Land Surface Temperature and Emissivity Separation from Cross-Track Infrared Sounder Data with Atmospheric Reanalysis Data and ISSTES Algorithm

1University of Chinese Academy of Sciences, Beijing 100049, China 2State Key Laboratory of Resources and Environment Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China 3Key Laboratory of Quantitative Remote Sensing Information Technology, Academy of Opto-Electronics, Chinese Academy of Sciences, Beijing 100094, China 4Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China 5Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Wulumuqi, Xinjiang 830011, China


Introduction
Land Surface Temperature and Emissivity (LST and LSE) are two key parameters in quantitative remote sensing and have been widely used in many fields such as meteorological and climate models, lithological mapping, and resources exploration [1,2].
Over recent decades, great effort has been made to retrieve the LST and LSEs from multispectral thermal infrared (TIR) data, and some typical algorithms have been successfully used to determine the LST and LSEs from space measurements [3].For example, the Split Window algorithm and Day/Night algorithm are used for the Moderate Resolution Imaging Spectroradiometer (MODIS), and the Temperature and Emissivity Separation (TES) algorithm is used for the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) [4][5][6][7].According to the current multispectral land products, the general accuracy of the LST can be approximately 1 K [7][8][9][10].However, in most algorithms, some empirical constraints on LSE are also the method for Temperature and Emissivity Separation are briefly described.Section 4 gives the results and Section 5 gives the discussion.Conclusions are provided in Section 6.

Study Area and Data
2.1.Study Area.To find a mostly cloud-free region, a study area with longitude from 1.4 ∘ W to 7.9 ∘ W and latitude from 38 ∘ N to 43 ∘ N is selected.The map of the study area generated from the Global Land Cover 2000 map produced by the Institute of Environment and Sustainability (IES) is shown in the red rectangle in Figure 1 [21].In this area, the main land covers are cultivated and managed areas, tree cover, shrub cover, artificial surfaces, and associated areas.

Cross-Track Infrared Sounder Sensor Data Records (CrIS SDRs).
The CrIS is a Fourier Transform Spectrometer (FTS) onboard the Suomi National Polar-Orbiting Partnership (S-NPP) Satellite, which was launched on October 28, 2011.It is designed with 1305 spectral channels over three wavelength ranges (see Table 1) and has a spatial resolution of 14 km at nadir.Two data formats are currently provided by CrIS: the interferogram measurements and calibration data in the form of Raw Data Records (RDRs) and the calibrated and geolocated data in the form of Sensor Data Records (SDRs).In this paper, only the LWIR band in CrIS SDRs, which were acquired in 2013, is actually used to retrieve the LST and LSEs.All the data can be obtained from NOAA's Comprehensive Large Array-data Stewardship System (CLASS) [22,23].

Data for Atmospheric Correction: Global Data Assimilation System (GDAS). The Global Data Assimilation System
(GDAS) is used by National Center for Environmental Prediction (NCEP) to place observations into a gridded model space to start or initialize weather forecasts with observed data.Dozens of atmospheric and land-soil variables are available in this dataset, from temperature, winds, and precipitation to soil moisture and atmospheric ozone concentration.In this paper, the GDAS analysis data in GRIB2 format is used, which is on a 1 ∘ × 1 ∘ longitude/latitude grid and generated globally every 6 h (0:00, 06:00, 12:00, and 18:00 UTC) [24].Radiometer Suite (VIIRS) is one of the five major Earthobserving instruments onboard the S-NPP.It provides full daily coverage on both the day and night sides of the Earth.VIIRS has 22 spectral bands covering the spectrum between 0.412 m and 12.01 m, including 16 moderate resolution bands (M-bands) with a spatial resolution of 750 m at nadir, 5 imaging resolution bands (I-bands) with a spatial resolution of 375 m at nadir, and one panchromatic day/night band (DNB) with a 750 m spatial resolution throughout the sea [25].

Data for
In this paper, the VIIRS LST EDRs are used for validating the LST retrievals, which are calculated with two types of algorithms: split-windows (SW) and optional dual-split window (DSW) [10].Compared with the ground measurements in four sites (Gobi, sand dune, and desert steppe), the average root mean square error (RMSE) and bias of VIIRS LSTs were approximately 2.74 K and 0.36 K in daytime and approximately 1.48 K and −0.58 K in nighttime, respectively [26].Although, as reported in [27], two problems were identified in the VIIRS LST EDR: (1) inaccurate spectral emissivity values used in the VIIRS algorithm, which are derived from fixed values depending on a limited number of surface types; (2) a nonrepresentative algorithm coefficients under hot and very humid conditions, the data used in our study are still reliable because most of the surfaces in our study area were the typical ones and the water vapor contents of the corresponding atmospheric profiles were all less than 3 g/cm 2 .

Atmospheric Infrared Sounder (AIRS) Emissivity Product.
Unlike the validation for LSTs, because no LSE product can be provided by the instruments onboard the S-NPP, the AIRS, which was also used as a reference instrument in designing the CrIS, is selected in our study for evaluating the LSE retrievals.
The AIRS is one of six instruments aboard Aqua, which was launched into the Earth orbit on May 4, 2002.It consists of 2378 infrared channels that cover 3.7-15.4m with a spatial resolution of 13.5 km at nadir [15].
In our study, only the Version 6 (v6) AIRS standard surface product, which contains retrieved estimates of the surface properties with a spatial resolution of 50 km and cloud and atmospheric information [28], is used for validating the LSEs.The current v6 surface retrieval algorithm actually uses a regression plus simultaneous solution approach to retrieve the spectral LSE, bidirectional reflectance, and LST.It was reported that, over Namib Desert, the absolute LSE differences between AIRS LSE product and ASTER and Lab data were 2.32 and 2.26%, respectively.Over Kalahari Desert, the differences were 0.68 and 2.26% [29].

Methodology
3.1.Basic Theory and Scheme.On the basis of radiative transfer theory, under clear-sky conditions the spectral radiance measured in the thermal infrared (TIR) band at the sensor level can be written as where  is the TIR channel;  ,at-sensor is the radiance at the sensor level;   is the Land Surface Emissivity;   is the Land Surface Temperature;   (  ) is the Planck Function at the temperature   ;  ,down and  ,up are the downwelling and upwelling atmospheric radiance, respectively;   is the total atmospheric transmittance.It is clear that if one wants to know the LST and LSEs, the atmospheric parameters in (1) must be provided in advance, which is also known as the process of atmospheric correction.For this purpose, the GDAS atmospheric reanalysis products and the fast radiative transfer model RTTOV are used in this paper [30].
Then, one can easily find that there are still  + 1 unknowns ( LSEs and 1 LST for  channels) in the RTE with only  equations; therefore, a Temperature and Emissivity Separation (TES) solution, such as the ISSTES algorithm in this paper, is also necessary for determining the LST and LSEs [31][32][33].
For the validations in our study, because no appropriate ground measurements at large scales for the study area are available, the cross-validation is used with the VIIRS LST EDRs and the AIRS emissivity product.In addition, due to different spatial resolutions between the VIIRS (750 m at nadir) and CrIS (14 km at nadir) data, a spatial collocation also needs to be done before the cross-validation.The same process is included in the cross-validation with the AIRS product too, which has a spatial resolution of 50 km at nadir.
The overall flowchart of this paper is shown in Figure 2.

Atmospheric Correction.
First, an interpolated NCEP profile from the global dataset should be obtained according to the coordinate and acquisition time of the CrIS pixel.
Next, obtain the entire pressure, temperature, and moisture profiles right above the ground and then run the RTTOV, a fast radiative transfer model, to calculate the atmospheric radiance values ( ,down and  ,up ) and transmittances (  ).
Here, to ensure the final accuracy of TES, the TIR band used in this paper is 800-970 cm −1 , which excludes the region with obvious ozone absorption.

Temperature and Emissivity Separation (ISSTES).
After correcting the atmosphere, the land leaving radiance can be calculated by where  ,land leaving is the land leaving radiance at the surface level.Now, only   and   are unknown in the RTE and   can be rewritten as a function of   : According to (3), if   is not accurately estimated, the corresponding LSE spectrum will exhibit sharp convexities or concavities, which are called atmospheric features that are caused by gas absorption [33].Because a typical emissivity spectrum is smoother than that with atmospheric features, the ISSTES algorithm has been used to iteratively retrieve the LSEs and LST from hyperspectral TIR data [12].
Firstly, an initial estimate  0 should be provided to calculate the initial LSEs, such as the max value of surface brightness temperatures.Next, a cost function should be defined for determining the LST and LSEs: with where  −1 ,   , and  +1 are three neighbor channels in the TIR band;  is the cost function;  ,land leaving is the measured radiance from CrIS;   ,land leaving is the estimated radiance at the sensor level with the emissivity of  , in each iteration.
Then, the optimal estimate of LST can be obtained by searching the minimum of the cost function  through an iterative process by changing  0 .After we obtain this optimal LST, the LSE spectrum can be easily derived from (3).Although some different cost functions for determining the optimal LST and LSEs have been proposed, it is found that the performance of ISSTES is not sensitive to the choice of the cost function [30,31].
Beyond that, a constraint of the maximum and minimum value of emissivity between 0 and 1 is also used in our study to ensure that all retrieved LSEs are in the physical range.

Cross-Validation for Land Surface Temperature (LST).
For the LST validation, as both VIIRS and CrIS are onboard the S-NPP, it is not necessary to consider the errors caused by the acquisition time.However, the different spatial resolution between CrIS and VIIRS data may lead to a scale effect problem [34,35].A simple collocation in space still needs to be performed in advance.
Firstly, for a given CrIS pixel, all the VIIRS pixels that fall in the spatial range of the CrIS pixel are selected.Next, all of the pixels with high quality (HQ) are selected through the VIIRS quality flag (QF).Finally, an arithmetic mean of the VIIRS LSTs is used as the actual CrIS LST for the given pixel.It should be noted that the calculated mean LST might be not representative if there are no sufficient valid VIIRS pixels with high quality.To solve this problem, a percent of HQ pixels (90%) is set to be a constraint to guarantee the credibility of the calculation of real LST.Furthermore, because of the lower spatial heterogeneity at nighttime, all datasets in this paper are acquired at nighttime to decrease the effect of the space matching [26,36].In addition, to better evaluate the results under different atmospheric conditions, 4 different months were selected to retrieve the LST and LSE, which also indicate the seasons of a year.For each month, the Root Mean Square Deviation (RMSD) of LSTs is approximately 0.84 K in February, and the bias is −0.07 K.In May, the RMSD and BIAS are approximately 1.39 K and 0.17 K, respectively.An RMSD of 1.63 K and a BIAS of −0.15 K are obtained in August.For November, the RMSD and BIAS are approximately 1.15 K and −0.11K, respectively.The overall RMSD of the LST retrievals in August is the worst in the 4 selected months, which might be caused by the higher water vapor content (WVC) in August.However, according to the results, the overall RMSD of the 4 month is only approximately 1.34 K with a bias of −0.06 K.In addition, the results in Figure 3 also show an obvious seasonal change on LSTs in a year.

Cross-Validation for the Land Surface Emissivity (LSE).
For the LSE validation, due to the different characteristics of AIRS and CrIS, such as the different spatial and temporal resolutions, there are not as many points as LSTs for crossvalidation.In fact, only the AIRS pixels with sufficient CrIS pixels in them, which cover 85% of the AIRS pixel range, are used for the cross-validation.In addition, a time constraint of 6 hours for acquisition time is also included in our study, but no limitations on the view angle are taken into account for obtaining a basic number of valid pixels.
To directly compare CrIS LSEs with AIRS, we interpolated the CrIS LSEs into identical channels in the AIRS LSE product from 800 to 970 cm −1 : 819.67 cm −1 (B1), 847.46 cm −1 (B2), 877.19 cm −1 (B3), 909.09 cm −1 (B4), and 943.4 cm −1 (B5).Figure 4(a) shows the comparison of the retrieved LSEs and AIRS product at each band, and Figure 4(b) shows a histogram of the differences between retrieved LSEs and AIRS LSEs.Detailed information of the comparison is provided in Table 2.
According to Table 2, the total RMSDs of the LSEs at each band are approximately 1.22-1.66%.The RMSD obviously decreases with the decrease (increase) in wavenumber (wavelength).The reason may be that at small wavenumbers the atmosphere is commonly much more transparent than at large wavenumbers in the selected TIR band.
From Figure 4(a), it is clear that the LSEs retrieved from November were with an obvious bias error, which indicates the ISSTES algorithm was more sensitive to the atmospheric correction under dry-cold conditions.Besides that, some singular points, which are circled with red lines, are also easily found in Figure 4(a), and all of them are from the month of May.For these points, the maximum difference of the channel LSEs can be larger than 5%, and there are many possible reasons for this: (1) the poor quality of the retrieved LSTs of the selected pixels; (2) the obvious differences in view angle between the CrIS and AIRS pixels; (3) the singular points caused by the inversion of RTE when the LST is close to the equivalent atmospheric temperature.However, the statistical results show that the total percentage of LSEs at each band remains larger than 80% with a mean difference of less than 2%.Details are shown in Table 3.In general, the overall accuracy of the LSE retrievals is comparable with the AIRS LSE product.According to the results in [27], the maximum error of AIRS product over desert was approximately 2%-3%.That is, for soil surfaces, the maximum error of the retrieved LSEs from CrIS data is approximately 2.3%-3.4%.This specific value will be even lower for other surfaces such as vegetation.On the other hand, unlike the few channel LSE values provided in the AIRS product, a continuum LSE spectrum is obtained simultaneously with the LST in our study.To show this result, a comparison of the mean LSEs of the selected pixels in May is shown in Figure 5.The solid red line indicates the mean ARIS LSEs, and the dotted red lines show the standard deviation of the mean LSEs.Similarly, the solid and dotted blue lines are the mean and standard deviation of the original CrIS LSEs, respectively.However, due to the misfits on atmospheric profiles, the LSE spectrum may be fluctuated by using the ISSTES algorithm.To decrease the uncertainty of atmospheric profiles on atmospheric correction and make the retrieved LSEs more practical for applications, a smoothed LSE spectrum, which is also showed in Figure 5 with green line, can be then obtained by using some mathematic methods.
As shown, when the mean LSEs are compared, the retrieved LSEs exhibit good shape consistency with the AIRS product.Different from the 5 channel LSEs in AIRS product in the range of 800-970 cm −1 , more spectral features can be contained in the retrieved LSE spectrum.It is clear that the AIRS LSE spectrum is more close to a near-gray surface, while obvious spectral changes, which are valuable for further analyses of atmospheric and surface properties, can be easily found in our retrieved LSE spectrum.

Discussion
Currently, a simultaneous solution approach is used to retrieve the atmospheric profiles together with the LST and LSEs from the CrIS data [20].To better eliminate the influence of the cloud, a Cloud-Clearing (CC) technique, which utilizes the CrIS radiance values within a FOR (3 × 3 Filed-Of-View, FOV), is included in the retrieval process.Thus, the released CrIS products are produced with a lower spatial resolution approximately 45 km.Due to the original purpose of the CrIS, the present approach focuses more on the atmospheric retrievals, which means there are more simplifications and approximations for the land parameters, such as the fixed infrared (IR) emissivities in the identification of the Clear FOV, the homogenous surface in each FOV cluster for the CC algorithm, and the prior constraints on both Microwave (MW) and IR surface emissivities for the physical retrievals [20].Consequently, the accuracies of the retrieved land surface parameters will be degraded if those underlying assumptions are violated.In addition, because a channel selection for CrIS data is adopted to speed up the retrieval process without losing obvious accuracies, the Advances in Meteorology retrieved LSEs are discrete.For example, just 12 IR LSEs, 12 IR surface reflectivities, and 1 LST, which are even not produced for users, are involved in the CrIS retrievals [20].Unlike the complicated simultaneous approach used to retrieve atmospheric profiles, LST, and LSEs, in this paper, a simpler method with two steps are used, (1) atmospheric correction and (2) TES, to retrieve just the LST and LSEs from the CrIS data.By correcting for the atmospheric effects using the atmospheric reanalysis products and the RTTOV, the atmospherically corrected CrIS measurements at the surface level within each of the FOVs are first obtained.On this basis, the LST and LSEs can be then retrieved with the ISSTES algorithm with a finer spatial resolution approximately 14 km at nadir.
Compared with the present approach, our method is more effective and provides comparable accuracies for both the LST and LSEs with a higher spatial resolution.In addition, as no assumptions except a smooth LSE spectrum, which is easy to be satisfied in the range of 800-970 for most typical materials, is necessary for ISSTES algorithm, the retrieved LST and LSEs are more reasonable [12].Furthermore, by smoothing the spectrum through mathematical methods, the retrieved LSEs are now given as a smoothed and continuous spectrum instead of a few channel LSEs, which is quite meaningful for various studies, such as object identification, resource exploration, process modeling, and weather forecasting [1,2].There is a reason to believe that, with the development of hyperspectral instruments, using hyperspectral data to retrieve the LST and LSEs will be increasingly more accurate and inevitable to promote the development of relevant studies.

Conclusions
As a subsequent instrument of AIRS, the CrIS will continue to provide accurate atmospheric profiles for enhancing weather forecasting models and will facilitate both short-and longterm weather forecasting.However, compared with studies on the atmosphere, little attention has been paid to the retrievals of surface parameters using CrIS data, which are also critical for determining accurate climate variables.
In this paper, to simultaneously retrieve a continuous LSE spectrum and the LST from the CrIS data with the ISSTES algorithm, the NCEP atmospheric reanalysis data were used to provide the information of necessary atmospheric profiles for driving RTTOV.In addition, because of the difficulty in acquiring adequate ground measurements at large scale for validation, a cross-validation is used in this paper with the VIIRS LST and the AIRS emissivity products.
The results show that the overall RMSD of LSTs can be less than 1.4 K. Considering the seasonal characters of atmospheric profiles, the RMSDs in May and August are larger than that of February and November, which may be caused by different amounts of water vapor in different seasons.When evaluating the retrievals of LSEs, because CrIS and AIRS have notably different spatial and temporal features, only the AIRS pixels covered with sufficient CrIS pixels within 6 hours of acquisition time are used in our study.The results show that the shapes of the retrieved LSE spectra are consistent with the AIRS product, and the overall RMSD is approximately 1.48%, which is consistent with the RMSD of 1.4 K on LSTs.Although some uncertainty remains in the atmospheric correction process and CrIS data, the relevant retrievals in our study can provide comparable accuracy with current multispectral products.More importantly, the corresponding LSEs in our paper are provided as a continuum spectrum and contain much more spectral information than all current LSE products.

Figure 1 :
Figure 1: Land surface covers in study area with a resolution of 1 kilometer generated from the Global Land Cover 2000 map.

Figure 2 :
Figure 2: Flowchart of Temperature and Emissivity Separation with CrIS data.

Figure 3
Figure3shows the comparison of the retrieved LSTs and VIIRS LSTs, and totally 29 days from 4 different months in 2013 were selected.For each month, the Root Mean Square Deviation (RMSD) of LSTs is approximately 0.84 K in February, and the bias is −0.07 K.In May, the RMSD and BIAS are approximately 1.39 K and 0.17 K, respectively.An RMSD of 1.63 K and a BIAS of −0.15 K are obtained in August.For November, the RMSD and BIAS are approximately 1.15 K and −0.11K, respectively.The overall RMSD of the LST retrievals in August is the worst in the 4 selected months, which might be caused by the higher water vapor content (WVC) in August.However, according to the results, the overall RMSD of the 4 month is only approximately 1.34 K with a bias of −0.06 K.In addition, the results in Figure3also show an obvious seasonal change on LSTs in a year.

Figure 3 :
Figure 3: Results of retrieved LSTs from CrIS data in 2 different months, 2013.Different colors indicate the different days: (a) LSTs in February; (b) LSTs in May; (c) LSTs in August; (d) LSTs in November.

Figure 4 :
Figure 4: The comparisons of LSEs between CrIS and AIRS: (a) scatterplots of LSEs in five bands for 2 months; (b) histograms of LSE differences between CrIS and AIRS.The red dashed lines mean the points that have a LSE difference of 0.02; the points circled with red solid lines are the singular ones.

Figure 5 :
Figure 5: An overview of the LSE retrievals in May with the ARIS LSE product.The solid red line indicates the mean ARIS LSEs, and the dotted red lines show the standard deviation of the mean LSEs.Similarly, the blue lines are the mean and standard deviation of the original CrIS LSEs, while the green ones are for the smoothed CrIS LSEs.

Table 1 :
Spectral resolution, frequency range, and number of channels of CrIS SDRs.

Table 2 :
Differences between CrIS and AIRS LSE product at 5 AIRS TIR bands.

Table 3 :
The detailed statistical information of LSEs at each of the 5 bands.