1. Introduction
The Earth faces in every moment with natural and human-induced changes and thus we have been striving to adapt to such changes for better life in future. Earth observing satellites and the remote sensing technology owing to advancements in science and technology allow us to continue to monitor the Earth. To predict the Earth’s climate and environmental changes by using a global numerical model, we need to prescribe the geophysical variables at present state. Surface temperature is one of such geophysical variables and known to be closely related to understanding the physical process of the exchange of energy and water on the Earth’s surface (Anderson et al., 2008). More importantly, because of its significance in the analysis of global warming, World Meteorological Organization (WMO) selects it as one of Essential Climate Variables (Bojinski et al., 2014).
Analysis of the surface temperature using the Earth observing satellites began with the operation of the Advanced Very High Resolution Radiometer (AVHRR) carried by the Television Infrared Observation Satellites (TIROS) and the National Oceanic and Atmospheric Administration (NOAA) satellites in the 1970s. The split-window algorithm (McMillin, 1975) using two thermal spectral bands of AVHRR has been widely used to derive the surface temperature. The advantage of the above algorithm is that we can calculate the surface temperature without any information of atmospheric profiles if we know the surface spectral emissivity a priori. However, we cannot apply this method for the Korea Multi-purpose Satellite (KOMPSAT)-3A infrared data since the KOMPSAT- 3A infrared payload instrument uses the single mid wave infrared (MWIR) spectral band for data acquisition. KOMPSAT-3A was successfully launched on March 25, 2015 by a Russian-Ukrainian Dnepr launch vehicle and carried two payload instruments that provide the multi-spectral images of 55 cm spatial resolution and the MWIR images of 5.5 m spatial resolution. KOMPSAT-3A MWIR measurements are made in the spectral range of 3.3–5.2 μm. It is important to note that the daytime measurements by MWIR sensors include both the reflected shortwave (0.2–5 μm) radiation and the emitted longwave (5–50 μm) radiation. Therefore, we should consider this point when calculating the surface temperature for this study.
In the past decades, a variety of algorithms has been developed to derive the surface temperature from satellite measurements (Gillespie et al., 1999; Li et al., 2013). Li et al. (2013) classified such algorithms into two categories with respect to the emissivity information: (1) retrieval algorithms with known emissivity (Cristόbal et al., 2009; Jiménez-Muñoz and Sobrino, 2003; Jiménez-Muñoz et al., 2009; Qin et al., 2001; Becker and Li, 1990; McMillin, 1975; Sobrino et al., 1994; Wan and Dozier, 1996; Prata, 1993; Sobrino et al., 1996; Sὸria and Sobrino, 2007) and (2) retrieval algorithms with unknown emissivity (Gillespie et al., 1999; Peres and DaCamara, 2005; Snyder et al., 1998; Valor and Caselles, 1996; Van de Griend and Owe, 1993; Sobrino and Raissouni, 2000; Jiang et al., 2006; Li and Becker, 1993; Li et al., 2000; Peres et al., 2010; Peres and DaCamara, 2004; Watson, 1992; Wan, 1999; Wan and Li, 1997; Barducci and Pippi, 1996; Gillespie et al., 1998; Gillespie et al., 2011; Borel, 1998; Borel, 2008; Wang et al., 2011; Aires et al., 2001; Aires et al., 2002; Wang et al., 2013; Li et al., 2007; Ma et al., 2000; Ma et al., 2002). They are also referred as deterministic and non-deterministic approaches, respectively (Hulley and Hook, 2011). We applied the first category of algorithm for this study. In addition, we note that a few studies were carried out regarding the derivation of surface temperature using the MWIR remote sensing data (Zhao et al., 2014; Tang and Wang, 2016), but even their studies are not the one applied the single spectral band data. Kim et al. (2019) recently demonstrated that the surface temperature can be retrieved from the MWIR single spectral band data of the National Aeronautics and Space Administration (NASA) Moderate Resolution Imaging Spectroradiometer (MODIS)/Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) airborne simulator (MASTER) (Hook et al., 2001). The purpose of this study is to derive the surface temperature from the KOMPSAT-3A MWIR data and further contribute to the development of surface temperature algorithms for the succeeding missions of KOMPSAT-7 and KOMPSAT-7A.
2. Methods and Data
We first introduce the physical principles of Planck’s law and the radiative transfer model and explain how to derive the surface temperature from the KOMPSAT- 3A MWIR data using these principles. We then describe the study area, KOMPSAT-3A satellite data, and some input data necessary for the radiative transfer model calculation.
1) Planck’s law and Radiative Transfer Model
Any object at an absolute temperature above 0 K emits the thermal radiative energy. According to Planck’s law, we can then express the emitted radiance (B), if the object is a blackbody, as follows:
\(B ( T ) = \frac { C 1 } { \pi \lambda ^ { 5 } [ e ^ { \frac { C 2 } { \lambda T } } - 1 ] }\) (1)
where λ is wavelength (m), T is surface temperature (K), C1 is 3.741775 × 10-22 W·m3·μm-1, and C2 is 0.0143877 m·K. Surface temperature obtained from Eq. (1) is the radiance temperature and known as skin temperature or brightness temperature. To calculate the surface temperature from Eq. (1) for any image pixel of interest, we should be able to derive B(T). B(T) is a component of the satellite observed TOA radiance that can be defined, at a given MWIR wavelength, as a sum of six components (Wan and Li, 1997; Schowengerdt, 2007):
\(\text {TOA radiance } = (L+1)_{TOA} = [\text {Ldir + Ldif +} \varepsilon B(T) +\rho \text {Idif]} \tau \text {+ Lpath + Ipath}\) (2)
where L and I represent radiances for shortwave (solar) components and longwave (infrared) components, respectively, Ldir is the unscattered (direct), surface- reflected solar radiance, Ldif is the down-scatterd, surface-reflected solar diffuse radiance, ε is surface emissivity, ρ is reflectance (1-ε, assuming Kirchhoff’s law), B(T) is the surface emitted radiance at surface (brightness) temperature (T), Idif is the downward atmospheric infrared radiance, τ is total transmittance, Lpath is the upward solar path radiance, and Ipath is the upward infrared path radiance (emitted by atmosphere). We can therefore derive B(T) while applying the MODerate resolution atmospheric TRANsmission (MODTRAN) radiative transfer model to solve Eq. (2).
For the above calculation, we used the MODTRAN 5.2 radiative transfer model (Berk et al., 2008) since it was available at work and efficient for the computational implementation. MODTRAN represents the U.S. Air Force standard moderate spectral resolution radiative transfer model for spectral range from the thermal infrared through the visible and into the ultraviolet (0.2 to 10,000 μm). MODTRAN uses a statistical band model to calculate spectral band transmittances, radiances, and fluxes. This statistical method is known to be in good agreement with the accuracy of a line- by-line algorithm: transmittance is generally better than ±0.005, thermal brightness temperature is better than 1 K, and radiance is approximately ±2%.
We need the input data for the MODTRAN radiative transfer model to calculate the surface emitted radiance from TOA radiance. Table 1 shows the major components of MODTRAN input data used for this study. For the atmospheric profiles such as pressure, temperature, and geopotential height, we used the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research reanalysis data, which were subsequently regenerated by NASA Goddard Space Flight Center (GSFC) for 26 pressure levels with 1- degree spatial resolution and 4-times daily temporal coverage. We then incorporated into the input data the KOMPSAT-3A Sensor Response Function (SRF), which was provided by a foreign vendor and classified into the restricted data by the Korea Aerospace Research Institute (KARI), and the values of the line-of-sight geometry as shown in Table 1. The Global 30 Arc- Second Elevation (GTOPO30) data from the United States Geological Survey (USGS) have been applied for surface elevation. The ground surface reflectance, one of important input data for the calculation of surface emitted radiances, will be described in Section 3) with more details.
Table 1. Major components of MODTRAN input data
2) Study Area and KOMPSAT-3A Satellite Data
To apply the radiometric calibration coefficients derived from the previous study (Kim, 2020), we use the same study area as before. The study area as shown in Fig. 1 includes the southern part of Salton Sea that lies in the southern California. It has different land cover types of natural objects such as water, sand, and agricultural (vegetated) land. We can therefore expect the various patterns of surface temperature produced from different land cover types due to their differences in surface emissivity. Salton Sea, meanwhile, has the merit of maintaining the NASA Jet Propulsion Laboratory (JPL) buoy (33.23°N, 115.82°W), where in-situ surface temperatures are measured every two minutes and can be used for comparisons with satellite derived results.
Fig. 1. KOMPSAT-3A level-1G image (590 x 685 pixels) data acquired over the southernmost part of Salton Sea in California on Nov. 14, 2015. This area of image serves as a study area.
The KOMPSAT-3A satellite acquired the image data of Fig. 1 on Nov. 14, 2015. The original spatial resolution of KOMPSAT-3A image data is 5.5 m, but they have been resampled to 30 m for public release. The current resampled image data consist of 590 × 685 pixels. Table 2 summarizes the coordinates of major points on the image. The radiometric quantization of each image pixel is 14 bits and thus the digital number (DN) of the image may range from 0 to 16,383. To retrieve the surface temperature from such KOMPSAT- 3A image data, we need to convert DN to the physical variable of radiance. We used the following Eq. (3) (Kim, 2020) to produce the TOA radiance image as shown in Fig. 2:
Table 2. Coordinates of KOMPSAT-3A level-1G image in Fig. 1
Fig. 2. KOMPSAT-3A MWIR TOA radiances (W·m-2·sr-1· μm-1) calculated by using Eq. (3).
\(TOA \text { radiance } = a \cdot DN ^ { 2 } + b \cdot DN + c\) (3)
where a=1.3e–8, b=–0.00015 and c=1.1. As mentioned earlier, we run the MODTRAN radiative transfer model employing the above TOA radiance image with other relevant data as input to calculate the surface emitted radiance and subsequently the surface temperature.
3) Emissivity Data
To perform the MODTRAN model calculation, we used the University of Wisconsin (UW) baseline fit emissivity database as an alternative input since no concurrent measurements for surface reflectance (i.e., – 1 emissivity) for KOMPSAT-3A image pixels at the time of its overpass were available. This database provides the global monthly emissivity map at 10 wavelengths (3.6, 4.3, 5.0, 5.8, 7.6, 8.3, 9.3, 10.8, 12.1, and 14.3 μm) with 0.05 degree spatial resolution (Seemann et al., 2008). The sources of the database are the NASA MODIS operational land surface emissivity product (https://www.icess.ucsb.edu/modis/EMIS/html/ em.html) and the laboratory measurements of surface emissivity such as the ASTER spectral library (Salisbury et al., 1994). The ASTER spectral library consists of data sources from the Johns Hopkins University spectral library, the NASA JPL spectral library, and the USGS spectral library.
Using the above UW emissivity (εi) database and the KOMPSAT-3A sensor response function (Ψi), we calculated the KOMPSAT-3A MWIR emissivity based on the following Eq. (4):
\(\varepsilon _ { \text { KOMPSAT-3A } } = \frac { \Sigma ( \Psi _ { i } * \varepsilon _ { i } ) } { \Sigma \Psi _ { i } }\) (4)
Fig. 3 shows the results of November 2015 for the global area (a) and for the present study area (b). It is notable that the emissivity pattern captures general features of natural materials in the southern California: high values over Salton Sea water, low values over sand (desert), and median values over agricultural land.
Fig. 3. KOMPSAT-3A MWIR emissivity of November 2015 derived from the UW emissivity database for the global area (a) and for the present study area (b).
3. Results and Discussion
Fig. 4 illustrates the surface temperature derived from the KOMPSAT-3A MWIR data using the MODTRAN radiative transfer model based on the method described in the previous section. As this time of image acquisition in the northern hemisphere shifts into winter, surface temperatures in the bottom left of lowland desert areas appear to be lower than those of Salton Sea and agricultural land. It is interesting to see that such differences between two areas cannot be found in the distribution of KOMPSAT-3A MWIR TOA radiances (Fig. 2). If we want to analyze this in detail, it is necessary to remind that 1) MWIR TOA radiances consist of reflected shortwave radiances and emitted longwave radiances and 2) surface temperature depends solely on the surface emitted longwave radiance.
Fig. 4. Surface temperature derived from the KOMPSAT3AMWIRdataofNov.14,2015usingtheMODTRAN radiative transfer model.
For the analysis of the above feature, we calculate the ratios of atmospheric radiances and surface emitted radiances to KOMPSAT-3A MWIR TOA radiances as shown in Fig. 5. We can see that the contribution of surface emitted radiances to TOA radiances is dominant and about 2 to 4 times larger than the atmospheric contribution. The above differences between two areas are also notable in the distribution of atmospheric and surface emitted components. This implies that these two components do not cause TOA radiances of lowland desert areas to be larger compared to other areas. Therefore, we will examine another important component contributing to TOA radiances, i.e., surface reflected radiances. As illustrated in Fig. 6, the differences between two areas reversely appear in the distribution of the ratio of surface reflected radiances to MWIR TOA radiances. The surface reflected radiances in lowland desert areas are relatively greater than Salton Sea and agricultural land. It becomes clear that surface reflected radiances significantly affecting MWIR TOA radiances result in differences of the geographical pattern between two areas. This example clearly demonstrates why we should be careful in the analysis of MWIR TOA radiances that include both shortwave and longwave radiation components.
Fig. 5. Ratios of (a) atmospheric radiances and (b) surface emitted radiances to KOMPSAT-3A MWIR TOA radiances.
Fig. 6. Ratio of surface reflected radiances to KOMPSAT3A MWIR TOA radiances.
Due to the lack of satellite-derived surface temperature data (e.g., Landsat and MODIS products) over the study area, we will make simple comparisons with available data. In-situ data are available at two websites: 1) Salton Sea (https://saltonsea.jpl.nasa.gov/) operated by NASA JPL based on buoy measurements 2) Sea Temperature Info (https://seatemperature.info/) based on satellite and in-situ data. Table 3 summarizes the comparisons of the KOMPSAT-3A MWIR estimate with the above data. The surface temperature extracted from the NASA JPL field data is the measured value close to the KOMPSAT overpass time (about 13:41 p.m.) and the KOMPSAT-3A MWIR estimate is the value of nearest-neighbor pixel (located at about 14 km southeast of the NASA JPL buoy). The results show that the current estimate is lower than the NASA JPL field data and Salton Sea data, differing by 2.2 K and 1.4 K, respectively. Although many factors including colocation issues among measurements and characteristics inherent in each data seem to make such differences, it is not possible to quantify them in detail.
Table 3. Comparisons of surface temperature over Salton Sea
4. Conclusions
Retrieval of the surface temperature from satellite infrared data is important in their applications and services. We have attempted to derive the surface temperature from KOMPSAT-3A MWIR data acquired over the southern California on Nov. 14, 2015, using the MODerate resolution atmospheric TRANsmission (MODTRAN) radiative transfer model. As described previously, we used the relevant input data for MODTRAN model such as UW emissivity, NCEP atmospheric profiles, and the solar and line-of-sight geometry at the time of KOMPSAT-3A overpass over the above area. Results of surface temperature reasonably demonstrated the seasonal geographical patterns over water, sand, and agricultural land: i.e., warmer surface temperatures (higher values) in Salton Sea and agricultural land relative to lowland desert areas. Such patterns are seen to be closely related to the surface emitted longwave radiances but cannot be found in the distribution of MWIR TOA radiances. We demonstrated in a subsequent analysis that surface reflected radiances affect more MWIR TOA radiances than surface emitted radiances do. This is why we should be careful in the analysis of MWIR TOA radiances that include both shortwave and longwave radiances, unlike typical thermal infrared radiances. For simple validation purposes, we compared the current estimate with two other measurements of NASA JPL field data and Salton Sea data. The current estimate differs with these datasets by 2.2 K and 1.4 K, respectively. Although many factors including colocation issues among measurements and characteristics inherent in each data might contribute to such differences, it is not possible to quantify them in detail. We rather suggest the future study on the validation of surface temperature derived from KOMPSAT-3A MWIR data in a comprehensive and systematic manner.
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