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SEVIRI data
Remote Sensing of Environment 91 (2004) 377 – 389 www.elsevier.com/locate/rse
Land surface temperature and emissivity estimation based on the two-temperature method: sensitivity analysis using simulated MSG/SEVIRI data Leonardo F. Peres *, Carlos C. DaCamara Centro de Geofı´sica da Universidade de Lisboa (CGUL) and Instituto de Cieˆncia Aplicada e Tecnologia (ICAT), Faculty of Sciences, University of Lisbon, Campo Grande, 1749-016 Lisbon, Portugal Received 3 July 2003; received in revised form 14 February 2004; accepted 27 March 2004
Abstract A feasibility study of land surface temperature (LST) and land surface emissivity (LSE) estimation is presented using METEOSAT Second Generation (MSG)/Spinning Enhanced Visible and Infrared Imager (SEVIRI) data, based on the two-temperature method (TTM). The performance of TTM was assessed by taking into consideration the noise in SEVIRI channels IR 10.8 and IR 12.0 as well as the errors in the atmospheric profiles. Imposed errors due to uncertainties on atmospheric information were generated based on the background error covariance matrix used in the assimilation scheme of the European Centre for Medium-Range Weather Forecasts (ECMWF) Global Circulation Model. TTM has provided LST values with averaged error bias [root-mean square error (RMSE)] ranging from 0.0 to 0.5 K (from 0.8 to 2.5 K) for geographical – seasonal model atmospheres stored in MODTRAN4 with water vapor content varying between 0.85 and 4.11 g cm 2. Obtained results suggest that TTM may be used as a complementary method to split-window (SW) algorithms over areas where LSE is not well known a priori. D 2004 Elsevier Inc. All rights reserved. Keywords: Land surface temperature; Land surface emissivity; Sensitivity analysis; MSG/SEVIRI
1. Introduction Land surface temperature (LST) is a key parameter in the physics of land surface processes because it is involved in the energy balance as well as in the evapotranspiration and desertification processes. LST is a good indicator of land degradation and climate change, and may be used for drought detection and impact assessment based on the estimation of indices of vegetation stress, especially designed to monitor vegetation health, moisture and thermal conditions (Kogan, 2001). LST information is therefore required for a wide range of applications and is of particular interest for the scientific communities dealing with both meteorological and climate models. Currently, the instruments on-board satellites working in the thermal infrared (TIR) are the only available operational systems capable to
* Corresponding author. Tel.: +351-21-750-0868; fax: +351-21-7500172. E-mail address: [email protected] (L.F. Peres). 0034-4257/$ - see front matter D 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2004.03.011
collect cost-effective LST data at spatial and temporal resolutions appropriate to most modeling applications. Although the use of satellite measurements appears to be very attractive, indirect measurements often bring up the complex mathematical issues associated to the inverse problems (Rodgers, 2000). The radiance measured is affected by surface parameters, namely, temperature and land surface emissivity (LSE), as well as by the thermal structure and composition of the atmosphere. An accurate estimation of LST from space data requires a proper characterization of the atmospheric influence (e.g., absorption and emission processes) as well as an adequate knowledge of LSE because natural surfaces do not act as blackbodies. A distinction between the effects of LST and LSE is not possible solely based on observations of the radiance emitted by the land surface. Even if the signal had been corrected from atmospheric influence, a single TIR measurement carried out in n spectral bands leads to n equations that are always less than the n + 1 unknowns (i.e., n spectral band LSE values plus one LST value). Without any a priori information, it is impossible to recover both surface param-
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eters, and the developed techniques differ according to the assumptions made in order to obtain the required additional information. Examples include the reference channel method (Kahle et al., 1980), the emissivity normalization method (Gillespie, 1985), the temperature spectral indices method (Becker & Li, 1990a), the spectral ratio method (Watson, 1992a), the alpha derived emissivity method (Kealy & Hook, 1993), the gray body method (Barducci & Pippi, 1996), the vegetation cover method (Valor & Caselles, 1996), the classification-based emissivity method (Snyder et al., 1998) and the temperature emissivity separation method (Gillespie et al., 1999). METEOSAT Second Generation (MSG), i.e., the new generation of geostationary meteorological satellites developed by the European Space Agency (ESA) in close cooperation with the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT), possesses a high temporal resolution (a new earth image every 15 min) together with a spatial resolution (3 km at subsatellite point) appropriate to regional to continental scales. In addition, the optical imaging radiometer on-board MSG, i.e., the Spinning Enhanced Visible and Infrared Imager (SEVIRI), presents spectral capabilities that are very similar to the TIR bands around 10.8 and 12.0 Am of the Advanced Very High Resolution Radiometer (AVHRR) on-board the National Oceanic and Atmospheric Administration (NOAA) series. These temporal, spatial and spectral characteristics make MSG/SEVIRI particularly suitable to the retrieval of environmental parameters that change rapidly in time (Cihlar et al., 1999), namely, LST and the diurnal cycle of LST (DCT). For instance, channels IR 10.8 and IR 12.0 allow using different methods for LST estimations, namely, the splitwindow (SW) technique (Becker & Li, 1990b; Wan & Dozier, 1996) and the two-temperature method (TTM) (Faysash & Smith, 1999, 2000; Watson, 1992b). The SW technique allows correcting the atmospheric effects on remotely sensed surface temperature and has been successfully applied to estimate sea surface temperature. Although the SW technique is simple and computationally efficient, it has the main disadvantage that small uncertainties in LSE may lead to high errors in LST. Therefore, usage of SW is constrained to areas where LSE is well known a priori (Gillespie et al., 1999). Methods, such as TTM, allow retrieving LST without a direct knowledge of LSE, and may therefore reveal to be especially adequate over areas where LSE is highly variable and SW cannot be accurately applied. In this respect, an assessment of the adequacy of TTM is worth being undertaken, and for this purpose, a feasibility study is here presented using simulated MSG/ SEVIRI data. Previous studies (e.g., Kealy & Hook, 1993; Liang, 2001; Watson, 1992a,b) have mainly focused on surface-leaving radiance, but to our knowledge, no assessment has been made on the required accuracy of the atmospheric correction. However, as remarked by Liang (2001), ‘‘the accuracy of atmospheric correction. . .will
eventually affect the separation of LST and emissivity,’’ and ‘‘it is a critical issue that we need to pay more attention to in the future’’. Accordingly, we have intended to perform a sensitivity study as close as possible to an operational environment, and therefore, the set of imposed errors due to uncertainties on atmospheric information was generated with the aim of reflecting realistic situations, e.g., by perturbing the profiles with values based on the background error covariance matrix used in the assimilation schemes of the Global Circulation Model operated at the European Centre for Medium-Range Weather Forecasts (ECMWF).
2. Method and data TTM is a physical method that allows for a simultaneous retrieval of LST and LSE from radiance measurements if surface is observed at least at two different temperatures. The method assumes that LSE does not change between observations and that atmospheric effects may be adequately estimated by means of a radiative transfer model (RTM). Assuming the Earth’s surface as a Lambertian emitter – reflector and neglecting atmospheric scattering, the radiance Rc (h), recorded in a given channel c by a sensor on-board a satellite observing the Earth’s surface under a zenith angle h, is given by the following relationship Z Z Rc ðhÞ ¼ fc ðkÞek Bk ðTs Þsk ðhÞdk þ fc ðkÞRuk ðhÞdk þ
Z
fc ðkÞ
ð1 ek Þ sk ðhÞEdk dk: p
ð1Þ
The first term on the right-hand side of Eq. (1) represents the radiance emitted by the surface that is attenuated by the atmosphere, fc(k), Bk(Tst), ek and sk(h), denoting the normalized spectral response function of the sensor in channel c, the emitted radiance given by Planck’s function for the surface temperature Ts, the spectral LSE and the spectral transmittance of the atmosphere at the zenith angle h, respectively. The second term represents the radiance emitted by the atmosphere towards the sensor, Ruk(h) denoting the spectral radiance emitted by the atmosphere at the zenith angle h along its upward path. The last term represents the downward atmospheric radiance that is reflected by the surface and then attenuated in its upward path to the sensor, Edk being the downward spectral atmospheric irradiance. It is worth noting (Sobrino et al., 1991) that Rc(h) may also be expressed in terms of channel-equivalent quantities, namely, ec, sc, Ruc and Rdc, i.e., Rc ðhÞ ¼ ec Bc ðTs Þsc ðhÞ þ Ruc ðhÞ þ Rdc ð1 ec Þsc ðhÞ:
ð2Þ
The atmospheric parameters sc(h), Ruc(h) and Rdc in Eq. (2) may be estimated based on information about the atmospheric state, namely, from humidity and temperature profiles, to be used as inputs to an RTM. Taking into
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account our assumptions, we are led to a system of 2n equations with n + 2 unknowns (i.e., n channel LSE values plus two LST values at each time) and such system may be solved when n>1. For instance, SEVIRI allows for sequences of observations in the two split-window channels (c1 = IR 10.8 and c2 = IR 12.0). Assuming that a pair of observations (performed at times t1 and t2) is available, then the four unknown surface parameters (i.e., LSE at c1 and c2, and LST at t1 and t2) may be obtained by solving a system of four equations, each one of the form given by Eq. (2). It is worth mentioning that the high temporal resolution of MSG/ SEVIRI system is expected to provide an adequate implementation of the method because significant changes in surface conditions (e.g., due to changes in soil moisture) are not expected to occur very often between two consecutive or close enough measurements. In order to properly solve the inversion problem, the solution must continuously depend on the data; that is, an arbitrarily small perturbation of the input data cannot lead to arbitrarily large perturbations in the output. In fact, measurement and model uncertainties may induce large variations in the solution, therefore making possible that an accurate solution of the inverse problem may not exist. This was indeed verified (Peres & DaCamara, accepted for publication) when the system of equations was solved algebraically. Measurement uncertainties have induced large variations in the solution resulting in unrealistic physical solutions (e.g., LST = 280.0 K and LSE = 1.30). In order to mitigate this effect, the above mentioned system of four equations was solved by the so-called least-square error method, i.e., by minimizing the following cost function f (x) 2X
ðetc Þ2
6 c¼c1 ;c2 6 t¼t1 ;t2 f ðxÞ ¼ 6 6 4 4
31=2 7 7 7 7 5
ð3Þ
that represents the root-mean square error (RMSE). In Eq. (3), the surface parameters x={xtc}={LSTt1,LSTt2, LSEc1, LSEc2} are adjusted in order to best match the radiance R˜ observed by the sensor to radiance R given by Eq. (2). The quality of the fit is measured by the Euclidean norm of the residual vector e = {etc}={R˜tc Rtc} and it is worth noting that e takes into account both measurement and model uncertainties. Measurement uncertainties arise from sensor performance (i.e., noise associated with the sensor) as well as from the data processing (e.g., radiometric calibration, atmospheric corrections) required to convert the sensor signal output into the parameters to be retrieved. Model uncertainties may arise from the assumptions made about the scene elements (e.g., assuming surfaces as homogeneous and isothermal, neglecting adjacency effects) that may not be consistent with the considered terrestrial surface. Model
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uncertainties also include the approximations made on radiative transfer computations (e.g., the Curtis – Godson scheme). Eq. (2) defines the so-called forward problem where we predict the radiance assuming that the surface parameter values are known. In turn, Eq. (3) characterizes the inverse problem where surface parameters are obtained by fitting the model to the observed radiances (Combal et al., 2002). A quasi-Newton optimization method was used to find the four unknowns that minimize f(x), i.e., the RMSE between R˜ and R. An initial guess vector x0 for the four surface parameters is required and an optimal direction of search is then established on the hypersurface defined by f(x), that leads to a new vector x. This process is reiterated until f(x) reaches its minimal value. In the ideal situation when there are no errors in the observations and the model gives an exact representation of the observed radiances, the cost function f(x) should reach zero. According to Goel and Sterbel (1983), a simple and practical approach to determine whether or not a given model is mathematically invertible consists in performing the following steps: (1) select a set of surface parameters LST and LSE; (2) use Eq. (2) to compute values of radiance; and (3) taking the computed values as perfect observations (i.e., error-free measurements), evaluate the surface parameters through the inversion of the model. The model is considered to be invertible if the estimated values are close enough to those used to simulate the observed radiances. Repeating the procedure for a large set of surface parameters may increase the confidence level of the decision. This procedure may be further generalized by perturbing the observations. Fig. 1 schematically shows the problem of LST and LSE estimation from observed radiance as well as the followed procedure to assess the performance of TTM. Simulations of observed radiances R˜ were obtained using MODTRAN4 (Berk et al., 2000), a well-known radiative transfer model that allows prescribing the surface parameters LST and LSE as well as defining the geometrical path and
Fig. 1. Schematic representation of the problem of LST and LSE estimation and of the procedure used to test the sensitivity of TTM.
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the sensor characteristics. The atmospheric contribution was computed using profiles of temperature and humidity that are stored in MODTRAN4 and constant differences of 2.0 K and 0.01 were prescribed for all pairs of LST (i.e., LSTt2=LSTt1+2.0 K) and of LSE (i.e., LSEc2 = LSEc1 + 0.01). It is worth noting that chosen differences were based on typical values found in operational applications. Because the system of four equations was always solved considering the four unknowns as independent quantities, there is no loss of generality and the adopted procedure has the advantage of allowing a two-dimensional representation of the space of solutions because the constraints define a plane P in the four-dimensional (4D) space of solutions that obviously contains the prescribed solution. Because, when using information from geostationary satellites (e.g., MSG/SEVIRI), the number of measurements may be significantly larger than the number of unknowns, we have also assessed the sensitivity of TTM to the number of measurements by simulating the overdetermined case when surface is observed at 11 different temperatures (2 11 = 22 equations with 2 + 11 = 13 unknowns). In all cases, validation was performed based on differences between obtained estimates of LST and LSE and the corresponding prescribed values.
3. Results and analyses Following Goel (1989), we will focus on some of the key issues that are relevant to any inversion problem, namely, local minima vs. global minimum, mathematical inversion of the model and stability of the solution. 3.1. The inversion problem TTM allows finding a unique set of parameter values [i.e., a global minimum of f(x)]. However, even when a unique solution does exist, several combinations of LST and LSE are also possible that lead to values of radiance that are quite alike to those associated with the correct values of LST and LSE. The existence of such combinations may result in local minima of f(x) turning difficult the determination of the global one. In such cases, the estimated values will strongly depend upon the initial guess x0 and may be quite erroneous. An example is given in Fig. 2a that depicts the behavior of the cost function on plane P (as defined in Section 2). Values of brightness temperature (BT) in channel IR 10.8 were used as initial guesses for LSTt1 and LSTt2 and a constant value of 0.90 was prescribed for LSE in both channels. The exact solution (LSTt1 = 292.0 K and LSEc1 = 0.97) is indicated in the figure by an asterisk that locates the global minimum where the cost function reaches zero. The obtained solution (corresponding to a local minimum of 1.9 10 5) is located at the tip of the arrow and errors of 2.9 K and 0.05 were respectively obtained for LSTt1 and LSE c 1 . It is worth emphasizing that, although the
Fig. 2. (a) Behavior of f(x) in mW m 2 sr 1 (cm 1) 1, as a function of 1 LSTt and LSEc1 and its dependence on the initial guess. The asterisk indicates the correct solution. (b) Zooming of the rectangular region marked in (a). Dots indicate the grid points.
corresponding residual norm is small (in absolute terms), the solution is by no means close to the exact solution. Fig. 2b depicts a zooming of a region of plane P around the exact solution and one may note a strip of local minima that have resulted from the discretization process in the vicinity of a trough line (thick curve). The existence of the line is a consequence of the coupling between LST and LSE for each channel and this problem is not solvable just by increasing the resolution of the grid cells. Because a proper choice of x0 is not obvious, a strategy has to be implemented that allows defining an adequate set of initial guess vectors. This may be achieved by defining a region of physically admissible solutions. Because constraints are usually based on an a priori knowledge of the physical problem, an analysis was performed on a set of values of LSE for a wide class of surface types and closed attention was paid to the relationship between LST and BT in channel IR 10.8.
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Constrains on LSE were derived from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) spectral library (data contribution from the Johns Hopkins University). This library is based on figures obtained from laboratory measurements of the spectral reflectance of different types of materials. An appropriate selection was performed on materials and the spectral LSE values were weighted by the spectral response functions of channels IR 10.8 and IR 12.0. As shown in Fig. 3, only 2.0% (1.0%) of materials have LSE values higher than 0.99 for channel IR 10.8 (IR 12.0) and 13.0% (0.6%) have values lower than 0.90. All vegetation, soils, water, manmade and sedimentary rock samples have values higher than 0.90 and the same occurs for 34 (out of 37) samples of metamorphic rocks. Values higher than 0.99 solely occur for some types of snow and frost. Accordingly, values of LSE were constrained to lie between 0.90 and 0.99. The imposed constraint on LST was based on results obtained using a set of simulations using three representative geographical – seasonal model atmospheres stored in MODTRAN4 (Table 1), namely, Mid-Latitude Summer (MLS), Mid-Latitude Winter (MLW) and Tropical (TROP). We have considered LST as varying around the air temperature at 2 m, Tatm, of each profile from Tatm 5.0 K to Tatm + 5.0 K in steps of 5.0 K. A value of 45j was assigned to the satellite zenith angle because it is representative in the case of MSG pixels over Europe. LSE was assumed to span from 0.90 to 0.98 in steps of 0.02. Obtained results are shown in Fig. 4, and accordingly, LST solutions were constrained to lie between BT and BT + 10.0 K (channel IR 10.8). The set of initial guess vectors was defined within the space of admissible solutions in steps of 1.0 K for LST and 0.01 for LSE resulting in a set of 110 initial guess vectors. In this case, very small errors of 0.006 K and 1.0 10 4 were obtained for the estimated values of LST and LSE, respec-
Fig. 3. LSE values in channels IR 10.8 and IR 12.0 for selected surfaces stored in the Johns Hopkins University directory at ASTER spectral library. The imposed constrain on LSE solution is delimited by the dashed line.
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Table 1 Some characteristics of the MLS, MLW and TROP atmospheric profiles Atmospheric profile
Water vapor content (g cm 2)
Air temperature at 2 m (K)
MLS MLW TROP
2.92 0.85 4.11
294.2 272.2 299.7
tively. Fig. 5 depicts the procedure of LST and LSE estimation using the constraints and the 110 initial guesses. 3.2. Sensitivity experiments Fig. 6 shows the histogram of errors for LST at time t1 and for LSE in channel IR 10.8 for a set of 72 simulations generated by error-free observations. The obtained RMSE was 0.05 for LST (at both times t1 and t2) and 0.001 for LSE in channels IR 10.8 and IR 12.0. Therefore, our results indicate that it is feasible to determine the surface parameters through the inversion of the model. The accuracy of the estimated surface parameters will essentially depend on the radiometric performance of the instrument as well on the performed atmospheric corrections, i.e., the determination of sc(h), Ruc(h) and Rdc. Accordingly, the performance of TTM was assessed taking into consideration the noise in SEVIRI channels IR 10.8 and IR 12.0 as well as the errors in the atmospheric profiles. The latter were based on the current ECMWF background error covariance matrix (Fillion & Mahfouf, 2000), and we have considered that the model based on Eq. (2) exactly describes the observed radiance and that the accuracy of the atmospheric correction does not depend on radiative transfer
Fig. 4. Relationship between LST and BT in channel IR 10.8 based on the set of simulated cases for three model atmospheres stored in MODTRAN4. For each model atmosphere, we represent the reference case (LST = Tatm) for five values of emissivity (middle line) as well as the two extreme cases (LST = Tatm F 5.0 K). Mid-Latitude Summer ( ), Mid-Latitude Winter (n) and Tropical (*). The dashed line indicates the upper bound of the imposed constrain on LST solutions.
.
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Fig. 5. Estimation of LST and LSE using 110 initial guesses. The dashed line delimits the space of admissible solutions.
model approximations. TTM performance was assessed based on the same simulated cases that were used to define the imposed constrain on LST. The used values for the noise equivalent delta temperature (NEDT) at 300 K for channels IR 10.8 and IR 12.0 were 0.11 and 0.15 K, respectively. These values are based on radiometric performances defined as short-term errors that include all factors (namely, random noise, stability of temperature of detectors, crosstalk and straylight, stability of gain and electromagnetic perturbation) affecting the radiometry during a single nominal repeat cycle (15 min duration) and applies to in-orbit conditions at End Of Live (EOL). The measured performance of SEVIRI is based on tests at satellite level that were complemented by a prediction of in-flight performances at EOL (Rogers, 2001). The abovementioned values of 0.11 and 0.15 were converted to 0.185 and 0.262 mW m 2 sr 1 (cm 1) 1, respectively, of noise equivalent delta radiance (NEDN). A simulation of the effects of satellite noise was then performed using a set of randomly generated signal level perturbations for each channel with normal distributions with zero mean and standard deviations equal to SEVIRI channel’s NEDN. Values of averaged error bias and RMSE for both welldetermined and overdetermined cases are shown in Table 2 for LST at time t1 and LSE in channel IR 10.8 but it is worth noting that the results are quite similar for all times and for both channels. In the well-determined case, values of averaged error bias (RMSE) for LST were 0.0 K (1.1 K), 0.1 K (2.0 K) and 0.1 K (0.8 K) for MLS, MLW and TROP, respectively, whereas for LSE estimation, the corresponding obtained values were 0.001 (0.030), 0.003 (0.040) and 0.006 (0.032). Figs. 7, 8 and 9 show histograms of errors for LST and LSE concerning MLS, MLW and TROP atmospheres. It may be noted that obtained results were almost the same for both well-determined and overdetermined cases suggesting that increasing the number of observations does not lead to significant improvements on
results. This aspect was emphasized in Peres and DaCamara (accepted for publication) when they have analyzed the effective rank of the problem and the degrees of freedom related to signal and to noise. Results also show that there is a negative correlation between the values of bias of LST and LSE, a feature that is expected to occur in simultaneous retrieval computations (Faysash & Smith, 1999, 2000). Because LST changes occurring every 15 min may be lower than the NEDT value, we have modeled the DCT following a method developed by Go¨ttsche and Olesen (2000). DCT was simulated in intervals of 15 min for three different types of surfaces, namely, continuous urban fabric, nonirrigated arable land and broadleaf forest (see Fig. 10). Results indicate that the LST difference for sequential observations is often lower than the NEDT value during nighttime and that, in such cases, the degrees of freedom of the measurement related to noise might be greater than those related to signal. On the contrary, combining observations with an interval of 1 h during daytime generally leads to
Fig. 6. Histogram of errors (estimation minus prescribed values) for LST at time t1 (a) and LSE in channel IR 10.8 (b). Bin sizes are 0.05 K and 0.001 for LST and LSE, respectively.
L.F. Peres, C.C. DaCamara / Remote Sensing of Environment 91 (2004) 377–389 Table 2 Results of sensitivity analysis related with signal-to-noise ratio for both well-determined and overdetermined cases Cases
Well-determined (2 times)
Overdetermined (11 times)
MLS LST RMSE 1.1 (K) Bias 0.0 LSE RMSE 0.030 Bias 0.001
MLW
TROP
MLS
MLW
TROP
2.0 0.1 0.040 0.003
0.8 0.1 0.032 0.006
1.0 1.8 0.8 0.0 0.1 0.1 0.028 0.037 0.032 0.001 0.002 0.005
Errors refer to LST at time t1 and LSE in channel IR 10.8.
adequate values of temperature difference (e.g., z 2.0 K). Brightness temperatures associated with modeled DCT were also computed for all atmospheric profiles and results suggest that differences in BT are good indicators for the choice of adequate time intervals between observations. Following Faysash and Smith (2000), a simple sensitivity study was first performed where the atmospheric parameters were perturbed by F 2%. Obtained errors for LST (LSE) were 3.6 K ( 0.04) for perturbations of 2%, and 2.1 K (0.01) for + 2%. The overestimation (underestimation) of LST in the case of negative (positive) perturbations is related to the fact that it compensates the respective decrease (increase) of the atmospheric parameters. As it was to be expected, an opposite behavior is observed with LSE. However, it is worth noting that the imposed perturbations of F 2% are not realistic because, on the one hand, atmospheric profile errors do not induce similar changes on
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the atmospheric parameters, and on the other hand, the transmittance sc(h) is negatively correlated with the upward and the downward atmospheric radiances Ruc(h) and Rdc; that is, an increase in sc(h) results in a decrease in both Ruc(h) and Rdc. A possible alternate way might consist in perturbing each level with values randomly taken from a normal distribution of zero mean and a standard deviation characteristic of the uncertainty. In this case, perturbations at a given level are assumed to be independent from those at others levels but such procedure is also not realistic. An extreme opposite procedure would be considering the perturbations to be perfectly correlated, e.g., by using perturbed profiles that are offset by given amounts (Tjemkes & Schemetz, 1998). In our case, we have decided to simulate more realistic perturbed profiles. Accordingly three sets of temperature and humidity perturbed profiles based on MLS, MLW and TROP were generated (see Fig. 11) based on the background error covariance matrix of the current operational 4D-Var data assimilation scheme at ECMWF. We have also computed the standard deviation for each vertical level (Fig. 12) and it may be noted that the minimum (maximum) error standard deviation for temperature occurs at the surface (stratosphere) for all profiles. Extreme values range from about 0.5 to 1.8 K for TROP and from 0.6 up to 4.9 K for both MLW and MLS. In the case of mixing ratio, the vertical profiles show a maximum of 2.2 g kg 1 at level 53 ( f 950 hPa) for TROP and 2.0 g kg 1 at level 49 ( f 850 hPa) for MLS. In the case of MLW, the profile of errors in standard deviation shows a
Fig. 7. Histogram of LST (upper panels) and LSE (lower panels) errors (estimation minus prescribed values) related with signal-to-noise ratio of channels IR 10.8 and IR 12.0 for MLS. Errors refer to LST at time t1 and LSE in channel IR 10.8. Left and right panels refer to the well-determined and the overdetermined cases, respectively. Bin sizes are 1.0 K and 0.02 for LST and LSE, respectively.
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Fig. 8. As in Fig. 7 but for MLW.
maximum of 0.6 g kg 1 at the surface and steadily decreases with height. The observed decrease of forecast errors of humidity near the surface may be explained by the low variability of humidity in the wet boundary layers (Fillion & Mahfouf, 2000). We have generated profiles with simultaneous perturbations on temperature and humidity, and in the case of MLS,
separate profiles of temperature and humidity were also considered in order to allow assessing the impact of each variable on the results. As shown in Table 3, values of averaged error bias (RMSE) for LST are less than 0.5 K (2.5 K), whereas for LSE, absolute values of averaged error bias (RMSE) are less than 0.010 (0.045). The previously mentioned negative
Fig. 9. As in Fig. 7 but for TROP.
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Fig. 10. Modeled DCT for continuous urban fabric (solid line), nonirrigated arable land (dotted line) and broadleaf forest (dashed line).
correlation between the bias in LST and LSE is worth noting again as well as the fact that increasing the number of observations does not contribute to obtain significant improvements on results. In the case of simultaneous perturbations on temperature and humidity, Figs. 13 –15 show histograms of LST and LSE estimation errors for MLS, MLW and TROP. As expected, the LST and LSE estimation errors due to perturbations on the humidity profiles are higher than those due to perturbations on temperature explaining the fact that the case of simultaneous
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Fig. 12. Standard deviation of errors of mass mixing ratio (solid curve) and temperature (dashed curve) for MLS (a), MLW (b) and TROP (c).
perturbations on humidity and temperature is very similar to the one when only humidity is perturbed.
4. Discussion and conclusions The major advantage of TTM is to enable for a simultaneous retrieval of LST and LSE. However, when using multitemporal methods such as TTM, one has to take into
Fig. 11. Comparison between the perturbed profiles (black curves) of temperature (upper panels) and humidity (lower panels) and respective reference profile (white curves) for MLS (left panels), MLW (middle panels) and TROP (right panels).
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Table 3 Results of sensitivity analysis related with perturbations imposed on atmospheric profiles for both well-determined and overdetermined cases Cases
Well-determined (2 times) a
LST (K) LSE
RMSE Bias RMSE Bias
b
Overdetermined (11 times)
MLS
MLS
MLS
MLW
TROP
MLSa
MLSb
MLS
MLW
TROP
1.0 0.1 0.020 0.002
2.0 0.5 0.034 0.006
2.1 0.5 0.035 0.006
2.4 0.2 0.045 0.005
2.5 0.3 0.040 0.010
0.9 0.1 0.019 0.002
2.0 0.5 0.034 0.005
2.1 0.5 0.034 0.005
2.2 0.1 0.041 0.004
2.5 0.4 0.039 0.008
Errors refer to LST at time t1 and LSE in channel IR 10.8. a Perturbation only on temperature profile. b Perturbation only on humidity profile.
account the technical problem related to the registration of multiple images from different times. These images should be spatially matched and the observations should be acquired with the same satellite-viewing angle. Because LST and LSE errors due to misregistration depend on the difference between the surface characteristics of the physical regions mistakenly matched, the error is expected to be small for homogeneous areas. Conversely, for heterogeneous areas, the error could be large depending on the variation of vegetation and soil proportions (i.e., mixed pixels) due to misregistration effects (Wan, 1999). Changes in the satellite-viewing angle will create differences in the projected surface that may lead to changes in magnitude of exposed bare soil, especially if the values of fractional vegetation cover are low. Currently, a large number of image-to-image registration algorithms is available in the literature (e.g., Brown, 1992; Fonseca & Manjunath, 1996; Le Moigne et al., 2002; Stone, 1999) and the selection of the most appropriate method depends on the type of data, the desired accuracy and the type of computing resources available (Le Moigne et al., 2002). Problems related to
registration are avoided when TTM is used with geostationary satellites like MSG because the satellite-viewing angle is always the same for each pixel. It is also worth emphasizing that TTM is especially adequate for MSG/ SEVIRI because of the advantages of high temporal frequency that contribute to mitigating the errors associated to the method hypothesis. Inversion methods that allow recovering both LST and LSE require independent atmospheric corrections, and therefore, both land surface parameters will strongly depend on atmospheric profile uncertainties. Vertical sounding instruments on-board satellites like the High Resolution Infrared Sounder (HIRS) and the Infrared Atmospheric Sounding Interferometer (IASI) provide simultaneous information of land surface measurements and vertical atmospheric profiles with a reasonable spatial resolution that may allow a suitable characterization of the atmosphere. In the case of instruments like the Moderate Resolution Imaging Spectroradiometer (MODIS) and IASI, it may be possible to estimate atmospheric temperature and water vapor profiles at 1 km resolution. Because there is no vertical sounding
Fig. 13. As in Fig. 7 but for perturbations imposed on MLS.
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387
Fig. 14. As in Fig. 13 but for MLW.
instrument on-board MSG, our estimations may be viewed as defining the base line for a preliminary assessment on the adequacy of algorithms to retrieve LST and LSE based on data with SEVIRI characteristics. Although TTM allows the separation of LST and LSE information from radiance measurements, and therefore, the solution may be uniquely determined by the data, the inverse problem is still an ill-posed problem because the
solution does not depend continuously on the data. The hypothesis assumed by TTM leads to a set of equations where the unknowns produce similar responses, and therefore, small perturbations in measurements (e.g., sensor noise, uncertainties in atmospheric profiles) may induce large errors in the solution. Accordingly, we have used a least-square optimization algorithm in order to stabilize the solution. The accuracy of the estimated surface parameters
Fig. 15. As in Fig. 13 but for TROP.
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was evaluated taking into consideration the noise in SEVIRI channels as well as the uncertainties in the atmospheric profiles that were based on the ECMWF background error covariance matrix. TTM has provided LST values with averaged error bias (RMSE) ranging from 0.0 to 0.5 K (from 0.8 to 2.5 K) for geographical – seasonal model atmospheres with water vapor content varying between 0.85 and 4.11 g cm 2. Obtained results suggest that TTM may be used as a complementary method to SW algorithms especially over areas where LSE is highly variable. Faysash and Smith (1999, 2000) have validated TTM using GOES8 measurements that were compared to in situ ground measurements made within the framework of the Atmospheric Radiation Measurement Program Cloud and Radiation Testbed (ARM CART). Because their validation conditions were totally different from ours, a direct comparison of results might be difficult. However, it is worth noting that their results are very similar to ours, and therefore, this may give a sounder indication on the performance of TTM. In that respect, LSE solution may be not stable enough because values of LSE averaged error bias (RMSE) range from 0.001 to 0.010 (from 0.028 to 0.045).
Acknowledgements We would like to thank the Institute for Applied Science and Technology of the Faculty of Sciences of the University of Lisbon (ICAT –FCUL) for providing the computing resources. The Portuguese Foundation of Science and Technology (FCT) has supported the research performed by the first author (Grant No. PRAXIS XXI/BD/21566/99). The research was performed within the framework of the Project Satellite Application Facility on Land Surface Analysis (LSA SAF), an R&D Project supported by EUMETSAT. The ASTER spectral library was available courtesy of the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California.
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L.F. Peres, C.C. DaCamara / Remote Sensing of Environment 91 (2004) 377–389 Sobrino, J. A., Coll, C., & Caselles, V. (1991). Atmospheric correction for land surface temperature using NOAA-11 AVHRR channels 4 and 5. Remote Sensing of Environment, 38, 19 – 34. Stone, H. S. (1999). Progressive wavelet correlation using Fourier methods. IEEE Transactions on Signal Processing, 47, 97 – 107. Tjemkes, S. A., & Schemetz, J. (1998). Radiative transfer simulations for the thermal channels of METEOSAT second generation, EUM TM 01. Valor, E., & Caselles, V. (1996). Mapping land surface emissivity from NDVI: Application to European, African, and South American areas. Remote Sensing of Environment, 57, 164 – 184.
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Land surface temperature and emissivity estimation based on the two-temperature method: sensitivity analysis using simulated MSG/SEVIRI data Leonardo F. Peres *, Carlos C. DaCamara Centro de Geofı´sica da Universidade de Lisboa (CGUL) and Instituto de Cieˆncia Aplicada e Tecnologia (ICAT), Faculty of Sciences, University of Lisbon, Campo Grande, 1749-016 Lisbon, Portugal Received 3 July 2003; received in revised form 14 February 2004; accepted 27 March 2004
Abstract A feasibility study of land surface temperature (LST) and land surface emissivity (LSE) estimation is presented using METEOSAT Second Generation (MSG)/Spinning Enhanced Visible and Infrared Imager (SEVIRI) data, based on the two-temperature method (TTM). The performance of TTM was assessed by taking into consideration the noise in SEVIRI channels IR 10.8 and IR 12.0 as well as the errors in the atmospheric profiles. Imposed errors due to uncertainties on atmospheric information were generated based on the background error covariance matrix used in the assimilation scheme of the European Centre for Medium-Range Weather Forecasts (ECMWF) Global Circulation Model. TTM has provided LST values with averaged error bias [root-mean square error (RMSE)] ranging from 0.0 to 0.5 K (from 0.8 to 2.5 K) for geographical – seasonal model atmospheres stored in MODTRAN4 with water vapor content varying between 0.85 and 4.11 g cm 2. Obtained results suggest that TTM may be used as a complementary method to split-window (SW) algorithms over areas where LSE is not well known a priori. D 2004 Elsevier Inc. All rights reserved. Keywords: Land surface temperature; Land surface emissivity; Sensitivity analysis; MSG/SEVIRI
1. Introduction Land surface temperature (LST) is a key parameter in the physics of land surface processes because it is involved in the energy balance as well as in the evapotranspiration and desertification processes. LST is a good indicator of land degradation and climate change, and may be used for drought detection and impact assessment based on the estimation of indices of vegetation stress, especially designed to monitor vegetation health, moisture and thermal conditions (Kogan, 2001). LST information is therefore required for a wide range of applications and is of particular interest for the scientific communities dealing with both meteorological and climate models. Currently, the instruments on-board satellites working in the thermal infrared (TIR) are the only available operational systems capable to
* Corresponding author. Tel.: +351-21-750-0868; fax: +351-21-7500172. E-mail address: [email protected] (L.F. Peres). 0034-4257/$ - see front matter D 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2004.03.011
collect cost-effective LST data at spatial and temporal resolutions appropriate to most modeling applications. Although the use of satellite measurements appears to be very attractive, indirect measurements often bring up the complex mathematical issues associated to the inverse problems (Rodgers, 2000). The radiance measured is affected by surface parameters, namely, temperature and land surface emissivity (LSE), as well as by the thermal structure and composition of the atmosphere. An accurate estimation of LST from space data requires a proper characterization of the atmospheric influence (e.g., absorption and emission processes) as well as an adequate knowledge of LSE because natural surfaces do not act as blackbodies. A distinction between the effects of LST and LSE is not possible solely based on observations of the radiance emitted by the land surface. Even if the signal had been corrected from atmospheric influence, a single TIR measurement carried out in n spectral bands leads to n equations that are always less than the n + 1 unknowns (i.e., n spectral band LSE values plus one LST value). Without any a priori information, it is impossible to recover both surface param-
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eters, and the developed techniques differ according to the assumptions made in order to obtain the required additional information. Examples include the reference channel method (Kahle et al., 1980), the emissivity normalization method (Gillespie, 1985), the temperature spectral indices method (Becker & Li, 1990a), the spectral ratio method (Watson, 1992a), the alpha derived emissivity method (Kealy & Hook, 1993), the gray body method (Barducci & Pippi, 1996), the vegetation cover method (Valor & Caselles, 1996), the classification-based emissivity method (Snyder et al., 1998) and the temperature emissivity separation method (Gillespie et al., 1999). METEOSAT Second Generation (MSG), i.e., the new generation of geostationary meteorological satellites developed by the European Space Agency (ESA) in close cooperation with the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT), possesses a high temporal resolution (a new earth image every 15 min) together with a spatial resolution (3 km at subsatellite point) appropriate to regional to continental scales. In addition, the optical imaging radiometer on-board MSG, i.e., the Spinning Enhanced Visible and Infrared Imager (SEVIRI), presents spectral capabilities that are very similar to the TIR bands around 10.8 and 12.0 Am of the Advanced Very High Resolution Radiometer (AVHRR) on-board the National Oceanic and Atmospheric Administration (NOAA) series. These temporal, spatial and spectral characteristics make MSG/SEVIRI particularly suitable to the retrieval of environmental parameters that change rapidly in time (Cihlar et al., 1999), namely, LST and the diurnal cycle of LST (DCT). For instance, channels IR 10.8 and IR 12.0 allow using different methods for LST estimations, namely, the splitwindow (SW) technique (Becker & Li, 1990b; Wan & Dozier, 1996) and the two-temperature method (TTM) (Faysash & Smith, 1999, 2000; Watson, 1992b). The SW technique allows correcting the atmospheric effects on remotely sensed surface temperature and has been successfully applied to estimate sea surface temperature. Although the SW technique is simple and computationally efficient, it has the main disadvantage that small uncertainties in LSE may lead to high errors in LST. Therefore, usage of SW is constrained to areas where LSE is well known a priori (Gillespie et al., 1999). Methods, such as TTM, allow retrieving LST without a direct knowledge of LSE, and may therefore reveal to be especially adequate over areas where LSE is highly variable and SW cannot be accurately applied. In this respect, an assessment of the adequacy of TTM is worth being undertaken, and for this purpose, a feasibility study is here presented using simulated MSG/ SEVIRI data. Previous studies (e.g., Kealy & Hook, 1993; Liang, 2001; Watson, 1992a,b) have mainly focused on surface-leaving radiance, but to our knowledge, no assessment has been made on the required accuracy of the atmospheric correction. However, as remarked by Liang (2001), ‘‘the accuracy of atmospheric correction. . .will
eventually affect the separation of LST and emissivity,’’ and ‘‘it is a critical issue that we need to pay more attention to in the future’’. Accordingly, we have intended to perform a sensitivity study as close as possible to an operational environment, and therefore, the set of imposed errors due to uncertainties on atmospheric information was generated with the aim of reflecting realistic situations, e.g., by perturbing the profiles with values based on the background error covariance matrix used in the assimilation schemes of the Global Circulation Model operated at the European Centre for Medium-Range Weather Forecasts (ECMWF).
2. Method and data TTM is a physical method that allows for a simultaneous retrieval of LST and LSE from radiance measurements if surface is observed at least at two different temperatures. The method assumes that LSE does not change between observations and that atmospheric effects may be adequately estimated by means of a radiative transfer model (RTM). Assuming the Earth’s surface as a Lambertian emitter – reflector and neglecting atmospheric scattering, the radiance Rc (h), recorded in a given channel c by a sensor on-board a satellite observing the Earth’s surface under a zenith angle h, is given by the following relationship Z Z Rc ðhÞ ¼ fc ðkÞek Bk ðTs Þsk ðhÞdk þ fc ðkÞRuk ðhÞdk þ
Z
fc ðkÞ
ð1 ek Þ sk ðhÞEdk dk: p
ð1Þ
The first term on the right-hand side of Eq. (1) represents the radiance emitted by the surface that is attenuated by the atmosphere, fc(k), Bk(Tst), ek and sk(h), denoting the normalized spectral response function of the sensor in channel c, the emitted radiance given by Planck’s function for the surface temperature Ts, the spectral LSE and the spectral transmittance of the atmosphere at the zenith angle h, respectively. The second term represents the radiance emitted by the atmosphere towards the sensor, Ruk(h) denoting the spectral radiance emitted by the atmosphere at the zenith angle h along its upward path. The last term represents the downward atmospheric radiance that is reflected by the surface and then attenuated in its upward path to the sensor, Edk being the downward spectral atmospheric irradiance. It is worth noting (Sobrino et al., 1991) that Rc(h) may also be expressed in terms of channel-equivalent quantities, namely, ec, sc, Ruc and Rdc, i.e., Rc ðhÞ ¼ ec Bc ðTs Þsc ðhÞ þ Ruc ðhÞ þ Rdc ð1 ec Þsc ðhÞ:
ð2Þ
The atmospheric parameters sc(h), Ruc(h) and Rdc in Eq. (2) may be estimated based on information about the atmospheric state, namely, from humidity and temperature profiles, to be used as inputs to an RTM. Taking into
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account our assumptions, we are led to a system of 2n equations with n + 2 unknowns (i.e., n channel LSE values plus two LST values at each time) and such system may be solved when n>1. For instance, SEVIRI allows for sequences of observations in the two split-window channels (c1 = IR 10.8 and c2 = IR 12.0). Assuming that a pair of observations (performed at times t1 and t2) is available, then the four unknown surface parameters (i.e., LSE at c1 and c2, and LST at t1 and t2) may be obtained by solving a system of four equations, each one of the form given by Eq. (2). It is worth mentioning that the high temporal resolution of MSG/ SEVIRI system is expected to provide an adequate implementation of the method because significant changes in surface conditions (e.g., due to changes in soil moisture) are not expected to occur very often between two consecutive or close enough measurements. In order to properly solve the inversion problem, the solution must continuously depend on the data; that is, an arbitrarily small perturbation of the input data cannot lead to arbitrarily large perturbations in the output. In fact, measurement and model uncertainties may induce large variations in the solution, therefore making possible that an accurate solution of the inverse problem may not exist. This was indeed verified (Peres & DaCamara, accepted for publication) when the system of equations was solved algebraically. Measurement uncertainties have induced large variations in the solution resulting in unrealistic physical solutions (e.g., LST = 280.0 K and LSE = 1.30). In order to mitigate this effect, the above mentioned system of four equations was solved by the so-called least-square error method, i.e., by minimizing the following cost function f (x) 2X
ðetc Þ2
6 c¼c1 ;c2 6 t¼t1 ;t2 f ðxÞ ¼ 6 6 4 4
31=2 7 7 7 7 5
ð3Þ
that represents the root-mean square error (RMSE). In Eq. (3), the surface parameters x={xtc}={LSTt1,LSTt2, LSEc1, LSEc2} are adjusted in order to best match the radiance R˜ observed by the sensor to radiance R given by Eq. (2). The quality of the fit is measured by the Euclidean norm of the residual vector e = {etc}={R˜tc Rtc} and it is worth noting that e takes into account both measurement and model uncertainties. Measurement uncertainties arise from sensor performance (i.e., noise associated with the sensor) as well as from the data processing (e.g., radiometric calibration, atmospheric corrections) required to convert the sensor signal output into the parameters to be retrieved. Model uncertainties may arise from the assumptions made about the scene elements (e.g., assuming surfaces as homogeneous and isothermal, neglecting adjacency effects) that may not be consistent with the considered terrestrial surface. Model
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uncertainties also include the approximations made on radiative transfer computations (e.g., the Curtis – Godson scheme). Eq. (2) defines the so-called forward problem where we predict the radiance assuming that the surface parameter values are known. In turn, Eq. (3) characterizes the inverse problem where surface parameters are obtained by fitting the model to the observed radiances (Combal et al., 2002). A quasi-Newton optimization method was used to find the four unknowns that minimize f(x), i.e., the RMSE between R˜ and R. An initial guess vector x0 for the four surface parameters is required and an optimal direction of search is then established on the hypersurface defined by f(x), that leads to a new vector x. This process is reiterated until f(x) reaches its minimal value. In the ideal situation when there are no errors in the observations and the model gives an exact representation of the observed radiances, the cost function f(x) should reach zero. According to Goel and Sterbel (1983), a simple and practical approach to determine whether or not a given model is mathematically invertible consists in performing the following steps: (1) select a set of surface parameters LST and LSE; (2) use Eq. (2) to compute values of radiance; and (3) taking the computed values as perfect observations (i.e., error-free measurements), evaluate the surface parameters through the inversion of the model. The model is considered to be invertible if the estimated values are close enough to those used to simulate the observed radiances. Repeating the procedure for a large set of surface parameters may increase the confidence level of the decision. This procedure may be further generalized by perturbing the observations. Fig. 1 schematically shows the problem of LST and LSE estimation from observed radiance as well as the followed procedure to assess the performance of TTM. Simulations of observed radiances R˜ were obtained using MODTRAN4 (Berk et al., 2000), a well-known radiative transfer model that allows prescribing the surface parameters LST and LSE as well as defining the geometrical path and
Fig. 1. Schematic representation of the problem of LST and LSE estimation and of the procedure used to test the sensitivity of TTM.
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the sensor characteristics. The atmospheric contribution was computed using profiles of temperature and humidity that are stored in MODTRAN4 and constant differences of 2.0 K and 0.01 were prescribed for all pairs of LST (i.e., LSTt2=LSTt1+2.0 K) and of LSE (i.e., LSEc2 = LSEc1 + 0.01). It is worth noting that chosen differences were based on typical values found in operational applications. Because the system of four equations was always solved considering the four unknowns as independent quantities, there is no loss of generality and the adopted procedure has the advantage of allowing a two-dimensional representation of the space of solutions because the constraints define a plane P in the four-dimensional (4D) space of solutions that obviously contains the prescribed solution. Because, when using information from geostationary satellites (e.g., MSG/SEVIRI), the number of measurements may be significantly larger than the number of unknowns, we have also assessed the sensitivity of TTM to the number of measurements by simulating the overdetermined case when surface is observed at 11 different temperatures (2 11 = 22 equations with 2 + 11 = 13 unknowns). In all cases, validation was performed based on differences between obtained estimates of LST and LSE and the corresponding prescribed values.
3. Results and analyses Following Goel (1989), we will focus on some of the key issues that are relevant to any inversion problem, namely, local minima vs. global minimum, mathematical inversion of the model and stability of the solution. 3.1. The inversion problem TTM allows finding a unique set of parameter values [i.e., a global minimum of f(x)]. However, even when a unique solution does exist, several combinations of LST and LSE are also possible that lead to values of radiance that are quite alike to those associated with the correct values of LST and LSE. The existence of such combinations may result in local minima of f(x) turning difficult the determination of the global one. In such cases, the estimated values will strongly depend upon the initial guess x0 and may be quite erroneous. An example is given in Fig. 2a that depicts the behavior of the cost function on plane P (as defined in Section 2). Values of brightness temperature (BT) in channel IR 10.8 were used as initial guesses for LSTt1 and LSTt2 and a constant value of 0.90 was prescribed for LSE in both channels. The exact solution (LSTt1 = 292.0 K and LSEc1 = 0.97) is indicated in the figure by an asterisk that locates the global minimum where the cost function reaches zero. The obtained solution (corresponding to a local minimum of 1.9 10 5) is located at the tip of the arrow and errors of 2.9 K and 0.05 were respectively obtained for LSTt1 and LSE c 1 . It is worth emphasizing that, although the
Fig. 2. (a) Behavior of f(x) in mW m 2 sr 1 (cm 1) 1, as a function of 1 LSTt and LSEc1 and its dependence on the initial guess. The asterisk indicates the correct solution. (b) Zooming of the rectangular region marked in (a). Dots indicate the grid points.
corresponding residual norm is small (in absolute terms), the solution is by no means close to the exact solution. Fig. 2b depicts a zooming of a region of plane P around the exact solution and one may note a strip of local minima that have resulted from the discretization process in the vicinity of a trough line (thick curve). The existence of the line is a consequence of the coupling between LST and LSE for each channel and this problem is not solvable just by increasing the resolution of the grid cells. Because a proper choice of x0 is not obvious, a strategy has to be implemented that allows defining an adequate set of initial guess vectors. This may be achieved by defining a region of physically admissible solutions. Because constraints are usually based on an a priori knowledge of the physical problem, an analysis was performed on a set of values of LSE for a wide class of surface types and closed attention was paid to the relationship between LST and BT in channel IR 10.8.
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Constrains on LSE were derived from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) spectral library (data contribution from the Johns Hopkins University). This library is based on figures obtained from laboratory measurements of the spectral reflectance of different types of materials. An appropriate selection was performed on materials and the spectral LSE values were weighted by the spectral response functions of channels IR 10.8 and IR 12.0. As shown in Fig. 3, only 2.0% (1.0%) of materials have LSE values higher than 0.99 for channel IR 10.8 (IR 12.0) and 13.0% (0.6%) have values lower than 0.90. All vegetation, soils, water, manmade and sedimentary rock samples have values higher than 0.90 and the same occurs for 34 (out of 37) samples of metamorphic rocks. Values higher than 0.99 solely occur for some types of snow and frost. Accordingly, values of LSE were constrained to lie between 0.90 and 0.99. The imposed constraint on LST was based on results obtained using a set of simulations using three representative geographical – seasonal model atmospheres stored in MODTRAN4 (Table 1), namely, Mid-Latitude Summer (MLS), Mid-Latitude Winter (MLW) and Tropical (TROP). We have considered LST as varying around the air temperature at 2 m, Tatm, of each profile from Tatm 5.0 K to Tatm + 5.0 K in steps of 5.0 K. A value of 45j was assigned to the satellite zenith angle because it is representative in the case of MSG pixels over Europe. LSE was assumed to span from 0.90 to 0.98 in steps of 0.02. Obtained results are shown in Fig. 4, and accordingly, LST solutions were constrained to lie between BT and BT + 10.0 K (channel IR 10.8). The set of initial guess vectors was defined within the space of admissible solutions in steps of 1.0 K for LST and 0.01 for LSE resulting in a set of 110 initial guess vectors. In this case, very small errors of 0.006 K and 1.0 10 4 were obtained for the estimated values of LST and LSE, respec-
Fig. 3. LSE values in channels IR 10.8 and IR 12.0 for selected surfaces stored in the Johns Hopkins University directory at ASTER spectral library. The imposed constrain on LSE solution is delimited by the dashed line.
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Table 1 Some characteristics of the MLS, MLW and TROP atmospheric profiles Atmospheric profile
Water vapor content (g cm 2)
Air temperature at 2 m (K)
MLS MLW TROP
2.92 0.85 4.11
294.2 272.2 299.7
tively. Fig. 5 depicts the procedure of LST and LSE estimation using the constraints and the 110 initial guesses. 3.2. Sensitivity experiments Fig. 6 shows the histogram of errors for LST at time t1 and for LSE in channel IR 10.8 for a set of 72 simulations generated by error-free observations. The obtained RMSE was 0.05 for LST (at both times t1 and t2) and 0.001 for LSE in channels IR 10.8 and IR 12.0. Therefore, our results indicate that it is feasible to determine the surface parameters through the inversion of the model. The accuracy of the estimated surface parameters will essentially depend on the radiometric performance of the instrument as well on the performed atmospheric corrections, i.e., the determination of sc(h), Ruc(h) and Rdc. Accordingly, the performance of TTM was assessed taking into consideration the noise in SEVIRI channels IR 10.8 and IR 12.0 as well as the errors in the atmospheric profiles. The latter were based on the current ECMWF background error covariance matrix (Fillion & Mahfouf, 2000), and we have considered that the model based on Eq. (2) exactly describes the observed radiance and that the accuracy of the atmospheric correction does not depend on radiative transfer
Fig. 4. Relationship between LST and BT in channel IR 10.8 based on the set of simulated cases for three model atmospheres stored in MODTRAN4. For each model atmosphere, we represent the reference case (LST = Tatm) for five values of emissivity (middle line) as well as the two extreme cases (LST = Tatm F 5.0 K). Mid-Latitude Summer ( ), Mid-Latitude Winter (n) and Tropical (*). The dashed line indicates the upper bound of the imposed constrain on LST solutions.
.
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Fig. 5. Estimation of LST and LSE using 110 initial guesses. The dashed line delimits the space of admissible solutions.
model approximations. TTM performance was assessed based on the same simulated cases that were used to define the imposed constrain on LST. The used values for the noise equivalent delta temperature (NEDT) at 300 K for channels IR 10.8 and IR 12.0 were 0.11 and 0.15 K, respectively. These values are based on radiometric performances defined as short-term errors that include all factors (namely, random noise, stability of temperature of detectors, crosstalk and straylight, stability of gain and electromagnetic perturbation) affecting the radiometry during a single nominal repeat cycle (15 min duration) and applies to in-orbit conditions at End Of Live (EOL). The measured performance of SEVIRI is based on tests at satellite level that were complemented by a prediction of in-flight performances at EOL (Rogers, 2001). The abovementioned values of 0.11 and 0.15 were converted to 0.185 and 0.262 mW m 2 sr 1 (cm 1) 1, respectively, of noise equivalent delta radiance (NEDN). A simulation of the effects of satellite noise was then performed using a set of randomly generated signal level perturbations for each channel with normal distributions with zero mean and standard deviations equal to SEVIRI channel’s NEDN. Values of averaged error bias and RMSE for both welldetermined and overdetermined cases are shown in Table 2 for LST at time t1 and LSE in channel IR 10.8 but it is worth noting that the results are quite similar for all times and for both channels. In the well-determined case, values of averaged error bias (RMSE) for LST were 0.0 K (1.1 K), 0.1 K (2.0 K) and 0.1 K (0.8 K) for MLS, MLW and TROP, respectively, whereas for LSE estimation, the corresponding obtained values were 0.001 (0.030), 0.003 (0.040) and 0.006 (0.032). Figs. 7, 8 and 9 show histograms of errors for LST and LSE concerning MLS, MLW and TROP atmospheres. It may be noted that obtained results were almost the same for both well-determined and overdetermined cases suggesting that increasing the number of observations does not lead to significant improvements on
results. This aspect was emphasized in Peres and DaCamara (accepted for publication) when they have analyzed the effective rank of the problem and the degrees of freedom related to signal and to noise. Results also show that there is a negative correlation between the values of bias of LST and LSE, a feature that is expected to occur in simultaneous retrieval computations (Faysash & Smith, 1999, 2000). Because LST changes occurring every 15 min may be lower than the NEDT value, we have modeled the DCT following a method developed by Go¨ttsche and Olesen (2000). DCT was simulated in intervals of 15 min for three different types of surfaces, namely, continuous urban fabric, nonirrigated arable land and broadleaf forest (see Fig. 10). Results indicate that the LST difference for sequential observations is often lower than the NEDT value during nighttime and that, in such cases, the degrees of freedom of the measurement related to noise might be greater than those related to signal. On the contrary, combining observations with an interval of 1 h during daytime generally leads to
Fig. 6. Histogram of errors (estimation minus prescribed values) for LST at time t1 (a) and LSE in channel IR 10.8 (b). Bin sizes are 0.05 K and 0.001 for LST and LSE, respectively.
L.F. Peres, C.C. DaCamara / Remote Sensing of Environment 91 (2004) 377–389 Table 2 Results of sensitivity analysis related with signal-to-noise ratio for both well-determined and overdetermined cases Cases
Well-determined (2 times)
Overdetermined (11 times)
MLS LST RMSE 1.1 (K) Bias 0.0 LSE RMSE 0.030 Bias 0.001
MLW
TROP
MLS
MLW
TROP
2.0 0.1 0.040 0.003
0.8 0.1 0.032 0.006
1.0 1.8 0.8 0.0 0.1 0.1 0.028 0.037 0.032 0.001 0.002 0.005
Errors refer to LST at time t1 and LSE in channel IR 10.8.
adequate values of temperature difference (e.g., z 2.0 K). Brightness temperatures associated with modeled DCT were also computed for all atmospheric profiles and results suggest that differences in BT are good indicators for the choice of adequate time intervals between observations. Following Faysash and Smith (2000), a simple sensitivity study was first performed where the atmospheric parameters were perturbed by F 2%. Obtained errors for LST (LSE) were 3.6 K ( 0.04) for perturbations of 2%, and 2.1 K (0.01) for + 2%. The overestimation (underestimation) of LST in the case of negative (positive) perturbations is related to the fact that it compensates the respective decrease (increase) of the atmospheric parameters. As it was to be expected, an opposite behavior is observed with LSE. However, it is worth noting that the imposed perturbations of F 2% are not realistic because, on the one hand, atmospheric profile errors do not induce similar changes on
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the atmospheric parameters, and on the other hand, the transmittance sc(h) is negatively correlated with the upward and the downward atmospheric radiances Ruc(h) and Rdc; that is, an increase in sc(h) results in a decrease in both Ruc(h) and Rdc. A possible alternate way might consist in perturbing each level with values randomly taken from a normal distribution of zero mean and a standard deviation characteristic of the uncertainty. In this case, perturbations at a given level are assumed to be independent from those at others levels but such procedure is also not realistic. An extreme opposite procedure would be considering the perturbations to be perfectly correlated, e.g., by using perturbed profiles that are offset by given amounts (Tjemkes & Schemetz, 1998). In our case, we have decided to simulate more realistic perturbed profiles. Accordingly three sets of temperature and humidity perturbed profiles based on MLS, MLW and TROP were generated (see Fig. 11) based on the background error covariance matrix of the current operational 4D-Var data assimilation scheme at ECMWF. We have also computed the standard deviation for each vertical level (Fig. 12) and it may be noted that the minimum (maximum) error standard deviation for temperature occurs at the surface (stratosphere) for all profiles. Extreme values range from about 0.5 to 1.8 K for TROP and from 0.6 up to 4.9 K for both MLW and MLS. In the case of mixing ratio, the vertical profiles show a maximum of 2.2 g kg 1 at level 53 ( f 950 hPa) for TROP and 2.0 g kg 1 at level 49 ( f 850 hPa) for MLS. In the case of MLW, the profile of errors in standard deviation shows a
Fig. 7. Histogram of LST (upper panels) and LSE (lower panels) errors (estimation minus prescribed values) related with signal-to-noise ratio of channels IR 10.8 and IR 12.0 for MLS. Errors refer to LST at time t1 and LSE in channel IR 10.8. Left and right panels refer to the well-determined and the overdetermined cases, respectively. Bin sizes are 1.0 K and 0.02 for LST and LSE, respectively.
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Fig. 8. As in Fig. 7 but for MLW.
maximum of 0.6 g kg 1 at the surface and steadily decreases with height. The observed decrease of forecast errors of humidity near the surface may be explained by the low variability of humidity in the wet boundary layers (Fillion & Mahfouf, 2000). We have generated profiles with simultaneous perturbations on temperature and humidity, and in the case of MLS,
separate profiles of temperature and humidity were also considered in order to allow assessing the impact of each variable on the results. As shown in Table 3, values of averaged error bias (RMSE) for LST are less than 0.5 K (2.5 K), whereas for LSE, absolute values of averaged error bias (RMSE) are less than 0.010 (0.045). The previously mentioned negative
Fig. 9. As in Fig. 7 but for TROP.
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Fig. 10. Modeled DCT for continuous urban fabric (solid line), nonirrigated arable land (dotted line) and broadleaf forest (dashed line).
correlation between the bias in LST and LSE is worth noting again as well as the fact that increasing the number of observations does not contribute to obtain significant improvements on results. In the case of simultaneous perturbations on temperature and humidity, Figs. 13 –15 show histograms of LST and LSE estimation errors for MLS, MLW and TROP. As expected, the LST and LSE estimation errors due to perturbations on the humidity profiles are higher than those due to perturbations on temperature explaining the fact that the case of simultaneous
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Fig. 12. Standard deviation of errors of mass mixing ratio (solid curve) and temperature (dashed curve) for MLS (a), MLW (b) and TROP (c).
perturbations on humidity and temperature is very similar to the one when only humidity is perturbed.
4. Discussion and conclusions The major advantage of TTM is to enable for a simultaneous retrieval of LST and LSE. However, when using multitemporal methods such as TTM, one has to take into
Fig. 11. Comparison between the perturbed profiles (black curves) of temperature (upper panels) and humidity (lower panels) and respective reference profile (white curves) for MLS (left panels), MLW (middle panels) and TROP (right panels).
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Table 3 Results of sensitivity analysis related with perturbations imposed on atmospheric profiles for both well-determined and overdetermined cases Cases
Well-determined (2 times) a
LST (K) LSE
RMSE Bias RMSE Bias
b
Overdetermined (11 times)
MLS
MLS
MLS
MLW
TROP
MLSa
MLSb
MLS
MLW
TROP
1.0 0.1 0.020 0.002
2.0 0.5 0.034 0.006
2.1 0.5 0.035 0.006
2.4 0.2 0.045 0.005
2.5 0.3 0.040 0.010
0.9 0.1 0.019 0.002
2.0 0.5 0.034 0.005
2.1 0.5 0.034 0.005
2.2 0.1 0.041 0.004
2.5 0.4 0.039 0.008
Errors refer to LST at time t1 and LSE in channel IR 10.8. a Perturbation only on temperature profile. b Perturbation only on humidity profile.
account the technical problem related to the registration of multiple images from different times. These images should be spatially matched and the observations should be acquired with the same satellite-viewing angle. Because LST and LSE errors due to misregistration depend on the difference between the surface characteristics of the physical regions mistakenly matched, the error is expected to be small for homogeneous areas. Conversely, for heterogeneous areas, the error could be large depending on the variation of vegetation and soil proportions (i.e., mixed pixels) due to misregistration effects (Wan, 1999). Changes in the satellite-viewing angle will create differences in the projected surface that may lead to changes in magnitude of exposed bare soil, especially if the values of fractional vegetation cover are low. Currently, a large number of image-to-image registration algorithms is available in the literature (e.g., Brown, 1992; Fonseca & Manjunath, 1996; Le Moigne et al., 2002; Stone, 1999) and the selection of the most appropriate method depends on the type of data, the desired accuracy and the type of computing resources available (Le Moigne et al., 2002). Problems related to
registration are avoided when TTM is used with geostationary satellites like MSG because the satellite-viewing angle is always the same for each pixel. It is also worth emphasizing that TTM is especially adequate for MSG/ SEVIRI because of the advantages of high temporal frequency that contribute to mitigating the errors associated to the method hypothesis. Inversion methods that allow recovering both LST and LSE require independent atmospheric corrections, and therefore, both land surface parameters will strongly depend on atmospheric profile uncertainties. Vertical sounding instruments on-board satellites like the High Resolution Infrared Sounder (HIRS) and the Infrared Atmospheric Sounding Interferometer (IASI) provide simultaneous information of land surface measurements and vertical atmospheric profiles with a reasonable spatial resolution that may allow a suitable characterization of the atmosphere. In the case of instruments like the Moderate Resolution Imaging Spectroradiometer (MODIS) and IASI, it may be possible to estimate atmospheric temperature and water vapor profiles at 1 km resolution. Because there is no vertical sounding
Fig. 13. As in Fig. 7 but for perturbations imposed on MLS.
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Fig. 14. As in Fig. 13 but for MLW.
instrument on-board MSG, our estimations may be viewed as defining the base line for a preliminary assessment on the adequacy of algorithms to retrieve LST and LSE based on data with SEVIRI characteristics. Although TTM allows the separation of LST and LSE information from radiance measurements, and therefore, the solution may be uniquely determined by the data, the inverse problem is still an ill-posed problem because the
solution does not depend continuously on the data. The hypothesis assumed by TTM leads to a set of equations where the unknowns produce similar responses, and therefore, small perturbations in measurements (e.g., sensor noise, uncertainties in atmospheric profiles) may induce large errors in the solution. Accordingly, we have used a least-square optimization algorithm in order to stabilize the solution. The accuracy of the estimated surface parameters
Fig. 15. As in Fig. 13 but for TROP.
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was evaluated taking into consideration the noise in SEVIRI channels as well as the uncertainties in the atmospheric profiles that were based on the ECMWF background error covariance matrix. TTM has provided LST values with averaged error bias (RMSE) ranging from 0.0 to 0.5 K (from 0.8 to 2.5 K) for geographical – seasonal model atmospheres with water vapor content varying between 0.85 and 4.11 g cm 2. Obtained results suggest that TTM may be used as a complementary method to SW algorithms especially over areas where LSE is highly variable. Faysash and Smith (1999, 2000) have validated TTM using GOES8 measurements that were compared to in situ ground measurements made within the framework of the Atmospheric Radiation Measurement Program Cloud and Radiation Testbed (ARM CART). Because their validation conditions were totally different from ours, a direct comparison of results might be difficult. However, it is worth noting that their results are very similar to ours, and therefore, this may give a sounder indication on the performance of TTM. In that respect, LSE solution may be not stable enough because values of LSE averaged error bias (RMSE) range from 0.001 to 0.010 (from 0.028 to 0.045).
Acknowledgements We would like to thank the Institute for Applied Science and Technology of the Faculty of Sciences of the University of Lisbon (ICAT –FCUL) for providing the computing resources. The Portuguese Foundation of Science and Technology (FCT) has supported the research performed by the first author (Grant No. PRAXIS XXI/BD/21566/99). The research was performed within the framework of the Project Satellite Application Facility on Land Surface Analysis (LSA SAF), an R&D Project supported by EUMETSAT. The ASTER spectral library was available courtesy of the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California.
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