Analysis of different models for atmospheric correction of meteosat infrared images. A new approach

Atmosphertc Research, 30 ( 1993 ) 1- 12

1

Elsevmr Science Pubhshers B.V, A m s t e r d a m

Analysis of different models for atmospheric correction of Meteosat infrared images. A new approach A.M. P6rez, P. Illera and J.L. Casanova Departamento de Fistca Aphcada I, Umverstdad de Valladohd, 47071, Valladohd, Spare (Recetved April 27, 1992, revised and accepted January 21, 1993 )

ABSTRACT A comparative study of several atmospheric correction models has been carried out As primary data, atmospheric profiles of temperature and humidity obtained from radiosoundlngs on cloud-free days have been used Special attention has been paid to the model used operationally in the European Space Operations Centre (ESOC) for sea temperature calculations_ The atmospheric correction lesuits are expressed in terms of the increase in the brightness temperature and the surface temperature A d~fference of up to a maximum of 1 4 degrees with respect to the correcnon obtained in the studied models has been observed_ The radiances calculated by models are also compared with those obtained directly from the satellite The temperature correctmns by the latter are greater than the former m practically every case. As a result of this, the operational cahbratmn coefficients should be first recalculaled if we wish to apply an atmospheric correctmn model to the satelhte data Finally, a new simphfied calculatmn scheme which may be introduced into any model is proposed. RESUMI2 On a compar6 les valeurs de la correction atmosph6nque obtenues par d~ff6rents modules Les donn6es d'entr6e des modules ont 6td des radlosondages r6ahs6s pendant certainsjours de c~el clair On a 6tudl6 sp6clalement le module que I'ESOC (Centre Europ6en pour les Op6ratlons Spatmles) Utdlse actuellement pour obtemr les temp6ratures de la surface de l a m e r Les r6sultats ont 6t6 analysts en fonctmn des dlff6rences entre la temp6rature observ6e depms le satellite et la temp6rature mesur6e au sol Ces dlff6rences atteignent un maximum de 1,4 :C entre les modules utdlS6S Les radiances th6onques ont 6galement 6t6 compar6es aux radiances mesur6es par le satellite La correctton de temp6rature donn6e par les radiances mesur6es par le satellite est consld6rablement sup6rleure h celle pr6vue par les modules La conclusion est qu'll faudralt modifier les coefficmnts de calibration op6ratlonnels pour I'utdlsatmn des radiances mesur6es par le satellite Enfin on propose un nouveau proc6d6 pour sJmphfier les calculs que l'on peut lntrodulre au seln de n'lmporte quel module de correction

INTRODUCTION

A large number o f meteorological satellites have an infrared channel with wavelengths between 10.5 and 12.5/lm located, therefore, in an atmospheric window. One o f the main uses o f this channel is the remeval o f surface tem-

0 1 6 9 - 8 0 9 5 / 9 3 / $ 0 6 00 © 1993 Elsevier Scmnce Pubhshers B V All rights reserved

2

k M PEREZ ET AL

peratures. This is due to this band having a high atmospheric transparency, which means that a large part of the radiation detected by the satellite comes from the earth's surface. Inevitably, however, there will also be a fraction of the radiation originating from the atmosphere itself. If this fraction is known, it may be added to that detected by the satellite, thus giving us the radiation which is emitted from the ground. By inverting the Planck's equation, surface temperature may be obtained. Numerous models exist for calculating atmospheric correction, most of them classified into two types: bichannel and monochannel. In bichannel models, the radiance coming from the surface is obtained from the radiances measured by the satellite in two appropriate different channels (Mc Millin, 1975; Price, 1984; Singh, 1984). For this type of models, the state of the atmosphere need not to be known. In the monochannel ones, an explicit calculation of the radiative transfer equation must be made (Price 1983; Schmetz, 1986). Despite the former being s~mpler, m many cases the application of a monochannel model is necessary, as is the case with the Meteosat satellite. This is because there is only one thermal channel located in the atmospheric window. Another type of models, called two-angle models, is also used by some authors (Mc Millin, 1975; Haupt et al., 1983; Singh, 1984) These models are based in the different radiances measured by the satellite from the same area observed under two different angles. Of course, they are only applicable in the case of polar satellites. Since we are only interested in the analysis of Meteosat images, only the monochannel methods will be dealt with. There are several atmospheric components which affect the emission-absorption processes in the atmosphere, water vapour being the main one. Ozone and carbon dioxide will be omitted in our study since their contribution is only 0 1 °C of atmospheric correction (Schmetz, 1986 ). Water vapour and temperature profiles have been obtained from radiosoundings. These have been carried out over several days at a single geographical point. However, for undisturbed synoptic conditions and given a relatively high horizontal homogeneity in the area studied (the Spanish plateau) it is believed that it will be possible to extend atmospheric correction to other points of the area. Indeed, this is the use of the calculation: to carry out the atmospheric correction on numerous points on the image from a single radiosounding (Price, 1983). For large areas, different radiosoundings may be interpolated. TOVS (TIROS-N Operational Vertical Sounder) data offers great support for this. This data, provided by the NOAA satellites, ~s used in order to derive atmospheric profiles (Smith et al, 1979 ). Our main objective has been to dispose of an adequate calculation for obtaining surface temperatures from Meteosat images. To this end, two things were necessary: firstly, to have at our disposal an atmospheric correction model. A number of models created by different authors were then taken for this study. Secondly, once obtained the atmospheric correction by a model, it is necessary to apply this correction to the radiance measured by the satellite

MODELS FOR ATMOSPHERIC CORRECTION OF METEOSAT INFRARED IMAGES

3

for obtaining surface temperatures in each pixel. So, a previous analysis of such radiance was necessary. At an operational level, the radiance provided by the satellite comes as a result of applying coefficients to the detected grey level. The calculation of these coefficients is carried out based on an external calibration. As it is described in Campbell (1982) the image of the total disc is divided into segments of 32x32 pixels. Segments of the sea surface are chosen. For each one of these, a theoretical radiance is derived by means of a radiative transfer model (Schmetz, 1986). The infrared counts, N, measured and averaged at each segment are equated with the theoretical radiance R and from there, the calibration coefficients C A L and S P C are obtained in accordance with the relation: R = CAL* ( N - S P C )

(l)

Our question is the following: if we wish to determine the land surface temperature considering smaller segments than those mentioned, will the existing atmospheric correction models reproduce at the height of the satellite the same radiance as that obtained from the operational coefficients? In order to ascertain this, we decided to compare the radiances obtained from the satellite with the theoretical radiances calculated by models. Three such models have been studied and referred to in the text by the names of their authors. APPLICATIONS OF SEVERAL ATMOSPHERIC CORRECTION MODELS TO THE METEOSAT SATELLITE

Any atmospheric correction scheme is based on the calculation of the different terms of the radiative transfer equation. For a cloud-free non-scattering and horizontally homogeneous atmosphere which is in local thermodynamic equilibrium, the integral form of this equation is: H

0

where In is the upward spectral radiance in a certain atmospheric level, z ( z ) is the atmospheric transmittance between a layer at height z and the satellite, O is the satellite viewing angle, B is the Planck function and H is the height of the satellite above the earth. The degree of complexity in the resolution of the equation depends on the model used to calculate the atmospheric transmittance. We have chosen three different models in order to analyze the results of different schemes in terms of temperature correction. The model proposed by Schmetz (1986) has been chosen as it is the model used operationally in the ESOC.

4

A M PE RE Z ET ~L

The second model is the one proposed by Price. This model is used In the estimations obtained from the NOAA satellites (Price, 1983 ) The third model is the one proposed by Tjemkes and Nieuwstadt (1990) This is a rigorous radiation model which estimates radiative exchanges between any two atmospheric levels. Schmetz and Tjemkes' models consider for water vapour, absorption due to lines as well as that due to the continuum. Schmetz's formulas for the cont i n u u m are based on those of Grassl ( 1976 ). For lines, the calculation of the transmittance is based in a previous exponential adjustment between transmittance and optical thickness using Lowtran-5 data. For spectral integration, Schmetz divides the 10.15 to 12.9 # m region into six bands of about 40 c m - ~ wave-numbers using an average transmittance in each band. Tjemkes' radiation scheme is a rigorous narrow band model The water vapour line absorption is modeled with the Goody band model (Tjemkes and Duynkerke, 1988 ), while the water vapour c o n t i n u u m absorption is evaluated from the empirical formulas of Roberts et al (1976). In the interval between 10.5 and 12.5 #m, they use a step function of 10 c m - I wave-numbers. The Price model is a simpler one as it only considers absorption in the continuum, also based on an approximation to the formula of Roberts (Price, 1983 ). For their application to Meteosat, it was necessary to include in the two last models, the filter function of Meteosat (Campbell, 1982 ) and the wavelength integration extended to the sensor detection band: /2

I(H,O)= t

0(2)

L(H,O)d2

where 0(;~) is the spectral response o f the infrared channel and ,~l and ,~2 are the hmlts o f the channel ( 10.5-12.5 jzm) E X P E R I M E N T A L DATA

In order to obtain primary data for the models, several radlosoundings were taken in the city of Leon (42o35 '10''N, 1 ° 5 7 ' 5 0 " W ) in the North of the Castilian Plateau In Spain. These were carried out during the months of July and August of 1991 about 9.00 U.T.C With the aim of considering cloud-free days, eleven radiosoundings have been chosen corresponding to July 12,16,24,26 and August 4,5,11,12,16,20,25. A second group of data is the series of Meteosat digital images at time of radiosoundings measurements. F r o m each image we have obtained an average grey level on a 7 × 7 pixel matrix, centred on the location point of the radiosoundings. A similar grey level was found when considering a smaller matrix due to the high horizontal homogeneity of the area. However, a larger

MODELSFORATMOSPHERICCORRECTIONOF METEOSATINFRAREDIMAGES

5

one was chosen to cover the horizontal displacement of the sonde during the radiosounding. RESULTS

(a) Analysis of the radiance measured by the satellite The methodology used was to compare the radiances at the height of the satellite obtained by different m e t h o d s . The first thing to be analyzed was the adaptation of the operational measurements of the satellite to our own conditions by means of a comparison of these with the results provided by the Schmetz model applied to the temperature and humidity profiles mentioned. The results obtained are shown in Fig. 1. In all cases, the theoretical radiance is greater than the experimental one. Cases 2 and 4, corresponding to July 16 and 26 were considered to be anomalous. Meteorological conditions were very similar to other days and yet the grey level was much higher (curiously, in those cases, the brightness temperatures provided by satellite are bigger than the surface temperatures ) From the radiance, the brightness temperature for both types of values has 2

RADIANCE (W/ld SR) 13.5

1,..30 125 120 115 110

7~

10.5

/\

100 95

/'

i' \

i

i

1

2

7/ /~ i\ i\ /\ / i/\\ /\ /\ rh,l \\ j\i\ r

r

|

3

4

5

7 t / f I i //

7

7, 7 lk-~ t i\ / fE I\ i~' i\

I\\

/\

-

,,~

/ /

I\, /,' /\ /k w~

tf

/

/\

\ /\

.....

\ \ /\ i\

/\\

I

i

t

i

i

t

6

7

8

9

10

11

sounding [77-/771SCHMETZ 1~"lTX-E~Op ERAT.

Fig. 1. Comparison of the experimental radiance obtained by the Meteosat satellite with that obtained theoretically by Schmetz's model.

6

,~. M P E R E Z ET A L

TABLE 1 Brightness t e m p e r a t u r e s in - C d e d u c e d from data of F~g 1 Sounding

7svt

I'B, Schmetz

182 Oper

I Bl-- IB2

12-7-91 16-7-91 24-7-9l 26-7-91 4-8-91 5-8-91 [1-8-91 12-8-91 16-8-91 20-8-91 25-8-91

19 5 28 2 16 4 14_3 292 27 3 225 21 3 19 9 19 6 24 9

17 6 23 9 14.0 13 3 24 I 23 4 195 19 0 18 4 15 1 22 1

16 8 28 5 12_6 16 8 21 2 22 4 17 4 16 9 17 7 13 5 20 8

0 8 -46 I 4 -3 5 29 10 2 1 2_1 0 7 16 [ 3

12.4

I

I

I

I

]

I

I

I

I

I

~

'

'

I

V'

'

'

/

t2

11.6

r/ /

/

R &

d i a n c e

-

/

it.2

L

/

iO. 8 m

i0.4

- Z I

tO 130

170 9re9 level

Fig_ 2 L e a s t s q u a r e f i t t i n g b e t w e e n t h e c a l c u l a t e d r a d i a n c e s in W m

2st

J a n d t h e grey levels.

MODELS FOR ATMOSPHERIC CORRECTION OF METEOSAT INFRARED IMAGES TABLE 2

Companson between the expenmental and the operational cahbratlon coefficients

Schmetz Operat.

CAL

SPC

0 0784651 0.0770156

4 7924 50

RADIANCE (W//M2 SR) 13.5

130

12.5

12.0

115

V~M I A i~r~l v IM,~'-J

11.0

10.5

10.0

i

|

i

1

!

'

,

i

!

i

1

2

3

4

5

?

8

9

10

11

17777~ Price

~

soundin 9 Tjernkes

Schmetz

~

Oper.

Fig 3. Comparison of radiance obtained from the three different theoretical models.

been obtained. The results are presented in Table 1. The differences between the two magnitudes are in some cases greater than 2 oC. Standard deviation between them is 1.06 °C. This means that if we apply the atmospheric correction given by the model to the brightness temperature provided by the satellite, the predicted surface temperatures will be less than the actual ones for the pixels matrix mentioned. In order to analyze more quantitatively the difference between both types o f results, the radiance obtained by the model was fitted to the grey level by Eq. ( 1 ). This is shown in Fig. 2. It is observed in Table 2 that the operational calibration coefficients differ slightly from the coefficients obtained by fitting. With the first one, calibration o f the image may be carried out on a large scale and the temperature o f a sea pixel correctly determined, as this varies

8

~, M PEREZ ET AL

TABLE 3 Temperate corrections calculated from the different models and from the radiance provided by the satellite infrared sensor Sounding

7sw

J7 a Prl

JTa Tjem

ATB Schm

.I l B ()per

12-7-91 16-7-91 24-7-91 26-7-91 4-8-91 5-8-91 11-8-91 12-8-91 16-8-91 20-8-91 25-8-91

19 5 28 2 16 4 14_3 29 2 273 225 21 3 19_9 196 24 9

I 1 2 8 15 0 4 3 5 2¢) 19 13 0 7 32 17

I9 40 2 2 0 9 4_7 38 28 22 I 5 4 I 2 7

19 4 2 2 3 10 5 I 40 30 22 I 5 45 2 8

26 - t) 3 ~8 -2 6 ~_0 S0 52 44 22 ~ l 40

very httle from one pixel to another. However, if the temperature of a specific land pixel is required, one must calculate calibration coefficients of one's own as this may vary considerably from one nelghbouring pixel to another.

(b) Comparison between models In this section, we seek a relative comparison of different atmospheric correction models with two objectives: to confirm previous results with other models and at the same time to analyze quantitatively the differences which arise when using models with different degree of accuracy. The models analyzed besides Schmetz's are Price's and Tjemkes'. The results are shown in Fig. 3. Atmospheric correction as the difference between brightness temperature and surface temperature, appears in Table 3. It may be seen that Schmetz's and Tjemkes' models give similar results for correchon. The difference is at most 0.4 ° C, being greater for the latter. With Price's model, the correction is smaller, 1.4 °C being the maximum difference with the Schmetz model. This quantity gives us an idea of the error introduced when neglecting hne absorption. DESCRIPTION OF A NEW SCHEME

Spectral radiation at the satellite level from a specific atmospheric level is given by the radiative transfer equation (Eq. 2). Multiplying both sides of this equation by the spectral response of the satellite and integrating over the wavelength range of the infrared sensor of Meteosat we obtain:

MODELS FOR ATMOSPHERIC CORRECTION OF METEOSAT INFRARED IMAGES

22

22

22

9

rH

(3) 21

21

21

"60

If we assume the transmittance independent of wavelength then Eq. (3) can be written as: 22

22

"rH 22

(4) 21

21

with ~= z(11.5 #m). This assumption may be justified in this particular wavelength region because no strong absorption lines are present (See Fig. 4). The three wavelength integrals in Eq. (4) have the same form: the integrand is the product of the spectral response and a Planck's function (our assumption is that the earth emits like a black body, this is, Io2=B~(To) and due to

tron~mt

l lonce

0.9

0.7

(3)

0.6

@.3 [email protected]

i

10.6

t

11.1

1

11,6

i

12.1

i

12.6

k(~m)

Fig 4 Dependence of the total atmospheric transmittance with the wavelength for the stud,ed models ( l ) Price (2) Tjemkes (3) Schmetz

10

,x M PI~REZ ET AL

TABLE 4

Comparison between the new proposed approach and the estimations of Schmetz's model Soundmg

12-7-91 16-7-91 24-7-91 26-7-91 4-8-91 5-8-91 11-8-91 12-8-91 16-8-91 20-8-91 25-8-91

3Ta *

AT a

18 4 1 2 3 10 50 3 9 2 9 2 2 15 4 5 2_7

19 42 2 3 10 5_1 4 0 30 2 2 15 4 5 2 8

Schmetz

*With lhe new scheme.

the definition of brightness temperature Isa~ =B~ (Ta). For this type of integrals the following approximation is used (Singh, 1984 ): t2

log

~aBad2 = a + b-~,

(5)

/I

For each temperature, a numerical calculation of the Integral m Eq. (5) with steps of 0.1 #m has been made. T was varied from - 50 to 100 ° C with increments of 1 ° C. The parameters a and b have been obtained by a least square fitting. The results for the infrared channel of the Meteosat satellite are: a=6.827115 b=-

1283.857

correlation r= - 0.999999 Replacing Eq. ( 5 ) in Eq. (4) we arrive at: -rH

F(TB)=F(To)+f F ( T ) d r r~)

with

F(T)=exp(a+b~,) If Ta and the atmospheric contribution are known, the surface temperature could easily be obtained by inverting F(T0).

MODELS FOR ATMOSPHERIC CORRECTION OF METEOSAT INFRARED IMAGES

11

The new calculation scheme proposed has been used in order to calculate atmospheric correction on eleven days of our study. In order to calculate transmittance at 11.5/tin the formulas used by Schmetz have been applied. Table 4 shows how this simple scheme gives very similar results to those provided by original Schmetz's calculation. The proposed scheme requires only a fraction of the computational effort as no spectral integration is required. SUMMARY AND CONCLUSIONS

The motivation for this study was the need for an adequate calculation of atmospheric correction for infrared Meteosat images. With this idea in mind, it has been verified that using the Meteosat operational calibration (obtained from the analysis of sea pixels and large areas) may lead to an error of several degrees when dealing with small land areas. A relative comparison has also been made of three different models in order to analyze the calculation of atmospheric correction with a greater or lesser degree of approximation. Future studies will aim at carrying out atmospheric correction of larger areas by means of interpolation among profiles. Finally, we presented a scheme which simplifies the calculation of atmospheric correction, by omitting the spectral integration over the sensor wavelengths. ACKNOWLEDGEMENTS

We would like to express our gratitude to J. Schmetz, S.A. Tjemkes and J.C. Price for providing their corresponding models.

REFERENCES Campbell, S., 1982. Vicarious calibration of Meteosat's infrared sensors Eur Space Agency J , 6: 151-162. Grassl, H., 1976. A new type of absorption m the atmospheric infrared window due to water vapour polymers. Beltr. Phys. Atmosph., 49 225-236 Haupt, I , Billing, H. and Jobst, S., 1983 Determination of sea surface temperatures and atmospheric correction values for infrared images on the base of data of the meteorological satelhte NOAA 5. Beitr Phys. Atmosph, 56(3). 295-321 McMilhn, L M , 1975. Estimation of sea surface temperatures from two infrared window measurements with different absorption J. Geophys Res., 80 (36): 5113-5117 Price, J.C., 1983, Estimating surface temperatures from satellite thermal infrared data--A simple formulanon for the atmospheric effect. Remote Sensing Environ., 13:353-361 Price, J.C 1984, Land surface temperature measurements from the spilt v¢lndow channels of the NOAA 7 Advanced Very High Resolution Radiometer. J. Geophys Res., 89 (D5): 72317237. Roberts, R.E., Selby, J.E.A. and Biberman, M., 1976 Infrared continuum absorpnon by atmospheric water vapour m the 8-12 a m window. Appl. Opt., 15 2085-2090.

12

\ M PEREZET ~L

Schmetz. J , 1986 An atmospheric-correction scheme for operational apphcat~on to Meteosat infrared measurements Eur Space Agency Journal, I 0 145-159 Smgh, S M , 1984 Removal of atmospheric effects on a plxel by plxel basis fiom the thermal infrared data from instruments on satelhtes The Advanced Ver~ High Resoluuon Radiometer (~.VHRR). lnt J Remote Sensing, 5( 1 )- 161-183 Smith, W.L, Woolf, H M , Hayden, C.M_, Wark, D Q and McMflhn, L M , 1979 The TIROSN operaUonal vertical sounder Bull Am Meteorol Soc, 60(10) 1177-1187 Tjemkes, S A and Duynkerke P_G, 1988 A new look at the Goody Band Model Bcm- Ph)s ~ l m o s p h , 6 1 ( 2 ) 105-113 Tjemkes, S A and Nleuwstadt, F, 1990 A long,~a~e l ad~atlon model for the nocturnal boundary layer J Geophys Res, 95(D1 ) 867-872