Parametrization of the effect of surface reflection on spectral infrared radiance measurements. Application to IASI

Journal of Quantitative Spectroscopy & Radiative Transfer 86 (2004) 201 – 214

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Parametrization of the e)ect of surface re*ection on spectral infrared radiance measurements. Application to IASI S. Heilliette∗ , A. Chedin, N.A. Scott, R. Armante Laboratoire de Meteorologie Dynamique, Ecole Polytechnique, Palaiseau 91128, Cedex, France Received 17 March 2003; accepted 12 August 2003

Abstract The recent launch of the Advanced Infrared Sounder (AIRS) on board EOS-Aqua and the scheduled launch of the Infrared Atmospheric Sounder Interferometer (IASI) on board the Meteorological Operational Satellite (METOP) in 2005 open interesting perspectives for remote sensing applications. Owing to their enhanced spectral resolution and sensitivity, this new generation of high-resolution infrared vertical sounders is ;rst aimed at improving the vertical resolution of temperature and water vapor pro;le retrievals needed by the weather forecasting community. Another important possible use of these instruments, in the context of the study of global warming, is to permit the retrieval of the concentrations of greenhouse gases like CO2 ; N2 O; CH4 , etc. In order to reach these two main objectives, improvement in the modeling of the radiative transfer is therefore necessary. One of the points which still needs some improvements is the contribution of the downward radiation re*ected by the surface back to the satellite which is often improperly accounted for in radiative transfer calculation to save computer time. In this article, we show how it is possible to simplify the problem through the computation of a spectrally dependent “e)ective” emissivity for which a simple parametrization is proposed, while preserving the accuracy of the results. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Surface re*ection; E)ective emissivity; High spectral resolution

1. Introduction The new generation of high-resolution infrared sounders like the Advanced Infrared Sounder (AIRS) recently launched on board EOS-Aqua and the Infrared Atmospheric Sounder Interferometer (IASI) to be launched on board the Meteorological Operational Satellite (METOP) in 2005 open promising perspectives for remote sensing applications. Improvement in the modeling of the radiative transfer is thus necessary to take bene;t fully from the greatly enhanced spectral resolution (2378 ∗

Corresponding author. Fax: +33-1-69-33-3005. E-mail address: [email protected] (S. Heilliette).

0022-4073/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2003.08.002

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channels and a spectral resolution ranging from 0.35 to 1:5 cm−1 for AIRS; 8461 channels and an unapodised spectral resolution of 0:25 cm−1 for IASI) and sensitivity of these new instruments. Surface emissivity is one of the important variables of the radiative transfer, not only because of its spectral variations, both over sea and over land but also because it directly in*uences the amount of radiation emitted and re*ected by the surface. Accurate line-by-line models have to properly account for this e)ect. However, taking into account the re*ection term adds to the computation burden. In this article, we show how it is possible to simplify the problem through the computation of a spectrally dependent “e)ective” emissivity. A parametrization of this e)ective emissivity is proposed. Under clear sky conditions (i.e. no clouds, no aerosols) and under the assumption of local thermodynamic equilibrium, the calculation of the monochromatic radiance I () emitted by the atmosphere leads to the integration of the radiative transfer equation which may be written in the following way:
1 I () = s ()s ()B(Ts ; ) + B(T (); ) d
+(1 − s ())s ()

s ()

1

s ()

B(T ( ); ) d ;

(1)

where () stands for the monochromatic transmission function between the satellite and the current level,  () for the monochromatic transmission function between the surface and the current level, s () for the monochromatic transmission function between the satellite and the surface, s () for the hemispherical directional emissivity of the surface, Ts for the skin surface temperature and B(T; ) for the usual Planck function. The ;rst and the second terms of Eq. (1) describe the up-welling radiance emitted by the surface of the earth and its atmosphere through the atmosphere. The third term deserves special attention. It corresponds to the down-welling radiance emitted by the atmosphere and re*ected by the surface back to the satellite. It is sometimes omitted since its contribution to the observed radiance is signi;cant only in relatively high transmission regions of the spectrum (transmission windows) and for values of s () signi;cantly di)erent from unity. Still, as radiance emitted in transmission windows is important to obtain information about the surface temperature or the lowest part of the atmosphere, a proper treatment of this last term is needed in order to obtain unbiased retrievals in particular of the surface skin temperature. It has also been shown that accounting properly for the surface emissivity in the solution of the inverse problem substantially and positively changes the retrieved meteorological pro;les [1]. 2. Eective emissivity concept It is possible to account for the last term of Eq. (1) by replacing the true emissivity s () by an “e)ective” emissivity se) () in the ;rst term of this equation, which can then be rewritten as
1 e) I () = s ()s ()B(Ts ; ) + B(T (); ) d: (2) s ()

From the comparison of Eqs. (1) and (2), it follows that
(1 − s ()) 1 e) s () = s () + B(T ( ); ) d : B(Ts ; ) s ()

(3)

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203

2 1.8 1.6 1.4

∆TB (K)

1.2 1 0.8 0.6 0.4 0.2 0 0

0.1

0.2

0.3

0.4

0.5 τs

0.6

0.7

0.8

0.9

1

Fig. 1. In*uence of the surface transmission on the re*ection term expressed in terms of brightness temperature KTB calculated for McClatchey’s MLS atmospheric pro;le and a constant true emissivity of 0.90.

The di)erence between the ;rst term of Eq. (2) and the ;rst term of Eq. (1) is the contribution of the surface re*ection to the outgoing radiance. Using the mean value theorem, this di)erence KI may be written as KI = (1 − s ())s ()(1 − s ())B(T˜ ; );

(4)

where T˜ is a frequency-dependent mean temperature. Using Eq. (4), it is easily seen that the re*ection term vanishes for very transparent transmission windows (s ≈ 1) or for very opaque portions of the spectra (s ≈ 0). In the ;rst situation, the atmosphere is so transparent that there is no radiance emitted and in the second situation the re*ected emission cannot reach the satellite because of the opacity of the atmosphere. Between these two extreme situations, the re*ection term is maximum near s ≈ 0:5 as it may be seen in Fig. 1 which shows the variation of the re*ection term KI , expressed in terms of brightness temperature KTB , versus the transmission function for the McClatchey’s Middle Latitude Summer (MLS) mean atmospheric situation. Using the new form of the re*ection term given by Eq. (4), we may rewrite Eq. (3) as B(T˜ ; ) (1 − s ())(1 − s ()): se) () = s () + (5) B(Ts ; ) Because of the occurrence of the factor (1 − s ()), this equation shows that the e)ective emissivity is essentially a decreasing function of the transmission. This can be seen in Fig. 2 which shows the e)ective emissivity calculated for the 8461 IASI apodised channels versus the transmission function for McClatchey’s MLS atmospheric pro;le and a constant true emissivity of 0.90. The description of the technical details of this calculation is postponed to Section 4. This result may seem to be counter-intuitive as we have already mentioned that the re*ection term is maximum around s ≈ 0:5. This comes from the fact that the re*ection term also depends on s . Therefore, a large di)erence

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0.98

εeff s (ν)

0.96

0.94

0.92

0.9

0

0.1

0.2

0.3

0.4

0.5 τs

0.6

0.7

0.8

0.9

1

Fig. 2. E)ective emissivity calculated for IASI apodised channels versus the transmission function for McClatchey’s MLS atmospheric pro;le and a constant true emissivity of 0.90.

1

0.98 0.94 0.90

0.99 0.98

Effective emissivity

0.97 0.96 0.95 0.94 0.93 0.92 0.91 0.9 900

1200

1500 1800 2100 Wavenumber (cm-1)

2400

2700

Fig. 3. E)ective emissivity calculated for IASI apodised channels for 3 constant values of the true emissivity using McClatchey’s MLS atmospheric pro;le.

between the e)ective emissivity and the true emissivity does not necessarily imply a great impact of the re*ection term on the observed radiance. Eq. (5) also shows that, even in the case of a constant true emissivity s , the e)ective emissivity e) s () is frequency dependent. Fig. 3 gives an idea of this frequency dependence. On this graph,

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we have plotted the variation of the e)ective emissivity versus the wavenumber for three values of a constant true emissivity: 0.90, 0.94 and 0.98. Fig. 3 also shows the great similitude between the variations of the e)ective emissivity for each value of the true emissivity. This arises from the fact that it is possible to introduce an invariant quantity K(), independent of the true emissivity:
1 se) () − s () B(T ( ); )  B(T˜ ; ) = d = (1 − s ()) (6) K() = 1 − s () B(Ts ; ) s () B(Ts ; ) relating se) () to s () se) () = s () + (1 − s ())K():

(7)

It is worth pointing out that this equation applies even if the true emissivity is frequency dependent as it is the case in reality. It is interesting to note that it is easily possible to range K(). First, it is obvious that K() ¿ 0. Furthermore, in most cases, we can assume that Ts ¿ T˜ . Therefore, recalling that the Planck function is an increasing function of the temperature at any frequency, it follows from Eq. (6) that 0 6 K() 6 1 − s ():

(8)

We can translate Eq. (8) in terms of the e)ective emissivity range of variation s () 6 se) () 6 s () + (1 − s ())(1 − s ()):

(9)

Parametrizing K(), which depends on the atmospheric pro;le considered, is the key to an easy determination of se) (). 3. Parametrization of the eective emissivity Knowledge of K(), as given by Eq. (6), requires that of T˜ () and s (). If the transmission function is known, we need an estimation of T˜ () which, as already pointed out, depends on the frequency. If the absorption in the transmission window considered is mainly due to the water vapor, which is often the case, one can reasonably assume that this temperature is not too far from the mean water vapor weighted temperature TQ de;ned as  Ps T (P)qw (P) dP T˜ () ≈ TQ = 0  Ps ; (10) q (P) dP w 0 where qw stands for the water vapor mass mixing ratio, P for the pressure and Ps for the surface pressure. If the spectral absorption is not essentially due to water vapor, T˜ () might be signi;cantly di)erent from TQ . For example, in the ozone absorption band around 9:5 m, T˜ () is much lower than TQ (the di)erence may reach about 30 K for a typical tropical atmospheric situation) because of the low temperature of the stratosphere where the absorption by the ozone molecule is essentially located. In such a case, the direct use of the true transmission function s () together with TQ instead of T˜ () in Eq. (6) leads to an erroneous estimate of K(). For this reason, we have investigated other

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parametrizations and found that expressing K() in terms of the integrated water vapor amount Qw , using a polynomial of degree two, is accurate enough in all cases: B(TQ ; ) [A() + B()Qw + C()Qw2 ] K() = (11) B(Ts ; ) with 1 Qw = g


0

Ps

qw (P) dP;

(12)

where g stands for acceleration of gravity. When the spectral absorption is essentially due to water vapor, Eqs. (11) and (6) mean that 1 − s () ≈ A() + B()Qw + C()Qw2 :

(13)

The constant term A() takes into account the mean absorption by all the minor gases other than water vapor, including ozone. B() and C() describe the absorption by the water vapor. The occurrence of the quadratic term is necessary to take into account the water vapor self-continuum absorption. When the spectral absorption is not essentially due to water vapor, for example in the ozone absorption band around 9:5 m, Eqs. (11) and (6) mean that B(T˜ ; ) (1 − s ()) ≈ A() + B()Qw + C()Qw2 : (14) B(TQ ; ) In this case, the polynomial expansion takes into account both the variation of the transmission function and the di)erence between T˜ and TQ as previously discussed. In all cases, starting from K(), TQ and Qw calculated for a representative set of pro;les, the coeRcients A(), B() and C() are determined for each channel by a linear regression (see Section 5 for detailed explanations). For remote sensing applications, it is important to take into account the in*uence of observation angle  in parametrization. From the dependence of transmission with respect to : s (; ) = s (; 0)sec  ;

(15)

if we assume that the absorption spectrum is dominated by water vapor, it then follows from Eqs. (13), (11) and (6) that the dependence of K() with  in parametrization is given by B(TQ ; ) {1 − exp[sec  log(1 − A() − B()Qw − C()Qw2 )]}: (16) K(; ) = B(Ts ; ) As a matter of fact, as it will be shown in Section 5, Eq. (16) remains suRciently accurate for our purpose in all cases. 4. Method of computation of the eective emissivity All the radiance spectrum calculations have been carried out using the Automatized Atmospheric Absorption Atlas (4A) line-by-line model [2–4] which is able to calculate such spectra with and without the re*ection term. The full radiance is represented by I↓↑ whereas the radiance obtained neglecting the re*ection term is denoted by I↑ . In order to calculate the e)ective emissivity se) ()

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207

corresponding to a given true reference emissivity 1 , for each atmospheric situation considered, we need to carry out three radiance spectrum calculations: two calculations without the re*ection term for the reference emissivity 1 and another emissivity 2 and one calculation with the re*ection term for the constant true emissivity 1 . De;ning KI as KI (; ) = I↑↓ (; 1 ) − I↑ (; );

(17)

it follows from Eq. (1) that this quantity depends on  in a simple way:
1 KI (; ) = s ()B(Ts ; )(1 − ) + (1 − 1 )s () B(T ( ); ) d s ()

= (; 1 ) + ():

(18)

The coeRcients (; 1 ) and () are easily calculated using KI (; 1 ) and KI (; 2 ). By de;nition, the e)ective emissivity associated with the true emissivity 1 zeroes KI . Thus, we can write (; 1 ) : (19) se) () = − () It is then straightforward to calculate K() using Eq. (6). Eq. (19) must be used with care because for opaque portions of the spectrum, the coeRcient () is almost zero. To avoid this problem, it is therefore necessary to introduce a threshold: if the emissivity Jacobian is greater than 0.2 then we use Eq. (19) to calculate the e)ective emissivity; in the opposite case, we simply put se) () = 1:0. 5. Results Using the previously described calculation method, e)ective emissivity spectra have been determined for 30 atmospheric pro;les selected within the Thermodynamic Initial Guess Retrieval (TIGR) climatological database in its latest version [5,6]. These 30 pro;les have been selected among 15 classes (2 by class, chosen randomly) obtained at the end of a clustering procedure (using temperature and water vapor pro;les) applied to TIGR and are representative of the whole database. All the e)ective emissivity spectra calculations have been carried out by simulating apodised IASI spectra. The coeRcients A(), B() and C() have been calculated, once and for all, for a nadir viewing angle and for each channel by linear regression using the 30 e)ective emissivity spectra of the learning set taken as reference. They may be applied to any atmospheric situation. In most of the cases, for a constant true emissivity s () = 0:98, the residuals of the regression, i.e. the di)erence between the calculated and the parametrized e)ective emissivity, are typically smaller than a few 10−3 . In Fig. 4, we show the residuals of the regression, for the tropical pro;le number 1 of the TIGR database which is part of the learning set. This pro;le is one for which the best results have been obtained. To illustrate the opposite situation, in Fig. 5 we show the residuals of the regression for the polar pro;le number 1962 of the TIGR database which is also part of the learning set. The worst results have been obtained for this very cold and dry atmospheric pro;le with a strong temperature inversion near the surface (about 15 K between 800 hPa and 1000 hPa). In order to test the ability of Eq. (16) to describe the dependence of the e)ective emissivity on the observation angle , we show in Figs. 6 and 7 the residuals of the regression for  = 45◦ and

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S. Heilliette et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 86 (2004) 201 – 214 0.0008 0.0006

eff εeff s - εpar

0.0004 0.0002

0 -0.0002

-0.0004 -0.0006 900

1200

1500

1800

2100

2400

2700

Wavenumber (cm-1)

Fig. 4. Residuals of the linear regression for the TIGR 2000 tropical pro;le number 1, a constant true emissivity of 0.98, and an observation angle of 0◦ .

0.008 0.006 0.004

eff εeff s - εpar

0.002 0 -0.002 -0.004 -0.006 -0.008 -0.01 900

1200

1500

1800

2100

2400

2700

Wavenumber (cm-1)

Fig. 5. Residuals of the linear regression for the TIGR 2000 polar pro;le number 1962, a constant true emissivity of 0.98, and an observation angle of 0◦ .

two independent mean pro;les from McClatchey: MLS for Fig. 6 and South Arctic Winter (SAW) for Fig. 7. The results are similar to those obtained for smaller observation angles. In Figs. 4–7 we have assumed a frequency-independent true emissivity s ()=0:98. In reality, emissivity is frequency dependent. In order to illustrate the application of our method to a more realistic situation, we have

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209

0.002

0.0015

eff

eff

εs - εpar

0.001 0.0005 0

-0.0005 -0.001 -0.0015 900

1200

1500

1800

2100

2400

2700

Wavenumber (cm-1)

Fig. 6. Residuals of the linear regression for McClatchey’s MLS atmospheric Pro;le, a constant true emissivity of 0.98, and an observation angle of 45◦ .

0.003

0.002

eff

eff

εs - εpar

0.001

0

-0.001 -0.002

-0.003 -0.004 900

1200

1500

1800

2100

2400

2700

Wavenumber (cm-1)

Fig. 7. Residuals of the linear regression for McClatchey’s SAW atmospheric Pro;le, a constant true emissivity of 0.98, and an observation angle of 45◦ .

applied our parametrization to a frequency-dependent sea emissivity as given by the widely used model of Masuda et al. [7]. The residuals obtained in such a case and for the tropical McClatchey’s pro;le are shown in Fig. 8. The relatively important di)erences observed in the vicinity of transition

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S. Heilliette et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 86 (2004) 201 – 214 0.01 0.008 0.006

0.002

eff

eff

εs - εpar

0.004

0 -0.002 -0.004 -0.006 -0.008 -0.01 900

1200

1500 1800 2100 Wavenumber (cm-1)

2400

2700

Fig. 8. Residuals of the linear regression for McClatchey’s Tropical atmospheric Pro;le, a frequency-dependent true emissivity corresponding to sea as modeled by Masuda et al. [7], and an observation angle of 0◦ .

between windows and opaque portions of the spectrum are related to the use of a threshold in the parametrization. The in*uence of these di)erences is quite small as the emissivity Jacobian is very low in these parts of the spectrum (see Fig. 10). For practical application of this parametrization, we are essentially interested in the accuracy of the spectra in terms of radiance or brightness temperature. For example, starting from a radiance spectrum calculated without the re*ection term for a reference constant emissivity ref and a given atmospheric pro;le, we are able to calculate the spectrum for any frequency-dependent emissivity for the same pro;le including the re*ection term, simply by writing I () = Iref () + (se) () − ref )J ;

(20)

where  J =

9I↑ 9

 = B(Ts ; )s ():

(21)

In Figs. 9–13, corresponding, respectively, to the previously considered atmospheric situations of Figs. 4–8, we have plotted a comparison of the error made omitting the re*ection term with the error made using Eq. (20) and the parametrization given by Eq. (16). Obviously, the systematic error made omitting the re*ection term is much greater than the error made using our approximate calculation method. Most of the time the latter error is smaller than 0:05 K and in the worst case the error reaches about 0:1 K. As can be seen in Figs. 11 and 12, our parametrization works quite well even for an angle of 45◦ . Our model is less accurate for cold and dry atmospheric situations

S. Heilliette et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 86 (2004) 201 – 214 0.4

211

up only parametrisation

0.35 0.3

Error (K)

0.25 0.2 0.15 0.1 0.05 0 -0.05

900

1200

1500 1800 2100 Wavenumber (cm-1)

2400

2700

Fig. 9. Comparison of the errors made neglecting the re*ection term and using our parametrized e)ective emissivity for the TIGR 2000 tropical pro;le number 1, a constant true emissivity of 0.98 and an observation angle of 0◦ .

0.4

up only parametrisation

0.35 0.3

Error (K)

0.25 0.2 0.15 0.1 0.05 0 -0.05

900

1200

1500 1800 2100 Wavenumber (cm-1)

2400

2700

Fig. 10. Comparison of the errors made neglecting the re*ection term and using our parametrized e)ective emissivity for McClatchey’s Tropical Atmospheric Pro;le, a frequency-dependent true emissivity corresponding to sea as modeled by Masuda et al. [7], and an observation angle of 0◦ .

like McClatchey’s SAW pro;le of Fig. 12 or the TIGR 2000 pro;le number 1962 of Fig. 13. Using a di)erent parametrization for each air mass type (tropical, polar, temperate, etc.) would probably lead to an improvement of our parametrization in these extreme situations.

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up only parametrisation

0.35 0.3

Error (K)

0.25 0.2 0.15 0.1 0.05 0 -0.05

900

1200

1500 1800 2100 Wavenumber (cm-1)

2400

2700

Fig. 11. Comparison of the errors made neglecting the re*ection term and using our parametrized e)ective emissivity for McClatchey’s MLS atmospheric Pro;le, a constant true emissivity of 0.98, and an observation angle of 45◦ .

0.3

up only parametrisation

0.25

Error (K)

0.2 0.15

0.1 0.05

0 -0.05

900

1200

1500 1800 2100 Wavenumber (cm-1)

2400

2700

Fig. 12. Comparison of the errors made neglecting the re*ection term and using our parametrized e)ective emissivity for McClatchey’s SAW atmospheric Pro;le, a constant true emissivity of 0.98, and an observation angle of 45◦ .

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213

0.3 up only parametrisation

0.25 0.2

Error (K)

0.15 0.1 0.05 0 -0.05 -0.1 -0.15 900

1200

1500 1800 2100 Wavenumber (cm-1)

2400

2700

Fig. 13. Comparison of the errors made neglecting the re*ection term and using our parametrized e)ective emissivity for the TIGR 2000 polar pro;le number 1962, a constant true emissivity of 0.98, and an observation angle of 0◦ .

6. Conclusion Improvement in the modeling of the radiative transfer, needed to fully take bene;t from the greatly enhanced spectral resolution and sensitivity of the new generation of high-resolution infrared sounders like the Advanced Infrared Sounder (AIRS) and the Infrared Atmospheric Sounder Interferometer (IASI), raises challenging problems. Among these problems, those linked with the surface emissivity are signi;cant because surface emissivity directly in*uences the amount of radiation emitted and re*ected by the surface and is spectrally variable both over sea and over land. Accurate line-by-line models have to properly account for this e)ect. In particular, taking into account the re*ection term is computationally expensive. In this article, we have shown how to simplify the problem through the computation of a spectrally dependent “e)ective” emissivity. A parametrization of this e)ective emissivity is proposed and applied to the IASI sounder. This parametrization is based upon the assumption that the variability of absorption in atmospheric windows is essentially due to water vapor, but also accounts for the e)ect of absorption by other gases. Using this parametrization, we are able to estimate the variation of the re*ection term versus the observation angle for any given thermodynamic pro;le. The accuracy of this parametrization, of the order of 0:05 K in most cases, is suRcient for most remote sensing applications and might even be improved by developing di)erent parametrizations for each air mass type which was not the case here. Acknowledgements This work has been supported by the European Community under contract EVG1-CT-2001-00056 (COCO Project), and by CNRS, CNES, and Ecole Polytechnique.

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References [1] Plokhenko Y, Menzel WP. The e)ects of surface re*ection on estimating the vertical temperature-humidity distribution from spectral infrared measurements. J Appl Meteorol 2000;39:3–14. [2] Scott N, ChWedin A. A fast line-by-line method for atmospheric absorption computations: the automatized atmospheric absorption atlas. J Clim Appl Meteorol 1981;20:802–12. [3] ChWeruy F, Scott N, Armante R, Tournier B, ChWedin A. Contribution to the development of radiative transfer models for high spectral resolution observations in the infrared. JQSRT 1995;53(6):597–612. [4] Scott N, ChWedin A, Armante R. The automatized atmospheric absorption atlas (4A) fast line-by-line model in 2003, in preparation. [5] ChWedin A, Scott N, Wahiche C, Moulinier P. The improved initialization inversion method: a high resolution physical method for temperature retrievals from the TIROS-N series. J Clim Appl Meteorol 1985;24:124–43. [6] Chevallier F, ChWedin A, Cheruy F, Scott NA. A TIGR-like atmospheric pro;le database for accurate radiative *ux computation. Q J R Meteorol Soc 2000;126:777–85. [7] Masuda K, Takashima Y, Takayama Y. Emissivity of pure and sea waters for the model of sea surface in the infrared windows regions. Remote Sensing Environ 1988;24:313–29.