Marco Matricardi
The introduction of clouds and aerosols in RTIASI
A
new version of RTIASI (Matricardi 2003), the ECMWF fast radiative transfer model
for the Infrared Atmospheric Sounding Interferometer (IASI), has been developed
that features the introduction of multiple scattering by aerosols and clouds. In RTIASI,
multiple scattering is parameterized by scaling the optical depth by a factor derived by
including the effect of backward scattering in the emission of a layer and in the transmission between levels (scaling approximation, Chou et al. (1999)).
Since the scaling approximation does not require explicit calculations of multiple scattering, the
computational efficiency of RTIASI can be retained. In fact, the radiative transfer equation for
multiple scattering is identical to that in clear sky conditions: the absorption optical depth, τa, is
~
replaced by the effective extinction optical depth,τe , defined as
τe = τ a + bτs
nc
Ltotal = ∑ Lovercast ( X s+1 − X s ) + Lclear (1− X n c +1)
s =1
(1)
where τs is the scattering optical depth and b is the integrated fraction of energy scattered
backward for incident radiation from above or below. If P (µ, µ′) is the azimuthally averaged
phase function, the scaling factor b can be written in the form
1
b=
2
1
0
∫ dµ ∫ P (µ,µ′) dµ′
0
(2)
–1
It should be noted that the scaling approximation rests on the hypothesis that the diffuse radiance
field is isotropic and can be approximated by the Planck function.
Layer
CFR (%)
1
0
2
50
3
0
4
30
5
80
6
0
7
0
Figure 4
Continental polluted
0.01
0.01
0.01
0.008
0.008
0.008
0.006
0.006
0.006
0.004
0.004
0.002
0
0
Wave number (cm-1)
0.002
0
800 1200 1600 2000 2400 2800
Wave number (cm-1)
200
Stratus (Maritime)
200
160
0.04
0.04
0.02
0.02
800 1200 1600 2000 2400 2800
0
800 1200 1600 2000 2400 2800
0
Wave number (cm-1)
800 1200 1600 2000 2400 2800
Wave number (cm-1)
Absorption coefficient
Scattering coefficient
200
160
120
Cumulus (Continental clean)
120
200
200
160
160
160
120
Cumulus (Maritime)
Cumulus (Continental polluted)
120
120
0.35
0.5
80
80
80
80
80
40
40
40
40
40
0
800 1200 1600 2000 2400 2800
0
Wave number (cm-1)
0
800 1200 1600 2000 2400 2800
Wave number (cm-1)
0
Wave number (cm-1)
Scattering coefficient
Extinction coefficient
Figure 2
800 1200 1600 2000 2400 2800
800 1200 1600 2000 2400 2800
0
Wave number (cm-1)
-25° to -30°
Absorption coefficient
-30° to -35°
-40° to -45°
-55° to -60°
1
1
1
1
1
0.8
0.8
0.8
0.8
0.8
0.6
0.6
0.6
0.6
0.6
0.4
0.4
0.2
0.4
0.2
800 1200 1600 2000 2400 2800
Wave number (cm-1)
0
0.4
0.2
800 1200 1600 2000 2400 2800
Wave number (cm-1)
Extinction coefficient
0
0.4
0.2
800 1200 1600 2000 2400 2800
Wave number (cm-1)
Scattering coefficient
0
0.2
800 1200 1600 2000 2400 2800
Wave number (cm-1)
0.9
1
1
2
3
4
5
6
The cloud distribution in each column
Aerosols – Desert – Tropical profile
Number density: global climatological value
4
Clear-Multiple stream
Scaling-Multiple stream
3
2
1
0
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
Number density: four times the global climatological value
4
3
2
1
0
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
Figure 5 The radiative impact of the Desert aerosol
type (black curve) and the error introduced by the scaling approximation (red curve) for the tropical profile for
two different aerosol number densities.
Cirrus – Height of cloud = 12km
Tropical profile – Single layer
20
Clear-Multiple stream
Scaling-Multiple stream
15
10
5
0
600
800
1000
1200
1400
2000
2200
2400
2600
2800
1800
2000
1600
Wave number (cm-1)
2200
2400
2600
2800
1600
1800
Double layer
20
15
10
5
0
600
800
1000
1200
1400
Figure 8 The radiative impact of the Cirrus cloud type
(black curve) and the error introduced by the scaling approximation (red curve) for the tropical profile for two different values of the cloud thickness.
Wave number (cm-1)
The absorption, scattering and extinction coefficient for the five water cloud types included in RTIASI-5.
-20° to -25°
0
800 1200 1600 2000 2400 2800
0.65
X1___ X2 ____________ X3 _______ X4 ______ X5_____________ X6 ___ X7
Wave number (cm-1)
0
800 1200 1600 2000 2400 2800
Wave number (cm-1)
Absorption coefficient
Figure 3 The absorption, scattering and extinction coefficient for a selected number of cirrus cloud types included in
RTIASI-5.
References
Amorati, R., and Rizzi, R., 2002: Radiances simulated in presence of clouds by use of a fast radiative transfer model and a
multiple-scattering scheme. Applied Optics, 41, No. 9, pp. 1604–1614.
Bauer, P., 2002: Microwave radiative transfer modelling in clouds and precipitation. Part I: Model description. Document No.
NWPSAT-EC-TR-005.
Chou, M-D., Lee, K-T., Tsay, S-C., and Fu, Q., 1999: Parameterization for Cloud Longwave scattering for Use in Atmospheric
Models. Journal of Climate, 12, pp. 159–169.
Hess, M., Kepke, P., and Schult, I., 1998: Optical Properties of Aerosols and Clouds: the software package OPAC. Bulletin of
the American Meteorological Society, 79, pp. 831–844.
Kahnert, F.M., Stamnes, J., and Stamnes, K., 2001: Application of the extended boundary condition method to homogeneous
particles with point-group symmetries. Applied Optics, 40, No. 18, pp. 3110–3123.
Macke, A., Mueller, J., and Raschke, E., 1996: Single scattering properties of Atmospheric Ice Crystals. Journal of the Atmospheric Sciences, 53, No. 19, pp2813–2825.
Matricardi, M., 2003: RTIASI-4, a new version of the ECMWF fast radiative transfer model for the Infrared Atmospheric Sounding Interferometer. ECMWF Technical Memorandum No. 425.
Brightness temperature difference (K) Brightness temperature difference (K)
(km-1)
0.06
The absorption, scattering and extinction coefficient for five of the aerosol types included in RTIASI-5.
Stratus (Continental)
(km-1)
0.06
Wave number (cm-1)
Extinction coefficient
Figure 1
0.08
0.004
0.002
800 1200 1600 2000 2400 2800
Desert
Urban
0.08
Brightness temperature difference (K) Brightness temperature difference (K)
Continental average
0.1
The accuracy of the scaling approximation has been assessed by comparing approximate radiances
(i.e. scaling approximation) with reference radiances computed using a 42-stream doublingadding algorithm (Bauer 2002). Spectra have been computed for a tropical and arctic air mass.
For each of the ten aerosol types included in RTIASI, we have considered vertical profiles representative of average and extreme conditions. The desert dust aerosol type has by far the largest
impact on the radiance. Figure 5 shows that for the extreme condition case the presence of
desert dust in a tropical air mass can result in a reduction of the top of the atmosphere clear-sky
radiance by 4 K in the thermal infrared and by 1.8 K in the short wave. The same figure shows
that errors introduced by the scaling approximation are less than 1 K in the thermal infrared and
less then 0.25K in the short wave. For the other aerosol types, errors introduced by the scaling
approximation never exceed 0.1 K. For all the water cloud types considered in RTIASI, errors
are typically less than 1K in the thermal infrared and below 4 K in the short wave. It should be
noted that for the cases considered here the presence of a water cloud in a tropical or arctic
air mass can result in a reduction of the top of the atmosphere radiance by 30K in the thermal
infrared and by up to 40K in the short wave. Results for a low level cloud (Stratus Continental)
and for a middle level cloud (Cumulus Continental Clean) are shown in figures 6 and 7 respectively. Finally, for the cirrus cloud type we found a remarkable agreement between approximate
and references radiances. Some of the results are illustrated in figures 8 and 9 where it can be
seen that for a tropical profile errors introduced by the scaling approximation never exceed 0.5
K whereas for an arctic profile errors are typically less than 0.1K. This can be explained in the
light of the fact that the phase function for ice crystals is characterized by a narrow and sharp
forward peak that results in a very small value of the b parameter and in the limit of b → 0 we
expect the reference and approximate radiances to converge since in this case the attenuation
of the radiance is only due to absorption.
Stratus (Continental) – Height of cloud = 2km
Tropical profile – Single layer
20
15
Clear-Multiple stream
Scaling-Multiple stream
10
5
0
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
Double layer
20
15
10
5
0
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
Wave number (cm-1)
Figure 6 The radiative impact of the Stratus Continental
cloud type (black curve) and the error introduced by the
scaling approximation (red curve) for the tropical profile
for two different values of the cloud thickness.
Brightness temperature difference (K) Brightness temperature difference (K)
(km-1)
Continental clean
Cloud displacement in each column
Fractional coverage 0
Column number
The RTIASI radiative transfer can include by default eleven basic aerosol components, five types
of water clouds and eight types of cirrus clouds. The database of optical properties for aerosols
and water droplets has been generated using the Lorentz-Mie theory for spherical particles taking
the microphysical properties assembled in the Optical Properties of Aerosols and Clouds (OPAC)
software package (Hess et al. 1998). The aerosols optical properties can be computed for any
mixture of the default eleven components or, alternatively, for ten aerosol types composed of
pre-defined mixtures of basic components representative of average and extreme conditions for
a range of climatological important aerosols. For cirrus clouds, a composite database has been
generated using the Geometric Optics method for large crystals and the T-matrix method for
small crystals. The publicly available codes developed by Macke et al. (1996) and Kahnert (2004)
have been used respectively. In either case, ice crystals have been assumed to have the shape
of a hexagonal prism randomly oriented in space. For cirrus clouds we have used the Heymsfield and Platt (1984) size distribution. To account for the radiative effects due to the presence
of small crystals, the Heymsfield and Platt distribution has been extrapolated to 4 µm using
the method described in Mitchell et al. (1996). For all the aerosol components and cloud types
included by default in RTIASI, the optical properties have been obtained based on microphysical
properties that, given their highly variable nature, do not necessarily reflect an actual situation.
For this reason, RTIASI allows the user to externally specify the values of the optical properties
used in the radiative transfer. In figure 1 we have plotted the absorption, scattering and extinction coefficient for the five most significant (in radiative terms) aerosol types. The same optical
properties for the five water clouds included in RTIASI are illustrated in figure 2 whereas for
cirrus clouds they are plotted in figure 3 where a selection of different temperature ranges has
been chosen.
(3)
Cumulus (Continental polluted) – Height of cloud = 6km
Tropical profile – Single layer
40
Clear-Multiple stream
Scaling-Multiple stream
30
20
10
0
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
2000
2200
2400
2600
2800
Double layer
40
30
20
10
0
600
800
1000
1200
1400
1600
1800
Wave number (cm-1)
Figure 7 The radiative impact of the Cumulus Continental Clean cloud type (black curve) and the error introduced
by the scaling approximation (red curve) for the tropical
profile for two different values of the cloud thickness.
Brightness temperature difference (K) Brightness temperature difference (K)
~
To solve the radiative transfer for a partly cloudy atmosphere (i.e. horizontally non-homogeneous), RTIASI uses a scheme (stream method, Amorati and Rizzi 2002) that divides the atmosphere
into a number of homogeneous columns. Each column is characterized by a different number of
cloudy layers, hence different radiative properties, and contributes to a fraction of the overcast
radiance that depends on the cloud overlapping assumption. To illustrate the stream method, we
give here an example where a seven layer atmosphere is considered. Once the cloud fractional
coverage in each layer is known (CFR in figure 4), we compute the cumulative cloud coverage,
Nnot (j), from layer 1 to layer j using the maximum-random overlap assumption. A cloud (blue
shaded region in figure 4) is then placed in layer j that covers the range from Nnot (j)–CFR(j) to
Nnot (j). To determine the number of columns, we consider all the cloud configurations that result
in a totally overcast column. In our example we obtain five, nc, overcast columns and one clear
column. Once the top of the atmosphere radiance has been computed for each homogeneous
column, the total radiance, Ltotal, is written as the sum of all the single column radiances weighted
by the column fractional coverage.
Brightness temperature difference (K) Brightness temperature difference (K)
Poster presented by Andrew Collard, ECMWF
ECMWF, Reading, UK
Marco.matricardi@ecmwf.int
Cirrus – Height of cloud = 12km
Arctic profile – Single layer
1.4
1.2
Clear-Multiple stream
Scaling-Multiple stream
1
0.8
0.6
0.4
0.2
0
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
2000
2200
2400
2600
2800
Double layer
1.4
1.2
1
0.8
0.6
0.4
0.2
0
600
800
1000
1200
1400
1600
1800
Wave number (cm-1)
Figure 9 The radiative impact of the Cirrus cloud type
(black curve) and the error introduced by the scaling approximation (red curve) for the arctic profile for two different values of the cloud thickness.