. In order to
answer question (2) posed in the Introduction, we use the same methods described in the
previous section, but include the effects of vegetation. This allows us to see how
vegetation affects the sensitivity of microwave brightness temperature to snow depth.
3.3.3 Measurement Scale Modeling
In order to quantify the effect of scale (if any) in PM remote sensing (i.e. question
3), we synthetically create multiple measurement scales in which we can conduct our
sensitivity analysis within a 1km x 1km ISA. Three different distributed spatial
observation methods were employed, at arbitrarily chosen footprint sizes of 100, 400, and
1000 meters, respectively. The antenna sampling patterns at these scales are shown in
Figure 7. The passive microwave observation was simulated by a weighted Gaussian
described by its Full Width Half Maximum (FWHM) spatial dimension. For an estimate
of the Tb at a point in space, we define a Gaussian inverse distance-weighted average
(GIDW) function (Li et al., 2012): (3.7)
The weights of the function can be found using the following equation
56
⎛ d2 ⎞
wi = exp ⎜ − i ⎟
⎝ σ ⎠
(3.8)
where di is the distance from the center of the footprint, and σ is the standard deviation of
the Gaussian function, and is given by the following relationship.
(3.9)
This function serves as a method by which we can estimate what the observed Tb should
be from a given antenna pattern and a high-resolution Tb simulation.
Figure 19: Illustration of FWHM sampling method utilized in order to study the effects of scale
on the microwave measurement at 100, 400, and 1000 meter resolution. The dimensions of each
square is 1km2. The different color (red to blue) represents the signal power of the simulated Tb
observation through Gaussian Inverse Distance Weighting.
The Tb at the specified location is determined using a linearly weighted combination
of observations taken from a set of sample points. Because of the spatial limitations of
the LiDAR-derived continuous snow depth data, as well as the snowpit data, the largest
PM observation that we are able to simulate has a diameter of 1000 meters. At each
pixel, we have a corresponding Tb that is simulated using MEMLS.
57
To increase
computational efficiency we aggregated the original 1.5 m pixels derived from LiDAR
data up to 10 m. Therefore, the “observation” is calculated using a summation of modeled
Tb at each pixel, multiplied by the distance weighting function. Therefore, the highest
weights are assigned to adjacent pixels near the center of the microwave footprint.
To address the effects of measurement scale on PM observations, we computed the
average Tb over the whole domain, at 10-meter resolution, and compare this true value to
the Tb that would be estimated by a radiometer observing our study area at different
measurement resolutions including 100, 400, and 1000 meters. We used equation (7) to
perform the aggregation to the three different spatial resolutions.
We validated our modeling efforts by comparing simulated and observed Tb
values. In a prior study using ground-based CLPX radiometer data, MEMLS modeled Tb
at 37 GHz, v-pol accuracy was approximately 5-10 K; specifically, mean absolute error
was 4.6 K, and the uncertainty due to grain size measurement precision and
transformation to correlation length was 9.7 K (Durand et al. 2008). While the fidelity of
MEMLS is not the focus of this paper, MEMLS accuracy could potentially affect the
results presented herein. The geographic location of each simulated observation is based
on the known geolocation of the actual microwave data. We use the same snow depths
described in section 2.1 at 10 m resolution. To simulate the passive microwave
observation, we use the Gaussian FWHM methodology that we previously described in
equation 7. We modeled each pixel within the ISA using the probabilistic multinomial
distribution as described in Section 3.3, and the vegetation was modeled according to
Section 3.2.
58
3.4 Results
In this section, we compare the results from different microwave modeling
scenarios over each study area. Several definitions will aid the presentation of the results.
First, we define signal as the magnitude of the change in Tb due to the different snow
and/or vegetation properties. Simply put, the signal represents the difference in Tb
between a snow covered vs. bare earth Tb measurement. Second, we define the sensitivity
to be the change in the slope of the previously defined signal, as a function of a change in
the snow properties.
3.4.1 Simulated Tb vs True Tb
The respective means of the simulated Tb and observed Tb were in agreement to
+/- 3 K for all ISAs except Fraser Alpine, where it was 5K (Figure 8).
59
Figure 20: Observed and estimated PSR radiance data from Fraser Alpine (a), Fraser Fool Creek
(b) , Rabbit Ears Buffalo Pass (c), and Rabbit Ears Spring Creek (d) ISAs. The red line is the
median of the dataset, whereas the whiskers extend to minimum and maximum data points not
considered outliers (no outliers were present).
The RMS error for each ISA ranged from a minimum of 2.3 K at Fraser Fool
Creek to a maximum of 14.8 K at Fraser Alpine. In Fraser Alpine ISA, we attribute the
large RMS error to the existence of a consistent negative bias in the microwave modeling
of vegetation free areas, typically between 10-15 K in value. It is interesting to note that
the variability of the scene Tb in each ISA was greater in model generated airborne Tb
than in the actual airborne Tb gathered during CLPX (Figure 9).
60
Figure 21: Observed(left) and estimated(right) PSR Tb data from Fraser Alpine as a function of
measured depth (top), the associated histograms of both(middle), and the cumulative distribution
function (bottom).
The reason for both the negative bias and difference in spatial variability could be
due to a multitude of causes, almost all of which are outside our control. These include
natural variability in the snowpack, subjectivity of the grain size measurements made by
61
different observers during CLPX, as well as the transformation from grain size to
exponential correlation length: the combined MEMLS uncertainty associated with the fit
between grain size and correlation length, and the uncertainty in the grain size
measurement was 10 K at 37 GHz in a related study using MEMLS and CLPX data
(Durand et al., 2008). Additionally, there exist ambiguities within the PSR data that lead
to decreased confidence in the geolocation procedure of the data itself. It is impossible to
investigate these anomalies without a robust reprocessing of the original navigation
datastream, which at the time of writing was unavailable.
3.4.2 Effects of Heterogeneous Snow Properties
Modeled Tb within the 1km x 1km area at FA ranges from 195-255 K for a total
range of ~60 K. Comparison of Figure 22b and Figure 22c indicates a strong spatial
correlation between the simulated Tb pattern and the ISA snowpit distribution. Indeed, the
coherence between Figure 22c and Figure 22b is clearly far higher than that between
Figure 10c and the snow depth (Figure 17). As an example, consider the northwest part
of the domain, which has fairly uniform snow depths (as indicated in Figure 17), but has
Tb varying from 200 – 235 K (in Figure 22c). The modeled microwave data seems to be
a function of the individual snowpits modeled at the different pixels.
62
Figure 22: Typical Voronoi diagram, where individual pixels are classisfied by distance to nearest
snow pit (a), where the different colors represent the different snowpits. A multinomial
distribution is used to map individual pixels to adjacent snow pits in a probabilistic manner,
where the probilities are a function of the spatial distance between pixel and snowpit (b). The
brightness temperature scene was then simulated as a function of snow properties only (c) and
vegetation contributions (d). In the figures above, the modeled site is Fraser Alpine. Brightness
temperatures are in kelvins.
To first order, the Tb variability in the Fraser Alpine ISA is dominated by the
stratigraphic properties of the different snowpits (such as grain size, density, etc), rather
than overall depth. If the dominating variable that influenced the Tb was snow depth, we
would expect to observe smooth trends in the brightness temperature signal that would
have high correlation with the trends in the snow depth shown in Figure 17. Visually,
63
this is not the case. We concede that our spatial representation of Tb mischaracterizes the
true patterns because we only have in situ measurements of snow properties at select
locations. However, for the purposes of this study, in which we seek to examine the
relationship between Tb and snow depth, it was an adequate representation of a spatially
continuous snowpack.
Our goal was to ascertain whether or not there is sensitivity to the overall snow
depth, despite the fact that spatial variations are dominated by stratigraphy (not depth), as
noted above. Figure 23 shows the mean modeled Tb versus the mean depth over the ISA,
using the methodology described in section 3.1. For the Fraser Alpine ISA, Tb averaged
over the entire ISA has a total range of ~30 K from the minimum to the maximum mean
snow depth (note that the aggregated range is much less than the total modeled range of
60 K). Once the depth is greater than 50 cm, the signal saturates and there is little
additional sensitivity to the increased depth.
64
Figure 23: The sensitivity of modeled PM observations to mean subpixel depth, in spite of
heterogeneous snow properties taken from different ISAs. Fraser Alpine and Fool Creek ISAs are
shown in (a) and (b), while Rabbit Ears Buffalo Pass and Spring Creek are shown in (c) and (d),
respectively.
The total range of Tb for the other three study areas are 32, 22, and 21 K for the FF,
RB, and RS study areas, respectively, and the saturation depths ranged from 50-102 cm.
For all study areas however, our analysis indicates that there still exists sensitivity to the
mean snow depth over the area, regardless of the heterogeneous nature of the snow
properties contained within each respective study area that we sampled (see Figure 23).
All of the study areas exhibit sensitivity to mean depth of snow, with the signal
65
variability ranging from 22 – 38 K depending on the native snow properties of each study
area. We note that the degree of sensitivity is not uniform over each study area, nor is it
linear with respect to depth, which could lead to ambiguity in SWE retrieval. In section
5.2, we examine the effect of PM sensitivity to depth in SWE retrieval.
3.4.3 Vegetation Effects
Figure 22c represents the Tb over the Fraser Alpine ISA solely as a function of the
different snowpack properties that were measured in situ during CLPX. The Northeast
corner of the ISA has modeled Tb ranging from 215-240 K. However in Figure 10d and
Figure 24c, with vegetation present, the subsequently modeled Tb ranges from 245-253
K, and the microwave signal attributable to the snow (as illustrated in Figure 22c) is
virtually masked. Thus, vegetation contributes its own emission (increasing Tb), and
attenuates the sensitivity of the Tb to snow (decreasing the range of signal); (Figure 22c,
d and Figure 24b).
66
Figure 24: Spatial comparison of observed PSR Tb (a), to the spatially continous modeled Tb field
(b), in kelvins. While we can model the spatially continuous Tb from depth and snow pit
measurements, we only have discrete measurements of PSR Tb. Note the anomolous cold PSR Tb
observations over the forested component of Fraser alpine (top left in figure 10a). This artifact
decreases our confidence in the geolocation procedures used for the PSR dataset.
Figure 25 shows the modeled sensitivity of Tb to depth using the methods
described in section 3.1 for four different snowpits, including (green lines) and neglecting
(blue lines) the vegetation. Vegetation radiative transfer calculations are discussed in
67
section 3.2 (see equation 5) The response of the modeled Tb to the snow depth ranges
from 20 – 30 K without vegetation, if vegetation is included, there are only a few kelvins
of change in Tb.
Figure 25: Estimated radiances (a) for different snow pits taken from Fraser Fool Creek ISA,
shown in blue. Vegetation is then added to the “scene”, with a transmissivity estimate of 0.55.
Radiances with vegetation shown in green. For comparison (b), the mean and standard deviation
of observed PSR Tb over snow covered areas in all the MSA’s was plotted against averaged
winter NDVI values obtained from MODIS imagery. As the vegetation (NDVI) values increase,
the signal attributable to snow is lost.
68
The experiments described in the previous paragraph assumed 100% forest cover
at a point scale. In reality, the different ISAs exhibit different fractional coverage. We
integrated the snow depth and Tb values simulated at 10 m up to the ISA scale (1 km2),
and repeated the sensitivity test by varying the mean snow depth; results are shown in
Table 3. From Table 3, the fractional vegetation coverage across the four ISAs ranged
from 0.36 at Fraser Alpine to 0.9 at Fraser Fool Creek. The Tb range for the four ISAs
excluding the effect of vegetation ranged from 8 K to 20 K. The Tb range including the
effect of vegetation ranged from 5.3 K to 9.6 K. The reduction in sensitivity due to
vegetation was estimated by comparing the Tb range with and without vegetation, and
dividing the change in Tb range by the total Tb range of unvegetated Tb . Fraser Fool
Creek was found to have a reduction in sensitivity to depth of 63 % attributed to
vegetation. Fraser Alpine has a vegetative fraction of 0.36, which corresponded to a
sensitivity reduction of 26 %. Rabbit Ears Buffalo Pass and Spring Creek ISAs had
sensitivity reductions of 23 and 34 %, which corresponded to vegetation fractions of 0.38
and 0.47, respectively.
Table 3: Sensitivity reduction attributable to vegetation within each of the four different ISAs.
Study Area Total Signal Attributed to Snow (K) Percentage of Forest Cover Total Signal (Including Vegetation) Sensitivity Reduction (%) Depth Range (cm) (min-­‐max) Fraser Alpine Fraser Fool Creek Rabbit Ears Buffalo Rabbit Ears Spring Creek 13 0.36 9.6 26 16-­‐128 20 0.90 7.5 63 17-­‐133 11 0.38 8.5 23 38-­‐307 8 0.47 5.3 34 25-­‐200 69
We then simulated the effect of partial forest cover on the modeled Tb at
incremental forest fractions over the entire spatial domain of different ISAs using
equations (5) and (6). We generated random spatial distributions of forest–covered pixels
at 0.2, 0.4 and 0.6 fractional coverage for each of four ISAs. The results of these
experiments are given in Table 4. For forest fractions as little as 20 percent, there exists
up to 6 K increase in Tb with respect to vegetation, while forest fractions of 0.6 exhibit up
to a 14 K increase in Tb. The Tb range at Fraser Alpine without vegetation is 15 K; for
0.2, 0.4, and 0.6 fractional vegetation cover, the range is reduced to 13 K, 10 K, and 6 K
respectively. At 60% vegetation cover for Fraser Alpine, the range is reduced to 40% of
the no-vegetation case. For the other three ISAs, the range for 60 % vegetation is reduced
to 30% - 60 % of the no-vegetation case.
Table 4: Total range of signal is shown at four different intensive study areas, as a function of
snow, and as a function of a mixed pixel scene.
70
To validate our vegetation methodology and examine the masking effect of
vegetation in observed Tb datasets, we plotted airborne PSR observations over snowcovered areas within the different MSAs vs. winter NDVI values obtained from 500
meter resolution MODIS imagery. The airborne microwave observations replicate our
modeled trend (Figure 25), where signal attributable to snow is lost as the NDVI values
increase. Note that the range variability is even more pronounced when NDVI is used as
the vegetation proxy, and at NDVI values of 0.4, there is a ~70 percent reduction in the
signal attributable to snow.
3.4.4 Effects of Measurement Scale
Figure 26 shows the average depth across each of the ISAs compared to the
average Tb as it would be estimated by a radiometer measuring at different measurement
resolutions, as illustrated in Figure 19. We define the difference between the true mean
Tb and the Tb measured from different spatial resolutions in terms of absolute error (AE).
All of these results are obtained without including any vegetation in the simulations. AE
values for Fraser Alpine ISA were the largest at the 1000 m scale and at full depth, but
only amounted to 3.1 K. Subsequent ISAs with decreased heterogeneity of snow
properties were studied, and smaller AEs were found, as a function of scale. At Rabbit
Ears Buffalo Pass ISA, the largest error, at 1000m resolution, only amounted to 1.4 K.
71
Figure 26: Sensitivity of the observations at different scales as a function of mean snow depth
(assuming no vegetation) at four different ISA’s (Fraser Alpine (a), and Fraser Fool Creek (b),
Rabbit Ears Buffalo Pass (b), Rabbit Ears Spring Creek (d), respectively.
Thus, sensitivity to mean snow depth exists for all ISAs regardless of subpixel
heterogeneity, and as the subpixel snow properties become more homogeneous in other
ISAs such as Rabbit Ears Buffalo Pass, the AE at all scales decreases concurrently (e.g.
Figure 26). These results seem to indicate that even large measurement scales would be
sensitive to the mean amount of SWE contained within the subpixel.
72
3.5 Discussion
The problem of the large spatial scale of PM measurements and the sub-pixel spatial
heterogeneity in snow properties is often cited as a major factor hampering
characterization of snowpack using microwave measurements (e.g. Derksen et al., 2005,
Tedesco et el., 2005). The model-based results presented in section 4.1 indicate that the
modeled response of the average Tb contains significant information about the average
depth within the same spatial domain despite sub-pixel variability in depth, grain size,
stratigraphy, and other snow properties. The results presented in section 4.3 indicate that
these relationships are relatively scale-independent; in other words, averaging from 100
m to 1,000 m does not significantly change the sensitivity of Tb to depth. Of course, as
the spatial scale of the microwave footprint increases to 10,000 m, there is in general
more likelihood of inclusion of vegetation, lakes, etc. While 1,000 m was the largest area
modeled in this study, we hypothesize that as long as vegetation, lakes, and other
complex microwave emissivity surfaces are not contained within the footprint, this
relationship will continue to hold at larger measurement scales. Recent observational
analysis supports this theory. Specifically, it was found that spaceborne microwave
observations are sensitive to magnitude of in-situ SWE contained within the radiometer
footprint (Li et al. 2012), provided the above-mentioned conditions are met. Given the
presence of this signal, an algorithm capable of retrieving snow depth despite the
complex relationships between Tb and depth is needed. This is an encouraging result.
Note that our results show sensitivity of the Tb to the mean depth within a Tb
measurement. Thus, one potential application is to combine the Tb with ancillary data that
73
would provide some information on the sub-pixel snow variability. The SWE
reconstruction from SCA imagery as described by e.g. Molotch & Margulis (2008) is one
such method, as is the Bayesian reconstruction of snow properties as described in Durand
et al. (2007). Thus, the microwave Tb could be used to estimate the spatially-averaged
depth or SWE, and SWE reconstruction could help to constrain the spatial pattern of
SWE.
While the saturation effect associated with deep snowpacks is a difficult problem to
overcome in PM remote sensing, our findings suggest that vegetation is arguably the
biggest problem facing utilization of PM measurements for mapping snow depth.
The signal-to-noise attributed to snow is reduced by vegetation and directly affects the
ability to measure SWE through passive microwave measurements alone. Incorporating a
Bayesian data assimilation (DA) framework in which vegetation is accounted for, along
with spatially varying snow properties is potentially one way of overcoming the
saturation effect of deep snow as well as vegetation. In a general DA framework, Tb is
forward modeled and combined with microwave and in situ snow observations to form an
optimal posterior estimate of snow properties, given the estimated uncertainties with the
modeled and measured datasets. Studies of this nature have been conducted with
promising results (Durand & Margulis, 2007; DeChant and Moradkhani, 2011; Andreadis
& Lettenmaier, 2012), and further application of such techniques are warranted. The
recent
GLOBSNOW
project
(http://www.globsnow.info)
merges
microwave
measurements with ground-based station observations of snow depth or water equivalent
74
(Pulliainen et al. 2006, Takala et al., 2011), which is an additional way to mitigate the
saturation effects associated with vegetation or deep snow.
Interestingly, our results seem to indicate that there is not significant coherence
between depth and Tb spatially (section 4.1); at these scales, our results indicate that
spatial Tb patterns are more controlled by stratigraphy and grain size. Nonetheless, our
results show that there is still sensitivity of Tb to the mean snow depth over spatial areas
of 1 km2. Thus, care should be taken when drawing conclusions drawn merely
from spatial Tb patterns in alpine areas.
3.5.1 The non-unique nature of the depth and Tb relationship
Given the heterogeneous nature of the snow properties at the sub pixel scale, our
modeling results indicate that there still exists sensitivity of the PM measurement to the
mean depth within the area bounded by the measurement scale. However, although there
exists measurement sensitivity to the mean depth in all cases, the estimates of the mean
Tb as a function of depth differ depending on the heterogeneity of the stratigraphic data
within the area. Looking again at Figure 26 for example, we observe that both Fraser
Fool Creek and Rabbit Ears Buffalo ISA clearly exibit sensitivity to changes in the
mean depth over a 1km x 1km area, however the observed Tb at Fraser Fool Creek are
offset by approximately 10-20 K from those at Rabbit Ears Buffalo Creek, in the same
range of depths. This is due to the difference in the snowpack properties at each site,
such as grain size and density. The snowpack observed in the Rabbit Ears ISAs exhibited
fairly homogenous snow properties, whereas the snowpack in Fraser Alpine ISA was
highly spatially variable. Therefore, due to the spatial variability of different snowpack
75
properties, it is somewhat futile to derive an inverse algorithm that purely relates SWE to
observed Tb, which does not take grain size, stratigraphy, and snow metamorphosis into
account. This is consistent with current attempts to include the effect of grain size in
SWE retrieval algrorithms (e.g., Kelly 2009, Tedesco & Narvekar , 2010, Takala et al.,
2011).
Another interesting effect that is seen in the modeling is the clear presence of the
saturation effect as the depth of snowpack increases. In all cases,we see that saturation of
the microwave signal is prevalent for snowpacks reaching 70-100 cm of snow depth,
which agrees with other studies that have been conducted with microwave measurements
(e.g., Foster et al., 2005; Tedesco & Narvekar , 2010). The lack of change in Tb, despite
increasing SWE, has the possibility to cause large errors in SWE estimates that are based
on gradient relationships, and we attempt to quantify this in the following section.
3.5.2 Uncertainty propogation in snow depth estimates
In order to understand how uncertainty propagates into snow depth estimates as a
function of PM observations, vegetation, and Tb gradient modeling, an ad hoc algorithm
was constructed using basic error propogation techniques. The Tb sensitivity was found
by modeling six individual snowpits at different depths, and finding the mean Tb vs.
depth relationship. By defining discrete depths, a gradient (
) can easily be calculated
to reflect the change in Tb with respect to snow depth. From this mean curve, we used the
simple error progogation algorithm below to calculate the uncertainty.
(3.10)
76
where
is approximated by 2 K, which is the clear-sky spaceborne AMSR-E
observation uncertainty. We repeated these results with and without vegetation; note
that vegetation cover was assumed to be continuous, rather than some fractional
vegetation. The sz results are shown in Figure 27 as a function of depth, and vegetation
presence. For a vegetation-free scene, and snow depths ranging from 0-60 cm, the
uncertainty in the depth prediction only ranges from 2-5 cm (9-12% of total depth).
However, as the snow depth increases from 60-120 cm, we see the uncertainty in the
snow prediction increase from 5 cm to 40 cm (45% of total depth), as a function of the
decrease in Tb gradient approaching the so called saturation depth. Furthermore, as the
depth is increased to 200 cm, the prediction of snow depth solely as a function of the Tb
gradient becomes problematic at best, with some uncertainty that are in excess of 138 cm
(69%).
Figure 27: Uncertainty modeling as a function of snow depth (cm) using snow properties from
six different snow pits (a). Blue corresponds to modeled snow scene, while green corresponds to
the same modeled scenes with vegetation imposed. The red “x” is the mean of the modeled snow
uncertainties. In (b), the mean uncertainties are shown with a bar graph for better visualization.
77
The effect of vegetation is very pronounced, in this context. When vegetation is added to
the scene, the depth uncertainty as a function of the Tb gradient jumps considerably, with
up to 25 cm of error at a snowpack depth of 60 cm (41%). At higher snow depths with
less Tb gradient, such as the range from 120-200 cm, the depth uncertainty as a function
of gradient are equivalent to the actual modeled snow depth, thus making the PM
observations of no value without additional ancillary information on the snowpack
parameters.
Because of the magnitude of its effect on SWE estimates derived from PM remote
sensing, further efforts should be devoted towards accurate parameterization of different
types of vegetation at the subpixel scale, preferably in the context of a globally available
land cover dataset. Indeed, this is mentioned in other literature (e.g. DeWalle and Rango,
2008) as a priority for improved PM algorithms. In order to fully exploit the
measurement technology available in PM remote sensing of snow, more effort should be
devoted to understanding the impact of vegetation on the Tb measurement and estimation
of SWE.
3.6 Conclusions and Future Work
The results presented herein show that passive microwave Tb are sensitive to
changes in spatial mean snow depth, regardless of spatial heterogeneity in snow
properties such as grain size, layering, and density. To first order, however, the spatial
patterns of observed Tb are more sensitive to grain size and stratigraphy than to depth.
Across three study areas, Tb decreases by 23-35 K as depth increased up to the signal
saturation depth, which ranged from 70-120 cm. With regard to vegetation sensitivity,
78
forest fractions (F) as little as 0.2 can modify the PM measurement by up to 10 K, and F
greater than 0.6 mask virtually all of the microwave signal attributable to snow.
Additionally, as the scale of the microwave measurement is increased, our results indicate
that the PM measurement remains sensitive to the subpixel mean depth, as modeled
measurement resolutions of 1000 meters only differ by 1.3 - 3.1 K as compared to
measurements obtained at 100 meter resolution over individual ISAs. Thus, the main
limitation for PM remote sensing of snow in mountainous areas seems to be the inclusion
of vegetation in the pixel, and the nature of its attenuating and bias characteristics.
Studies at individual ISAs with fractional forest coverage found that sensitivity to snow
depth was reduced by 23-63 percent due to presence of vegetation, which leads to
significant errors in depth retrieval when not taken into account. With no a priori
knowledge of snowpack properties, or a method by which subpixel vegetation can be
classified and modeled accordingly, SWE estimates derived from PM remote sensing
estimates will continue to be characterized by large uncertainty in complex mountain
environments.
Further studies should be conducted in an attempt to understand how microwaves
interact and propagate through mountain snowpacks. Of course, correct radiative transfer
modeling will only result from accurate measurement of grain size. Thus, improved
methods of characterizing grain size are important for enhancing existing RT models of
snow and SWE estimation. Further analysis should also be conducted concerning the
metamorphism of snow throughout the winter months, as a result of external and internal
forces which drive the transformation of snowpack properties. Until metamorphism of
79
the snowpack properties can be accurately modeled with measured and/or modeled
meterological data, accurate SWE estimation from PM measurements will continue to
exhibit large uncertainty.
Lastly and perhaps most importantly, characterization of
subpixel vegetation effects by use of an appropriate global remote sensing dataset would
likely improve SWE estimates from PM remote sensing observations.
80
Chapter 4 Macroscale Vegetation Effects
Vegetation coverage (Hallikainen et al., 1992; Schmugge & Jackson, 1992;
Chang et al., 1996; Foster et al., 2005; Langlois et al., 2011) complicates the Tb – SWE
relationship, due to the fact that in-scene vegetation masks the time-varying response of
PM Tb to snow properties (Hallikainen et al., 1984). Consequently, SWE retrievals
derived from PM Tb observations in vegetated areas are often characterized by large
errors and uncertainty (Hall et al., 1982; Chang et al., 1996; etc). The motivation of this
chapter is to identify areas where Tb could be used to characterize snow accumulation and
to identify where the Tb will be dominated by vegetation, and therefore not of use for
snow characterization. This is accomplished by estimating the vegetation transmissivity
through the use of Tb observations and a globally available vegetation dataset.
We first review the radiative transfer model physics pertaining to vegetation and
snow, the existing transmissivity models, and their use in SWE retrieval in forested areas.
We then describe the datasets and methodology used to derive an empirical vegetation
transmissivity model based on PM Tb variability and parameterized via the Leaf Area
Index. Finally, we use the new model to predict areas in which SWE retrieval based on
PM Tb measurements is feasible.
81
4.1 Background
Vegetation has a direct influence on the measured microwave radiation over a
snow-covered scene. Research has shown that the PM Tb sensitivity to snow in forested
areas is lower than that in non-forested areas by approximately 50% (Hallikainen et al.,
1992). Hallikainen et al. (1988) showed that annual variations in brightness temperature
in forests in Finland are small at the 10, 18, and 37 GHz frequencies for both horizontal
and vertical polarizations. In the 37 GHz frequency used in this study, vegetation is a
strong absorber of microwave radiation, and areas with vegetation cover usually show
higher Tb values due to the strong microwave emission from the vegetation itself.
By masking the emission from snow-covered landscapes and contributing its own
emission, vegetation can directly affect PM SWE retrieval algorithms. In this regard,
over-story vegetation is a primary source of error in PM SWE retrieval (Foster et al,
2005). Since a typical spaceborne PM footprint measured at 37 GHz is on the order of
100 km2 or larger, microwave footprints over mountainous regions can often be expected
to contain vegetation with varying degrees of density and type. Goïta et al. (2003)
proposed a linear mixture algorithm which takes into account the fraction of each land
cover type (deciduous, coniferous, sparse woodland and open areas) within the PM pixel.
Derksen et al. (2005) provided an extensive validation of the work of Goïta et al. (2003),
using a suite of land cover sensitive SWE retrieval algorithms, with per-grid cell SWE
estimates produced as the sum of the SWE values obtained from each land cover
algorithm weighted by the percentage land cover type within each grid cell. Foster et al.
(2005) assigned smaller SWE retrieval uncertainty to low (<20%) and high (>80%)
82
fractional forest cover, while large error bars were assigned to pixels with medium values
for fractional forest cover, due to the complexity of decoupling the contribution of the
PM signal due to scattering from the underlying snow and emission from trees. The
percentage of forest cover in a PM pixel was calculated from the total number of forest
classification pixels at 1 km divided by the total number of pixels. The current
operational Advance Microwave Scanning Radiometer-Experiment (AMSR-E) SWE
algorithm uses a linear mixture of forested and non-forested pixels, the forested
component being parameterized with global forest fraction data available from Boston
University International Geosphere-Biosphere Programme data (Tedesco & Narvekar,
2010), yet vegetation remains a difficult problem to overcome in the retrieval process. A
transmissivity map has been generated as part of GlobSnow (a global SWE estimation
project) but it is based on optical imagery and global land cover information, and is
mainly used for optical snow extent retrieval (Solberg et al., 2010).
The difficulties associated with remote sensing inversion for snowpack
characterization has motivated the application of data assimilation and Bayesian methods,
but even these methods are not immune from vegetation issues.
Whether Tb is
assimilated directly (Durand et al., 2009; Andreadis et al., 2008) or indirectly through
empirical relationships which link snow depth and/or SWE to Tb (De Lannoy et al., 2010;
Takala et al., 2011), vegetation must, in some way, be accounted for in the assimilation
process. This is usually accomplished via physical or empirically-based vegetation
models.
83
Efforts have been made to generate physical and empirical models of vegetation
transmissivity, with varying degrees of success. At the most basic level, a vegetation
layer can be modeled as a mixture of air and plants; however plant materials have very
complex dielectric behavior (Pampaloni, et al., 1986; Wegmuller et al., 1995). Roy et al.
(2012) presented a simplified radiative transfer model, generally called the τ–ω model,
for boreal forests in Canada. The main variable which they used to parameterize the
vegetation is the vegetation transmissivity ( γ ), which is closely related to the optical
thickness ( τ ) of the vegetation. Defining the vegetation transmissivity for the purpose
of enhancing retrieval of SWE derived from PM remote sensing has been studied
previously (e.g. Kurvonen & Hallikainen, 1997). Much of the previous literature has
focused on retrieving vegetation transmissivities using intensive ground sampling
methods in which some metric of biomass, most often stem volume, is examined
(Kruopis et al., 1999; Pardé et al.,2005; Langlois et al., 2011). However, the in-situ
measured biomass variables are difficult and tedious to make in the field, and impractical
(if not impossible) at large scales. Langlois et al. (2011) suggested implementing a
standard and thorough vegetation transmissivity model in order to improve global SWE
retrieval algorithms. However, there is no unified vegetation metric that has been used in
the literature to parameterize the vegetation transmissivity, which is globally available in
both the spatial and temporal domains. Thus, the motivation for this work is to determine
what relationships exist between PM Tb and a globally available vegetation dataset,
specifically LAI, using a data driven approach. By examining the spatial and temporal
variability in the PM Tb signal as a function of LAI, we aim to formulate a new model of
84
transmissivity as a function of LAI, and ultimately better understand the uncertainty in
SWE retrievals from PM Tb measurements over vegetated areas.
4.2 Data and Methods
To examine the effect of vegetation on spatial and temporal microwave Tb
variability, we used passive microwave observations at both airborne and spaceborne
measurement scales.
4.2.1 NASA CLPX
The NASA Cold Land Processes Experiment (CLPX) was a multi-sensor, multiscale field campaign conducted in parts of Colorado in 2002-2003 designed to extend
knowledge of local-scale processes to regional and global scales (Cline et al., 2002). The
goal was to use microwave remote sensing to measure critical components of the
terrestrial cryosphere, including snow pack characteristics, and the freeze/thaw state of
the land surface (http://www.nohrsc.nws.gov/~cline/).
Within a framework of nested
study areas ranging from 10,000 m2 to 160,000 km2, intensive ground, airborne, and
spaceborne observations were collected. The large regional study area (LRSA) was the
focus of this study, and encompassed an area of 160,000 km2 (Figure 28).
85
Figure 28: Digital elevation model (DEM) of the study area (with inset of the continental USA)
showing flight tracks where the PSR airborne dataset was collected (black lines) as part of CLPX.
The AMSR-E data was collected over the entire study area. Elevations are in meters.
The study areas were chosen to represent the different alpine, subalpine and prairie
environments found globally, with varying snowpack and vegetation characteristics
4.2.1.1 Airborne PSR Data
In this study, we analyzed the Tb at 37 GHz collected by the airborne NOAA
Polarimetric Scanning Radiometer (PSR) passive microwave imager. We chose vertical
polarization for both the airborne and spaceborne PM Tb datasets because it is frequently
used in SWE retrieval algorithms, and is less affected by incidence angle, which varies
86
significantly in complex terrain characteristic of our study area. Data were collected
during the first and third Intensive Observation Periods (February 23-25, 2002, February
19– 25, 2003) of the NASA Cold Land Processes Experiment-1 (CLPX-1),
(http://www.nohrsc.nws.gov/cline/clpx.html), which were characterized by dry snow
conditions. The airborne microwave data was gathered at an incidence angle of ~55
degrees from nadir (Stankov et al., 2008), the same as AMSR-E.
The calibration
uncertainty for PSR is typically given as 1-2 Kelvin, depending on frequency, whereas
AMSR-E has a published 1σ of 1 K (Lobl, 2001). The size of the PSR microwave
footprint varied depending on the frequency, as well as the flying height above ground
and orientation of the aircraft. At 37 GHz, the frequency used in this study, the spatial
resolution of the microwave footprint was typically on the order of 110-270 meters in
size (Tedesco et al., 2005; Vander Jagt et al., 2013). As can be seen in Figure 29, the
PSR observations are irregular in spatial coverage, due to the conical scanning geometry
of the PSR radiometer (Stankov et al., 2008).
87
Figure 29: Example of the characteristic sampling pattern of the PSR dataset as collected during
the CLPX (here shown over the Rabbit Ears MSA), draped over a DEM, with elevations in
meters (top). The sampling density within each 500 meter pixel varied spatially, as seen in
(bottom). Plots are shown to scale.
Some areas with scan overlap had high sampling densities (n>50 per 0.25 km2),
while other areas were relatively sparse (n<10 per 0.25 km2). For the purposes of this
study, we gridded the PSR measurements to 500 meter resolution using drop in the
bucket interpolation and took the mean and variance of all Tb measurements that fall
within each pixel in order to examine subpixel variability of the airborne PSR data as a
function of vegetation coverage. We calculated the correlation coefficient between the
88
subpixel variability and number of subpixel observations to ensure that the variability
wasn’t biased by the number of observations within the pixel. With an R2 value of 0.026,
the number of observations per grid cell explains less than 3% of the overall Tb
variability.
4.2.1.2 Spaceborne AMSR-E Data
In addition to the airborne PSR data collected as part of the CLPX, we utilized
data from the spaceborne Advanced Microwave Scanning Radiometer (AMSR-E) aboard
the NASA Earth Observing System (EOS) Aqua satellite. Tb data gathered using the
AMSR-E sensor is a main input into SWE retrieval algorithms (Kelly et al., 2003;
Tedesco et al., 2010) and has been used extensively for cryospheric study; however, the
AMSR-E sensor failed in October of 2011 and is no longer operational. AMSR-2 was
launched in early 2012 and will provide mission continuity. For the spaceborne
measurements, we used the AMSR-E L2A swath dataset with the 36.5V_Res.4_Tb (notresampled) data field from 2002-2003 winter snow season (November 2002-March
2003). We used the 36.5 GHz, vertical polarization without any resampling to the NASA
EASE grid, as is often done with AMSR-E Tb measurements (Li et al., 2012). Native
AMSR-E footprints are ellipses with a semi-major axis of 14km and a semi-minor axis of
8km.
The orientation of the footprint depends on the satellite orbit characteristics,
specifically the ascending and descending track. AMSR-E passes over the same place on
earth twice a day, one pass is in the ascending direction while the other in the descending
direction, however we only used nighttime passes in an attempt to maximize dry snow
conditions. We gridded the AMSR-E footprints to nominal resolutions of 10 x 10 km, for
89
the purpose of this study, using bicubic interpolation. Because the AMSR-E footprints are
already spatially coarse in nature, it is somewhat futile to examine sub-grid variability by
aggregating the spaceborne measurements to a larger scale. Using the approximate
native resolution, we instead used the temporal variability for each AMSR-E pixel as a
proxy for evaluating the effect of vegetation on observed PM Tb. Thus, the airborne and
spaceborne PM datasets are complementary and independent in nature for robust model
determination, with both subpixel/spatial (airborne) and temporal (spaceborne) coverage.
4.2.2 Remotely Sensed Vegetation Indices
While there is existing literature that describes the MODIS derived LAI product
(Running et al., 2006;Wang et al., 2004), it is helpful to at least give some background on
the algorithm which is used in this study, and suggested for incorporation into complex
SWE retrieval algorithms. Leaf Area Index (LAI) is a dimensionless quantity that
characterizes plant canopies, and is defined as the one-sided green leaf area per unit
ground surface area in broadleaf canopies (Running et al., 1996). In coniferous forests,
different definitions for LAI have been used such as half of the total needle surface area
per unit ground surface area (Chen et al., 1992), and the total needle surface area per unit
ground
area.
LAI
is
used
to
predict
photosynthetic
primary
production,
evapotranspiration, and as a reference tool for crop growth. For our vegetation dataset,
we used the level-4 MODIS MCD 15A3 global Leaf Area Index (LAI) product, which is
composited every 4 days at 1-kilometer resolution on a Sinusoidal grid. This product is
derived from the Surface Reflectance Product, and the Land Cover Type product from
both the Aqua and Terra platforms.
90
The MODIS LAI retrievals are performed by comparing observed and modeled
surface reflectances for a suite of canopy structures and soil patterns that covers a range
of expected natural conditions. Best quality LAI retrievals are performed with a main
radiative transfer (RT)-based algorithm; in the case of its failure, lesser-quality retrievals
are generated by an empirical backup algorithm based on LAI and the normalized
difference vegetation index (Myneni et al. 1997). The estimation of surface parameters
from satellite observations is a challenging task. Even when properly calibrated and
atmospherically corrected data are available, the linkages between surface reflectance and
canopy variables such as LAI are not straightforward as noise due to measurement
geometry and soil properties can be substantial. Estimation of global leaf area index using
radiative transfer is largely motivated by practical considerations and to a lesser extent by
accuracy (Myneni et al., 1997).
Examination of the MODIS LAI metadata revealed that the backup MODIS
algorithm is used almost exclusively throughout our study domain during the winter
season. This is likely due to the presence of snow, which can produce uncertainties in the
main retrieval algorithm. To validate whether the backup LAI algorithm was adequate
for our study, we examined the temporal variability of the algorithm on a pixel-by-pixel
basis to determine whether or not the distributed LAI solution was stable. Because the
product is distributed every four days, we aggregated the LAI solution by month, and
computed the average pixel variability. Of the winter months, the overall variability is
lowest in the month of January, and highest in March, likely due to the increasing
incident solar flux, and greening at lower elevations (Figure 30).
91
Figure 30: Monthly variability in the LAI within the CLPX LRSA (2002-2003) during the winter
months (top). LAI values over the LRSA for seven days from the month of January (bottom).
Therefore, we used the January LAI product as the vegetation proxy for which to
compare with our passive microwave datasets. Because the LAI values could potentially
be contaminated during winter months due to snow canopy interception, we selected the
maximum LAI value during the month of January from the 7 different LAI retrievals at
each pixel in order to minimize the effects of canopy interception on the LAI pixels.
92
Thus the “greenest” pixel over that time-series is selected, since there is no practical way
to validate whether snow exists in the canopy over such a large study domain. We
performed an ad hoc visual comparison of the LAI and in-situ vegetation density using
visible-band imagery from the USGS National Hydrography Dataset. Overall, the LAI
algorithm agrees well with the vegetation density, as shown in Figure 31.
93
Figure 31: Visible images corresponding to the following different LAI values, 0, 2, 4, and 6
(clockwise from top left). The locations of each image are shown in the bottom figure.
94
4.2.3 SNODAS SWE
We used SWE output from the NOAA National Weather Service's National
Operational Hydrologic Remote Sensing Center (NOHRSC) SNOw Data Assimilation
System (SNODAS). SNODAS is a modeling and data assimilation system developed by
NOHRSC to provide the best possible estimates of snow cover by integrating snow data
from satellite and airborne platforms and ground stations with model estimates of snow
cover (Carroll et al. 2001). SNODAS has 1 km spatial resolution and 24-hour temporal
resolution. To approximate the peak snow accumulation, SNODAS SWE from March
15th, 2003 was used.
This date is typically chosen as a proxy for peak snow
accumulation over a snow season.
4.2.4 Transmissivity Estimation
At the 37 GHz frequency used in this study, the total emission from a two-layer
medium (snow and forest) can be well approximated using a simple radiative transfer
model, as described in previous literature (e.g. Langlois et al., 2011). The Tb above a
vegetated, but snow-covered scene ( Tbsv ) can be modeled in the following manner,
assuming negligible reflectivity from vegetation:
Tbsv = Tbsstv + Tbv + tv (1− ess )(1− tv )T v
where Tbss is the Tb attributable to snow only,
the brightness temperature of the vegetation,
and
(4.1)
tv is the vegetation transmissivity, Tbv is
ess is the emissivity of the snow surface,
T v is the physical temperature of the vegetation. Looking at Equation (1) above, we
95
see that the third term is of considerably less magnitude than the first two, typically <5 K
in numerical experiments (not shown), and for the purposes of this study can be
neglected. The simplified form is then given by:
Tbsv = Tbsstv + Tbv
(4.2)
Or equivalently,
Tbsv = Tbsstv + (1− tv )Tv
(4.3)
Assuming that the vegetation transmissivity is a constant value for each grid cell, the
variability in the quantities in Equation (3) can be modeled in the following manner:
σ T2 sv = σ T2 ss tv2 + (1− tv )2 σ T2 v
b
b
(4.4)
We remind the reader that for airborne PSR data, σ T2 sv corresponds to the subgrid spatial
b
variability of Tb measurements within one 500x500 m grid cell whereas for spaceborne
AMSR-E data, σ T2 sv corresponds to the temporal variability of Tb measurements from
b
one 10x10 km grid cell over an entire winter season, as shown in Figure 32.
96
Figure 32: The variability in observed Tb ( σ 2 sv ) for one grid cell is calculated based on the
Tb
temporal variation over the winter season for spaceborne AMSR-E data, whereas for airborne
PSR measurements, we use subgrid spatial variation due to the lack of temporal sampling.
Equation 4 cannot be solved explicitly for transmissivity without accounting for
σ T2 ss and σ T2 v on the right side of Equation 4. To estimate the temporal variability of the
b
vegetation temperature ( σ T v ) in Equation 4, we used available in-situ meteorological
2
data that was collected as part of the CLPX study (Elder & Goodbody, 2004). Nine
identical meteorological towers were located in different areas throughout the CLPX
study area. At each site, measurements were made at 10 m above ground level (air
97
temperature, relative humidity, radiation, leaf wetness, wind speed, and direction).
Meteorological observations were recorded at a 10-minute temporal resolution between
20 September 2002 and 1 October 2003, although data were not necessarily continuous
throughout this time period for all towers. We calculated the average air temperature
across the nine stations over the entire snow season. The average, minimum and
maximum (averaged to ten-minute temporal resolution) of the stations is shown in Figure
33.
Figure 33: The green line and the blue lines correspond to the mean, minimum and maximum
observed air temperature from the 9 meteorological sites respectively, from a subset of the Nov
2002-March 2003 dataset.
We use this air temperature variance to approximate the vegetation temperature
variance,
σ T2 v , over our study area. Moreover, we accounted for the uncertainty in the
estimate
σ T2 v , by increasing σ T2 v with variance of the difference between the maximum
and minimum temperatures across the nine stations for each ten-minute interval. To
98
ensure that
σ T2 v
is entirely removed from our data, we take a conservative approach and
subtract the entire
σ T2 v
from the left side of equation 4 , rather than
σ T2 v scaled
by
(1− tv )2 , thus
σ T2 sv − σ T2 v = σ T2 ss tv2
b
(4.5)
b
It is impossible to directly estimate σ T2 ss for each individual grid cell because
b
only σ T2 sv is observed. However, using the properties of variance estimation (Navidi,
b
2008), we can derive an equivalent form of Equation 5 by binning all grid cells according
to their respective LAI, and taking the variance within each bin, i.e.:
var ⎡⎢σ T2 sv − σ T2 v ⎤⎥ = var ⎡⎢σ T2 ss ⎤⎥ tv4 ∈{ LAI =1... n}
⎣
⎦
b
⎣
b
⎦
(4.6)
The implied assumption in (6) is that tv is constant within each LAI bin. To estimate
var ⎡⎢σ T2 ss ⎤⎥ , we compute var ⎡⎢σ T2 sv − σ T2 v ⎤⎥ for LAI = 0 and assume it is representative
⎣ b ⎦
⎣ b
⎦
for pixels with higher LAI values. The transmissivity is then estimated by:
tv = 4
var ⎡⎢σ T2 sv − σ T2 v ⎤⎥
⎣
b
var ⎡⎢σ T2 ss ⎤⎥
⎣ b ⎦
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⎦
(4.7)
Note that equation (7) is applied slightly differently when calculating tv from the airborne
and spaceborne data. For calculation of tv from the airborne microwave measurements,
the
σ T2 v
within a 500 m pixel can be assumed be to be negligible.
4.3 Results and Discussion
4.3.1 Estimation of transmissivity from brightness temperature variability
Figure 34 shows the observed spatial variability in the airborne Tb dataset, and the
temporal variability in the spaceborne Tb datasets plotted as a function of LAI. As can be
seen, an inverse relationship clearly exists between σ T2 sv and LAI.
b
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Figure 34: Variance of Tb with respect to LAI (a). The spaceborne AMSR-E Tb data is shown in
blue, as compared to the airborne PSR (red). The empirically derived transmissivity from PSR
(red) and AMSR-E (blue) were fit to an exponential curve for model generation, using non-linear
least squares (b). The X’s denote the LAI cutoff values for the different measurement scales.
Each PSR datapoint in the figure represents the sub-grid spatial variability in Tb
within each 500 x 500 meter pixel (see Figure 32 for reference). Note that each 500 m
pixel has a single, integer LAI value, whereas the AMSR-E footprint averaging leads to
mixed-pixels of non-integer values in Figure 34a. For both airborne and spaceborne
datasets, the PM Tb data appears to follow an exponential relationship with respect to
LAI, with the variability in Tb decaying to minimal levels at LAI values greater than 4.
101
As can be seen in Figure 34, there is a discontinuity in the lower bound of the spaceborne
dataset ( σ T2 sv < 28 K), which is an artifact of the removal of air temperature, as described
b
in equation 6. Additionally, the airborne PSR datasets were collected during a relatively
short time window (a total of 5 days), thus it is unlikely to exhibit the same magnitude of
variability as compared to the AMSR-E measurements, which were taken over the entire
winter season.
The transmissivity for each integer LAI bin was computed according to equation
6 above. Once the transmissivity had been computed as a function of LAI, we fit an
exponential model to the transmissivity estimates, in order to create an effective
transmissivity model, as shown in Figure 34. The two-term exponential model had the
following form, y = aebx +cedx , where x corresponds to LAI, and a, b, c, and d are model
parameters fitted by a non-linear least squares regression. The two term exponential
model was used because there are likely multiple decay processes occurring
simultaneously, therefore a one-term exponential model did not adequately describe the
decay rate. For airborne datasets, we used a model fit with x = LAI -1 in order to best fit
the data. Transmissivity derived from airborne (PSR) measurements is significantly
greater than that derived from spaceborne (AMSR-E) data, although both exhibit the
same exponential decay. This is an interesting finding, and is consistent with the fact that
the spatial averaging of the AMSR-E antenna magnifies the effects of vegetation on the
transmissivity. To ensure that this result was not influenced by different physiographic
features within the study area, we computed the correlation coefficients between σ T2 sv
b
102
and variables such as elevation and slope. With R2 values of 0.01 for elevation and
0.008 for slope, the correlation does not appear strong enough to affect this methodology.
Additionally, while our transmissivity model is derived from different principles than that
of Langlois et al. (2011), the saturation values for the transmissivity at 37 GHz are
similar in magnitude, thus providing some measure of validation against existing models.
To validate the AMSR-E transmissivity model with alternate Tb data, we
processed the same LRSA for the winter seasons of 2004 and 2005, using an AMSR-E 37
Ghz v-pol Tb timeseries from November 1-March 15th, and examining the temporal
variability in Tb of each pixel. The snow season of 2005 in Colorado was higher than
average (http://www.co.nrcs.usda.gov/), while the 2003 and 2004 snow seasons were
lower than average (~75%), thus providing a robust manner in which to test our
transmissivity modeling hypothesis. The same processing methods were used as
described in sections 3.1-3.3. As shown in Figure 35, the 2004-2005 observed temporal
Tb variability as a function of LAI is very similar to that from 2003. Additionally, the
transmissivity estimates derived from the 2004-2005 PM Tb using equation 6 closely
match the modeled transmissivity values from 2003 and exhibit the same exponential
decay, with an R2 value of 0.85.
103
Figure 35: Scatter plot of the observed Tb variability from 2004 and 2005 as compared to LAI
(a). The transmissivity derived from the 2004 and 2005 AMSR-E data (y-axis), as compared to
the predicted transmissivity from the exponential model(x-axis), with an R2 value of 0.85 (b).
4.3.2 Mapping passive microwave-retrievable SWE
For exponentially decaying quantities, the e-folding length is defined as the
distance at which a variable decays to 1/e of its original value. Here, we used the efolding length of the Tb variability as a simple cutoff for where microwave remote
sensing of snowpack is no longer practical due to signal masking by vegetation. Note that
104
future work is required to better define whether 1/e is the correct cutoff; the sensitivity to
this assumption is examined later in this paper. The LAI cutoffs are 1.8 for AMSR-E and
4.7 for PSR, respectively, based on the e-folding length of the transmissivity signal.
We then classified our study area using a binary map of “SWE retrievable” areas using
the SNODAS SWE product. Due to the differing LAI cutoffs, separate maps of airborne
and spaceborne microwave retrievable areas were constructed; these are shown in Figure
9.
Figure 36: The retrievable land area for both airborne (a) and spaceborne (b) PM remote sensing.
The blue pixels correspond to optimal areas for PM SWE retrieval, whereas red is suboptimal
(due to vegetation coverage). The bottom figure has been gridded to the approximate spatial
resolution of AMSR-E measurements. The horizontal line in the top figure corresponds to
MODIS LAI tile boundaries.
105
We used the maps shown in Figure 36 to quantify the total microwave retrievable
SWE in the study area that can be characterized via spaceborne and airborne microwave
remote sensing. Over the entire study area, 88.9 percent of the land area is retrievable
with airborne methods, which corresponds to 74.3 percent of the total SWE that exists at
peak SWE accumulation based on the amount of SWE in retrievable areas relative to the
total SWE of the entire area. With spaceborne data, 52.8 percent of the land area and
35.5 percent of the SWE is retrievable.
In our study domain, there is 57,744 km2 less
land area for SWE retrieval from spaceborne vs airborne PM methods.
We quantified the total amount of SWE accumulation that can be characterized
from airborne and spaceborne measurements for major Colorado river basins, including
the Yampa, Upper Colorado, Gunnison, Arkansas, Rio Grande, Delores, and North Platte
Rivers. For each basin, we estimated the percentage of land area, and the percentage of
SWE available (based on the SNODAS product) for PM remote sensing based on the LAI
thresholds. For example, the areas that are microwave retrievable via airborne remote
sensing in the Upper Colorado, along with the March 15 SWE from SNODAS is shown
in Figure 37.
106
Figure 37: Upper Colorado river basin delineated into optimal (blue) and suboptimal (red) bins
based on the MODIS LAI , at airborne resolution (a). The corresponding basin SWE, as obtained
from SNODAS, is shown as well (b), with units in mm.
The results for all basins are summarized in Figure 38 and Table 5. Of the river
basins examined, the Yampa has the highest percentage of both land area and SWE
retrievable via PM based remote sensing techniques, with 96.8 percent of the land area
and 86.5 percent of the SWE available for PM remote sensing at airborne observation
resolution: at spaceborne resolution, 88.1 percent of the land area and 51.2 of the SWE is
107
retrievable. In more vegetated basins, the percentage of retrievable land area and SWE is
much lower, with only 68.9 and 64.5 percent of SWE retrievable using airborne
observations, and 21 and 16 percent of SWE retrievable at spaceborne resolutions in the
upper Colorado and upper Gunnison basins, respectively. This disparity is quite intuitive
upon visual inspection, as the Yampa River basin is characterized mainly by expansive
grass and shrublands, with intermittent deciduous and evergreen forests scattered
throughout the more mountainous areas. In contrast, the upper Colorado River basin is
characterized by dense coniferous forests in both valleys and upland areas, with much
lower amounts of grass and/or shrubland, especially in areas with relatively high snow
accumulation.
108
Figure 38: Major river basins of Colorado with elevation in meters(a), with percentages of SWE
(from SNODAS) accessible to PM remote sensing techniques at airborne (cyan) and spaceborne
(black) resolutions(b). River basins are the Yampa, upper Colorado, upper Gunnison, Arkansas,
North Platte, and Delores, respectively (from left).
For the Yampa and upper Colorado, the amount of area retrievable is much greater than
the SWE retrievable; this is because areas with the deepest snow accumulation often
109
occur in forested areas. Thus the relatively low LAI values for the Upper Colorado in
Figure 37 tend to correlate with areas with relatively low SWE accumulation.
Table 5: Major river basins of Colorado, with percentages of area accessible to PM remote
sensing techniques (according to LAI), and the associated retrievable SWE (from SNODAS) at
both airborne (AB) and spaceborne (SB) measurement scales.
% Obs
% SWE Obs
% Obs
% SWE Obs
River Basin
Latitude
Longitude
(SB)
(SB)
(AB)
(AB)
Yampa
40.524
-107.22
88.1
51.2
96.8
86.5
Colorado
38.62
-106.87
41.3
21.0
77.2
68.9
Gunnison
38.79
-107.7
57.3
16.0
83.9
64.5
Arkansas
38.54
-106.6
0.08
31.0
74.4
74.8
Rio Grande
37.5
-106.1
51.9
41.3
92.9
88.8
North Platte
40.96
-106.2
73.6
48.3
85.4
73.6
Delores
38.39
-108.8
18.6
0.06
85.9
70.4
4.4 Discussion and Conclusion
4.4.1 Discussion
In this study, we calculated an effective transmissivity that is based entirely on the
variability of airborne and spaceborne measured Tb. The derived model appears to be in
agreement with a recently published dataset by Roy et al. (2012), however the models are
parameterized with different vegetation metrics, thus a true comparison is impossible
without additional data. Existing empirically based transmissivity models (e.g. Kurvonen
& Hallikainen, 1997; Kruopis et al., 1999, Langlois et al., 2011) mainly use biomass
110
metrics such as stem volume, which are not available on a global scale, whereas the LAI
parameterization used in this study is available globally with both high spatial and
temporal resolution.
While it is clear that the spatio-temporal Tb variability in these data do indeed correlate
with vegetation via the LAI (R values of -0.85 and -0.74 for airborne and spaceborne
measurements, respectively), the correlation may not imply causation. The decay of
spatial Tb variance from the airborne measurements with increasing LAI may also be
caused by other factors such as the fact that the trees reduce hillslope scale (e.g. 100+ m)
spatial variability in snowpack properties by reducing the effect of wind on scour and
drifting. Thus, we would expect a priori that there would be somewhat less variance in
the Tb of the snow under the vegetation. In our analysis, we hypothesize that this has the
effect of reducing the snow Tb variance in vegetated areas. This would cause our analysis
to underestimate the vegetation transmissivity. Thus, our transmissivity estimates are
conservative, and the percent of microwave-retrievable SWE should be interpreted as a
worst-case value. In other words our results and the associated caveats support the
conclusion that at least 35.5 % of the SWE within the CLPX LRSA is microwaveretrievable at spaceborne resolution.
Another topic worthy of discussion is the e-folding method by which we
delineated where the variability in the seasonal Tb falls below a certain defined threshold
and no longer provides useful information for SWE retrieval. Because the transmissivity
threshold directly determines the LAI cutoff and thus the amount of SWE that can be
measured, uncertainty in this threshold impacts the overall fidelity of our results. For
111
example, with spaceborne Tb retrievals, the e-folding distance of the transmissivity curve
corresponded to an LAI cutoff value of 1.8.
However, if we extend the threshold to
lower transmissivity values, we can calculate the change in retrievable SWE over our
study domain. Figure 39 shows the change in SWE retrievability as the LAI cutoff value
increases from 1.8 to 3.8. The currently selected value of LAI=1.8 corresponds to
retrievability of 35.5 percent of the overall SWE within the LRSA study area. However,
as the transmissivity threshold is dropped, and the LAI cutoff value increased, there is a
dramatic increase in the overall SWE retrievability, reaching 81.8 percent at an LAI value
of 3.8 for spaceborne observations.
112
Figure 39: By varying the LAI cutoff threshold which defines adequate variability in the PM Tb
signal (a) for SWE retrieval, we can estimate the total percentage of SWE that is retrievable over
our study area(b), as a function of changing LAI.
By applying the methodology described herein to spaceborne Tb measurements,
future studies can identify areas where vegetation will likely mask the Tb signal, and thus
effectively decrease the uncertainty of the snow properties derived from PM Tb inversion.
Vegetation masking could also be used within large scale, hemispheric SWE retrieval
113
algorithms such as GlobSnow that weigh satellite radiometer derived information with an
observational first guess from weather station measurements.
Regions with low
microwave transmissivity and high vegetation density could have relatively low
weighting applied to the PM observation-based retrieval and high weighting applied to
the in-situ weather stations. Thus, it represents an effective and easily integrated
contribution to large scale assimilation studies involving PM Tb and SWE, as vegetation
is often a constituent of snow covered areas.
While such vegetation masking is a
beneficial processing step, improvements in estimates of SWE and other snow properties
from PM inversion is also dependent on two other entities; namely the accuracy of snow
model physics that are used to relate physical snow properties to Tb. and the scaling
processes that occur as measurement resolution transitions from in situ to spaceborne
scales. However, in recent years, forward radiative transfer models (Wiesmann &
Mätzler, 1999; Liang et al., 2008; Lemmetyinen et al., 2010) have arguably advanced to
the point of being able to accurately characterize microwave Tb at the point scale, given
accurate estimates of snow grain size and layering (Durand et al., 2008). Thus, as
improvements are made in the modeling and characterization of snow states, SWE
retrieval capabilities should increase in spite of reduced PM Tb variability in vegetated
areas. Moreover, recent work has shown that the sensitivity of Tb measurements to SWE
is not inherently dependent upon spatial scale (Vander Jagt et al., 2013).
The contribution of this study is to not only advance understanding of the physical
processes and interactions between vegetation, snow and Tb, but also attempt to quantify
its effects in an applied manner as it relates to water resources. Because our assumptions
114
are conservative, throughout, we hypothesize that more than 35.5% of the total SWE
accumulation is spaceborne microwave retrievable within our LRSA study domain.
Refining this estimate will require further work in development of models of microwave
vegetation transmissivity as a function of readily-available datasets, such as LAI. Studies
such as Langlois et al. (2011) and Roy et al. (2012) have been critical in advancing this
field; further such studies are necessary. Furthermore, estimates of the vegetation
properties themselves, such as LAI, need further improvement in mountainous areas.
4.4.2 Conclusion
We calculated a conservative estimate of microwave vegetation transmissivity
using MODIS LAI data. Separate relationships with respect to LAI were developed with
airborne (PSR) and spaceborne (AMSR-E) passive microwave datasets. An interesting
result of this analysis is the apparent non-linear contribution of vegetation as a function of
measurement resolution. Our study suggests that at spaceborne PM measurement scales,
the impact of vegetation at microwave wavelengths aggregates in a way that causes a
reduction in Tb variability, and equivalently transmissivity, as compared to higher
resolution airborne measurements. Further studies should be conducted in an attempt to
understand why this apparent non-linearity exists, which should lead to improvements in
modeling at different spatial resolutions.
We validated our transmissivity model independently using microwave Tb from a
small(2004) and large snow year (2005) in Colorado. The derived transmissivity values
were well-correlated with the exponential model, resulting in an R2 value of 0.85.
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We used the model to predict areas where SWE is microwave retrievable. This is
of particular relevance for the snow research community using passive microwave data in
SWE retrieval algorithms and data assimilation schemes. We found 87.8% of the land
area, and 74.3% percent of the snow water equivalent contained within the LRSA is
found in areas below the LAI values which limit PM remote sensing of SWE at airborne
PM resolution, whereas 46.2 percent of the land area and 35.5 percent of the SWE is
retrievable at spaceborne PM resolution. Thus, PM based techniques should remain a
valuable tool for assessing the snow accumulation in those areas, and lends credence to
continued efforts towards this objective.
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Chapter 5 Conclusion
5.1 Research Findings and Contribution
5.1.1 Microstructure Characterization
Utilizing in-situ measurements of snowpack properties and a forward microwave
modeling framework, predicted Tb was compared against observed Tb to determine the
efficacy of the different methods for characterizing microstructure utilizing the
microwave emission model of layered snowpacks (MEMLS), a commonly used RTM for
layered snowpack. It should be noted that overall sample size (two) was small, due to the
difficulty of making these labor intensive measurements in the field.
In Chapter 2, it was detrmined that using MEMLS with measurements of S is
more attractive than using MEMLS with measurements of Dg, for several reasons. First,
measurements of S are repeatable and objective, while measurements of Dg vary from
observer to observer, and are highly subjective. Second, in this study, the MAE of the Tb
simulations using Dg is roughly four times that when using the objective measurements of
S. Lastly, MEMLS simulations forced with S are capable of replicating the observed Tb if
the theoretical relationship between Le and S is modified with an empirical constant. In
this study, it was found that the empirical constant suggested by Brucker et al. (2011)
provides the optimal fit between observed Tb and those predicted by MEMLS when
relating S to Le.
117
All of this has implications for utilization of microwave measurements in
characterizing SWE. Microwave inverse algorithms calculate estimates of SWE and grain
size (Tedesco & Narvekar, 2010), and these grain size estimates must be validated in the
course of algorithm development. Moreover, grain size prognostic models (Flanner &
Zender, 2006) are a critical component of radiance assimilation schemes (Durand et al.,
2009); as the models typically prognose S, a robust link between S and Le is required for
coupling to MEMLS. Objective characterization of snow microstructure in forward
radiative transfer modeling is critical in being able to accurately calculate SWE from
measurements of microwave radiance.
5.1.2 Scaling Issues (PM)
The results presented herein show that passive microwave Tb are sensitive to
changes in spatial mean snow depth, regardless of spatial heterogeneity in snow
properties such as grain size, layering, and density. To first order, however, the spatial
patterns of observed Tb are more sensitive to grain size and stratigraphy than to depth.
Across three study areas, Tb decreases by 23-35 K as depth increased up to the signal
saturation depth, which ranged from 70-120 cm. With regard to vegetation sensitivity,
forest fractions (F) as little as 0.2 can modify the PM measurement by up to 10 K, and F
greater than 0.6 mask virtually all of the microwave signal attributable to snow.
Additionally, as the scale of the microwave measurement is increased, our results indicate
that the PM measurement remains sensitive to the subpixel mean depth, as modeled
measurement resolutions of 1000 meters only differ by 1.3 - 3.1 K as compared to
measurements obtained at 100 meter resolution over individual ISAs. Thus, the main
118
limitation for PM remote sensing of snow in mountainous areas seems to be the inclusion
of vegetation in the pixel, and the nature of its attenuating and bias characteristics.
Studies at individual ISAs with fractional forest coverage found that sensitivity to snow
depth was reduced by 23-63 percent due to presence of vegetation, which leads to
significant errors in depth retrieval when not taken into account. With no a priori
knowledge of snowpack properties, or a method by which subpixel vegetation can be
classified and modeled accordingly, SWE estimates derived from PM remote sensing
estimates will continue to be characterized by large uncertainty in complex mountain
environments.
Further studies should be conducted in an attempt to understand how microwaves
interact and propagate through mountain snowpacks. Of course, correct radiative transfer
modeling will only result from accurate measurement of grain size. Thus, improved
methods of characterizing grain size are important for enhancing existing RT models of
snow and SWE estimation. Further analysis should also be conducted concerning the
metamorphism of snow throughout the winter months, as a result of external and internal
forces which drive the transformation of snowpack properties. Until metamorphism of
the snowpack properties can be accurately modeled with measured and/or modeled
meterological data, accurate SWE estimation from PM measurements will continue to
exhibit large uncertainty.
Lastly and perhaps most importantly, characterization of
subpixel vegetation effects by use of an appropriate global remote sensing dataset would
likely improve SWE estimates from PM remote sensing observations.
119
5.1.3 Vegetation Contributions
We calculated a conservative estimate of microwave vegetation transmissivity
using MODIS LAI data. Separate relationships with respect to LAI were developed with
airborne (PSR) and spaceborne (AMSR-E) passive microwave datasets. An interesting
result of this analysis is the apparent non-linear contribution of vegetation as a function of
measurement resolution. Our study suggests that at spaceborne PM measurement scales,
the impact of vegetation at microwave wavelengths aggregates in a way that causes a
reduction in Tb variability, and equivalently transmissivity, as compared to higher
resolution airborne measurements. Further studies should be conducted in an attempt to
understand why this apparent non-linearity exists, which should lead to improvements in
modeling at different spatial resolutions.
We validated our transmissivity model independently using microwave Tb from a
small(2004) and large snow year (2005) in Colorado. The derived transmissivity values
were well-correlated with the exponential model, resulting in an R2 value of 0.85.
We used the transmissivity model to predict areas where SWE is microwave
retrievable. This is of particular relevance for the snow research community using
passive microwave data in SWE retrieval algorithms and data assimilation schemes. We
found 87.8% of the land area, and 74.3% percent of the snow water equivalent contained
within the CLPX LRSA in Colorado is found in areas below the LAI values which limit
PM remote sensing of SWE at airborne PM resolution, whereas 46.2 percent of the land
area and 35.5 percent of the SWE is retrievable at spaceborne PM resolution. Thus, PM
120
based techniques should remain a valuable tool for assessing the snow accumulation in
those areas, and lends credence to continued efforts towards this objective.
121
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Appendix A: Estimating Spatially Continuous Snow Properties
One of the main objectives of this study was to investigate how subpixel heterogeneity
affects the observed Tb, as a function of scale. Thus, it was desirable to obtain a method
by which all of the snowpit data within each ISA could be utilized with the spatiallydistributed LIDAR depth estimates in a way that most closely represents the true
variability of snowpack found in mountainous environments. There is a large amount of
existing literature that has attempted to predict the variability of different snow properties
using geostatistical (Erxleben et al. 2002) as well as physiographic methodology
(Molotch et al., 2006, Anderton et al., 2002). In general, while some of these efforts have
been successful to a degree, the results still do not necessarily capture the true
spatialvariability associated with snow properties. For example, in Erxleben et al. (2002)
, only 18–30% of the observed variability in snow depth was resolved in different CLPX
ISAs. For this reason, we take an alternative approach in order to represent the spatial
variability of snow properties in our modeling efforts.
We spatially distributed all of the snowpits over an ISA using a Voronoi scheme,
in which each individual 1.5 m pixel is assigned snowpack characteristics based on its
spatial proximity to the nearest snowpit. The Voronoi cell Vk associated with the site Pk
is the set of all points in X whose distance to Pk is not greater than their distance to the
140
other sites Pj, where j is any index different than k. Therefore, we created a simple
algorithm by which data from the nearest snowpit adjacent to the individual pixel can be
mapped into the pixel while preserving the true depth of that pixel.
The snowpit
stratigraphic layers are simply linearly scaled based on the difference between the pixel
snow depth to the actual pit depth.
Using a traditional Voronoi scheme creates
unrealistically sharp boundaries in the resulting snowpit map (Figure 22). To avoid this
unrealistic spatial distribution, we added noise to the Voronoi scheme by means of a
multinomial distribution, which has desirable statistical properties for our experiment. A
multinomial experiment consists of n repeated trials, where each trial has a discrete
number of possible outcomes. On any given trial, the probability that a particular
outcome will occur is constant. In our case, we assigned probabilities to each pixel based
on the distance to adjacent snow pits, with a total of n different outcomes (see Figure
22b) corresponding to the n snowpits.
The snowpack then assumes a probabilistic
nature, which is more representative of the natural variability than is typically observed.
It should also be noted that we omitted a small amount of snowpit data, due to certain
undesirable characteristics for spatial representation of snowpack. For example, of the
eight snowpits shown in Figure 16 which comprised a subset of the overall snowpit
samples, pits 1 and 7 exhibit a single snow layer of 3-4 cm, with a corresponding pex of
0.05 mm. Scaling this pit depth to a value of 50 cm in the way described in section 3.3.1,
the resulting stratigraphic model for that pixel would be unrealistic, because those
specific properties are only found in shallow, single layered snowpack. Because these
shallow pit snow properties were only found in select areas with little snow
141
accumulation, we reasoned that a deep snowpack would not be characterized by these
conditions, and thus would be poorly represented if shallow snow pit properties were
used in the depth mapping function. Because of this, we omitted excessively shallow
snowpit properties from our analysis using a simple search criteria.
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