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Land surface temperature (LST) is one of the key parameters in the physics of land surface processes at local/global scales. In this paper, a LST retrieval method was proposed from airborne multispectral scanner data comparing one mid-infrared (MIR) channel and one thermal infrared (TIR) channel with the land surface emissivity given as a priori knowledge. To remove the influence of the direct solar radiance efficiently, a relationship between the direct solar radiance and water vapor content and the view zenith angle and solar zenith angle was established. Then, LST could be retrieved with a split-window algorithm from MIR/TIR data. Finally, the proposed algorithm was applied to the actual airborne flight data and validated with in situ measurements of land surface types in the Baotou site in China on 17 October 2014. The results demonstrate that the difference between the retrieved and in situ LST was less than 1.5 K. The bais, RMSE, and standard deviation of the retrieved LST were 0.156 K, 0.883 K, and 0.869 K, respectively, for samples.
© 2015 Optical Society of America
1. Introduction
Land surface temperature (LST) plays an important role in land-surface processes on regional and global scale [1–3 ]. LST is also a good indicator for studying the greenhouse effect and the energy flux between the atmosphere and the ground [4,5 ]. However, it is impractical to obtain LST values over large areas using ground measurements due to the complexity of land surfaces. Fortunately, satellite data offer the possibility of measuring LST over the globe with sufficiently high temporal resolution and complete spatially averaged rather than point values with the development of remote sensing technology [6].
Many methods have been proposed to estimate LST from thermal infrared (TIR) remotely sensed data, such as the single channel algorithm [7], split-window algorithm [1,8–12 ], day/night algorithm [13,14 ], temperature-independent spectral index algorithm [15], spectral ratio [16], maximum–minimum difference (MMD) method [17], ASTER TES method [18], et al. Meanwhile, the studies on LST retrieval from mid-infrared (MIR) and TIR data have also been conducted. A split algorithm with three TIR channels and one MIR channel was proposed by [19] to retrieve LST from Spinning Enhanced Visible and Infrared Imager (SEVIRI) data. The Visible Infrared Imaging Radiometer Suite (VIIRS) workgroup developed a dual split window day/night LST algorithm using 2 TIR bands (10.8μm and 12μm) and 2 MIR bands (3.75μm and 4.0μm) in which a solar zenith angle cosine correction during the daytime was used to correct the solar radiation [20]. Theoretically, the main difficulty in LST retrieval from the MIR data is that the radiance measured during daytime in the MIR spectrum contains not only the thermal radiation emitted by the surface, but also the solar radiation reflected by the surface. Therefore, the removal of solar radiation is an essential requirement for LST retrieval. Prior knowledge of accurate atmospheric and surface bidirectional reflectance information should also be supplied to improve the retrieval accuracy.
The objective of this study is to develop a method to retrieve LST from one MIR channel (3.7~4.8μm) and one TIR channel (7.7~9.5μm) from airborne flight data. This paper is organized as follows: Section 2 describes the LST retrieval method using MIR and TIR channels. Section 3 introduces the study area, flight data and the in situ data. The proposed method is applied to simulated and actual flight data in Section 4. The conclusion is drawn in Section 5.
2. Methodology
2.1 Basic theory
Under local thermodynamic equilibrium during a clear-sky day, the radiative transfer equation (RTE) in the MIR region (3~5μm) can be written as [6,15 ]:
Without the effect of solar radiation, RTE in TIR region (8~14μm) can be written as:
where is the radiance measured by thermal sensor in channel i and is the Planck function. is the brightness temperature. and are surface emissivity and temperature, respectively. is the atmospheric transmittance from ground to sensor. and are the upwelling and downwelling atmospheric radiance, respectively. and are the upwelling and downwelling solar diffusion radiance from the atmospheric scattering of solar radiance. is the surface bidirectional reflectance. is the solar radiance at ground level, where is the solar irradiance at the top of the atmosphere (TOA). is the atmospheric transmittance from the sun to the ground. , , and are the viewing zenith angle, solar zenith angle, and azimuth angle, respectively.Equation (1) can be rewritten as follows:
where is the radiance after extracting the reflected solar direct radiance, is the equivalent brightness temperature. includes the surface-leaving radiance and the upwelling and downwellling atmospheric/solar diffusion radiance. is the direct solar radiance, which does not include the influence of surface bi-directional reflectance.2.2 LST retrieval method from MIR and TIR channels
From RTE, the daytime MIR radiance contains not only the radiance emitted by the land surface and atmosphere but also the solar radiance reflected by the land surface. To retrieve LST from MIR and TIR data, the direct solar radiance should be estimated first to eliminate the effect of solar radiation, and then a split window method is developed to estimate the LST with the radiance that eliminate the solar direct influence ().
2.2.1 Estimation of direct solar radiance in the MIR spectrum
To retrieve LST from the daytime MIR data, the estimation of direct solar radiance is the premise becasue the measured radiance will be strongly affected by solar. It is also a difficult task because the direct solar radiance portion in RTE is coupling of the bi-directional reflectivity of the surface (), the solar radiance at ground level () and the transmittance from the ground to the sensor ().
From the previous study, the atmospheric transmittance can be expressed as a function of water vapor content (WVC) [21]:
where the fitting coefficients a, b, c are functions of the viewing zenith or solar zenith angle. The atmospheric transmittance from the ground to the sensor had a proportional relation to under the same atmospheric conditions (Fig. 1 ). In addition, it can be seen from the solar radiation, i.e., , the direct solar radiation reaching the surface in the MIR channel can be expressed as a linear function of cosine of SZA.
Fig. 1 The statistical relationship between cos(SZA) or 1/cos(VZA) and the direct solar radiation simulated by MODTRAN code under the Mid-Latitude Summer atmosphere.
The MODTRAN 4.0 radiative transfer code was used to simulate the radiances in terms of the channel filter functions to obtain the coefficients. The VZAs were set to be 0°, 33.56°, 44.42°, 51.32°, 56.25°, and 60° (corresponding values of 1/cos(VZAs) were 1, 1.2, 1.4, 1.6, 1.8, and 2.0), respectively, to have 1/cos(VZAs) sampled with a step of 0.2. The SZAs were set as 0°, 25.84°, 36.87°, 45.57°, 53.13°, and 60° (cos(SZAs) are 1, 0.9, 0.8, 0.7, 0.6, and 0.5, respectively). In total, 705 atmospheric profiles with the atmospheric bottom temperature (Ta) of 250~310 K and the WVC of 0.06~5.39 g/cm2 extracted from the TOVS Initial Guess Retrieval (TIGR) database, and six MODTRAN standard atmospheres were used for the analysis. Figure 1 is the simulated result under the Mid-Latitude Summer atmosphere.
The direct solar radiance in Eq. (3) can be expressed as the function of WVC, SZA and VZA [21]:
where and are fitting coefficients.It is assumed that the surface is Lambertian and that the bi-directional reflectivity of the surface () can be estimated by surface emissivity (εi), i.e., = (1-εi)/π. The direct solar radiance reaching the sensor can be calculated by.
2.3.2 LST retrieved from MIR and TIR channels
Based on the differential atmospheric absorption in two TIR channels in 10~12.5μm, a split window method was improved for LST retrieval from the TIR data by expressing LST as a linear function of the brightness temperatures Ti and Tj measured in the two adjacent TIR channels. In consideration of the similar RTEs in MIR and TIR without the influence of solar direct radiance, this paper extends the split-window method to the MIR and TIR spectral region for LST retrieval without the effect of direct solar radiance. The method is expressed as:
with , .where , , , , , and are fitting coefficients which can be derived from simulated data. and are the TOA equivalent brightness temperatures in one TIR channel and one MIR channel. and are the LSEs in channel and , respectively. ε is the averaged emissivity, and is the emissivity difference between the MIR and TIR channels.
It should be noted that from Eq. (3) and (4) with the definition of T' the method removes the dependence of the RTE on the solar direct radiance, but it still contains dependence on the solar diffuse irradiance that is not removed at all. In this paper, the determination of the coefficients of the split-window algorithm considers the impact of the solar diffuse irradiance.
3. Study area and data
3.1 Study area
To evaluate the in-flight performance of the remote sensing data obtained with thermal sensors onboard an airborne platform, a comprehensive field campaign was carried out at the Baotou site on 17 October 2014. The Baotou site (Fig. 2 ) is located in Urad Qianqi, Inner Mongolia, in northern China at a latitude of 40.85°N and a longitude of 109.6°E [22]. The land covers in the study area included cropland, herbaceous land, trees, shrubland, grassland, sparse vegetation, urban areas, bare ground and water body. Ulansuhai Lake is the only body of water body that is located in the northwestern section of the study area; its temperature measured at the time of the airborne overpass was used to validate the retrieval results by using our proposed method. The Baotou site receives little precipitation and has a high percentage of cloud-free days. The study area has a continental climate that is characterized by four seasons and a large diurnal temperature variation. The annual average temperature and rainfall are 6~7°C and 200~300 mm, respectively. It has an average ground elevation of 1290 m above sea level. During the field campaign, the flight altitude was 1.7 km above ground level, obtaining a swath width of 0.6 km and the spatial resolutions of the MIR and TIR sensors were 2 m.
3.2 Airborne data
The MIR and TIR sensors were developed by the Shanghai Institute of Technical Physics, Chinese Academy of Sciences. Both sensors are array cameras (320 × 256 detectors). The main specifications of the sensors are presented in Table 1 .
Table 1. Main specifications of the thermal sensors
Figure 3 shows the main study area from airborne images acquired on October 17, 2014 at 12:40 (local time), and the artificial permanent target area and the portable target area are highlighted. The permanent targets are composed of a knife-edge target and a fan-shaped target. The knife-edge target consists of four uniform regions, with the same size of 48 m × 48 m and can be used in radiometric calibration, dynamic range and response linearity assessments for optical payloads.
Fig. 3 The main study area of Baotou site. The images were obtained from the at-sensor radiance in visible bands acquired on October 17, 2014 at 12:40 (local time).
3.3 In situ data
(1) Targets and in situ LST measurements
Field campaigns are very important for validating or testing the algorithms developed for retrieving a certain biogeophysical parameter from spaceborne or airborne data [23]. Ground LST measurements for the validation of airborne-derived LST products were performed at the Baotou site during the field campaign in 2014. Because most of the Earth's surface is heterogeneous, high-quality ground validation data are limited to few surface types, such as lakes, silt playas, grasslands and agricultural fields in dedicated campaigns [24–26 ]. Moreover, it is also necessary to observe the surface at several points to reduce measurement uncertainty.
Several natural scenes (Fig. 4 ), including water body, bare soil, sand and vegetation, together with the white gravel permanent target and the black portable target, were chosen at the test site to evaluate the LST retrieved from the MIR/TIR data. It should be noted that permanent targets are paved with white, gray and black gravel. However, in this campaign, only the white gravel target is used because the minimum diameter of 10 mm of the white gravel renders it the best uniform of the surface. The emissivity of the white gravel surface is higher than 0.9 in the MIR and TIR spectra.
At the Baotou site, the in situ ground LST measurements were carried out simultaneously with the flight. Several ground radiometers were distributed within the area and deployed at nadir to capture the natural variability of ground LSTs, and the temporal sampling interval was 1 second. Then, the continuous measurements were averaged to determine LST. SI-111 thermometers with a spectral range of 8~12 µm were used to measure the temperature of the soil, sand, vegetation, white gravel, and black portable target. The temperatures of the water body were measured by 4 KT-15 thermometers fixed on a hemispherical frame (Fig. 4a). The surface temperature was measured at an altitude of approximately 1.5 m. Table 2 describes the main characteristics of the measurement targets. Table 3 summarizes the main technical characteristics of the thermal instruments. Emissivity measurements were performed using a 102F Fourier Transform Infrared Spectroradiometer (FTIR) with a spectrum covering from 2 to 16 μm, a spectral resolution of 4 cm−1, and a field of view (FOV) of 4.8°.
Table 2. Main specifications of the measurement targets
Table 3. Main technical specifications of the thermal instruments
(2) Atmospheric profile
During the ground LST measurement campaigns, a radiosonde balloon with standard instruments was launched half an hour before the plane overpass to obtain the atmospheric temperature and water vapor profiles. The balloon reached a height of 10 km within one hour. Local radiosondes provide an accurate description of the atmospheric state spatially and temporally coincident with the airborne measurement. These parameters were provided in 50 pressure levels with an interval of 200 m.
(3) Water vapor content
To estimate the surface temperature from the airborne flight data, the WVC was also measured with an automatic CIMEL CE-318 sunphotometer with nine channels at nominal wavelengths of 340, 380, 440, 500, 670, 870, 936, 1020, and 1640 nm. The WVC was derived using the Angstrom law. The measured value of WVC at the time of the airborne data acquisition was 0.72 g·cm−2.
4. Results and discussions
4.1 Result of the estimated direct solar radiance
From Eq. (6), the direct solar radiance including transmittance term can be estimated as the function of WVC, SZA and VZA, and the fitting coefficients can be obtained from the simulated data (see Table 4 ). Figure 5 shows the scattering figure of the estimated and true direct solar radiance simulated by MODTRAN using TIGR atmospheric database in MIR channel to evaluate the accuracy of direct solar radiance for wet- and dry-atmospheres. The root mean square errors (RMSE) were 0.0084 and 0.0102 W/(m2·sr·μm), and the correlation coefficients (Rs) are 0.999 and 0.987 for WVC of 0~1.5 g/cm2 (dry atmosphere) and 4~5.5 g/cm2 (wet atmosphere), respectively. Clearly, good accuracy can be obtained from this method. Compared with wet atmosphere, a better accuracy is shown in dry atmosphere
Table 4. Fitting coefficients for the direct solar radiance estimation
4.2 Result of LST retrieval from simulated data
To develop the LST retrieval method, the at-sensor radiances should be simulated. The radiative transfer code MODTRAN 5.0 was used to obtain the radiances for the MIR and TIR channels in terms of the spectral response functions. In total, 705 atmospheric profiles, which extracted from the TOVS Initial Guess Retrieval (TIGR) database with an atmospheric bottom temperature (Ta) of 250~310 K and a WVC of 0.06~5.39 g/cm2 were used to develop the algorithm. The surface temperatures were changed from Ta-5 K to Ta + 15 K with a step of 5 K. Seventy different emissivities from the Johns Hopkins University (JHU) Spectral library, including soils, vegetation, and water, were used in the simulation. The VZAs were set as 0°, 33.56°, 44.42°, 51.32°, 56.25°, and 60°, respectively, and the SZAs were set as 0°, 25.84°, 36.87°, 45.57°, 53.13°, and 60°, respectively.
Figure 6 shows the RMSEs between the simulated and estimated LST as functions of the secant VZA for different sub-ranges using the simulated data. For two water vapor sub-ranges, 0~1.5 g/cm2 (dry atmosphere) and 4~5.5 g/cm2 (wet atmosphere), the RMSEs were less than 1.3K for dry atmosphere, and less than 2.8K for wet atmosphere. We can see that for dry atmosphere the retrieval accuracy was good; however, its accuracy was slightly lower for wet atmosphere. In addition, the RMSEs increased with VZA.
LSE is the key input parameter to retrieve LST, and its uncertainty will be influenced on the retrieval accuracy of LST [27]. A Gaussian random distribution error, where the mean of the distribution was 0 and the standard deviation is 0.01, was added to emissivities. Table 5 shows the effect of emissivity on the accuracy of LST retrieval at the condition of VZA = 0°. The LST retrieval errors were the difference between the LSTs retrieved from LSE-uncertainty-added conditions and those determined from no-LSE-uncertainty conditions, and its errors varied from 0.59 K to 0.99 K by assuming that the uncertainty of the emissivity was 0.01. Figure 6 shows the retrieval accuracy for dry atmosphere better than that of wet atmosphere, while Table 5 gives that the effect of emissivity uncertainty on the LST retrieval errors is similar for dry- and wet- atmospheres, except high temperature condition (305~320K).
Table 5. Effect of the emissivity uncertainty (Δε = 0.01) on LST retrieval (VZA = 0°)
4.3 Validation based on ground LST data
4.3.1 Data processing
In this study, the method was applied to flight data on October 17, 2014 over the study area in Baotou covered by vegetation, water, sand, and bare soil. Due to the influence of the attitude and speed of spacecraft and the Earth's rotation, the image would undergo a certain degree of geometric distortion, such as compression, distortion, stretching and offsetting, compared with the actual position of ground target pixels. Hence, to obtain an accurate location of the image pixels, an elastic band-to-band registration method proposed by [28] was used for the airborne MIR and TIR images. As a key input parameter for LST retrieval, LSE was estimated by the supervised classification method. Six categories, i.e., vegetation, water, roads, building, sand and bare soil, have been classified. The LSEs in the MIR and TIR channels were obtained by integrating emissivity spectral curves measured by 102F with spectral response function. The SZA for every pixel can be calculated using an equation, i.e., , with the information on latitude and longitude, where θ is the solar zenith angle. h is the hour angle at the local sidereal system. δ is the solar declination. is the local latitude. The VZA of each pixel can be acquired according to the field of view (FOV) of the sensor and the pixel numbers. WVC can be extracted from the atmospheric profiles acquired by radiosonde at the imaging time. After data processing, the LSTs can be derived using Eq. (6) and validated with in situ measurements over these targets.
4.3.2 LST estimation from ground-based measurements
It should be noted that the in situ temperature data collected by KT-15 or SI-111 thermometers are the brightness temperatures at ground level () rather than the actual surface temperature (). From RTE, because at ground level τ≈1 and ≈0 are assumed, the surface emissivity values (ε) can be measured in situ, and the relationship between and can be expressed by:
where is the land surface emissivity, is the downwelling atmospheric radiance, and B is the Planck function. Downwelling atmospheric radiance can be calculated by MODTRAN 5.0 using the atmospheric profile measured by radiosonde. To obtain the actual LST, the measurements made by the broadband KT-15 or SI-111 instruments must be corrected for the downwelling atmospheric radiance. First, given an estimated surface temperature, the at-surface spectral radiance was calculated using Eq. (8) with the downwelling spectral radiance and the measured emissivity. Then, the broadband radiance was obtained by integrating the spectral radiance with the response function of the instruments at a given temperature. Finally, this temperature was iteratively adjusted until the calculated radiance was equal to the measured radiance, and this final temperature was the actual LST of the targets [27].4.3.3 Validation
The in situ land surface temperature measurements of the six targets were used to evaluate the accuracies of the method of the flight data. From the flight data, it can be seen that due to the small size of the portable black target and the significance of temperature difference between the target and the background, the adjacent effect will introduce large influences on validation. Thus, the portable black target was not used for validation in the following. For the other five targets, the pixels were selected to yield the average temperature with the temporal strategy of ± 5 min and spatial sampling strategy of 5 × 5 pixels centered on the measurement targets. Each target was covered by two flight strips during the flight period. Table 6 provides the detailed view time of each target.
Table 6. Validation results in the study area
Figure 7 and Table 6 are the retrieved and measured LSTs, which show a better agreement. The bais, RMSE and standard deviation (STDEV) of the retrieved LSTs were 0.156 K, 0.883 K, and 0.869 K, respectively for all the five samples, including water, bare soil, vegetation, sand, white gravel. The differences between the retrieved and in situ LST were smaller than 1.5 K. Vegetation and water body show the best validation results with errors of less than 1.0 K. It should be noted that the white gravel used for validation shows a better accuracy of less than 1.5K.
Fig. 7 Comparison of the LST retrieved using our proposed method with the validating LST for different samples.
5. Conclusions
In this study, a new algorithm for LST retrieval is proposed from airborne flight data in one MIR and one TIR channel. To retrieve LST more accurately, two steps were followed: first, the relationship between the direct solar radiance and the atmospheric WVC, VZA, and SZA, was established to remove the influence of direct solar radiance in MIR spectrum. The RMSEs of direct solar radiance were 0.0084 and 0.0102 W / (m2·sr·μm) for dry atmosphere and wet atmosphere, respectively. A high accuracy of estimated direct solar radiance was obtained in this paper. Second, a split-window algorithm was proposed to remove the atmospheric effect and retrieve the land surface temperature. Finally, the proposed algorithm was applied to actual flight data and validated with in situ measurements for various land surface types. The validation results showed a better accuracy between the estimated and measured LST, and were smaller than 1.5 K. It indicates that the proposed method is helpful in estimating land surface temperature, and also solves the problem of solar radiation with the aid of land surface emissivity as a priori knowledge. Future work will focus on more airborne and spaceborne sensors, such as TASI, AHS, MODIS, and VIIRS.
Acknowledgments
This work was supported partly by the National Natural Science Foundation of China (NSFC) under Grant 41371353 and by the National High Technology Research and Development Program of China under Grant No. 2014AA123201 and No. 2014AA123202. The authors thank the anonymous referees for their comments and suggestions, which have significantly improved the article.
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