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ATMOSPHERIC SCIENCE LETTERS
Atmos. Sci. Let. 7: 9–14 (2006)
Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/asl.122
Assessing vertical resolution requirements for
operational weather radar data quality
Marion P. Mittermaier,* Anthony J. Illingworth and Robin J. Hogan
Department of Meteorology, University of Reading, Reading, UK
*Correspondence to:
Marion P. Mittermaier, Met
Office, FitzRoy Rd, Exeter,
EX1 3PB, UK.
E-mail: marion.mittermaier@metoffice.gov.uk
Received: 27 September 2005
Revised: 19 January 2006
Accepted: 26 January 2006
Abstract
High-resolution, 0.28◦ beamwidth range-height-indicator (RHI) data are used to simulate
the reflectivities measured at various ranges by an operational radar with a 1◦ beamwidth.
It is found that the sampling is optimal when the elevation increments equal the beamwidth.
Larger increments lead to an unacceptable loss of information. Copyright  2006 Royal
Meteorological Society
Keywords:
oversampling; brightband; scan sequence
1. Background
Operational radars scan in a sequence of plan position
indicator (PPI) scans at different elevations producing
a volume scan. The aim is to obtain information on the
radar reflectivity at various heights. If the sole purpose
of collecting and processing radar data were to obtain
surface estimates of precipitation, then scanning in
the rain at a single elevation as close to the ground
as possible (without contaminating the signal with
clutter) would be the solution. Very often this is not
possible because at increasing ranges the low altitude
level of the melting layer coupled with the earth’s
curvature means that the beam is no longer in the
rain, and some knowledge of the vertical profile of
reflectivity (VPR) is needed to infer the rainfall rate
at the ground.
Multiple elevation data are essential for determining the shape of the VPR, forming the basis for VPR
correction schemes that correct for melting effects
and ice, assisting in the discrimination between stratiform and convective precipitation processes, determining the development stage of thunderstorms as in the
GANDOLF forecasting scheme (Pierce et al., 2000)
and deriving Doppler wind fields. The reflectivity at
higher altitudes in the ice contains additional information. Hogan et al., (2006) reported that the error in
the ice water content retrieved from radar reflectivity (taken between 10 and 40 km from the radar) is
about +50%/−33% between −20 and −10 ◦ C, rising
to +100%/−50% for temperatures less than −40 ◦ C.
Converting these percentage errors to their logarithmic equivalents suggests that if the reflectivity Z in
the ice is known to be better than 1.5 dB (rounded
from 1.76 dB), it can be used to evaluate the performance of the ice parameters in operational numerical
weather prediction (NWP) models, and ultimately be
assimilated into such NWP models.
Copyright  2006 Royal Meteorological Society
The challenge of providing adequate information for
downstream applications and users of radar data is one
shared by all operational radar networks and is, fundamentally, a function of the underlying climatic regime,
radar location relative to the terrain and also system
specifications. In recent years Westrick et al. (1999)
and Brown et al. (2002) discussed NEXRAD radar
scan strategy needs in terms of high-altitude radar
locations and obtaining accurate echo top heights. Others like Novák and Kráčmar (2002) discuss the implementation of an interlaced scan strategy, first proposed
by Vasiloff et al. (1987). Still others describe the Canadian National Radar Network (Joe and Lapczak, 2002)
and the South African networks (Terblanche et al.,
1999), both using more than ten elevations scanning
up to between 24 and 45◦ with rapid update times of
the order of 5 min. In the United Kingdom, the radar
network consists of 11 C-band radars (at the time of
study) with a 1◦ beamwidth (Harrison et al., 2000).
One of the two standard four-elevation scan strategies
is used; either 0.5, 1, 1.5 and 2.5◦ (with some oversampling), or the other 0.5, 1.5, 2.5 and 4◦ (with no
oversampling).
In this letter we investigate the potential benefits
of oversampling on data quality to provide a better
representation of the VPRs for use in brightband
correction schemes and to estimate ice water content
in the ice. We use the UK radar network to illustrate
the method.
2. Beam geometry and range effects
To place the problem of sampling a varying VPR
with an operational radar in perspective, we consider
an idealised profile, which is a simplified version
of that used by Kitchen et al. (1994) and which
has a constant reflectivity of 20 dBZ in the rain,
10
M. P. Mittermaier, A. J. Illingworth and R .J. Hogan
a brightband 700-m deep with a peak reflectivity
of 28 dBZ and a constant reflectivity lapse rate
of 3 dB·km−1 above the brightband as shown in
Figure 1(a). To simulate the sampling that would
be achieved by the operational Met Office radars,
this profile template is convolved with a Gaussian
beamwidth having a two-way full-power effective
beamwidth of 1◦ , and the resulting VPRs at 20, 40, 60
and 80 km are shown. Pure beam broadening effects
cause the peak value of reflectivity to fall to 36.5,
35.2, 35.3 and 33.6 dBZ , respectively. At a range
of 80 km the smearing out of the echo leads to an
apparent increase of 1 dB in the reflectivity of the rain
at a distance of 600 m below the true bottom of the
brightband. For a 12-dB brightband enhancement, the
equivalent distance at this range is 850 m.
Figure 1(a) was compiled with a 3 dB·km−1 slope
above the brightband. Convolution with the beam
pattern also introduces a constant positive bias to the
resulting reflectivities above the brightband in the ice,
but the magnitude is dependent on the steepness of
the lapse rate of reflectivity. This bias is shown in
Figure 1(b) as a function of range and for the three
lapse rates of 3, 6 and 9 dB·km−1 . Steeper slopes
imply a larger positive bias at progressively closer
ranges. This increase appears to be nearly linear with
range for smaller lapse rates, but becomes increasingly
non-linear as the lapse rate increases. For small lapse
rates the effect is negligible, with biases <0.15 dB,
while for the steeper gradient of 6 dB·km−1 we can
derive Z with the accuracy of 1.5 dB (required for
estimating ice water content) out to a range of 80 km,
and for gradients of 9 dB·km−1 this accuracy limit is
reached at a range of 60 km.
The idealised profiles in Figure 1(a) are of very high
resolution (10 m), but resampling at selected heights
corresponding to a few elevations and reconstructing
the profiles using these few values will introduce differences between the original and the reconstructed
one. The differences will depend on where the resampling is performed in height, and also on the range.
4.5
Ideal
20 km
40 km
60 km
80 km
4
Height (km)
3.5
3
2.5
2
1.5
1
0.5
14
16
18
3.5
3
Bias (dB)
20
22
24
26
28
30
Reflectivity factor (dBZ)
(a)
3 db.km-1
6 db.km-1
9 db.km-1
2.5
4.1. Significant echo height distribution
1.5
1
0.5
(b)
20
A database of 981 range-height-indicator (RHI) scans
sampling nine events between August and December
2000 were used. The data were collected using the 3GHz dual-polarisation Doppler weather radar located
at Chilbolton (51.14 ◦ N and 1.44 ◦ W), southern England (see Goddard et al., 1994). The 25-m antenna
provides a 0.28◦ beamwidth. Typically, the RHI scans
have 0.1–0.2◦ elevation steps between 0–30◦ . Data
are collected to a range of 90 km with a 300-m range
resolution. Figure 2 shows a typical RHI from the
database.
Only VPRs with reflectivities greater than 12 dBZ
at the lowest level, and below the freezing level, of
a particular scan sequence were considered, chiefly
because the main focus here is on rainfall. The
threshold corresponds to a rainfall rate of 0.2 mm·h−1
(Marshall and Palmer, 1948). Freezing level height
forecasts from the mesoscale version of the Met Office
Unified Model (UM) were used to ensure that the
lowest beam was in the rain.
4. Studying the effects of oversampling
2
0
3. Description of high-resolution radar data
30
40
50
60
Range (km)
70
80
Figure 1. (a) The Nimrod VPR template convolved with a 1◦
beam at 20, 40, 60 and 80-km range showing beam broadening
effects. (b) Biases introduced in the ice due to beam pattern
convolution as a function of range and VPR slope
Copyright  2006 Royal Meteorological Society
The echo distribution in the vertical was analysed
using the RHI database. This was done to determine
up to which height the radar coverage is required to
capture the most important features and the maximum elevation that is required to provide this coverage. Cumulative distributions of the frequency of
occurrence of significant reflectivities (≥12 dBZ in
the rain) were calculated. These distributions, shown
in Figure 3(a) and (b), are presented in two ways, first
as a distribution in height and then as a function of
elevation angle. The data are sorted into 10-km range
bins of either 500-m height bins from 0 to 9 km,
Atmos. Sci. Let. 7: 9–14 (2006)
Vertical resolution requirements for operational weather radar data quality
11
Figure 2. Example of a high-resolution RHI for 2 November 2000 at 09 : 13 UT showing radar reflectivity factor
Figure 3. Cumulative distributions of the frequency of occurrence of echoes in the RHI database exceeding 12 dBZ as a function
of height in (a) and as a function of elevation in (b). Contours are every 0.1 between 0 and 1. (c) The fraction of the area within a
range of 80 km, which is sampled for four different radar elevations as a function of altitude. It is desirable to sample 2 km higher
than the brightband (see text)
or 0.5◦ elevation bins from 0 to 30◦ . At least 90%
of significant reflectivities appear to be found below
4 km at all the ranges up to 90 km from (a). From
(b) it can be seen that to achieve this 90% level of
coverage at 20 km, an elevation of 15◦ is required.
This requirement decreases rapidly with range, and
Copyright  2006 Royal Meteorological Society
elevations less than 5◦ are sufficient for ranges greater
than 60 km to achieve the same 90% margin. Given
the wide spectrum of data included in this data set,
a suggested maximum height of 5 km would come
close to including most reflectivities of relevance for
the VPR related applications.
Atmos. Sci. Let. 7: 9–14 (2006)
12
M. P. Mittermaier, A. J. Illingworth and R .J. Hogan
4.2. Scan sequence selection
4.3. Error analysis
The aim of implementing a volume scan is to gain a
three-dimensional representation of the radar area. If
coverage up to, say, 5-km above ground level (AGL)
were required, then for a maximum elevation of 4◦
this is only possible at ranges greater than 60 km. For
a maximum elevation of 2.5◦ this is only achievable
beyond 100 km from the radar. Yet the 0.5◦ base scan
is below 1 km up to 70 km, below 2 km up to 110 km,
and below 3 km AGL up to 150 km range.
Base scan is a site-specific parameter and as such
will not be discussed here. On the basis of observational evidence Smyth and Illingworth (1998) showed
that it is desirable to sample up to a height of at
least 2 km above the brightband height to distinguish
between different ice processes, and to discern whether
the VPRs are convective or stratiform; an important
consideration when attempting to estimate the surface
rainfall rate. Aggregation gives a strong signature in
the 1–2 km above the brightband for stratiform VPRs.
In the United Kingdom, freezing level height forecasts (typically t + 4h forecasts) from the UM are used
in the operational VPR correction scheme (Harrison
et al., 2000). Their use was evaluated by Mittermaier
and Illingworth (2003) and the rms of the height
in the brightband was found to be less than 150 m,
which is well within the specification needed for
the correction scheme. Errors for the European Centre for Medium-range Weather Forecasts (ECMWF)
northern hemisphere forecasts were also comparable
to those obtained for the UM at longer lead times
(12–36 h).
To assess the impact of increasing the maximum
elevation angle on radar areal coverage, consider
Figure 3. The figure shows the fraction of radar area
that is covered within a range of 80 km from the radar,
given four different maximum elevations, 2.5, 4, 8
and 16◦ . Therefore, if the freezing level were at 1 km
AGL, then a 2-km coverage above the brightband
height means that the radar needs to sample up to
3 km, so for a maximum elevation of 2.5◦ and a
maximum range of 80 km, only 26% of the radar
area would be sampled. With a 4◦ maximum elevation
71% of the radar area is sampled. For 8◦ the area
increases to 93%, and for 16◦ 98% of the area at
3 km is sampled. Notice that the incremental increases
in coverage grow smaller as the maximum elevation
increases.
One way of studying the effect of oversampling
is to nest several equally spaced scan sequences
spanning the same elevation interval. Starting with
a coarse sequence (effectively undersampling), each
of the other sequences is nested, providing progressively finer resolution data until a resolution near
that of the Chilbolton radar of 0.28◦ is reached.
Here, minimum and maximum elevations of 0.5 and
4.5◦ were used. This elevation interval was then
sampled at 0.33, 0.5, 0.67, 1, 1.33 and 2◦ producing scan sequences of 13, 9, 7, 5, 4 and 3 tilts,
respectively.
The high-resolution RHIs were convolved with a 1◦
beamwidth Gaussian beam pattern, and then resampled
according to the nested sequences to investigate
the effect of oversampling the same elevation angle
interval.
By linearly interpolating the resampled profiles
back onto the original high-resolution heights, error
statistics can be calculated. As all sequences are
sampling the same height ranges at various resolutions,
it is possible to calculate the mean root-mean-squared
difference (rmsd ) in dB averaged over height; as a
function of constant elevation angle separation, and
for different horizontal ranges from the radar. This is
plotted in Figure 4. The 95th percentile rmsd is also
plotted as an indication of the maximum error.
The graph yields some surprising results. It would
appear that the oversampling at 0.33◦ as compared to
2◦ would result in only a very small mean decrease
(∼0.4 dB) in the rmsd error. The maximum mean
error is lowest when the elevation step separation
is about the same as the beamwidth. The mean
rmsd increases in range, but beyond 70 km the beam
broadening effects produce a smoothing or damping
effect for the elevation steps greater than 1◦ , so that
the errors are seen to decrease slightly with elevation
step separation.
So why does oversampling at 0.33◦ not improve
Z ? Calculating the mean over the height range does
not show height intervals where the errors are greater
than or less than this mean value. The brightband
is typically at 1–2 km, so that at 80-km range most
elevations are sampling in the ice. Values of Z in the
ice above the brightband are not well related to the
values of Z in the rain (e.g. Fabry et al., 1992), so for
VPRs there is little to be gained from knowing Z in the
ice more accurately. This was confirmed by Kitchen
(1997) who showed that for VPR correction only small
Copyright  2006 Royal Meteorological Society
8
Mean rmsd in height (dB)
7
20 km
40 km
60 km
80 km
Max
6
5
4
3
2
1
0
0.33 0.5 0.66
1
1.33
2
Elevation step separation (°)
Figure 4. The mean rmsd in dB averaged over height as a
function of elevation step angle separation, for different ranges
from the radar. Also shown is the 95th percentile rmsd, quoted
as the maximum error
Atmos. Sci. Let. 7: 9–14 (2006)
Vertical resolution requirements for operational weather radar data quality
13
Figure 5. The rmsd centred on the brightband peak for different elevation step angle separations at 20, 40, 60 and 80 km
gains can be made by using information from upper
beams. Accordingly, the maximum error is related to
how well the sampling captures features such as the
brightband, which is the ‘problem area’. It is therefore
useful to zoom in on the height interval 500 m on
either side of the brightband peak and compute the
rmsd every 100 m between the high-resolution profiles
and the resampled and linearly interpolated profiles to
gauge the effect of oversampling. This is plotted in
Figure 5 at 20, 40, 60 and 80-km range for the six
nested scan sequences.
Figure 5 shows that the incremental improvements
become progressively smaller with increasing overlap between successive beams. Once the angle separation is less than the beamwidth, only very small
improvements are possible. It does, however, show
that locally, in the ‘problem area’ around the bright
band, there are benefits when oversampling and keeping the angle separation less than, or at most equal
to, the beamwidth. Error reductions of 0.5 to 1 dB at
ranges beyond 40 km are achievable when changing
the steps from 1◦ to 0.66◦ steps, but the remaining
Copyright  2006 Royal Meteorological Society
error of about 4 dB cannot be reduced further by
using even smaller steps. In all instances, reducing the
step separation yields a progressively more accurate
representation of the brightband peak. For instance,
reducing the sampling volume from 1◦ to 0.66◦ , and
increasing the number of elevation steps would be beneficial for the case of rain advecting into the radar
domain, benefiting from both increased information
(more samples in the vertical), and a reduced error.
This could be important for various applications ranging from detecting severe convection to brightband
correction algorithms.
The errors 0.5 km above the brightband peak are
more complicated, because in the aggregation zone
extending 1 km above the brightband the reflectivity
gradient is initially steeper and then relaxes to a lower
value. As a result the interpolation between the sample
at the height of the brightband maximum and at a
height 2–3 km above for ranges over 60 km with the
2◦ sampling step can lead to occasional reduction in
error for this coarse resolution, but on balance the net
effect is still negative.
Atmos. Sci. Let. 7: 9–14 (2006)
14
M. P. Mittermaier, A. J. Illingworth and R .J. Hogan
5. Concluding summary
as part of various projects. We also thank the Met Office for
supplying the UM output and especially Malcolm Kitchen who
provided the motivation for the work. Funding for the first
author was provided by the Met Office and the Environment
Agency under contract PB/B3567.
In the preceding sections a method for testing and
comparing different scan strategies has been presented.
Central to the method is the coarsening or ‘upscaling’
of high-resolution, narrow beamwidth RHI data to
simulate operational radar beamwidths.
The method provides flexibility in scan strategy
design (the number and spacing of elevation steps
between base scan and maximum elevation), constrained only by the beamwidth of the high-resolution
data, in this case 0.28◦ . For this study the method was
used to design nested scan sequences to test the impact
of oversampling and increased information content.
General conclusions include:
• Elevation steps equal to the beam width appears to
be the optimal solution and is acceptable in terms
of data coverage.
• Oversampling has very limited benefits; separating
the radar beams elevations by 0.66◦ for a 1◦
beamwidth radar leads to a slight improvement in
the inferred VPR, but only beyond 60-km range.
• Undersampling with the elevation steps greater than
the beam width leads to a rapid degradation of the
inferred vertical profile and should be avoided.
• The observed value of Z in the ice is generally
within 1.5 dB of the true value, which is sufficient
for deriving ice water content unless the vertical
gradient of reflectivity exceeds 9 dB·km−1 .
• Calculating a distribution of significant reflectivity
(above 12 dBZ ) is helpful in determining the minimum height of the radar sampling volume. For this
study at least 90% of significant reflectivities are
found below 4 km at all ranges up to 90 km.
This analysis is based on UK network radar specifications. Nevertheless, the figures presented may be
applicable to radars with similar specifications elsewhere. In the United Kingdom, besides the benefits to the current Nimrod operational VPR correction scheme, future amendments to the scheme may
require more information about the slope of reflectivity
in the ice. Radar-rainfall rates have been assimilated
into the UM via a latent heating scheme for several
years, and this is shown to be beneficial (Jones and
Macpherson, 1997). Any future plans to assimilate
three-dimensional radar data, especially the assimilation of radar-derived ice water content into NWP
models, would also be facilitated by increasing the
information content in the ice.
Acknowledgements
We thank the Chilbolton Observatory, a part of the Rutherford
Appleton Laboratory for use of the 3-GHz radar data collected
Copyright  2006 Royal Meteorological Society
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Atmos. Sci. Let. 7: 9–14 (2006)
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