REMOTE SOUNDING OF TEMPERATURE AND HUMIDITY IN THE
PRESENCE OF CLOUDS
*
*
**
Cristina Prates , Stefano Migliorini , Stephen English and Ed Pavelin***
*University of Reading, PO BOX 243, Reading, RG6 6BB, United Kingdom
**ECMWF, Reading, United Kingdom
***Met Office, Exeter, United Kingdom
Abstract
To date, the radiative transfer models that are used to assimilate infrared cloudy radiances are based
on simple cloud schemes in which clouds are assumed to be single-layer grey bodies of negligible
depth. Observations show that the majority of cloud formations found in the atmosphere are more
complex than the single layer configuration. Comparisons with Advanced Very High Resolution
Radiometer (AVHRR) have shown that even a modest increase in complexity of the cloud model
should increase by 28 % the amount of data that could be assimilated more effectively. However the
impact of this extra data remains unknown.
A new cloud scheme enabling an additional cloud layer (two-layer cloud representation) to be treated
in a one-dimensional variational retrieval (1D-Var) has been developed and tested using IASI
measurements. In this new scheme the infrared effects are modelled by means of four cloud
parameters (effective cloud fraction and cloud top pressure for two possible cloud layers) and are
retrieved simultaneously with temperature and humidity profiles.
The new cloud scheme is compared against the old one using both observed and simulated IASI
measurements. The cluster information based on a detailed radiance analysis of co-located AVHRR
pixels inside each IASI field of view, important to define the scene type (e.g. overcast, partially
covered), is used in this study as an independent source of information to characterise the cloud
formation within IASI pixel. The impact of the new cloud model, and the cause of this impact, are
presented.
.
INTRODUCTION
Satellite sounding measurements are an important source of information for numerical weather
prediction systems (NWP) since they provide valuable information on the vertical structure of
atmospheric temperature and humidity. The assimilation of those observations has initially focused on
clear-sky conditions leading to the discard of information which may be important.
In recent years, the awareness that cloudy areas are often meteorologically sensitive and the
availability of a new generation of advanced infrared sounders instruments have encouraged the NWP
community to take steps towards the assimilation of cloudy radiances. However, this is a more difficult
problem than the assimilation of clear-sky radiances because it requires the parameterisation of
radiative cloud effects within the observation operator (radiative transfer models).
Currently, the radiative transfer models that are used to assimilate infrared cloudy radiances in
operational centres are based on the so-called emissivity type approach where no explicit scattering is
included. In this approach clouds are normally assumed to be single-layer grey bodies of negligible
geometrical depth (e.g. at Met Office (Pavelin et al, 2008) and at ECMWF (McNally, 2009)).
In this paper the single-layer approach used in the Met Office, described below, is assessed using
retrievals from IASI observations and comparing them with co-located Advanced Very High Resolution
Radiometer (AVHRR) observations. A new cloud scheme enabling an additional cloud layer (two-layer
cloud representation) to be treated in a one-dimensional variational retrieval (1D-Var) has been
developed and tested using both observed and simulated IASI measurements. The new cloud scheme
is compared against the old one using IASI measurements. The cluster information based on a
detailed radiance analysis of co-located AVHRR pixels inside each IASI field of view is used in this
study as an independent source of information to characterise the cloud formation within IASI pixel.
TECHNIQUE TO ASSIMILATE CLOUDY RADIANCES AT MET OFFICE
The radiance measured at the top of the atmosphere for a given wavelength, ν, L ( ) , considering
the emissivity type approach where a single layer grey body cloud (i.e. cloud emissivity does not
change with the wavelength) is assumed, can be calculated by the following expression:
Cld
LCld ()  (1  N c )LCl ()  N c LOp (, p c )
(1)
where N c is the product between cloud geometrical fraction, N, and cloud emissivity,  c , known as
effective cloud fraction (ECF), L () is the cloud-free radiance and L (, p c ) the radiance
Cl
Op
corresponding to overcast conditions with an opaque cloud (i.e. the cloud layer is assumed to be a
perfect emitter) whose top is at pressure pc (cloud top pressure, CTP). Therefore the cloud IR radiative
effects are modelled by means of two cloud parameters: effective cloud fraction (ECF) and cloud top
pressure (CTP).
In the Met Office the IASI radiances are processed through a 1D-Var scheme before being assimilated
in 4D-Var (Hilton et al., 2009). The two cloud parameters are obtained externally by 1D-Var and
passed as fixed parameters to the global assimilation scheme whereby are used to constrain the
forward calculations. However, just the channels whose jacobians peak above cloud top are effectively
used in the 4D-Var assimilation.
The Met Office 1D-Var dimensional scheme is a standalone retrieval for nadir-viewing passive satellite
instruments. The 1D-Var state vector contains temperature and humidity at fixed pressure levels (43 in
case of temperature and 26 for humidity), 4 surface variables (2m-temperature, 2m-specific humidity,
skin temperature and surface pressure) and two cloud parameters (ECF and CTP).
The Met Office forecast model provides the background information for both the profiles and surface
variables and for those fields the first guess is set equal to the background information. For the cloud
parameters as no information is available from the NWP model the background errors for ECF and
CTP are assumed to be large (  ECF  1 and  CTP  1000hPa ) and the values itself are fixed
(ECF=0.5 and CTP=500 hPa).
The fact that cloudy retrieval is a highly non-linear problem requires that a good description of the
initial cloud quantities should be provided. Hence the first guess for cloud parameters are estimated
from the observations using the minimum residual method (Eyre & Menzel, 1989), which is based on
the best fit between observed radiances and forward-modelled cloudy radiances using a set of IR
channels. The minimization is done by using the Levenberg-Marquardt algorithm.
ASSESSEMENT OF 1D-VAR RETRIEVALS ERRORS
The strategy followed to assess the limitations associated with the simple representation of cloud
radiative effects that is currently used for 1D-Var cloudy radiance retrievals is based on comparing the
IASI retrievals with observations from an independent source as well as by utilising simulated
observation experiments.
Intercomparison with AVHRR cluster information
Over sea, scenes observed by satellites exhibit inhomogeneities that result mainly from the presence
of cloud in the instrument’s field of view (FOV). AVHRR radiance cluster analysis (Cayla, 2001) can
provide valuable information to define the scene type and is utilised here as an independent source of
information to characterise clouds within IASI FOV. IASI retrievals are compared with AVHRR colocated cluster information over the ocean. The pixel heterogeneity is characterised by the number of
clusters (maximum of 7) inside each IASI pixel; the higher the number of clusters the higher the pixel
heterogeneity is.
Data set:
The data chosen for the study was acquired from three hours before to three hours after 00 UTC on 4
May 2010; only IASI pixels over sea with available AVHRR cluster information were considered.
Distribution of the data according to the number of AVHRR clusters (maximum of 7) inside each IASI
FOV is shown in Figure 1, for cloudy retrievals only. The clouds retrieved by 1D-Var were classified
according to the position of their tops: high (above 500hPa); medium (between 500hPa and 800hPa);
and low (below 800hPa). Homogeneous scenes (1 cluster), which corresponds to overcast pixels, are
just a small portion of the occurrences (slight above 5%); pixels with one- or two-cloud layers (i.e. 2 or
3 clusters) are the most frequent in the sample. High clouds are the predominant type in most of the
groups. Assuming that pixels with a total number of 3 AVHRR clusters are likely to have more than a
single-layer cloud (or to correspond to a two- or three-cloud layers) a model dealing with an extra
cloud layer can mean that more 28% of the data are being dealt in a more appropriate way.
Figure 1: Distribution of IASI cloudy pixels (as determined by 1D-Var) according to the number of AVHRR clusters
inside each IASI FOV. The cloudy pixels were grouped in three categories: high, medium and low, referring to the
height of the cloud top. The sample contains only pixels over sea.
Model space results:
The retrieved profiles for temperature and humidity from the same data set have been compared
statistically with background profiles for different cloud types (as determined by 1D-Var) and different
degrees of pixel heterogeneity (as defined by AVHRR radiance cluster analysis). The results obtained,
particularly for high clouds (see Figure 2), illustrate well the limitations of 1D-Var cloud model. The
increase of bias and standard deviation with increase of pixel heterogeneity is evident. For multi-layer
cloud formations (i.e. 2 or more clusters) the retrieval is warming considerably the mid and upper
troposphere. This feature is linked to a positive bias in observation minus background brightness
temperature differences (not shown here) for channels that peak between 300-600hPa.
Figure 2: Statistics of 1D-Var retrieval for high clouds: standard deviation (left) and bias (right) of difference between
retrieved and background temperature profile calculated according to AVHRR cluster information. The sample sizes
and the respective maximum standard error is also displayed (#n and σmax, respectively).
Observation space results:
Statistics of the differences between observed minus calculated brightness temperature using the
retrieved profiles and cloud parameters were also computed for different cloud types and different
degrees of pixel heterogeneity. For high clouds for example, the results exhibit a spectral variability
(not shown). The CO2 channels, which normally peak on high troposphere or lower stratosphere,
display small bias even for cases of high pixel inhomogeneity. On the other hand, the atmospheric
window channels, very sensitive to lower troposphere, show a spectral variation in the bias that
becomes more pronounced in cases of multiple cloud layers (3 or more clusters). Both grey (spectrally
independent) and single-layer assumptions for high clouds lead to poor results in the window region
for multilayer cloud formations.
Simulated cloud experiments
A very common situation in the atmosphere is to have a semi-transparent ice cloud on top of lowerlevel water cloud. In this particular case it is likely that the retrieval cloud top under this single-layer
assumption will be placed between the two cloud layers (Baum & Wielicki, 1994). Some simulated
experiments were carried out by combining different cloud configurations to assess the errors that
single-layer assumption can have on situations where two cloud layers are present in the atmospheric
column. Various combinations of cloud emissivity (via the ECF parameter) and cloud height were
tested.
The results obtained show that larger errors are found in cases where a layer of transmissive clouds is
above a layer of thick clouds. It was also verified that in cases where the uppermost cloud is optically
thin (lower values of ECF) the cloud top is positioned between the two layers (see right plot in Figure
3). This effect is stronger if the second layer is optically thick (not shown here).
Figure 3 shows the results obtained from an ensemble of run for two different cloud configurations
both with two cloud layers, but in one the uppermost layer is nearly opaque (ECF=0.9) and in the other
is optically thin (ECF=0.5). It is also worth noting that the lower the retrieved cloud top the larger the
temperature bias is.
Figure 3: Statistics of 1D-Var retrieval obtained from a set of 200 pseudo IASI observations for a two layer cloud
configuration with the cloud tops positioned at 396hPa and 565hPa (depicted by orange horizontal lines). The plot on
the left refers to the case of an optically thick uppermost cloud (ECF=0.9) and the one on the right to an optically
thin uppermost cloud (ECF=0.5). The lowermost cloud is a semitransparent cloud (ECF=0.5) for both cases. The mean
and standard deviation of temperature errors (T-Ttruth) are in green and red respectively, solid refers to retrieved values
and dash to the background. The mean CTP of the retrieved and first guess are represented respectively by the
horizontal solid blue lines and horizontal green dash lines.
THE NEW CLOUD MODEL: TWO-LAYER APPROACH
The radiance measured by the satellite at a given wavelength, ν, L () , in presence of two
independent cloud layers with cloud-top pressures, p1 and p2 (with p1<p2) and effective cloud fraction
Ne1 (= N c1 ) and Ne2 (= N c2 ), respectively, can be written as:
cld
Lcld ()  (1  N e1 )(1  N e2 )Lclr ()  N e1Lop (p1 , )  N e2 (1  N e1 )Lop (p 2 , )
(2)
where L () is the cloud-free radiance, and L (, p) the radiance corresponding to overcast
conditions with an opaque cloud whose top is at pressure p. Note that in this approximation the clouds
are assumed to be grey bodies with negligible depth and randomly overlapped (the probability that
different cloud layers overlap each other is proportional to the horizontal extent of each of the cloud
layers, i.e. cloud fraction).
clr
op
The radiative transfer model (RTTOV) used within 1D-Var was modified in order to accommodate the
two new cloud variables (ECF2 and CTP2 for the additional cloud layer) required for the calculations
of the cloudy radiances (equation 2). The 1D-Var scheme was extended in order to retrieve the two
additional state vector variables present in the new cloud model. The background values for the cloud
parameters were set to fixed values (ECF1=0.5, ECF2=0.5, CTP1=500hPa and CTP2=750hPa). The
background errors assumed for the cloud parameters have the same magnitude for both layers (
 ECF  1 and  CTP  250hPa ). The minimum residual method that provides the first guess for the
cloud parameters within 1D-Var has been modified accordingly and estimates for the four cloud
parameters are calculated.
COMPARISON WITH SINGLE-LAYER APPROACH
A similar methodology to the one employed to assess the 1D-Var single-layer retrieval errors was
adopted here to assess the performance of the new cloud layer model; the retrievals using the twolayer cloud representation were compared against the ones from single-layer assumption using both
simulated experiments and observed radiances from IASI.
Simulated cloud experiments
The 1D-Var retrievals under single-layer assumption when there are two cloud layers in the
atmospheric column in which the uppermost is optically thin lead to considerable errors in the cloud
top position as well as in the atmospheric profiles. Some simulated experiments were carried out by
combining different atmospheric conditions and cloud configurations in order to assess the
performance of the new cloud model. The results obtained show that in cases where there is a semitransparent cloud on top of a lower cloud (semi-transparent or opaque) the new cloud model
represents on average better the truth than the single-layer approach.
Figure 4 displays the statistics computed on model space for both single and two-layer-cloud 1D-Var
retrievals obtained from a set of 200 ensemble runs for a particular case of two layer cloud
configuration. The mean retrieved CTP for both layers is quite accurate and shows an improvement
relative to single layer retrieval. The bias and the standard deviation in the retrieved temperature
profile are smaller for the two-layer-cloud retrieval. It is worth mentioning that the statistics computed
in observation space show a good agreement between the calculated radiances and the observations
for both cases and no evident differences were found in the two situations despite the vertical
difference seen in temperature (not shown).
Observed radiances
The results from simulated experiments demonstrate the superiority of the two-cloud-layer approach
for idealised situations where two cloud layers are present. It is important to investigate whether the
two-layer cloud approach can also bring some improvements relatively to the single layer approach in
the realm of observations. To accomplish that the new cloud algorithm was applied to observed IASI
data and a statistical study was perform based on the AVHRR cluster analysis similarly to what has
been presented for the single layer operational retrievals.
Figure 4 : Statistics of 1D-Var retrievals using the single-layer cloud approach (left) and the two-layer cloud
representation (right). The retrievals were obtained from an ensemble of 200 pseudo IASI observations where the truth
is characterised by two cloud layers at 396hPa and 565hPa (horizontal orange lines) with ECF values equal to 0.3 and
0.5, respectively. The mean and standard deviation of temperature errors (T-Ttruth) are in green and red respectively,
solid refers to retrieved values and dash to the background. The mean CTP of the retrieved and first guess are
represented respectively by the horizontal solid blue lines and horizontal green dash lines.
The statistical study, based on the same observation dataset as previously, provide us with some
insights on how the new scheme performs with real data. The most interesting result was obtained for
the statistics on model space for high cloud type. Figure 5 displays those statistics for the temperature
profiles which can be compared against the ones obtained for 1D-Var single-layer approach shown in
Figure 2. It is readily apparent from the comparison that the two-layer-cloud retrievals exhibit smaller
bias and standard deviation in the temperature profile particularly for pixels characterised by high
heterogeneity, i.e. the ones that are likely to correspond to a multi-layer cloud formation. The results
on observation space do not differ much from each other and the fit to observations is generally quite
good for homogeneous scenes (not shown here).
CONCLUSIONS AND FUTURE WORK
AVHRR cluster information showed that the majority of cloud formations found in the atmosphere are
more complex than the single-layer representation assumed and it is not by chance that those are
precisely the situations where larger errors in the single-layer retrieval were found.
The experiments performed with simulated IASI measurements clearly demonstrate that two-layer
cloud model can offer improvements in situations where the uppermost cloud is thin (ECF<0.5) which
is promising as those are the situations where single-layer approach performs worse. Furthermore, the
comparison against the old cloud scheme using IASI observed radiances shows that the two-layer
model is able to reduce considerably the bias and standard deviation of retrieved temperature profile
for pixels with multi-layer clouds without detriment to retrievals in single-layer cloud occurrences.
Although the inclusion of an extra cloud layer in the representation of clouds reduces substantially the
temperature bias it can be argued that it is still too big with respect to observation error to allow
assimilation of channels below the cloud top. Nevertheless, the fact that the two-layer cloud model is
able to provide a better estimate of the top cloud position in cases of two-layer formations represents a
valuable input to the Met Office assimilation system to prevent assimilating channels contaminated by
the clouds.
Figure 5: Statistics of 1D-Var retrieval using the two-layer-cloud representation for high clouds (CTP above 500hPa).
Standard deviation (left) and bias (right) of difference between retrieved and background temperature profile calculated
according to AVHRR cluster information.
A well-known limitation of the scheme is the fact that some retrievals of cloud can be obtained in dry
regions of the atmospheric column since the retrieved cloud is not physically related to the
temperature and humidity profiles. Constraints based on the thermodynamic relation between clouds
and relatively humidity are worth being investigated. Another important issue is the validation of the
two-layer-cloud model with campaign data where a more complete description of the cloud formations
and of the temperature and humidity profiles are available. The Variational Assimilation of Cloud
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Affected Radiances (VACAR) campaign data are being considered for a future validation study.
REFERENCES
Baum, B. A., & Wielicki, B. A. (1994). Cirrus cloud retrieval using infrared sounding data: multilevel
cloud errors. J. Appl. Meteor. , 33, pp 107-117.
Cayla, F.-R. (2001). AVHRR radiances analysis inside IASI FOV’s. CNES internal report (IA-TN-00002092-CNE).
Eyre, J. R., & Menzel, W. P. (1989). Retrieval of cloud parameters from satellite sounder data: a
simulation study. J. Appl. Meteor. , 28,pp 267-275.
Hilton, F., Atkinson, N. C., English, S. J., & Eyre, J. R. (2009). Assimilation of IASI at the Met Office
and assessment of its impact through observing system experiments. Q.J.R. Meteorol. Soc. , 135, pp
495-505.
McNally, A. (2009). The direct assimilation of cloud-affected satellite infrared radiances in the ECMWF
4D-Var. Q.J.R. Meteorol. Soc. , 135, pp 1214-1229.
Pavelin, E. G., English, S. J., & Eyre, J. R. (2008). The assimilation of cloud-affected infrared satellite
radiances for numerical weather prediction. Q. J. R. Meteorol. Soc. , 134, pp 737-749.
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For details see the following webpage: http://www.faam.ac.uk/index.php/current-future-campaigns/past-campaigns/177-vacarvariational-assimilation-of-cloud-affected-radiances