Journal of
Hydrology ELSEVI E R
Journal of Hydrology 188-189 (1997) 788-814
Land surface temperature estimation based on NOAA-AVHRR data during the HAPEX-Sahel experiment H e n r i k Steen A n d e r s e n University of Copenhagen, Institute of Geography, Oster Voldgade 10, DK-1350 Copenhagen K, Denmark
Abstract Accurate estimation of land surface temperature can be regarded as an important prerequisite of the global or regional monitoring of water, energy, and radiation budgets. An accurate estimation of land surface temperature involves correction for both the atmospheric and the surface emissivity effect. Combined ground truth, radiosonde and remote sensing data from the HAPEX-Sahel experiment have been used to evaluate three existing AVHRR-based split-window models designed for land surface temperature estimation and an algorithm for emissivity difference estimation. Local or regional model coefficients have been determined on the basis of simulated AVHRR measurements. The applied model for the emissivity difference determination turned out to be very sensitive under situations with medium to high water vapour content. It was found that results from the three models compared well except at large view angles. In semi-arid regions with high atmospheric water vapour content the atmospheric effect accounts for almost 90% of the correction whereas the emissivity effect typically accounts for 10%. An absolute evaluation was not performed, but comparison with ground truth data showed that the model-predicted temperatures were well within the expected range.
1. Introduction The land surface temperature results from the energy exchange at the surface and satellite-based monitoring of the land surface temperature (LST) can be regarded as an important prerequisite o f regional or global observations of surface water, energy and radiation budgets. Accurate LST estimates may be used as input to simple statistical models used for estimation of evapotranspiration as described by Sandholt and Andersen (1993) or serve as validation of more elaborate models. LST maps can also be understood as an important data layer in geographical information systems (GIS) as described by Begh and Sogaard (1993), and it may be anticipated that linkage to other environmental 0022-1694/97L$17.00 © 1997- Elsevier Science B.V. All rights reserved PH S0022-1694(96)03171-X
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GIS data layers, e.g. fractional vegetation cover and soil type maps, will optimize the exploitation of satellite-measured thermal IR radiation in the future. Satellite-based monitoring of a fast responding system such as the Earth's surface requires information with high temporal resolution. At present, data from the Advanced Very High Resolution Radiometer (AVHRR) flown on the NOAA series of satellites may be one of the most important information sources because of the orbit and sensor characteristics, which permit daily global coverage of reflected and emitted radiation from the Earth-atmosphere system. The objective of this paper is to analyse the ability of existing AVHRR-based splitwindow models to accurately determine LST in a semi-arid environment, where both surface and atmospheric conditions may limit the usefulness of such models. This work is based on data obtained during the HAPEX-Sahel Experiment, which took place in Niger in 1991-1993, with an Intensive Observation Period (IOP) in August-October 1992. The experiment combined ground truth and remote sensing data with hydrological and meteorological modelling techniques. It aims to improve the parametrization of land surface-atmosphere interactions at the GCM grid scale and to improve large-scale estimates of relevant surface characteristics and surface energy, water and momentum fluxes (Goutorbe et al., 1994). Although the satellite measurements of thermal radiation are made in an atmospheric window, e.g. the 10-12/xm window, where absorption is at minimum, the influence of atmospheric absorption and emissions on the surface temperature signal is not negligible. In the IR part of the electromagnetic spectrum, water vapour is the principal factor for atmospheric effects. The water vapour content of the atmosphere varies both in time and space, and consequently will also vary the atmospheric effect. This calls for robust algorithms which are capable of handling this varying effect. A large number of papers have dealt with the problems of producing accurate sea surface temperature estimates, preferable within 0.3 K (e.g. Deschamps and Phulpin, 1980; Barton, 1983; LlewellynJones et al., 1984; McClain et al., 1985; Castagn6 et al., 1986). Very recently, i.e. during the last 10 years, a growing attention toward accurate estimation of land surface temperature has evolved (e.g. Price, 1984; Becker, 1987; Cooper and Asrar, 1989; Wan and Dozier, 1989; Becker and Li, 1990; Sobrino et al., 1991; Kerr et al., 1993a; Coil et al., 1994c). Even if an uncertainty of 1 K is acceptable for the LST estimation, it is in most cases impossible to use an algorithm developed for sea surface temperature estimation directly. This is a consequence of the significant differences between the two problems. In the case of sea surface temperature retrieval the emissivity effect is small and not very variable. It may be taken into account through a constant term of about 0.5 K. Land surface emissivities are typically lower than 1.0 and vary with both wavelength and view angle. In addition, the land surface temperature field within a pixel is generally very inhomogeneous compared with that for the sea surface. This is mainly due to differences in the thermodynamic properties of the two media, i.e. the much lower thermal diffusivity and the lower level of evaporation which characterize the land surface. This means that simple extension to the land surface of the method developed for sea surface temperature measurements would lead to unacceptable errors (Wan and Dozier, 1989). Cooper and Asrar (1989) evaluated six atmospheric correction models developed primarily for sea surface applications over a taUgrass prairie area. They compared the computed surface temperature with
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H.S. Andersen~Journalof Hydrology 188-189 (1997) 788-814
in situ measurements and found that only one of the models was within _+ 3 K. These results underlined both the necessity for emissivity correction and the regional character of the split-window model coefficients. Therefore, to obtain accurate LST estimates from space, it is necessary to correct for both the atmosphere and emissivity. However, when we deal with variable atmospheric conditions and land surfaces with variable spectral emissivities, the unknowns always outnumbers the independent radiance measurements of the Earth-atmosphere system (Wan and Dozier, 1989). Perhaps the two most used atmospheric correction models in connection with data from the AVHRR are the so-called dual-channel split-window and single-channel model. Both methods have advantages and disadvantages. For the single-channel method to apply it needs a very accurate description of the atmospheric state, i.e. the vertical distribution of temperature, humidity and pressure, and the number of often crucial assumptions which concern surface emissivity is limited to one. Radiosonde data are often used to describe the state of the atmosphere, and the method gives very satisfactory results provided the radiosonding is synchronous and co-located with satellite measurements. The use of radiosondes is hampered by the insufficient density of the network in some areas, by lack of timing and by poor representativeness (Kerr et al., 1993a). On the other hand, the use of the split-window method eliminates the need for knowledge about the atmospheric state but it emphasizes the need for a proper description of the surface emissivity; i.e. the emissivity for both channels must be known. However, the splitwindow models' independence of radiosonde data makes them very useful in an operational context. In Section 2, the basic radiation transfer equations are briefly presented, and Section 3 reviews three recently proposed split-window models, which were specially designed for estimation of LST. Section 4 and Section 5 describe the data processing and the results.
2. Atmospheric correction Because the atmosphere is not completely transparent, even in the least absorbing regions of the thermal IR spectrum, the outgoing spectral radiance of the Earth will be influenced not only by the Earth's surface but also by the composition and thermal structure of the atmosphere. A complete radiative transfer model of the atmosphere would account for both the absorption and emission of the atmosphere. 2.1. The radiation transfer equation
The following model describes the atmospheric correction for a cloud-free and planeparallel non-scattering atmosphere under local thermodynamic equilibrium (LTE). For the most important radiatively active gases, LTE holds for pressures greater than 0.1 mbar. Under LTE conditions with no scattering, Kirchhoff's law states that the source function in the radiative transfer equation is equal to the Planck function, and the LTE concept allows the definition of a local temperature at any point of the medium. If the atmosphere can be described as plane-parallel and non-scattering and the surface is Lambertian, which is generally not the case (Nerry et al., 1988), then the radiance measured by a satellite sensor
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at channel i can be defined as --,['sat =
°~(x)exBx(Ts)rX(O)d X
I
7r
•I
(1-e (X)Li(O') (O')sin20'dO'dX
where L× is radiance, X is wavelength, 0 is the zenith angle, fi is the normalized response function which characterizes the sensor, r× is the spectral atmospheric transmission, e x is the spectral surface emissivity, p is the pressure and subscript s stands for surface. The first term in Eq. (1) describes the surface contribution, the second term is the atmospheric contribution along the upward path and the last term is the atmospheric contribution along the downward path, reflected by the surface and attenuated along the upward path. To express Eq. (1) for a given satellite channel i it is necessary to define a channel emissivity (e i) and a channel transmissivity O'i)- Although e i depends on the temperature, Becker and Li (1990) have shown numerically that the variation of ei with Ts is negligible, i.e. within 2 x 10"4; furthermore, Becket and Li (1990) also showed that the variation of the channel transmissivity with temperature is negligible, i.e. within 10 -3. To simplify Eq. (1) even more, the downward radiation may be considered independent of azimuth directions and the Planck function for channel i may be defined as
Bi(T)=
J/.~(~,)Bx(T)dX lr
(2)
Ll(hem)= r J~ Lk(O')sin(20')dO' where L 1(hem) is the downward hemispherical radiance. Now it is possible to write for a given channel i, after integration with the normalized response function, Bi(T)=ei'ri(O)Bi(Ts)+
If f/(X)Llx(O)d)~+ 1 -ei~rri I f f,-(~,)Llx(hem)dX or
(3)
B i ( T ) = eiT"i(O)Bi(Ts) + L~(O)+ 1 - eiri(O)L~(hem)
When measurements are taken in the atmospheric window, the first term of Eq. (3) will be affected least, whereas the relative importance of the second term will be very variable depending upon the vertical structure of the atmosphere. The third term is related to surface characteristics: when ei approaches unity the contribution approaches zero.
2.2. The split-window model The differential absorption method is widely used to correct satellite-measured temperature measurements taken at either two different spectral windows or at two
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H.S. Andersen~Journalof Hydrology 188-189 (1997) 788-814
different angles. The essence of the method is that the radiance attenuation caused by atmospheric absorption is proportional to the radiance difference of two simultaneous measurements with distinct conditions (McMillin, 1975). The split-window algorithm simply consists of a linear combination of the thermal channels, which gives a surface temperature corrected for atmospheric contribution, for an n-channel instrument. For a two-channel instrument, it is normally written as
Ts = T4 +At + Al (1"4- Ts)
(4)
where A0 and A l are coefficients often determined by regression. Here T4 and/'5 refers to brightness temperatures from AVHRR Channels 4 and 5, but generally speaking the two measurements should be taken in an atmospheric window, where absorption is low and due to the same gases. If these conditions are met, the transmittance for the two channels will be slightly different but the atmospheric temperatures will be approximately equal and therefore ignored. To derive the split-window model from the radiative transfer Eq. (3), a number of simplifications have to be made; i.e. the linearization of both the water vapour transmittance and the Planck function. These simplifications put constraints on the general applicability of the split-window model and both approximations may be invalid in tropical semi-add regions, where a pronounced temperature gradient and large atmospheric water vapour content may exist. The method works because, in theory, the value of coefficient A i is independent of the temperature profile as well as the amount of water vapour present. However, this is only true if the total absorption is relatively small so that the linear approximations hold. For moist atmospheres at large view angles this may call for an additional correction term such as A2(T4 - Ts)lcos(O) (McMillin and Crosby, 1984). The validity of the linearization of the Planck function lies in the fact that the main contribution to the atmospheric radiance comes from the lowest layers of the atmosphere. Here the layer temperature 7": is close to the mean atmospheric radiative temperature Ta. Furthermore, the surface temperature T~ must be close to Ta. Lineadzation of the water vapour transmittance relies on water vapour absorption being small in the atmospheric window. Then it is possible to assume that the transmittance from the top of the atmosphere to altitude z depends linearly on the amount of water vapour in the vertical column between the same levels. Therefore, to derive the split-window equation it is assumed that r(0) = 1 - kiw/cos(O), where ki is a weighted absorption coefficient. Becker and Li (1990) showed that the linear dependence of transmittance on wlcos(O) is valid for 0 < 50 and w < 3 g cm -2, and that the values of k4 and k5 corresponded to those of Price (1984). Similar results have been calculated for actual radiosonde data from the HAPEX-Sahel experiment, i.e. k4 = 0.1382 (r 2 = 0.95) and k5 = 0.1727 (r 2 = 0.93) for 0 -< 45 ° (see Fig. 1). If the view zenith angle was restricted to 65 ° or less, the r 2 decreased to 0.87 and 0.78, respectively. Therefore, it is assumed appropriate to restrict 0v to lie within ___45 °.
3. Estimation of land surface temperature Over land surfaces, atmospheric and emissivity effects are coupled, owing to the reflection of downwelling atmospheric radiation at the surface. The emissivity effect
H.S. Andersen~Journalof Hydrology 188-189 (1997) 788-814
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1"
0 . 9 ............................................................................................................ 0.8 ............................................................................................................. 0.7 ............................................................................................................
L-r', 0 . 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .=
. ' = " " = ............... , ° ..
•
Hi~ ta tii
................................................
~ ................
0.5
"~o.4
~....~
. .Sdl!l[ ,it. Ii,ll..ll P
........................................
.......
==
a .....................
- ~ ........ ,,------~-----ii----li .............................
0.3 ......................... , ......,....=a[_......m.m_m.l..NL....~.................................... ii n dlu
0 . 2 ........... - I ............ • ................................................................................. 0.1 .............................................................................................................
o
1.o
l'.s
2'.o
2'.s
3'.o
3's
40
Water Vapour Content (g/cm2)
•
Channel4
~"
Channel5
I
Fig. 1. lllustration of the linearization of the water vapour transmittance. Data are calculated for the radiosondes shown in Table 1 for view zenith angles within 45 °.
will decrease with increasing water vapour content in the atmosphere because of the stronger influence of atmospheric radiance (Coil et al., 1994c). The perturbation effects on the split-window algorithm when used over land surfaces are mainly the following: surface emissivity is a priori unknown and different from unity; spectral variability of the surface emissivity may be high; the surface temperature also has a very high spatial variability, even at scales smaller than the resolution of AVHRR; a distinct gradient between air and surface temperature may exist (Kerr et al., 1993a). Furthermore, Sobrino et al. (1991) theoretically demonstrated that a global split-window is not possible for at least two reasons: (1) the variability of land surface emissivity; (2) the influence of atmospheric conditions on the split-window coefficients. It is therefore important to look for an optimized regional split-window model combined with better knowledge of the surface conditions.
3.1. The emissivity effect If the effect of the atmosphere is correctly calculated, the surface temperatures T , and T~5obtained in each channel only depend on the emissivity in each of these channels. From a physical point of view, T~ should be the same whatever the channel is. If the emissivity difference is close to zero, and if the atmospheric conditions are known, then with the two channels of AVHRR, it is possible to obtain both surface temperature and surface emissivity. In that case, there are indeed two measurements and two unknowns. However, if nothing is known about emissivity, it is impossible to obtain Ts, i.e. one must know or assume the values of ~4, ~5 or e, Ae. This is a consequence of the missing equation concept occurring in spectral IR radiometry (Becker and Li, 1990). Land surface emissivity may range from 0.90 to 1.0, and it depends on the roughness and other physical parameters of the surface such as its moisture content. Because of the
H.S. Andersen~Journalof Hydrology 188-189 (1997) 788-814
794
existence of multiple scattering within a developed vegetation canopy, the emissivity of a vegetated surface will approach a black body (Salisbury and D'Aria, 1994). Labed and Stoll (1991) also noted that emissivity increased rapidly with vegetation height and density. For a number of soil samples, Nerry et al. (1988) showed that e for AVHRR Channels 4 and 5 ranges from 0.96 to 0.98, with Ae ranging from - 0.02 to 0.006. Coil et al. (1994c) used ~4 = 0.982 and ~5 = 0.986 for a vegetated surface and e4 = 0.956 and ~5 = 0.967 for a sand surface. Measurements from La Crau over a dry surface with very sparse vegetation gave ~4 = 0.957 and e5 = 0.976 (Labed and Stoll, 1991). According to Coil et al. (1994b), spectral measurements of different sandy soil samples were performed by the University of Strasbourg (GSTS) during the Hapex-Sahel lOP. The resulting mean emissivity was approximately 0.975 and the emissivity difference was small (approximately 10-4), which is similar to the spectral difference for vegetation. The large range of surface temperatures and emissivities that may exist within a pixel makes the definition of effective emissivity and temperature difficult. The error of split-window LST estimations by the emissivity effect is of the order (Becker, 1987) AT = 501 - e _ 300 e4 - e5
(5)
6
It is seen that if Ae > 0 the error introduced by ~ < 1 is decreasing; however, if Ae < 0 it is increasing. The latter is often the case for bare soil, whereas z~e is often positive for vegetated surfaces. It is important to note that the spectral emissivity effect is six times larger than the average emissivity effect. For vegetation and bare soil as defined above, Eq. (5) gives AT = 2.03 K and AT = 5.43 K, respectively; indeed a considerable effect. However, Eq. (5) is only strictly valid for low to medium water vapour content. For high water vapour content AT will be smaller, as will be shown below.
3.2. Split-window adopted for land surfaces Since about 1990, attempts have been made to formulate an extended version of the split-window model, which includes both the atmospheric and emissivity effects and is therefore well suited for accurate LST estimation. In this paper, three existing models will be analysed by means of data obtained during the HAPEX-Sahel lOP. Sobrino et al. (1991 ) linearized the emissivity dependence of the split-window coefficients A0 and A j in terms of the emissivity difference Ae = ~ 4 - tE5and e4- This was done for an interval of E 4 ranging from 0.94 to 0.99 and an interval of Ae from - 0.01 to 0.01. Sobrino et al. showed that coefficient A i is less affected by emissivity than isA0. They concluded that the dependence of the view zenith angle can be avoided, but the dependence of A 0 and A I on atmospheric moisture (seasonal and regional variation) must be kept. In continuation of this work, Coil et al. (1994c) proposed an extension to the general version of split-window where the offset B is a function of emissivity:
Ts= Ta +Ao +A1(Ta- Ts) + B(~) with B(~) = ~(I - e) + fl,%
(6)
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The parameters ct and/~ depend on the state of the atmosphere and surface temperatures; i.e. ct = (b4 - bs)ar5 and/~ = a~'sbs, where a = [1 - r4(0)]/[r4(0) - rs(0)], bi is given by
(ni-lT~_Tlai)[l_ri(O=O)]
bi = -T7 -+'Yi ni k,
(7)
ni
where T~ is the surface brightness temperature, 7~ represents the ratio of the hemispherical downwelling radiance and the downwelling radiance at nadir, and ni is a channeldependent parameter. Coil et al. (1994c) analysed the variation of B(e) with respect to water vapour content and emissivity effects and showed that ot can be taken as a constant but/3 is a function of water vapour content. The model was tested for a large range of simulated surface and atmospheric conditions. The atmospheric water vapour content was varied from 0.4 to 3.2 g cm -2, the view zenith angle was set to 0 °, 30 °, or 50 ° and three surface types (emissivity conditions) were included, i.e. blackbody, vegetation and desert (see Coll et al. (1994c) for details). The model fitted the simulated data with an r.m.s, value of 0.47 and residuals were in the approximate range from 1 to - 2 K. Becker and Li (1990) analysed, by the use of observed and standard atmospheric profiles, the validity of the radiation transfer equation and determined the emissivity effect on the split-window coefficients A0 and A 1- They also derived theoretical equations, which showed that the actual surface temperature can be expressed as a linear combination of T4 and T5 with coefficients depending on spectral emissivities but not on atmospheric conditions: Ts =Ao -I
P(T4+Ts) M ( T 4 - T s ) 2 ÷ 2
with (1 - ~ ) + A ~ P= 1+o~--~- ~-~
(8)
M = 3 / + ~ , (1 - e ) + B , A__~ e E
E2
Eq. (8) includes a first-order emissivity correction through M and P. The model was tested for subarctic and mid-latitude atmospheric conditions; the view zenith angle was set to 0 °, the mean emissivity ranged from 0.9 to 1, and the emissivity difference covered the interval - 0.016 to 0.016, Becker and Li found that Eq. (8) is valid over a large range of temperatures and atmospheric conditions and that if emissivities are known one can obtain the surface temperature with good accuracy, i.e. within - 0.57 to 0.37 K. Later, Sobrino et al. (1994) evaluated Eq. (8) for a much larger range of atmospheric, viewing and surface conditions and found an r.m.s, value of 1.4 K with a maximum residual of 8.7 K. It is worth noting that, to calculate the actual surface temperature from Eq. (6) or Eq. (8), some knowledge of Ae and e has to be assumed. Kerr et al. (1993a) used a slightly different approach and suggested a semi-empirical split-window model for land surfaces primarily designed for arid and semi-arid areas, where vegetation may be very sparse and the temperature high. The rationale behind the method is that the actual surface temperature, for a pixel with a given distribution of
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H.S. Andersen~Journal of Hydrology 188-189 (1997) 788-814
vegetation and bare soil expressed by a vegetation fraction, can be described as a linear combination of the surface temperature for a fully vegetated pixel and the surface temperature for a bare soil surface pixel. The method takes into account the effect of the vegetation fraction through the parameter C: Ts = TvC + Tsoil(1- C) Tv =Ta+Av(T4-Ts)+Bv
(9)
Tsoil= T4 +Asoil(T4 - T5) + BsoiJ where C is the vegetation fraction and subscripts v and soil stand for vegetation and bare soil, respectively. It was assumed that Ae and e for a fully vegetated surface can be approximated by the values for a sea surface so A v and By are obtained from a sea surface temperature algorithm. The coefficients AsoiJ and Bsoil for bare soil were found using ground measurements.
4. Selection of a local split-window model Major difficulties are involved in creating a combined set of ground and satellite measurements. Because of the large temperature variability that can exist within a given pixel, it is extremely difficult to establish a ground temperature sampling programme that can provide data which are comparable with the areal-integrated satellite measurements. This problem affects both the analysis and the validation of a given splitwindow model. Therefore split-window coefficients are often determined using simulated data. Radiosondes launched during the HAPEX-Sahel IOP were used as input to a simulation of AVHRR Channels 4 and 5 top of the atmosphere radiance measurements. The surface boundary conditions were chosen so that the simulations covered a typical range of surface types with respect to temperature, mean emissivity, emissivity difference and view angle variations. Furthermore, the surface was assumed to be Lambertian. For most surfaces this approximation is not valid. At local scale both emissivity and surface temperature are angular dependent, mainly owing to surface structure (Prata, 1994). However, the influence at the scale of an AVHRR pixel may be difficult to assess and model. The simulated data set may therefore be used to analyse the performance of splitwindow models in a semi-arid region characterized by high surface temperatures and high water vapour content in the atmosphere. 4.1. Simulations of satellite measurements Radiances measured at the top of the atmosphere by the AVHRR Channels 4 and 5 were simulated by the use of LOWTRAN-7 (Kneizys et al., 1988) for a number of specific surface and atmospheric conditions. To cover a typical range of atmospheric temperatures, pressure and humidity profiles, radiosonde measurements were used. LOWTRAN-7 numerically solves the first two parts of Eq. (I), and the reflective part has been calculated separately.
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Actual surface conditions were approximated by varying the spectral surface emissivity and the surface temperature. The channel emissivity was varied from 0.9 to 1.0 with a step of 0.002, and the emissivity difference was varied from - 0.02 to 0.02 with a step of 0.004. The surface temperature was varied from 305 to 335 K with a step of 2 K, and the view zenith angle was varied from 0° to 45 ° with a step of 15°. The emissivity and temperature interval are assumed to cover the majority of surface conditions occurring during a typical rainy season in the Sahel at the time corresponding to an NOAA 11 afternoon passage. The radiosonde measurements were conducted by the Centre National de Recherches Mrtrorologiques (Bergue and Bessemoulin, 1993), France, through the intensive observation period from 17 August to 12 October 1992 and made available through the HAPEX-Sahel Information System (Prince et al., 1995). The balloons were launched from Hamdalley within the West Central site (Goutorbe et al., 1994; Prince et al., 1995),
Table 1 Summary of calculations made on the radiosonde data Radiosonde no.
Time
Water vapour (g cm-2)
Precipitable water (g cm-2)
Atmospheric temperature T~ (K)
Atmospheric temperature T~ (K)
Radiance L~ (hem) (roW m -z)
Radiance L t (hem) (roW m-2)
920821 920825 920827 920829 ~ 920902 920903 920906 ~ 920909 920910 920912 920913 920914 920916 920917 920918 920922 920925 920926 920928 920930 921003 921007 ~ 921008 a 921009 a 921012
14:59 15:05 15:01 15:01 14:55 13:52 15:28 14:50 14:55 14:55 14:58 14:56 14:57 14:54 14:59 14:35 15:00 15:01 15:130 15:01 14:59 15:01 15:00 15:00 14:59
3.133 3.378 2.751 3.545 3.28 2.697 2.971 2.05 2.711 2.497 2.551 2.955 2.639 2.075 1.942 2.157 2.141 2.19 1.551 2.717 2.614 1.316 1.718 2.402 2.753
4.455 4.88 4.161 5.081 4.552 3.856 4.181 2.9 3.798 3.635 3.593 4.285 3.772 2.999 2.767 3.027 3.045 3.024 2.115 3.8 3.789 1.878 2.356 3.258 3.885
295.7 291.4 289.25 291.85 291.35 293 294.5 296.55 294.3 293.6 296.15 291.95 293.65 294.6 295.85 295.9 296.4 298.1 298 293.5 291.95 295.05 297.25 296.85 295.85
296.5 292 289.85 292.55 291.95 293.7 295.25 297.45 295 294.4 297.1 292.7 294.35 295.45 296.85 296.7 297.2 298.9 299.15 294.25 292.6 295.75 298.4 297.65 296.65
62.62 61.2 47.57 64.79 62.53 51.71 59.03 41.9 55.52 48.8 53.62 54.46 51.82 40.8 40.5 44.56 42.96 47.41 34.09 53.13 48.52 26.49 37.07 52.11 55.35
88.17 86 69.26 90.9 87.33 51.71 83.93 61.67 79.5 71.04 77.29 78.27 74.9 60.09 59.76 65.42 63.2 69.21 34.09 76.72 70.83 38.8 54.78 75.4 79.67
aThe selected radiosondes. The water vapour content is the pressure-corrected moisture content. Precipitable water content is the integration of mixing ratio with height. Mean precipitable water content is 3.564 gcm-~, with a standard deviation of 0.822; mean water vapour content is 2.509 g cm -2, with a standard deviation of 0.560. The atmospheric temperature is calculated from Tai = Bi - I [L~ ~(0 = 0)]/[ 1 - ¢i(0 = 0)]. The downward hemispherical radiance is defined Ll(hem ) = ~-ffo/~ Li l (0')sin(20')d0.
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H.S. Andersen~Journal of Hydrology 188-189 (1997) 788-814
typically from 07:00 to 17:00 h UT at 2 h intervals. The radiosondes were instrumented as described by Bergue and Bessemoulin (1993). Measurements were taken every 5 s from the surface up to approximately 20000 m, leading to a total number of around 20000 measurements per profile. As a first step, 25 radiosonde profiles taken around 15:00 h UT were analysed and five representative profiles were selected for further analysis (see Table 1). The selection was based on the calculated water vapour content supplemented with cloud cover and cloud type information from Niamey airport. LOWTRAN-7 was used for the analysis and for the simulation. LOWTRAN-7 can accept up to 34 profile levels. The original profile data set was therefore reduced by definition of 34 levels with varying vertical extension in such a way that the vertical resolution was best in the low levels, because most of the water vapour is situated within the first 3 - 4 kin. The radiosonde profiles were supplemented with data from the LOWTRAN-7 tropical model atmosphere, i.e. gas and aerosol profile data. The aerosol content was assumed to be of rural type corresponding to a meteorological visibility of 23 lon. Radiance output from LOWTRAN-7 was weighted with the normalized sensor response functions which characterize the AVHRR/2 sensor Channels 4 and 5 onboard NOAA 11 as defined by Walter (1988). Conversion from the AVHRR simulated radiance to temperature was facilitated by the construction of a lookup table. The temperature interval of the lookup table was limited to 270-340 K with a resolution of 0.05 K, which is considered appropriate in this case. Table 1 provides a summary of the radiosonde characteristics. It is seen that the water vapour content (Wv) can vary from 1.32 to 3.54 g cm -2 with a mean value of 2.51 g c m -2. A strong temporal variation is evident, although low values, i.e. Wv < 2.0, tend to occur at the end of the IOP. In the derivation of the split-window model it is assumed that the atmospheric temperature for the two channels is approximately equal, i.e. Ta4 ~ Tas; the results in Table 1 show that they are fairly close, i.e. within 1 K. The maximum effect of the reflective part of Eq. (1) is approximately equivalent to 1 K.
4.2. Calculation of local coefficients. The simulated data set was used to determine the coefficients for Eq. (6) and Eq. (8). The set of equations were solved by the least-squares method. The results for several scenarios are shown in Table 2 and Table 3. The separation of atmospheric and emissivity correction in Eq. (6) permits an inclusion of a view angle correction term A 2(T4 - Ts)/cos(O). This addition leads to an improvement, both in terms of r.m.s, and range. However, if off-nadir viewing conditions are included, the opposite result emerges, probably because of the addition of parameter A 2 to Eq. (6). The residuals for both models including emissivity correction varied with the emissivity difference; the residuals were at a minimum around Ae = 0 and increased toward _+ 0.02, with the residuals for AE = - 0.02 being largest and the variation being largest for Ae < 0, where the aggregated effect of emissivity is at maximum. The coefficients ot and/~, which determine the emissivity correction for Eq. (6), can be estimated by regression as shown in Table 2 or by use of radiosonde data through the calculation of Ti and bi. To evaluate the variation of ot and/~ for a range of possible atmospheric and surface conditions, they have been calculated for the five test radiosondes,
H.S. Andersen~Journal of Hydrology 188-189 (1997) 788-814
799
Table 2 Coefficients determined for Eq. (6), for f o u r different scenarios
Conditions 0 (deg) Ae Ts (K)
-< 45 1.0 0 305-335
-< 45 1.0 0 305-335
0 0.91 - 1.0 ± 0.02 305-335
-< 45 0.91 - 1.0 ± 0.02 305-335
- 0.3859 2.8651 0 0 0
- 0.2629 1.8202 0.8713 0 0
0.0361 2.6158 0.0 56.49 - 110.02
- 0.1584 1.8185 0.8440 56.49 - 110.48
0.7081 89.38 4.63 0.982
0.3848 98.75 2.51 0.9947
0.7109 84.97 5.79 0.9753
0.7663 82.35 6.71 0.9936
Coefficients A0 At A2 c~
Residuals r.m.s. Within 1 K (%) Range r2
R a n g e is highest m i n u s lowest residual.
The results are shown in Table 4 and Fig. 2. It is clear, as was also found by Coil et al. (1994c), that tx is relatively constant but/3 can vary with a factor of 3-4. The relative importance of the emissivity difference as predicted by Eq. (5) is still evident from the o~ and/3 values, although the effect is damped in cases of high atmospheric water vapour content. However, for the majority of situations shown in Table 1 o~ ~- 50 and/3 ~ 70 may apply, but for atmospheric conditions with low water vapour content large errors can result
Table 3 Coefficients determined for Eq. (8), for three different scenarios
Conditions 0 (deg) e A~ Ts (K)
0 1.0 0 305-335
0 0.91 - 1.00 ± 0.02 305-335
-< 45 0.91 - 1.00 ___ 0.02 305-335
- 0.0052 0 0 6.2780 0 0
- 0.0052 0.1680 - 0.4380 6.2681 - 0.1587 22.5874
- 0.0052 0.1536 - 0.4580 6.5572 2.0441 23.6765
0.2794 100.0 1.18 0.9974
0.6031 90.85 4.89 0.9961
0.8538 80.27 7.54 0.9916
Coefficients A0 /3 "/' a' /3'
Residuals r.m.s. Within I K (%) Range r2
R a n g e is highest m i n u s lowest residual.
800
H.S. Andersen~Journalof Hydrology 188-189 (1997) 788-814
Table 4 Calculated ot and/3 values for various water vapour contents and brightness temperatures Radiosonde date
Wp (g cm-2)
T* (K)
ct
/3
29 August
5.08 5.08 5.08 5.08 3.86 3.86 3.86 3.86 4.18 4.18 4.18 4.18 1.88
305 315 325 335 305 315 325 335 305 315 325 335 305 315 325 335 305 315 325 335 305 315 325 335
39,59 45.42 51.24 57.07 45.34 49.88 54.42 58.97 41.92 47.04 52.15 57.28 52.35 54.85 57.34 59.83 48,92 52.05 55.18 58.31 44.89 49.16 53.51 57.85
29.19 39.17 49.14 59.11 51.08 62.24 73.4 84.56 40.4 51.46 62.52 73.59 106.42 116.52 126.62 136.72 1DO.1 113.11 126.11 139.11 55.38 67.27 79.17 91.06
3 September
6 September
7 October
1.88
1.88 1.88 2.36 2.36 2.36 2.36 3.26 3.26 3.26 3.26
8 October
9 October
140
.
-
o
o
120 .......... ; ..................................................................................................... e e,
100
...............
: ...........
~. . . . . . . . . . . . .
÷
~:.............
, ............................................ '," ,,
......................................................................
e . . . . . . . . . . . . . . .
~cl" 8 0
!
.
....................................
4
60
...........
i ...............................
40
.............
i ............................................................
1.5
w'"":
.......................................
!
2.0
i
......................
2.5 3.0 3.5 4.0 4.5 Precipitable Water Content (g/cm2)
"a
°l~
:
!;.~
5.0
..........
..........
5.5
]
Fig. 2. Values of a and ~ for various amounts of precipitable water content and four temperatures, i.e. 305 K (low points), 315 K, 325 K and 335 K (high points).
H.S. Andersen~Journal of Hydrology 188-189 (1997) 788-814
801
from using these mean values, depending on the surface type. Apparently, the tx and/3 values determined by regression tend to favour situations with low water vapour content. Alternatively, the split-window coefficients calculated for e = 1 may be used in connection with a separately estimated ot and/3 value, for example, based on the relation of ol and/~ to water vapour content, as indicated in Fig. 2. The resulting influence of ct and/3 variations on the value of B(e) is shown in Fig. 3 for vegetation and sand. The effect of the emissivity correction is large in the case of sand especially because Ae = - 0.01 and relatively low for vegetation because A¢ is small. It is also seen that the emissivity correction increases with decreasing water vapour content because the effect of emissivity on the surface emissions is increasingly compensated by the surface reflection of downward atmospheric radiance when the water vapour content in the atmosphere is high. It is worth noting that emissivity measurements over bare soil or sand during the IOP of HAPEX-Sahel gave a Ae of the order of 10 -4, which will lead to B(e) = 1 K, so the result for sand shown in Fig. 3 may be regarded as the upper limit.
5. Application to HAPEX-Sahel AVHRR data As mentioned
above, the orbital and radiometric
m a k e s it v e r y w e l l s u i t e d f o r a g r o c l i m a t o l o g i c a l
configuration
monitoring.
of NOAA-AVHRR
In particular, the temperature
signal may be used to establish both radiation and energy balance components. this will require evaluation
accurate
surface
of the performance
temperature
estimates
of the available
set gathered during the HAPEX-Sahel
and consequently
split-window
models.
However, a thorough
The unique
data
lOP may be used to partly fulfil these requirements.
4' ,l, 3.5 ..........
o
~- ............................................................................... o
o
~,, . . . . . . . . . . . .
,b
i
3 ........................................................................................
$-:_..........
o
2.5 ............ ~............. ~............ ~......."------~........ ~ ................ ~............. ::............ nn 2- ............................................................................................
-~ . . . . . . . . . . . . ;o
1.5 ......... ~-~ ........ "al" ~ ............ : ............. i............. :............. ~............. :............. • ; .~ ; . 1............................ : ............ "...... ""-'-: ........ ~,...... g ....... :............ -' ........... 0.5 1.5
2.0
2.5 3.0 3.5 4.0 4.5 Precipitable Water Content (g/cm2)
I m
Vegetation
*
Sand
5.0
5,5
[
Fig. 3. The emissivity effect calculated for vegetation and sand or bare soil for varying amounts of precipitable water content and surface temperature, i.e. 305 K (low points), 315 K, 325 K and 335 K (high points). The emissivity for sand is assumed to be E4 = 0.956 and e 5 = 0.967; for vegetation e 4 = 0.982 and e 5 = 0.986 were used.
802
H.S. Andersen~Journalof Hydrology 188-189 (1997) 788-814
The three different split-window models (Eq. (6), Eq. (8) and Eq. (9)) with local or regional coefficients, as outlined in Section 4, have been tested with A V H R R afternoon data acquired during the HAPEX-Sahel IOP and the results were compared with ground measurements of surface temperature. Unfortunately, mainly because of cloudcontaminated data and view angle restrictions, the number of afternoon A V H R R scenes with related ground truth data from the sites during the lOP is very limited. 5.1. Satellite data processing Geometrical and radiometric uncorrected A V H R R data were acquired from the HAPEX-Sahel Information System (Kerr et al., 1993b; Prince et al., 1995) and corresponding TBUS orbital information was obtained and processed by CHIPS (Andersen et al., 1992). The thermal calibration, including the non-linearity correction, followed the procedure outlined by Walter (1988). The calibration coefficients for visible and near-IR data were chosen from Teillet and Holben (1994) and assumed constant during the HAPEX-Sahel experiment. The orbital description was improved by a visual adjustment of the individual scenes so a navigational accuracy better than one pixel was gained. Based on the orbital information and the site positions given in Table 5, A V H R R data from the individual sites were extracted for a 3 km by 3 km window from the calibrated 10 bit data and accumulated in a database. This implies that the number of different pixels used for each 3 km by 3 km window will vary with the along-scan position of the site. All site data were flagged 'cloudy' or 'cloud free' after a close visual inspection. The visible and near-IR data from A V H R R Channels 1 and 2 were atmospherically corrected using the 5S/SMAC model (Rahman and Dedieu, 1994; Tanr6 et al., 1990). Input to the atmospheric correction of A V H R R Channels 1 and 2 is given in Table 6. For all sites the vegetation fraction was approximated by (Kerr et al., 1993b; Coil et al., 1994b) C=
NDVImax - NDVI NDVImax - NDVImi n
(10)
Table 5 Position in UTM coordinates relative to Zone 31 and description of applied sites HAPEX Site
Site no.
Easting(m)
Northing(m)
Surfacetype
Super-site
1 2 3 4 5 6 7 8 9 lO 11
465227.2 464827.8 466992.8 447331.6 453250 454394.6 447453.5 424040.6 418099.4 417578.4 393300.3
1499333. l 1497379.6 1497800.8 1497371.7 1498558.9 14929i 5.8 1496720. l 1464133.6 !464427.4 1459377.6 i 525485.4
Fallow Millet Millet 2 Fallow Degraded fallow Tiger bush Millet Millet Fallow Tiger bush Millet
Central East
no.
6756 6754 6954 5 i 54 5655 5750 5 i 53 2924 2424 2319 0179
Central West
South Danguey
H.S. Andersen~Journalof Hydrology 188-189 (1997) 788-814
803
Table 6 Input values to the atmosphericcorrection of AVHRR Channels I and 2 Date
Precipitable water (g cm-2)
Aerosol optical depth (at 0.55 gin)
Ozone content (cm)
03 Sep. 92 06 Sep. 92~ 14 Sep. 92~ 28 Sep. 92' 05 Oct. 92d 06 Oct. 92d 07 Oct-92
3.856 4.181 4.285 2.115 3.9 2.8 1.89
0.258 0.3 0.422 0.825 0.35 0.35 0.355
0.25 0.25 0.25 0.25 0.25 0.25 0.25
Aerosol optical depth guessed. b Aerosol optical depth from 13.9. c Aerosol optical depth from 10:00h UTC. d Aerosol optical depth guessed and precipitable water content from ECMWF. The sun photometer measurements of optical depth were provided by Dr. D. Tanr& University of Lille. where NDVImax and NDVImi° were assigned values of 0.77 and 0.11, respectively (see Begue (1991)). It should be noted that N D V I in Eq. (10) is calculated from atmospherically corrected visible and near-IR reflectance factors. 5.2. Estimating the emissivity difference As stated above, both Eq. (6) and Eq. (8) need a priori values for the mean emissivity and emissivity difference. This information might be obtained from land surface type maps if it is possible to relate the individual surface types to values of e and A~. At least two reasons make this approach very difficult: the scarcity of surface emissivity measurements and problems with the definition of effective values for inhomogeneous areas. Another way to proceed is to try to estimate E and/or Ae directly from satellite data. As mentioned above, the missing equation problem in thermal remote sensing requires that ancillary data must be available. Both Becker and Li (1990) and have suggested methods that can estimate e and/or Ae from satellite data and information about the atmospheric state. Here, only the method recently proposed by Coil et al. (1994c) and analysed by Coil et al. (1994a) will be tested. Coil et al. (1994c) proposed a method for the determination of the emissivity difference on the scale of an A V H R R pixel by use of the same data as used for the LST determination. The method requires an a priori estimation of the effective emissivity (e) on a pixel scale, and an accurate description of the atmospheric state at the time of the satellite passage. The method was tested and analysed by Coll et al. (1994b) and Coil et al. (1994a). The following outline of the method follows the derivation described by Coil et al. (1994a). The idea is that if a temperature difference (T~ - T~) still exists after correction for the atmospheric effect, then this difference can be related to an emissivity difference. The brightness temperature at surface level T~ can be defined as Bi(T*) = eiBi(T) + (1 - ei)~yiL~(0 = O)
(11)
804
H.S. A n d e r s e n ~ J o u r n a l
of Hydrology
188-189
(1997)
788-814
where 3'i is a channel- and atmosphere-dependent parameter that relates the hemispherical downweUing radiance to the nadir downwelling radiance. Linearization of the Planck function and the definition of an atmospheric temperature T ~ i , namely, B i ( T ~ i ) = L ~ ( O = 0)/[1 - r i ( O = 0)] leads to a formulation for the difference between the actual surface temperature and the surface brighmess temperature: T-T~=
1-eib
(12)
i
given that ei is close to unity. The difference between the brightness temperature for Channels 4 and 5 can be expressed as a function of the mean emissivity, the emissivity difference and the atmosphere. The emissivity difference can therefore be estimated by Ae = (T,~ - T ~ ) - (1 - e)(b 5 - b4)
(b5 +b4)/2
(13)
Given an a priori value of e and knowledge of the state of the atmosphere it is possible to estimate Ae; T/* = [ B i ( T i ) - L l ( O ) ] l r i ( O ) a n d b i can be calculated by use of an atmospheric model and radiosonde data. Fortunately, the influence of ~ on the calculation of A~ is relatively small. The accuracy of the description of the atmospheric state is, however, very important. This means that the radiosonde data must be close both in space and time to the AVHRR data. The estimation of A¢ has been tested for five sets of satellite and radiosonde data, i.e. on the 6, 14 and 28 September and 7 October. The necessary a priori value of ~ has been approximated by the use of vegetation fraction C, namely, e = C¢v + (1 - C)esoil. It was assumed that e , = 0.984, taken from Coil et al. (1994c), and for bare soil the mean value of the measurements performed by the University of Strasbourg (GSTS) during the IOP was used, ~soil = 0.975. Only one of the test days showed reasonable results, namely 28 September. In the case of 3, 6 and 14 September, the precipitable water content in the
7 tl 6.00
i L
......... ~.......... ~......... ! .......... ! ......... i .......... '. ......... ":.......... ! ......... ~..........
,
~
...........i..
i
"
~
i......... i i .......... .
j
~
~
,
l i i i
2 . 0 0 . . . . . . . . . .
