QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY
Q. J. R. Meteorol. Soc. (in press)
Published online in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/qj.84
Ice hydrometeor microphysical assumptions in radiative
transfer models at AMSU-B frequencies
A. M. Doherty,a * T. R. Sreerekha,b† U. M. O’Keeffea and S. J. Englisha
a
b
Met Office, Exeter, UK
University of Bremen, Bremen, Germany
ABSTRACT: Comparisons between two radiative transfer models, ARTS and RTTOV, showed that results in the presence
of scattering from ice hydrometeors are highly dependent on assumptions made about the ice microphysics, specifically
the size distribution and the density of the ice particles. This paper presents the results of a comparison study between a
number of different treatments for the ice microphysics in RTTOV. Of the approaches considered, the combination of a
size-dependent density (larger ice particles are less dense) and a size distribution treatment based on the cloud temperature
and ice water content give the best approximation for the cases examined. Further work is planned in other regimes to see
if this approach can be applied more widely.  Crown Copyright 2007. Reproduced with the permission of Her Majesty’s
Stationery Office. Published by John Wiley & Sons, Ltd
KEY WORDS
satellite data; microwave; scattering; NWP
Received 27 September 2006; Revised 21 March 2007; Accepted 28 March 2007
1.
Introduction
For many years, Numerical Weather Prediction (NWP)
centres have been assimilating microwave radiances from
satellites. However, the data used have been limited to
clear fields of view because these cases are far simpler
to model than cloudy cases. NWP requires an observation operator for each assimilated observation type to
link the observed variable with physical atmospheric variables. In the case of satellite radiances, this operator is
a Radiative Transfer Model (RTM). An RTM requires
atmospheric profiles in order to model the upwelling radiation at the Top Of the Atmosphere (TOA). When the
radiation observed is only absorbed and emitted by the
atmosphere, as in the cloud free case, modelling is relatively straightforward. However, when thick cloud is
present microwave radiation is also scattered and this
proves far more difficult to model. The problem is partly
the complexity of the calculation, which makes models
solving the full scattering Radiative Transfer Equation
(RTE) very expensive, and partly the lack of knowledge about the parameters on which scattering depends,
namely the spatial distribution of cloud hydrometeors and
the microphysics of those hydrometeors. In this paper we
focus on ice hydrometeors, which have a strong scattering
effect on microwave frequencies above ∼85 GHz.
There are a number of methods of solving the RTE
in an RTM, many of which employ approximations to
reduce the cost and make models viable for NWP. These
* Correspondence to: A. M. Doherty, Met Office, FitzRoy Road,
Exeter, EX1 3PB. E-mail: [email protected]
† Present address: Met Office, Exeter, UK.
include the Eddington approximation (e.g. Kummerow,
1993), Monte-Carlo methods (e.g. Davis et al., 2005) and
discrete ordinate techniques (Emde et al., 2004). Many
comparisons between RTMs have been made, mainly at
lower frequencies where scattering effects are less pronounced (e.g. Smith et al., 2002) but also more recently
at higher frequencies in order to look at the effects of
scattering (e.g. Kim et al., 2004). These show that given
accurate inputs, different approaches to solving the equation of radiative transfer perform to a similar standard.
Other studies such as Skofronick-Jackson et al. (2002)
show that assumptions about microphysical parameters
have a significant effect on the calculated TOA brightness
temperature (BT). In scattering conditions RTMs calculate upwelling TOA microwave radiances using single
scattering parameters (extinction, albedo and the asymmetry matrix) which are dependent on the ice microphysics, but the calculation of which is fundamentally
independent of the radiative transfer problem itself. All
RTMs contain assumptions about the microphysics of the
cloud hydrometeors, and it is here that the main uncertainties in simulating TOA BT arise, rather than in the
approach to radiative transfer. Parametrizations of microphysics should be as accurate as possible, but above all
they should be consistent with the model providing the
input profiles and the model calculating the single scattering parameters. This opinion is also given in the COST
712 report on microwave remote sensing in clouds and
precipitation (Czekala et al., 2000).
Atmospheric profiles, including those of cloud hydrometeors, can be obtained from an NWP forecast model.
However, this rarely provides information on the bulk
 Crown Copyright 2007. Reproduced with the permission of Her Majesty’s Stationery Office.
Published by John Wiley & Sons, Ltd.
A. M. DOHERTY ET AL.
microphysical properties of clouds. If information is
available it is diagnostic, not prognostic (Li et al., 2005).
In the Met Office Mesoscale model, used in this case to
generate inputs to the RTM, the prognostic variables are
cloud ice and a liquid plus vapour variable; everything
else is diagnostic.
The shape, size distribution, permittivity and density of
the particles within an ice cloud are unknown and must be
parametrized or approximated. These have a significant
impact on the results of the RT calculations (Hogan
et al., 2000; Skofronick-Jackson et al., 2002). The bulk
microphysics of clouds has been investigated by many
measurement campaigns, both airborne (e.g. Baum et al.,
2005) and ground-based (e.g. Shupe et al., 2005), and has
been found to be highly variable both in time and space,
from cloud to cloud and even within individual clouds
(Hogan et al., 2000; Benedetti et al., 2003; Gayet et al.,
2004). Czekala et al. (2000) concluded that knowledge
of bulk microphysical hydrometeor properties and their
relation to individual hydrometeor optical properties is
one of the key areas where effort is required in this field.
Aircraft measurement campaigns have been the most
common approach for investigating ice cloud microphysics. Many parametrizations have been developed
using data sets from such campaigns which link atmospheric variables to the unknown microphysical parameters. For instance, McFarquhar and Heymsfield (1997)
used temperature and ice water content to parametrize
the size distribution of ice particles in tropical cirrus and
Field et al. (2005) carried out a similar analysis to obtain
particle size distribution (PSD) parametrizations for midlatitude stratiform cloud. However, in many RTMs and
NWP centres, less flexible PSDs are still in use, such
as those of Marshall and Palmer (1948) and Sekhon and
Srivastava (1970). The need for variability is addressed
by dividing hydrometeors into a number of categories
(rain, snow, hail, graupel, cloud liquid and cloud ice)
and applying a different size distribution and maximum
and minimum size to each type. There is no consensus
in the literature as to which approach is best.
Ice hydrometeor density has generally been approximated as a constant in radiative transfer and cloud resolving models. Variability has been introduced by categorizing ice hydrometeors into different types, each with its
own constant density. This is a crude approximation as
the density of a snow or ice particle is not independent
of its size (Heymsfield et al., 2004). Density relations
have been extensively studied through the use of aircraft
data, with mass–size parametrizations being developed by
Heymsfield et al. (2004), Brown and Francis (1995) and
others. Hogan et al. (2000) examined some of these density relations and investigated the effect of a 40% error
in density on retrieval of frozen hydrometeor diameter
and ice water content (IWC) using dual frequency radar.
They found that the density assumption is a larger source
of error in retrieving diameter than either crystal habit
or the shape of the size distribution. However, they did
not reach a conclusion about which mass–size relation
best parametrizes density for any particular situation and
stress the importance of resolving this issue for remote
sensing applications in precipitating cloud.
It should be noted that one set of parametrizations
is not going to be appropriate for all situations and
the microphysical information available from operational
models is not currently sufficient to allow a choice to be
made between available schemes.
In this paper a number of parametrizations of the
density and size distribution of ice hydrometeors is
examined. Investigation is undertaken of their effect
on scattering RT calculations at microwave frequencies (the frequencies of the channels of the Advanced
Microwave Sounder Unit B (AMSU-B) instrument, i.e.
89–183 GHz) in the RTTOV model (Saunders et al.,
1999). The assumption is made that at frequencies below
200 GHz ice particles can be approximated by spheres,
allowing the application of Mie theory. Although the
assumption of spheres will introduce errors to the calculations, these are thought to be smaller than those associated with the other uncertainties. This approximation is
widely used in other work recorded in the literature (e.g.
Brown et al., 1995; Hogan et al., 2000; Bennartz and
Petty, 2001). Hogan et al. (2000) quote an error of less
than 15% in calculations of scattering parameters using
a T-matrix code by assuming spherical particles compared to using more realistic shapes such as hexagonal
columns and plates or dendritic snowflakes. The expense
of using these more complex scattering models precludes
their use in NWP, and no prior information is available
about which shape would be more suitable. Given that
Hogan et al. (2006) quote an error of roughly 40% in
the derivation of IWC from radar due to the uncertainty
in the shape of the size distribution, the error introduced
by the assumption of spherical particles is of secondary
importance.
Section 2 describes the AMSU-B instrument. The
RTMs are described in Section 3. Section 4 presents one
of the case studies used in the comparisons. Section 5
describes the density and PSD models used in this study.
Section 6 presents the results of the comparisons using
different microphysics in RTTOV and Section 7 gives the
summary and conclusions.
2.
AMSU-B
AMSU-B is a side-scanning nadir-viewing instrument,
which is part of the Advanced Television Infrared Observation Satellite (TIROS) Operational Vertical Sounder
(ATOVS) suite carried on the NOAA polar orbiting
satellites NOAA 15–18. It has five channels numbered
as AMSU channels 16–20, with AMSU channels 1–15
belonging to the AMSU-A instrument. The AMSU-B
channels are sensitive to atmospheric water vapour and
hydrometeors and their weighting functions peak at different altitudes throughout the atmosphere. In standard
atmospheric conditions, AMSU channel 16 (89 GHz) is
a surface channel and channel 17 (150 GHz) peaks low
in the atmosphere with a large contribution from the surface. The other channels peak successively higher in the
 Crown Copyright 2007. Reproduced with the permission of Her Majesty’s Stationery Office.
Published by John Wiley & Sons, Ltd.
Q. J. R. Meteorol. Soc. (in press)
DOI: 10.1002/qj
ICE HYDROMETEOR MICROPHYSICS FOR RADIATIVE TRANSFER
atmosphere starting with channel 20 (183 ± 7 GHz) at a
water vapour burden of about 10 kg m−2 , then channel
19 (183 ± 3 GHz) and channel 18 (183 ± 1 GHz) at
the highest altitude, at a water vapour burden of about
0.8 kg m−2 (Staelin, 1987).
AMSU-B has a field of view of 1.1° corresponding
to a nadir resolution of 16 km (Muller et al., 1994).
Each AMSU-B scan line takes 2.67 s to complete with
90 fields of view per line. The maximum scan angle
of AMSU-B is 48.3° , and the innermost scans are at
0.55° . AMSU-B is a total power radiometer and measures
the combined horizontal and vertical polarization of
the incoming radiation. The proportion of the measured
radiation that is vertically polarized is 100% at nadir
and decreases with increasing scan angle (Saunders et al.,
1995).
The cross-track scanning nature of the AMSU-B instrument means that it records measurements with variable
polarization along the scan. There is also a representation
of spatial cloud variability along the scan and off-nadir
effects due to the slant path of the observation. These
effects are assumed to be of secondary importance to the
signals presented in this paper from variations in the ice
microphysical assumptions.
3.
Radiative transfer models
3.1. RTTOV
Radiative Transfer (RT) for the Television infrared observation satellite Operational Vertical Sounder (TOVS)
(RTTOV) is a fast RTM developed by the EUMETSAT Satellite Application Facility for NWP (http://www.
metoffice.gov.uk/research/interproj/nwpsaf/index.html)
for use with nadir viewing instruments such as AMSU
(Saunders et al., 1999). RTTOV 8.7 (http://www.
metoffice.gov.uk/research/interproj/nwpsaf/rtm/index.
html) was released in November 2005. It includes the
ability to model microwave scattering in the presence of
snow and ice cloud (Bauer et al., 2006). RTTOV assumes
a plane parallel atmosphere and spherical hydrometeors,
allowing the use of Mie Theory. The scattering calculations are solved using the delta-Eddington approximation (Wu and Weinman, 1984; Bauer, 2002) and surface
emissivity is calculated using FASTEM-3 (English et al.,
2003). The Maxwell-Garnett approach (Maxwell-Garnett,
1904) is used to account for the fraction of an ice particle
comprising ice, liquid water or air and to calculate the
refractive index.
RTTOV 8.7 requires temperature, pressure and humidity profiles plus profiles of four hydrometeor types: rain,
snow, liquid cloud and ice cloud. A Marshall-Palmer size
distribution (Marshall and Palmer, 1948) is assumed for
the precipitating hydrometeors and a modified gamma
distribution for the cloud hydrometeors. The density of
the ice hydrometeors is constant and set to 0.9 g cm−3
for ice and 0.1 g cm−3 for snow. In the work presented
in this paper, RTTOV 8.7 was modified to allow the use
of different size distributions and densities.
3.2. The Atmospheric Radiative Transfer System
(ARTS)
ARTS is an RTM developed by the University of Bremen for use with upward, downward and limb viewing
instruments. It deals with scattering by solving the full
vector radiative transfer equation using a multi-stream
solution, so it is a slower model than RTTOV but more
exact in its calculations (Sreerekha et al., 2002). ARTS
uses spherical Earth geometry and in the version used
here is run in one-dimensional mode using the discrete
ordinate iterative method (Emde et al., 2004).
For the ARTS results shown in this paper, FASTEM
was implemented to calculate surface emissivity over the
ocean (English and Hewison, 1998) and the McFarquharHeymsfield PSD was adopted for ice hydrometeors
(McFarquhar and Heymsfield, 1997). Ice density was
a constant at 0.91 g cm−3 . Ice hydrometeor refractive
indices were calculated using data from Warren (1984).
Liquid cloud hydrometeors were also considered in
the RT calculations, although precipitating hydrometeors
were not. As a result, the liquid hydrometeors input to
ARTS differed from that used in RTTOV as rain was not
included. However, ice inputs were identical as RTTOV
was also adjusted to accept only one frozen hydrometeor
type.
In a separate study (Courcoux et al., 2006), ARTS
and RTTOV have been compared using identical microphysics. The comparisons showed very close agreement
between the two RTMs (∼1 K) when identical assumptions were made.
4.
Case study
A number of case studies over the UK were chosen for the
purposes of investigating the effect of ice hydrometeor
microphysical assumptions in RTTOV. The case study
from 25 January 2002, 13 UTC, when a frontal system
with thick ice cloud and heavy rain was present over the
UK, is presented here. The input profiles for the RTMs
were obtained from the Met Office Mesoscale model,
which has a horizontal resolution of 12 km. The forecast
fields were for a 13 UTC forecast and the NOAA 16
overpass was at 13:32, so there is a discrepancy of 32 min
between model and observation times. Figure 1 shows the
Advanced Very High Resolution Radiometer (AVHRR)
infrared (IR) image for this case.
As error analysis of the Met Office model forecast
fields is not an aim of this paper, we make the assumption
that these fields can be assumed to be without bias in the
following.
5.
Ice microphysical assumptions
There are a number of treatments for size distribution and
density of ice hydrometeors available in the literature.
 Crown Copyright 2007. Reproduced with the permission of Her Majesty’s Stationery Office.
Published by John Wiley & Sons, Ltd.
Q. J. R. Meteorol. Soc. (in press)
DOI: 10.1002/qj
A. M. DOHERTY ET AL.
Figure 1. AVHRR IR image for case study showing a strong frontal system across the UK.
However, we have no information about separate ice
hydrometeor types in the input files used from the Met
Office Mesoscale model, and consider all ice hydrometeor types together. In this paper, there is no distinction
between, for example, cloud ice, snow, graupel and hail.
5.1.
ρ = 8.74×10−4 exp (−0.625 D 2 )+4.5×10−5 . (2)
3. A density treatment from Brown and Francis (1995)
based on aircraft data from midlatitude cirrus:
Density treatments
Constant ice hydrometeor density is often used in cloud
resolving models, and is used in the released versions of
RTTOV and ARTS (Section 3). However, atmospheric
ice hydrometeors can be aggregates comprising ice,
air and liquid in differing quantities. Generally, the
density of ice hydrometeors decreases with increasing
size (Heymsfield et al., 2004). To account for this, a
number of expressions for density ρ as a function of
particle diameter D have been developed. Three are
considered here. All of the following equations are in
SI units (ρ in kg m−3 , D in m).
1. The parametrization used in the Unified Model at the
UK Met Office:
ρ = 0.132 D −1 .
2. A parametrization based on aircraft data from stratiform precipitating mixed phase cloud (Jones, 1995):
(1)
ρ = 0.035 D −1.1 .
5.2.
(3)
Particle size distributions (PSD)
As outlined in Section 3, RTTOV 8.7 uses a MarshallPalmer size distribution for snow and a modified gamma
distribution for ice. For the purposes of this paper, snow
and ice are treated as a single hydrometeor type with a
single size distribution. A number of PSD parametrizations are investigated for use with this single ice hydrometeor type. PSDs examined include the modified gamma
distribution and a new treatment developed by Field et al.
(2005). This new treatment is based on aircraft data gathered over the UK and calculates the size distribution
of the ice hydrometeors using the IWC and temperature
within the cloud.
 Crown Copyright 2007. Reproduced with the permission of Her Majesty’s Stationery Office.
Published by John Wiley & Sons, Ltd.
Q. J. R. Meteorol. Soc. (in press)
DOI: 10.1002/qj
ICE HYDROMETEOR MICROPHYSICS FOR RADIATIVE TRANSFER
6. Comparison of different ice microphysical
assumptions
Table I outlines the microphysical assumptions used in
RTTOV for the purposes of this paper.
The histogram in Figure 2 shows the frequency of
each BT bin in the case study for ARTS and RTTOV
simulations and for observations. ARTS and RTTOV
both agree well with observations for BTs greater than
∼250 K. However, RTTOV does not agree so well with
observations at lower temperatures where the scattering
signal from ice hydrometeors is found. The lowest
RTTOV BT is 245 K, while the observations and ARTS
simulations fall as low as 220 K.
BT maps for channel 20 (183 ± 7 GHz) of the output
from RTTOV experiment 1 and from ARTS for the case
study are shown in Figure 3.
Three points can be noted from Figure 3:
1. Both RTMs reproduce the broad structure seen in the
observations. The frontal system across the British
Isles is clearly visible in both simulations.
2. The smaller scale features seen in the observations
are not reproduced exactly by either model. This is
probably due to discrepancies in the forecast fields,
which may not be accurate on smaller scales and
which are 32 min before the ATOVS overpass.
3. There is greater agreement in structure between the
two models than compared to observations, but there
Table I. RTTOV configurations.
Experiment
1
2
3
4
5
6
Density
Size distribution
0.1 g cm−3
0.5 g cm−3
0.5 g cm−3
8.74 × 10−4 exp (−0.625 D 2 )
+4.5 × 10−5
0.132 × D −1
0.132 × D −1
Modified Gamma
Modified Gamma
Field et al. (2005)
Modified Gamma
Modified Gamma
Field et al. (2005)
800
Frequency
600
400
solid line=RTTOV
dotted line=ARTS
dashed line=obs
200
0
200
220
240
260
280
300
Brightness Temperature (K)
Figure 2. Histogram of experiment 1: RTTOV, ARTS and observed
channel 20 BTs.
is a significant difference in the magnitude of the
scattering signal. This difference in the model outputs
may come from either the approach to radiative
transfer or from the basic microphysical assumptions.
We cannot comment on the agreement between the
models until we know how much these assumptions
affect the results of the radiative transfer.
The effective radius is an input parameter to ARTS.
This can be varied to effectively tune ARTS to agree
closely with observations, as seen in Figure 2, or to
agree closely with RTTOV, simply by using a smaller
assumed effective radius. Since agreement between modelled results and observations is better at higher BTs
(<5 K difference), it is likely that the problem arises
from the ice microphysical assumptions in RTTOV and
not from the method of solving the radiative transfer
equation.
Choosing a realistic size distribution and density for ice
hydrometeors is difficult as these quantities differ from
cloud to cloud and even within clouds (Korolev et al.,
2001). The effect of the assumptions is demonstrated
by the BT plots in Figure 4 which show the difference
between channel 20 RTTOV BT for experiments 2 and 3
(same density but different size distribution) and between
experiments 2 and 4 (same size distribution but different
density).
The top two panels in Figure 4 show that BT variablity
due to changes in microphysical assumptions is very high.
The maximum difference between experiments 2 and 3
(same density, different PSD) is of the order 20 K and
for experiments 2 and 4 (same PSD different density) it
is of the order 50 K. It is often larger than the signal seen
from cloud itself (∼15 K for channel 20). This sensitivity
to assumed microphysics was also seen by SkofronickJackson et al. (2002) in their comparison of microwave
BTs in different cloud parametrizations for convective
situations.
In the bottom panel of Figure 4, the difference between
simulated and observed BT for experiment 6 is shown.
Some of the differences are due to the time offset between
the AMSU-B overpass and the forecast fields used in the
models (32 min). Errors in the forecast fields themselves
will also generate errors in the simulated BT, no matter
how well the RTM performs.
Figure 5 shows a histogram of the frequency of occurrence of each BT for each of the six RTTOV experiments
at the lower end of the BT range. This BT range has been
magnifed as this is where the scattering signal for ice
hydrometeors is seen and where the greatest differences
exist between the experiments. This plot depicts how,
of all the parametrizations considered here, experiment 6
matches observations most closely. There is still a discrepancy of more than 10 K at the lowest BTs, showing
that this parametrization does not completely reproduce
the observed ice scattering signal. At the highest BTs,
experiment 6, in common with all the RTTOV experiments, overestimates the BT by about 1 K (not shown).
 Crown Copyright 2007. Reproduced with the permission of Her Majesty’s Stationery Office.
Published by John Wiley & Sons, Ltd.
Q. J. R. Meteorol. Soc. (in press)
DOI: 10.1002/qj
A. M. DOHERTY ET AL.
Obs
Channel 20 experiment 2 – experiment 3
ARTS
−21
−18
−15
−12
−9
−6
−3
0
RTTOV
Channel 20 experiment 2 – experiment 4
−59
−49
−40
−30
−20
−10
0
channel 20 BT (K)
220
228
236
244
252
260
268
276
Figure 3. Observed, ARTS and RTTOV experiment 1 BT, for channel
20.
Observed minus simulated BTs were calculated for
each point in the case study for each experiment. The
data were then sorted into nine categories defined by
the ice water path (IWP) and liquid water path (LWP)
as outlined in Table II. The mean and standard deviation
were calculated for each bin. These are shown in Figure 6
for channels 16, 17 and 20 for bins 1, 3, 7 and 9.
Figure 6 shows that, as expected, all experiments
perform similarly when the IWP is below 25 g m−2
(cross and star symbols). However, the bins with
IWP >500 g m−2 (triangle and diamond symbols) show
Observed – Experiment 6 RTTOV BT channel 20
−26
−17
−9
0
8
16
25
Figure 4. Top panel: difference between RTTOV channel 20 simulations
for experiments 2 and 3. Middle panel: difference between RTTOV
channel 20 simulations for experiments 2 and 4. Bottom panel:
difference between observed channel 20 BT and RTTOV simulations
for experiment 6.
large variations between experiments. Experiments 2 and
3, with the ice particle density of 0.5 g cm−3 show the
largest difference from observations, confirming that this
density is an unreasonably large assumption if applied to
 Crown Copyright 2007. Reproduced with the permission of Her Majesty’s Stationery Office.
Published by John Wiley & Sons, Ltd.
Q. J. R. Meteorol. Soc. (in press)
DOI: 10.1002/qj
ICE HYDROMETEOR MICROPHYSICS FOR RADIATIVE TRANSFER
comparison of ch 20 TBs
250
Frequency
200
150
100
50
0
180
RTTOV expt 1
RTTOV expt 2
RTTOV expt 3
RTTOV expt 4
RTTOV expt 5
RTTOV expt 6
Observation
200
220
240
Brightness Temperature (K)
260
Figure 5. Histogram of RTTOV channel 20 BTs for all experiments
and the observations.
all ice hydrometeors. Figure 6 shows that experiment 6
has comparable mean and standard deviation to experiments 1, 4 and 5. Noting evidence from Figure 5, it
can be concluded that experiment 6 fits the observed
behaviour most closely.
7.
Figure 6. Mean and Standard Deviation of observed minus simulated
BT from the case study for each of 4 IWP and LWP bins. Results are
shown for channels 16, 17 and 20 for each experiment.
Summary and conclusions
A number of different parametrizations for the ice
hydrometeor microphysics were implemented in RTTOV.
The resulting simulated BTs were compared with observations and with ARTS output for a number of case
studies using input fields from the Met Office Mesoscale
model. The results for one of the case studies are presented in this paper. The comparisons highlight the sensitivity of the RTMs to the assumptions made about the
density and size distribution of the ice hydrometeors.
Of the parametrizations examined, a density of ρ =
0.132 D −1 and the Field size distribution (experiment 6)
was identified as the best fit to observations across a range
of measures. When comparisons of the mean and standard
deviation of differences were examined, experiments
1, 4, 5 and 6 performed well and consistently. When
comparisons were made in the form of histograms of BT
to overcome mislocation problems, experiments 3 and
6 provided the closest approximations to observations.
Given these results, experiment 6 was identified as the
best of the parametrizations examined. However, none of
the experiments fully captures the natural variation of BT
seen in the observations. It is possible that some errors
are introduced through the use of forecast model fields
as input. While we have made the assumption throughout
this work that a forecast model can be taken as a biasfree reference, the profiles may include errors. Both the
density and PSD treatments used in experiment 6 have the
benefit that they are dependent on other cloud parameters,
namely temperature and IWC for the PSD and particle
size for the density. This makes them more flexible and, if
the relations between the known and unknown parameters
are valid for the conditions in which they are used, more
realistic. When using the experiment 6 parametrization,
Table II. LWP and IWP bins.
Bin number
IWP limits
LWP limits
1
2
3
4
5
6
7
8
9
<25 g m−2
<25 g m−2
<25 g m−2
25 g m−2 < IWP <500 g m−2
25 g m−2 < IWP <500 g m−2
25 g m−2 < IWP <500 g m−2
>500 g m−2
>500 g m−2
>500 g m−2
<25 g cm−2
25 g m−2 < LWP < 500 g m−2
>500 g m−2
<25 g m−2
25 g m−2 < LWP < 500 g m−2
>500 g m−2
<25 g cm−2
25 g m−2 < LWP < 500 g m−2
>500 g m−2
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Number of points
1850
874
103
1204
1584
584
159
1478
164
Q. J. R. Meteorol. Soc. (in press)
DOI: 10.1002/qj
A. M. DOHERTY ET AL.
no particle size is required from the forecast model: only
temperature and IWC.
The parametrizations presented here have been tested
for case studies over the UK only. Comparisons under
other meteorological conditions should be made to ensure
assumptions are valid in a range of situations and
climatological zones.
Acknowledgements
The authors would like to acknowledge Brett Candy for
help gathering the case study data, Paul Field for guidance using the Field et al. (2005) size distribution and
Pete Francis for assistance applying the microphysical
assumptions. Thanks also to the ARTS Radiative Transfer
Model developers and Peter Bauer for help with RTTOV.
References
Bauer P. 2002. Microwave radiative transfer modeling in clouds and
precipitation. Part I: Model description. NWPSAF Document No.
NWPSAF-EC-TR-005.
Bauer P, Moreau E, Chevallier F, O’Keeffe U. 2006. Multiplescattering microwave radiative transfer for data assimilation
applications. Q. J. R. Meteorol. Soc. 132: 1259–1281.
Baum BA, Heymsfield AJ, Yang P, Bedka ST. 2005. Bulk Scattering
Properties for the Remote Sensing of Ice Clouds. Part I:
Microphysical Data and Models. J. Appl. Meteorol. 44: 1885–1895.
Benedetti A, Stephens GL, Haynes JM. 2003. Ice Cloud Microphysics
Retrievals from Millimeter Radar and Visible Optical Depth Using
an Estimation Theory Approach. J. Geophys. Res. 108: D11: Art.
No. 4335.
Bennartz R, Petty G. 2001. The Sensitivity of Microwave Remote
Sensing Observations of Precipitation to Ice Particle Size
Distributions. J. Appl. Meteorol. 40: 345–364.
Brown PRA, Francis PN. 1995. Improved Measurements of the Ice
Water Content in Cirrus Using a Total-Water Probe. J. Atmos.
Oceanic Technol. 12: 410–414.
Brown PRA, Illingworth AJ, Heymsfield AJ, McFarquhar GM, Browning KA, Gosset M. 1995. The Role of Spaceborne Millimetre Wave
Radar in the Global Monitoring of Ice Cloud J. Appl. Meteorol. 34:
2346–2366.
Courcoux N, Doherty A, Sreerekha TR. 2006. Comparison of Radiative
Transfer Models for AMSU-B in the Presence of Clouds. NWPSAF
Document No. NWPSAF-MO-VS-020.
Czekala H, Bauer P, Jones D, Marzano F, Tassa A, Roberti L,
English S, Bapista P, Mugnai A, Simmer C. 2000. Clouds and
Precipitation, Pp 37–68 in Cost Action 712, Radiative Transfer
Models for Microwave Radiometry. Final report of Project 1, Matzler
C (ed). Office for Official Publications of the European Communities:
Luxembourg.
Emde C, Buehler SA, Davis C, Eriksson P, Sreerekha TR,
Teichmann C. 2004. A Polarized Discrete Ordinate Scattering
Model for Simulations of Limb and Nadir Longwave Measurements
in 1D/3D Spherical Atmospheres. J. Geophys. Res. 109: D24,
doi:10.1029/2004JD005140.
English SJ, Hewison T. 1998. A fast generic millimetre wave emissivity
model. Proc SPIE 3503: 288–300.
English S, Jupp A, Candy B, Bobbington D, Holt A. 2003. Capability
and requirements for polarimetric radiometry in numerical weather
prediction for surface wind analysis. First progress report for ESA
contract ref. no. CAO/CB/02.1025.
Field PR, Hogan RJ, Brown PRA, Illingworth AJ, Choularton TW,
Cotton RJ. 2005. Parameterization of ice-particle size distributions
for mid-latitude stratiform cloud. Q. J. R. Meteorol. Soc. 131:
1997–2017.
Gayet JF, Ovarlez J, Shcherbakov V, Strőm J, Schumann U, Minikin
A, Auriol F, Petzold A, Monier M. 2004. Cirrus cloud microphysical
and optical properties at southern and northern midlatitudes during
the INCA experiment. J. Geophys. Res. 109: D20: Art. No. D20206.
Heymsfield AJ, Bansemer A, Schmitt C, Twohy C, Poellot MR. 2004.
Effective Ice Particle Densities Derived from Aircraft Data. J. Atmos.
Sci. 61: 982–1003.
Hogan RJ, Illingworth AJ, Sauvageot H. 2000. Measuring Crystal Size
in Cirrus Using 35- and 94-GHz Radars. J. Atmos. Oceanic Technol.
17: 27–37.
Hogan RJ, Mittermaier MP, Illingworth AJ. 2006. The Retrieval of Ice
Water Content from Radar Reflectivity Factor and Temperature and
its Use in Evaluating a Mesoscale Model. J. Clim. Appl. Meteorol.
45: 301–317.
Jones DC. 1995. Validation of scattering Microwave Radiative Transfer
Models using an aircraft radiometer and ground-based radar. PhD
Thesis, University of Reading, Department of Meteorology.
Kim MJ, Skofronick-Jackson GM, Weinman JA. 2004. Intercomparison
of Millimeter-Wave Radiative Transfer Models. IEEE Trans. Geosci.
Remote Sensing 42: 1882–1890.
Korolev AV, Isaac GA, Mazin IP, Barker HW. 2001. Microphysical
properties of continental clouds from in situ measurements. Q. J. R.
Meteorol. Soc. 127: 2117–2151.
Kummerow C. 1993. On the Accuracy of the Eddington approximation
for radiative transfer at microwave frequencies. J. Geophys. Res. 98:
2757–2765.
Marshall JS, Palmer WM. 1948. The distribution of raindrops with size.
J. Meteor. 5: 165–166.
Maxwell-Garnett JC. 1904. Colours in metal glasses and in metallic
films. Philos. Trans. R. Soc. London 203: 385–420.
McFarquhar GM, Heymsfield AJ. 1997. Parameterization of tropical
cirrus ice crystal size distributions and implications for radiative
transfer: results from CEPEX. J. Atmos. Sci. 54: 2187–2200.
Muller BM, Fuelberg HE, Xiang X. 1994. Simulations of the
Effects of Water Vapour, Cloud Liquid Water, and Ice on AMSU
Moisture Channel Brightness Temperatures. J. Appl. Meteorol. 33:
1133–1154.
Saunders RW, Hewison TJ, Stringer SJ, Atkinson NA. 1995. The
radiometric characterization of AMSU-B. IEEE Trans. Microwave
Tech. 43: 760–771.
Saunders R, Matricardi M, Brunel P. 1999. An Improved Fast
Radiative Transfer Model for Assimilation of Satellite Radiance
Observations. Q. J. R. Meteorol. Soc. 125: 1407–1425.
Sekhon R, Srivastava R. 1970. Snow Size Spectra and Radar
Reflectivity. J. Atmos. Sci. 27: 299–307.
Shupe MD, Uttal T, Matrosov SY. 2005. Arctic Cloud Microphysics
Retrievals from Surface-Based Remote Sensors at SHEBA. J. Appl.
Meteorol. 44: 1544–1562.
Skofronick-Jackson GM, Gasiewski AJ, Wang JR. 2002. Influence of
Microphysical Cloud Parameterizations on Microwave Brightness
Temperatures. IEEE Trans. Geosci. Remote Sensing 40: 187–196.
Smith AE, Bauer P, Marzano FS, Kummerow CD, McKague D,
Mugnai A, Panegrossi G. 2002. Intercomparison of Microwave
Radiative Transfer Models of Precipitating clouds. IEEE Trans.
Geosci. Remote Sensing 40: 541–549.
Sreerekha TR, Buehler S, Emde C. 2002. A simple new radiative
transfer model for simulating the effect of cirrus clouds in the
microwave spectral region. J. Quant. Spectrosc. Radiat. Transfer 75:
611–624.
Staelin DH. 1987. Capabilities of the Advanced Microwave Sounding
Unit. Space systems possibilites for a global energy and water cycle
experiment. Appendix B. WMO publication.
Warren SG. 1984. Optical constants of ice from the ultraviolet to the
microwave. Appl. Opt. 23: 1206–1225.
Wu R, Weinman JA. 1984. Microwave Radiance from Precipitating
clouds containing aspherical ice, combined phase and liquid
hydrometeors. J. Geophys. Res. 89: 7170–7178.
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Q. J. R. Meteorol. Soc. (in press)
DOI: 10.1002/qj