Surface Temperature Retrieval from MASTER Mid-wave Infrared Single Channel Data Using Radiative Transfer Model

Abstract

Surface temperature has been derived from the MODIS/ASTER airborne simulator (MASTER) mid-wave infrared single channel data using the MODerate resolution atmospheric TRANsmission (MODTRAN) radiative transfer model with input data including the University of Wisconsin (UW) emissivity, the National Centers for Environmental Prediction (NCEP) atmospheric profiles, and solar and line-of-sight geometry. We have selected the study area that covers some surface types such as water, sand, agricultural (vegetated) land, and clouds. Results of the current study show the reasonable geographical distribution of surface temperature over land and water similar to the pattern of the MASTER L2 surface temperature. The thorough quantitative validation of surface temperature retrieved from this study is somehow limited due to the lack of in-situ measurements. One point comparison at the Salton Sea buoy shows that the present estimate is 1.8 K higher than the field data. Further comparison with the MASTER L2 surface temperature over the study area reveals statistically good agreement with mean differences of 4.6 K between two estimates. We further analyze the surface temperature differences between two estimates and find primary factors to be emissivity and atmospheric correction.

1. Introduction

Surface temperature is an essential variable necessary to understand the physical process of the exchange of energy and water on the Earth’s surface (Anderson et al., 2008). It also helps to analyze the climate change such as global warming and thus is selected as one of Essential Climate Variables by the World Meteorological Organization (WMO). Scientists want to find how an increase of greenhouse gases in the atmosphere influences the melting of glacier and the natural ecosystem. Such global monitoring of environmental changes requires the remote sensing of surface temperature from space with adequate spatial and temporal resolution.

Monitoring of surface temperature began with the analysis of data from the Advanced Very High Resolution Radiometer (AVHRR) carried by the Television Infrared Observation Satellites(TIROS) and the National Oceanic andAtmosphericAdministration (NOAA) satellites in the 1970s. Thereafter, there have been numerousstudies on surface temperature retrieval using thermal infrared (TIR) data (Prata et al., 1995; Li et al., 2013).According to Li et al.(2013), the methods ofsurface temperature retrieval can be categorized into two groups: retrieval with known emissivity and retrieval with unknown emissivity. The retrieval with known emissivity has further classification depending on the number of available spectral channels. On the other hand, a few studies of surface temperature retrieval using mid-wave infrared (MWIR) data have been performed (Zhao et al., 2014; Tang and Wang, 2016) but these are not the single-channel method.This study pertainsto the single-channel method.The use of MWIR channel seems to have pros and cons. The MWIR channel provides a potential advantage in surface temperature retrievalsince it is considered less sensitive to errors in emissivity determination than the TIR channel (Salisbury and D’Aria, 1994; Mushkin et al., 2005). On the contrary, a major disadvantage isthat MWIR measurements include both solar and thermal components. Therefore, it requires the subtraction of solar components when retrieving surface temperature. In this study, we seek to implement such concept to derive surface temperature from the MWIR single channel (e.g., KOMPSAT MWIR) data by using radiance components calculated from the radiative transfer model.

2. Method and Data

We first examine the features of atmospheric gas absorption that are essential to understand the basic principles of remote sensing. Fig. 1 shows the atmospheric transmittance in association with atmospheric gas absorption in the MWIRspectralrange (3-5 μm).It is notable to see the following two features: 1) no transmission occurs in between 4.2 μm and 4.4 μm due to strong CO₂ absorption, 2) atmospheric window exists in the 3.5-4.1 μm range. More details about atmospheric gas absorption can be found in the literature (Goody and Yung, 1989).

Fig. 1. Atmospheric transmittance in association with species in the MWIR spectral range. The MODTRAN radiative transfer model uses the following input conditions: US standard atmosphere with no clouds and rain, solar zenith angle of 60°, surface reflectance of Algodones Dunes.

1) Method

To derive the surface brightness temperature from the Earth-atmosphere system, we need to understand the radiative transfertheory and Planck’slaw.The basic radiative transfer equation takes the following form (Chandrasekhar, 1960):

\(-\frac{d I}{\kappa \rho d s}=I-\frac{j}{\kappa}\)       (1)

where I, j, κ, ρ, and s represent the specific intensity (radiance), the source function coefficient, the mass absorption coefficient, the density of the material, and the path length,respectively. Planck’slaw describesthe blackbody radiance as a function of wavelength and temperature as follows:

\(\mathrm{B}(\mathrm{T})=\frac{C 1}{\pi \lambda^{5}\left[e^{\left.\frac{C 2}{\lambda T}-1\right]}\right.}\)       (2)

where λ = wavelength (m), T = temperature (K), C1 = 3.741775×10^-22W·m³ ·μm^-1 , andC2 = 0.0143877 m^·K.

We retrieve the surface brightnesstemperature using the above principle and Planck’s law. This study focuses on the surface brightnesstemperature retrieval based on the single channel MWIR measurements, assuming the surface emissivity to be given. The surface brightness temperature means the black body temperature (T) in Equation (2).

The radiative transfer modelsimulatesthe observed radiance (L_obs) by sensor with realistic atmospheric profiles,surface properties, and sensorresponse function. The following sensorresponse function (SRF) has been incorporated:

\(\text { Lobs }=\frac{\int \psi(\lambda) L(\lambda) \mathrm{d} \lambda}{\int \psi(\lambda) d \lambda}\)       (3)

where ψ = SRF and L(λ) = totalradiance incident upon sensor (W/m² /sr/μm). Using these calculated radiative components, we estimate the black body radiance at surface and then calculate the surface brightness temperature.

We have used the MODTRAN 5.2 radiative transfer model with the relevant input data to calculate the radiation components. MODTRAN (Berk et al., 2008) represents the U.S. Air Force standard moderate spectral resolution radiative transfer model forspectral 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, radiance, 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%

2) Remote Sensing Data

As for the observed remote sensing data, we have used the MASTER data in the MWIR spectral range (Hook et al., 2001). Some characteristics of the MASTER instrument and spectral information are given in Table 1 and Table 2, respectively. More information on ancillary and calibration is available on the MASTER website (https://master.jpl.nasa.gov/). Although the total number of the MASTER MWIR channels is 15 from channel 26 to channel 40, we selected the channel 38 (4.9672 μm) due to the availability of emissivity data and the atmospheric absorption.

Table 1. Characteristics of the MASTER Instrument

Table 2. Spectral Information of the MASTER MWIR Channels

Fig. 2 showsthe MASTERlevel-1Bbrowse images acquired by ER-2 aircraft on May 28, 2015. The entire image strip consists of 716 pixels (cross-track) by 12,209 scan lines(along-track); however,forsimplicity, we illustrate some portion of the image including our study area.The image includesthe Salton Sea area and the part ofAlgodones Duneslocated in the southeastern portion oftheCalifornia.The sand dune region appears to be bright white on visible and dark (hot) on infrared. Instead, Salton Sea is dark on visible and white (cold) on infrared. We can also identify the low-level clouds over the southern part of Salton Sea as seen in browse images, except the 11.18 μm case.

Fig. 2. The MASTER level-1B browse images acquired on May 28, 2015 over the Salton Sea of Southern California: flight number 15-943-00, track number 7. Note that the top of the image points toward southeast.

To demonstrate the results for different surface types within reasonable computational hours, we selected the study area of 716 × 716 pixels asshown in Fig. 3. It containssome surface types: i.e., water,sand, agricultural (vegetated) land, and clouds. It also includesthe NASAJPLSalton Sea buoy (33.22532°N, 115.82425°W), where in-situ surface temperatures are measured every two minutes. The numeric values in Fig. 3 represent the observed radiances by MASTER channel 38 (4.9672 μm). The pattern appears to be similar to that of MWIR channel 30 in Fig. 2.

Fig. 3. Study area (716 × 716 pixels) depicting the radiance values observed by the MASTER channel 38.

3) MODTRAN Input Data

The MODTRAN input data are composed ofsensor response, atmospheric profiles, line-of-sight geometry, and ground surface properties. The accuracy, temporal and spatialresolution ofthe input data affect the quality of MODTRAN output and thus the surface brightness temperature.

Fig.4 showstheMWIRMASTERSRFsimplemented in the MODTRAN model. Note that the curve for channel 26 is the same as channel 32 and thus only 14 curves are displayed.The atmospheric absorption in the path length of the lab measured SRF curves has been removed and smoothed at the NASAAmes Research Center.

Fig. 4. SRFs for the MASTER MWIR channels

To provide the atmospheric profilessuch as pressure, temperature, and geopotential height, we employed the NCEP/National Center for Atmospheric Research (NCAR) reanalysis data, which were subsequently regenerated by NASA/GSFC for 26 pressure levels with 1 degree spatial resolution and 4-times daily temporal coverage. For the line-of-sight geometry information, we used the MASTER ancillary data that included aircraft altitude, pixel elevation, solar zenith angle,sensor zenith angle, and solar azimuth angle.The solar zenith and azimuth angles at the time of observation are 15.3 and 219.2 degrees, respectively. Since no in-situ measurements for surface reflectance or emissivity at the time of the MASTER data acquisition are available, we used the UW baseline fit emissivity database as an alternative. These data have 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 (MOD11) and the laboratory measurements ofsurface emissivity such as the ASTER spectral library. The ASTER spectral library therein includes data from the Johns Hopkins University spectral library, the Jet Propulsion Laboratory spectral library, and the U.S. Geological Survey spectral library. Since the center of the MASTER channel 38 (4.97 μm) is close to 5.0 μm, we used the surface emissivity data for 5 μm asshown in Fig. 5. Despite the spatial resolution, it appears to capture the emissivity features of natural materials.The maximum value of emissivity (0.978) occurs over the Salton Sea water while the minimum value (0.892) is found over desert areas. The emissivity of agricultural land, typically 0.95, lies in between them.

Fig. 5. Surface emissivity for the study area. It is extracted from the UW infrared land surface emissivity data for 5 μm in May 2015.

3. Results and Discussion

Although the MASTER instrument produces data from 15 channelsin the MWIR spectral range, we can not apply the current method for all spectral channels due to atmospheric absorption. To demonstrate this point, we performed the simple MODTRAN run with the following input conditions: US standard atmosphere with no clouds and rain,solar zenith angle of 60°, surface reflectance of Algodones Dunes, boundary temperature of 288.15 K, and the MASTER SRF. The results are shown in Fig. 6. We omitted the surface temperature for channel 26 (3.1477 μm) since the channel input information is the duplicate of channel 32 (4.0677 μm). It is worthy to note that due to strong absorption by CO2 (Fig. 1) the significant deviation occurred for channel 33 (4.2286 μm), so the calculation for channel 34 (4.3786 μm) was not done. We therefore suggest that the current method be used for the MWIR MASTER data of 12 channels except for channel 26, channel 33, and channel 34. However, these 12 usable channels would be further reduced to two or three if we consider the availability of the UW emissivity database at a given wavelength.Thisis why we selected the channel 38 (4.9672 μm) for this study.

 

Fig. 6. Surface temperature forthe MASTER MWIRchannels computed by MODTRAN.

Before discussing the results from this study, it is important to examine the following two points regarding the assessment of surface temperature: 1) how well the total radiance calculated by the MODTRAN model, denoted as L_model, matches with the MASTER radiance measurements, L_MASTER, and 2) analysis of radiance components to understand the dominant factors in calculating surface temperature. If L_model differs significantly from L_MASTER for some reason, this would be a primary source for the surface temperature error. Therefore, such differences should be adjusted before estimating the surface temperature. To demonstrate this point, we define and calculate the model-observation scale factor (MOSF) as L_MASTER/L_model. Fig. 7 shows the results of MOSF for the study area. Overall, the MODTRAN model calculations underestimate total radiance values compared to the MASTER measurements. Large differences between model and observation take place over desert and bare soils, while small differences are found over Salton Sea and agricultural land. Such differences originate from the accuracy of input parametersforthe MODTRAN modelrun,specifically emissivity and atmospheric profiles.They appearto be greater over desert and bare soils, compared to those over Salton Sea and agricultural land, as we will discuss shortly in terms of contributions of each radiance component. For example, there are some differences between in-situ measurements (0.96 ~ 0.98 at 4.9672 μm) ofsand fromAlgodones Dunes, Kelso Dunes, and White Sand and the UW emissivity (089 ~ 0.91) of sand areas in Fig. 5. According to Li et al. (2013), the use of underestimated emissivity by 7% herein can produce, by reducing surface emission, about 3.5 K errors in surface temperature.

Fig. 7. Model-observation scale factor(MOSF), LMASTER/Lmodel, for the study area.

Fig. 8 shows the results of radiance components calculated from the MODTRAN model with MOSF adjustments. We find that the dominant component of L_model is the thermal component, which is an order of magnitude greater than the solar component. The atmospheric radiance represents the sum of both solar and thermal path radiances with the thermal scattered and then ground reflected radiance. The ground reflected radiance among three components does not significantly contribute to the observed radiance (i.e., MASTER Radiance) and the primary components are the surface emitted radiance and the atmospheric radiance.

Fig. 8. Radiance components calculated from the MODTRAN model with MOSF adjustments using the MASTER radiance.​​​​​​​

Although the surface emitted radiance is slightly greater than the atmospheric radiance, the radiances of Salton Sea and agricultural land in each component are smaller than those of desert and bare soils. Moreover, it would be meaningful to see the geographical patterns ofthe contribution of each component to the MASTER radiance on a pixel basis asshown inFig. 9.Contributions (ratio) ofsurface emitted radiances over Salton Sea and agricultural land are greater (>65%) than those over desert and bare soils. On the contrary, contributions of atmospheric radiances over Salton Sea and agricultural land are less than the counterparts of desert and bare soils. It is also known that the emissivity uncertainties over Salton Sea and agricultural land are lessthan those of desert and bare soils. Therefore, the estimation of surface temperatures over Salton Sea and agricultural land is considered more reliable than those of desert and bare soils.

Fig. 9. Geographical patterns of the ratio of each component to the MASTER radiance.​​​​​​​

Fig. 10 demonstratesthe surface temperature derived from the MASTER channel 38 data, using the MODTRAN radiative transfer model with the input data described in the previous section. We can see the homogeneous pattern of surface temperatures over water compared to land. As expected, the low surface temperatures over Salton Sea and agricultural land are contrasted with the high surface temperatures over other land cover types. The surface temperature in the region with low-level clouds appears to be enhanced due to the greenhouse effect of clouds.

Fig. 10. Surface temperature derived from the MASTER channel 38 data using MODTRAN.​​​​​​​

Since the complete validation ofsurface temperature for the study area is not possible due to the lack of insitu measurements, we simply compare with the following two data sets as currently available: the NASAJPLin-situ measurementsin Salton Sea and the MASTERL2 surface temperature products.The Salton Sea website at the NASA JPL (https://saltonsea.jpl. nasa.gov/) provides the access to some of field data including surface temperature. We used this field data for comparison and summarized the resultsin Table 3. In comparison with field data, we find that the present estimate (channel 38) is higher (+1.8 K) and the MASTER L2 surface temperature (channel 44) is slightly lower (-0.7 K). It would be inappropriate to draw an overall conclusion from this single point comparison but the bias from field data appears to be small over the high emissivity surface like Salton Sea. The NASA JPL MASTER L2 products are generated based on the ASTERTemperatureEmissivitySeparation (TES) algorithm (Hulley and Hook, 2011; Gillespie et al., 1998), using TIR spectral bands. We extracted the surface temperature from the MASTER L2 products for the study area (Fig. 11).

Table 3. Validation of surface temperatures at the Salton Sea buoy (33.22532°N, 115.82425°W). Deviations from field data are given in parenthesis

Fig. 11. Surface temperature from the MASTERL2 products.​​​​​​​

Comparisons of the present estimate with the MASTER L2 surface temperature (channel 44 surface temperature) are summarized in Table 4. Their mean and range differences are 4.6 K and 18.5 K,respectively, though the statistically good correlation (r=0.9398) between two estimates exists. The MASTER L2 surface temperature has higher values of mean and standard deviation than the present estimate. The map of differences (not shown) further reveals the pattern similar to MOSF shown in Fig. 7 in that large differences occur over desert and bare soils and small differences appear in Salton Sea and agricultural land. We will discuss next some uncertainties or limitations related to such differences.

 Table 4. Comparison of surface temperature (Channel 38) with the MASTER L2 surface temperature (Channel 44). The center of the MASTER channel 44 is located at 9.104 μm

We consider the following factors as potential sources of the above surface temperature differences: the MASTER radiances, surface emissivity, TES algorithmused fortheMASTERL2 surface temperature, and atmospheric correction. The maximum surface temperature difference (17.1 K) is larger than the contrast between desert and Salton Sea. It is however difficult to analyze the exact contribution of each factor, so that we rather examine the scale of impact by each factor. There might be concern on uncertainties in the MWIR MASTER radiances. It isreported that theTIR MASTER channels were well calibrated (< 0.3 K) and no radiometric validation was performed for the MASTER MWIR channels due to the low signal to noise (Hook et al., 2001). Nevertheless, we expect that the MASTER channel 38 does not undergo the low signal to noise problem caused by atmospheric absorption as shown previously (Fig. 6).

The surface emissivity used in each algorithm differs fromthe true value at a given wavelength and thusthese differences produce the surface temperature differences between two estimates. We presume, in channel 38 case, that the surface temperature bias could be within 3.5 K, which is caused by 7% emissivity difference as previously discussed for desert. For the TES algorithm applied for the MASTER L2 surface temperature, the retrieval accuracy for emissivity and surface temperature is within 1.5% and 1.5 K, respectively (Gillespie et al., 1998).

There are two aspects of the uncertainty associated with atmospheric correction. One is the uncertainty related to atmospheric profiles and the other is the way that the atmospheric radiance is appropriately subtracted from total radiance. Since both algorithms used the same source of atmospheric profiles, the degree of their uncertainties in deriving surface temperature remains the same. The corrected radiance (about 0.6 W/m2/sr/μm) by MOSF in channel 38 case is equivalent to about 7.5 K change in surface temperature. However, unlike the present estimate, the MASTERL2 surface temperature was derived without adjusting the total radiance difference between model and observation while performing the atmospheric correction. Considering the maximum difference of two surface temperature products and the overall contribution of factors in the above, we can infer that the magnitude of unadjusted atmospheric correction for the MASTER L2 product is about 4 K, which is not negligible. Therefore, we suggest that the correction should be made properly for the atmospheric radiance proportional to the observed total radiance.

4. Conclusions

Surface temperature has been derived from the MASTER MWIR single channel data using the MODTRAN radiative transfer model with input data including UW emissivity, NCEP atmospheric profiles, and solar and line-of-sight geometry. Despite some issues and concerns such as the removal of solar components and the availability of emissivity, we demonstrate that the MODTRAN results with the best available input data can produce the reasonable geographical distribution of surface temperature over land and water.

The thorough quantitative validation of surface temperature retrieved from this study is extremely limited due to the lack of in-situ measurements. One point comparison at the Salton Sea buoy shows that the present estimate is 1.8 K higher than the field data. The comparison with the MASTER L2 surface temperature further reveals that the MASTER L2 surface temperature has higher values, with mean differences of 4.6 K, than the present estimate. We further analyze the surface temperature differences between two estimates and find primary factors to be emissivity and atmospheric correction. These are simple comparisons using currently available data as preliminary validation efforts. Therefore, more ground truth data are needed to make a reasonable conclusion for validation of products from this study.