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Atmos. Sci. Let. 6: 160–163 (2005)
Published online 27 September 2005 in Wiley InterScience ( DOI: 10.1002/asl.110
Modelling of downwelling long-wave radiation using cloud
fraction obtained from laser cloud-base measurements
G. G. Rooney*
Met Office Field Site, Cardington Airfield, Shortstown, Bedford, MK42OSY, United Kingdom
*Correspondence to:
G. G. Rooney, Met Office Field
Site, Cardington Airfield,
Shortstown, Bedford, MK42OSY,
United Kingdom.
A method is described for the estimation of downwelling long-wave radiation in both cloudy
and clear-sky conditions. This method uses an estimate of cloud fraction, obtained from
the output of a laser cloud-base recorder, to modify the clear-sky emissivity as calculated
from standard near-surface measurements.  Crown Copyright 2005. Reproduced with the
permission of Her Majesty’s Stationery Office. Published by John Wiley & Sons, Ltd.
long-wave radiation; cloud fraction; laser cloud-base recorder; emissivity
Received: 6 October 2004
Revised: 17 March 2005
Accepted: 18 July 2005
1. Introduction
As the number and proportion of automatic
(unmanned) weather observing sites increases, both
in the United Kingdom and farther afield, the Met
Office and others are examining ways to maximise
the usefulness of the data from these sites. One example of this is the development of algorithms to derive
cloud amounts from laser cloud-base recorder (LCBR)
data (Kärkkäinen, 1997). The Met Office has a project
currently running to see how co-located pyrgeometer
measurements of atmospheric downwelling long-wave
radiation (DWLW) can be used to improve the estimate of cloud amount from this method (see also
Aviolat et al., 1998).
The work described here, however, addresses the
counter-question: can the output of an LCBR be used
to derive an estimate of atmospheric DWLW? One reason for looking at this is that DWLW measurements
are not routinely made at observing stations; however,
such information could now be useful for running
site-specific surface models. For example, the Met
Office Surface Exchange Scheme (MOSES; Essery
et al., 2001) for the modelling of surface and subsurface heat and moisture fluxes is available in standalone form, designed to be forced by observations (or
estimates) of downwelling long-wave and short-wave
radiation, precipitation, temperature, pressure, humidity and windspeed. Most of these are available now
from many stations in the United Kingdom, and if an
LCBR-derived DWLW estimate was sufficiently accurate, then data from these stations could be used to
evaluate or augment site-specific forecasts.
2. Model of atmospheric downwelling
long-wave radiation
The model used here is based on the simple model
by Crawford & Duchon (1999, hereafter CD99). The
basis of this is the empirical relationship of Brutsaert
(1975) between effective clear-sky atmospheric emissivity εc , and near-surface temperature and vapour
pressure, T and e respectively,
εc = 1.24(e/T )1/7
where T is in degrees Kelvin and e is in millibars
CD99 improve on this by introducing the cloud fraction φ, and taking the actual atmospheric emissivity ε
to be an intermediate value between the clear-sky εc
and the cloudy value assumed to be unity, that is,
ε = φ + (1 − φ)εc
They then model φ as
φ = (Ic − Im )/Ic
where Ic is the clear-sky solar irradiance and Im is
the measured solar irradiance. For this study, Ic was
obtained according to the method described by CD99
as a function of solar zenith angle, sun–earth distance,
atmospheric pressure and dewpoint.
Finally, DWLW is obtained from ε and the nearsurface temperature as
DWLW = εσ T 4
There are two things to note about the method
of CD99. Firstly, the dependence of the model on
Im restricts this improved scheme to daylight hours
only. Secondly, the modification of the original model
does not involve any consideration of cloud height,
but only cloud fraction.
 Crown Copyright 2005. Reproduced with the permission of Her Majesty’s Stationery Office. Published by John Wiley & Sons, Ltd.
Modelling of DWLW radiation using LCBR cloud fraction
3. Cloud fraction from LCBR
An alternative source of data that may be used to
estimate cloud fraction φ is the output of a LCBR.
These instruments are deployed at many observing
stations, and operate both night and day. Deriving
φ from LCBR output would therefore enable the
modelling of DWLW at all times, not during daytime
only as is the case with the CD99 method.
3.1. Exponential-decay algorithm
The Met Office and others have developed skycondition algorithms (SCAs) to obtain a description of
cloud cover from the output of an LCBR. These SCAs
are reasonably complex and are generally applied in
real time. The Met Office algorithm is known as
the exponential-decay algorithm (EDA). This name
reflects its response to forcing with a step function, which is to increase the estimated cloud cover
from zero to approach 8 oktas exponentially with a
timescale of order 1 h.
The output of the EDA consists of the height
and integer number of oktas of each cloud layer
identified, up to a maximum of three cloud layers.
However, only the total cloud fraction is required for
the DWLW model used here. To combine more than
one cloud layer, conditions of both maximum overlap
and random overlap of layers have been applied (the
cloud fraction from the former being a lower bound
to that from the latter). The results from each of these
will be presented for comparison.
The EDA software was available for use in this
study, however the simpler ‘convolution’ method was
also applied to the LCBR data, and results from both
these methods will be presented in what follows.
4. Comparison with data
4.1. Description of data
Data for comparison of the models described above
were recorded at the Met Office Field Site (Met
Research Unit), at Cardington, Beds, United Kingdom
during the 6 month period between 27 May 2003 and
26 November 2003.
The data consist of pressure, screen temperature and
humidity (from which vapour pressure and dewpoint
were obtained according to standard formulae), downwelling short-wave and long-wave radiation components, and cloud height. All of these except the cloud
height were logged at 4 Hz before being reduced to
15 min means. The cloud height was recorded at 30 s
intervals and passed at this frequency to the EDA,
which gives the output at the same frequency. Both
the EDA output and the raw cloud height were then
sampled down to 15 min intervals before being used
as described in Sections 3.1 and 3.2 respectively.
The short-wave and long-wave radiation components were measured using a Kipp & Zonen CM22
pyranometer and a Kipp & Zonen CG4 pyrgeometer respectively. The CG4 was mounted on a solar
tracker, which uses a small ball on an arm to shade
the dome of the instrument from direct solar radiation.
The cloud height was recorded using a Belfort model
7013C ceilometer (manufactured by TransTechnology
3.2. Convolution method
It is also worthwhile considering what can be achieved
without SCA software. In this case, a simpler method
may be applied which captures some of the features
of the EDA. This process first reduces the LCBR
output of cloud height to a simple binary series L(t),
indicating the presence or absence of cloud. The
LCBR software returns a zero value when no cloud
is detected, so L(t) is obtained simply by setting
every non-zero number in the output timeseries to
unity. L is then convoluted with an exponential-decay
function D(t) = e −t /τ and normalised to produce the
new estimate of cloud fraction,
C (t) = L ∗ D(t)
φ(t) = C (t)/max(C )
The decay timescale τ used here was 3.75 min, i.e.
one-quarter of one 15-min timestep between points
(see Section 4.1). With this timescale, forcing with
a step function produces a fractional cover value of
approximately 0.9 after six timesteps (1.5 h), which is
comparable to the response of the EDA.
 Crown Copyright 2005. Reproduced with the permission of Her
Majesty’s Stationery Office. Published by John Wiley & Sons, Ltd.
4.2. Results and discussion
The results presented here are a comparison of the
cloud fraction and consequent DWLW as obtained
from the four methods described above: CD99,
exponential-decay algorithm with maximum overlap
(label EDA-MO), exponential-decay algorithm with
random overlap (label EDA-RO) and convolution
(label CONV). The first of these is based on measurements of solar irradiance and can be used during
daytime only; the last three are based on measurements of cloud height and can be used at all times.
The DWLW obtained from the clear-sky formulation
of Brutsaert (1975) will also be presented to enable
the contribution of the cloud data to be assessed (label
Firstly, the correlation coefficients between cloud
fractions obtained by different methods are presented
in Table I. There is a high degree of correlation
between the cloud fractions obtained by various methods from the LCBR data, but less between each of
these methods and that based on the solar-irradiance
data. This difference is perhaps not surprising since
the LCBR methods all yield results on the basis of
Atmos. Sci. Let. 6: 160–163 (2005)
G. G. Rooney
Table I. Correlation coefficients between cloud fractions
obtained by different methods. Note that the CD99 entries
are for correlation of daytime points only
clouds that have passed directly overhead, whereas the
pyranometer-based method will derive its results from
cloud cover in the area of sky between the instrument
and the sun. Obviously, this area will never be overhead in the United Kingdom and will be close to the
horizon near the start and end of the day.
Secondly, the DWLW from each method is compared with that measured by the CG4 in Table II. The
results from all these are an improvement on the clearsky model B75, and the figures for bias indicate that
the cloudy models all predict more DWLW overall
than B75, which is to be expected. In general, the
cloudy models show a high degree of correlation with
observations, with r.m.s.e. values of a similar magnitude. The bias of the CD99 method is the smallest,
between one-half and one-third of those of the LCBRbased methods.
Despite the relative simplicity of these methods,
the degree of accuracy compares favourably with
that derived from modelling or climatology. In a
comparison of DWLW obtained from various General
Circulation Models with observations from numerous
sites around the world, Wild et al. (2001) find the
average bias in four out of the five models studied
to be greater than 10 Wm−2 . They also state that
±10 Wm−2 is the best estimate of the accuracy of
measurements obtained from a global network of
DWLW measurements (see also McArthur, 1998).
Morcrette (2002) states that this accuracy is also
the level required for data to be useful in climate
studies. Gupta et al. (1999) estimate the uncertainty of
monthly average long-wave fluxes to be approximately
15 Wm−2 in their discussion of a climatology of the
surface radiation budget recently derived from satellite
It thus appears that the methods of DWLW modelling presented here are sufficiently accurate and that
they may be usefully employed in the generation of
Table II. Statistics for comparison of observed DWLW with
that produced by each of the models. The convention used
is that a positive bias means model overprediction compared
to observations. Note that the CD99 entries are for daytime
points only
Bias (Wm−2 )
r.m.s.e. (Wm−2 )
 Crown Copyright 2005. Reproduced with the permission of Her
Majesty’s Stationery Office. Published by John Wiley & Sons, Ltd.
data for modelling studies. In addition, it may be that
data generated in this way are also better than those
derived from modelling or climatology because these
data are based on local measurements. Thus, for example, if they are combined with other data from the
same site for use in model forcing, it may be hoped
that the combination is relatively self-consistent, so
that increased DWLW is associated with higher nighttime temperatures, reduced solar irradiance during the
day, etc.
Finally, the information derived from the LCBR
data in this study has been limited to cloud fraction
only, as this is easily incorporated and compared with
the method of CD99. It is to be expected that if the
information on cloud height were to be integrated
in the modelling in some way, perhaps as a further
modification to εc , then the model accuracy could be
improved. It is hoped that this may be the subject of
a longer investigation to be carried out in the future.
5. Conclusions
Six months of data have been used to test the accuracy
of cloud fraction derived from LCBR measurements
in a model of atmospheric DWLW. It appears that
this method produces results comparable to those of
Crawford and Duchon (1999), which are based on
pyranometer measurements. Both these methods are
an improvement on the simple clear-sky emissivity
model from which they are derived. The LCBR
method is additionally advantageous in that it can
produce a sufficiently accurate estimate of long-wave
radiation at all times and not daytime only, and is
therefore potentially useful for model forcing and/or
I am grateful to the following people for their help and advice:
Dave Bamber, Phil Hignett, James McGregor, Mike Molyneux
and Stewart Nightingale. Constructive comments from the
anonymous referees are also gratefully acknowledged.
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 Crown Copyright 2005. Reproduced with the permission of Her
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Atmos. Sci. Let. 6: 160–163 (2005)
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