A Physics-Based Method to Retrieve Land Surface ... - IEEE Xplore

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 54, NO. 8, AUGUST 2016

A Physics-Based Method to Retrieve Land Surface Temperature From MODIS Daytime Midinfrared Data Bo-Hui Tang, Member, IEEE, and Jie Wang

Abstract—The midinfrared (MIR) spectral region (3–5 μm), which penetrates most haze layers in the atmosphere and is less sensitive to variations in atmospheric water vapor, seems to be appropriate for retrieving land surface temperature (LST). However, there are currently few studies of LST retrieval with MIR data because it is difficult to eliminate solar irradiance from the total energy measured in the MIR during the daytime. This paper proposes a physics-based method to retrieve LST from MODIS daytime MIR data. The bidirectional reflectivity describing the reflected solar direct irradiance is determined using the method by Tang and Li. The directional emissivity, representing the surface emitted radiance, is determined by a kerneldriven bidirectional reflectance distribution function model, i.e., RossThick-LiSparse-R. Intercomparisons using the MODISderived LST product MYD11_L2, for the Baotou experimental site in Urad Qianqi, Inner Mongolia, China, have a maximum root-mean-square error (RMSE) of 1.69 K and a minimum RMSE of 1.31 K, for four scenes of MODIS images. Furthermore, in situ LSTs measured at the Hailar field site in northeastern Inner Mongolia, China, were also used to validate the proposed method. Comparisons of the LSTs retrieved from MODIS daytime MIR data and those calculated using in situ measurements have a bias and RMSE of −0.17 K and 1.42 K, respectively, which indicates that the proposed method can accurately retrieve LST from MODIS daytime MIR data. Index Terms—Daytime, land surface temperature (LST), midinfrared (MIR), MODIS.

I. I NTRODUCTION

L

AND surface temperature (LST) is a key variable controlling fundamental biospheric and geospheric interactions between the Earth’s surface and its atmosphere [1]. It is also one

Manuscript received January 28, 2016; revised March 9, 2016; accepted March 20, 2016. Date of publication April 21, 2016; date of current version June 1, 2016. This work was supported in part by the National Natural Science Foundation of China under Grant 41571353 and Grant 41231170 and in part by the “Strategic Priority Research Program” Climate Change: Carbon Budget and Relevant Issues of the Chinese Academy of Sciences under Grant XDA05040204. (Corresponding author: Bo-Hui Tang.) B.-H. Tang is with the State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China, and also with the Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China (e-mail: [email protected]). J. Wang is with the State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China, and also with the University of Chinese Academy of Sciences, Beijing 100049, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2016.2548500

of the most important parameters in the physics of land-surface processes at local to regional or global scales [2]. Knowledge of LST provides important information for many studies, such as evapotranspiration, climate change, surface energy budgets, hydrological cycle, vegetation monitoring, urban climate, and environment change [3]–[9]. Consequently, the ability to accurately determine LST over large spatial and temporal scales is essential to many applications [10]. Estimation of LST from satellite observations in the thermal infrared (TIR, i.e., 8–14-μm window) has been ongoing for several decades, and LST retrieval accuracy has been significantly improved. Currently, many algorithms have been proposed and developed to estimate LST from polar-orbit satellite data [11]–[17] and geostationary satellite data [18]–[20]. Li et al. [21] comprehensively reviewed the current algorithms and grouped them into three categories, i.e., single-channel methods, multichannel methods, and multiangle methods, providing that the land surface emissivities (LSEs) are known a priori. They noted that the retrieval of LST from space is mathematically underdetermined and unsolvable. Although the solution of the radiative transfer equation (RTE) sets becomes deterministic via assumptions and constraints on the LSEs, LST retrieval remains unstable due to the high correlations of the measurements in the TIR region. The introduction of the midinfrared (MIR) channels into LST retrieval can significantly reduce the correlation of the RTE sets and greatly improve the accuracy of the estimated LST [22]. The MIR spectral region (3–5 μm) has many advantages with respect to the TIR spectral region. In contrast to TIR, MIR can better penetrate most of the haze layers (except dust) in the atmosphere [23] and is less sensitive to variations in water vapor in the atmosphere [24]. Mushkin et al. [25] extended surface temperature and emissivity retrieval to the MIR using the multispectral thermal imager and found that LST retrieved from MIR is only half as sensitive to errors in LSE as those retrieved from TIR. Consequently, it seems to be more appropriate to retrieve LST from MIR rather than TIR data. However, measurements in the MIR region at satellite altitudes during the daytime consist of a combination of both reflected radiance due to solar irradiance and emitted radiance from both the surface and the atmosphere. The reflected solar irradiance is on the same order of magnitude as the radiance emitted by the surface and the atmosphere, which makes it difficult to eliminate the solar effect on LST retrieval in the MIR. This is because the separation of solar irradiation from the total energy measured in the MIR requires not only accurate atmospheric

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TANG AND WANG: PHYSICS-BASED METHOD TO RETRIEVE LST FROM MODIS DAYTIME MIDINFRARED DATA

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area has a cold temperate semihumid and semiarid continental monsoon climate with a mean annual temperature of −2 ◦ C and a mean annual rainfall of approximately 350 mm. This site was chosen because it is homogeneous and fully covered by grass. This site is very suitable for the validation of LST retrieved from satellite data. B. MODIS Satellite Data

Fig. 1. Locations of the study areas.

information but also knowledge of the bidirectional reflectivity of the surface. The uncertainties in such information may lead to larger errors in the LST retrieved from MIR data. Therefore, there are currently few studies of LST retrieval using MIR data. Qian et al. [26] recently proposed retrieving LST solely from the nighttime MIR data observed by an airborne hyperspectral scanner (AHS). Zhao et al. [27] developed a split-window method to retrieve daytime LST from two MIR channels of the AHS. However, the LSEs were determined using a supervised classification method. The uncertainty of this classification may introduce large errors into the LST retrieval. The objective of this paper is to develop a physics-based method to retrieve LST from the MODIS daytime MIR data. Section II introduces the study areas and data sets, including the satellite data and in situ measurements. Section III presents the radiative transfer theory in the MIR region and describes the methodologies associated with the determinations of bidirectional reflectivity and directional emissivity. Section IV gives the results of LST retrieved from MODIS daytime MIR data. Preliminary validations using the MODIS LST product MYD11_L2 and in situ measurements are also presented in this section. Finally, the conclusions are given in Section V. II. S TUDY A REAS AND DATA S ETS A. Study Areas Two field experimental sites were chosen as study areas. Fig. 1 shows the locations of the sites (red rectangles). The first study area, i.e., the Baotou experimental site, is located in Urad Qianqi, Inner Mongolia, in northern China, between latitudes 40◦ 45’ N and 40◦ 54’ N and longitudes 109◦15’ E and 109◦40’ E. The area has a semiarid temperate continental climate with a mean annual temperature of 6 ◦ C and a mean annual rainfall of approximately 288 mm. Most of the soil in this area is sandy loam and silt loam. The site was chosen because there is a series of cloud-free MODIS data available over this region and the land cover of the area is diverse, including cropland, grassland, open shrubland, and barren or sparsely vegetated areas. In addition, it has an average ground elevation of 1290 m above sea level, and the atmosphere is quite clean. The second study area, i.e., the Hailar field site, is located in Northeastern Inner Mongolia, China (49◦ 21’ N, 120◦ 07’ E). The central area of the study site is approximately 0.4 km2 . The

MODIS is a passive imaging sensor aboard the NASA EOS Terra satellite launched in 1999 and the Aqua satellite launched in 2002. The instrument consists of 36 spectral channels covering the visible and infrared wavelengths, from approximately 0.4 to 14.0 μm [28]. MODIS is intended to satisfy a diverse set of atmospheric, oceanographic, and terrestrial science observational requirements. The data used in this work were the MYD021KM, MYD03, MYD35_L2, MYD07_L2, and MYD11_L2 product files provided by the NASA GSFC Level 1 and Atmosphere Archive and Distribution System (LAADS) (http://ladsweb.nascom.nasa.gov/data/search.html). The MYD021KM products, which are Earth View data with 1-km resolution at nadir calibrated by the MODIS Characterization and Support Team, include top-of-the-atmosphere (TOA) radiances and reflectances. The MYD03 products provide geodetic latitude, longitude, solar zenith and azimuth angles, and satellite zenith and azimuth angles, for each 1-km sample. MYD35_L2 is a cloud mask product that assigns a clearsky confidence level (i.e., clear, probably clear, uncertain, and cloudy) to each IFOV. MYD07_L2 is an atmospheric profile product, providing temperature and moisture profiles with a spatial resolution of 5 km at nadir for 20 vertical atmospheric pressure levels. MYD11_L2 is a land surface temperature/ emissivity (LST/E) product, providing per-pixel LST and LSE values at 1-km resolution, and is used to validate the LST estimated from the MIR data. C. In Situ Measurements The in situ experimental campaigns were conducted at the Hailar field site. To ensure that the ground measurements of LST were representative at the satellite pixel scale, four SI-111 infrared radiometers, which were manufactured by Apogee Instruments, Inc., USA, were uniformly installed at an interval of 120 m at the field site. The SI-111 sensors measured the TIR radiance in the 8.0–14.0-μm domain and obtained brightness temperatures with an absolute accuracy of ±0.2 K. The sensors, with a FOV of 44◦ , were mounted at a height of 2.0 m to observe an area of approximately 2.0 m2 . An additional SI-111 sensor was directed toward the sky at 53◦ with regard to the zenith and measured the downwelling atmospheric radiance, which was used to correct for the reflected atmospheric component [29]. Fig. 2 gives one photograph of the SI-111 infrared radiometers installed at the field site to illustrate the field measurement. All measurements were recorded every 10 s and were stored as 30-s averages. Furthermore, to reduce the influence of the external environment on the measured infrared radiance, a wireless net observation system was adopted to transfer the radiances to a computer terminal.

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Inverting (2) and combing (1) gives Bi (Ti )−Ratm_i ↑−Rs Ts =

Fig. 2. Photograph of SI-111 infrared radiometers installed at the field site.

D. DEM Data To calculate the real atmospheric path length between the targets and the sensor, digital elevation model (DEM) data with 90-m resolution provided by the NASA Shuttle Radar Topographic Mission (SRTM) were used. The SRTM provides DEMs for over 80% of the Earth, and the vertical error of the DEM is reported to be less than 16 m. These data are currently distributed free of charge by the USGS and are available for download from the National Map Seamless Data Distribution System or the ftp site (http://srtm.csi.cgiar.org/SRTM_v41/SRTM_Data _GeoTIFF). The DEM data were resampled at 1-km resolution to match the MYD021KM data. III. M ETHODOLOGY A. Radiative Transfer Theory for the MIR On the basis of radiative transfer theory for a cloud-free atmosphere in thermodynamic equilibrium, the daytime channel radiance Bi (Ti ), which was observed at the TOA by a MIR channel (3–5-μm window) of the sensor onboard a satellite, is approximately [30] s ↑ Bi (Ti ) = Bi (Tg_i )τi + Ratm_i ↑ +Ratm_i

(1)

where Ti and Tg_i represent channel brightness temperatures observed in channel i at TOA and at ground level, respectively. Bi is the Planck function, τi is the total atmospheric transmit↑ is tance along the target to the sensor path in channel i, Ratm_i the thermal-path atmospheric upwelling radiance in channel i, s and Ratm_i ↑ is the thermal-path upward radiance resulting from the scattering of solar radiation. Bi (Tg_i ) is the channel radiance in channel i at ground level, which can be written as s Bi (Tg_i ) = εi Bi (Ts )+(1−εi) Ratm_i ↓ + Ratm_i ↓ +ρbi Ris (2) where εi (i.e., LSE; hereafter, εi is used interchangeably with LSE) is the directional channel emissivity in channel i; Bi (Ts ) is the radiance emitted by a blackbody with land surface temperature Ts (i.e., LST; hereafter, LST is used interchangeably with Ts ); Ratm_i ↓ is the channel downward atmospheric radiance, which is defined as 1/π times the total downward atmospheric s irradiance; Ratm_i ↓ is the channel downward solar diffusion radiation over the hemisphere divided by π; ρbi is the surface bidirectional reflectivity in channel i, which is usually referred to as the surface bidirectional reflectance distribution function (BRDF); and Ris is the solar irradiance at the ground level in channel i. All terms in (1) and (2) are angular dependent. For simplicity, the angular expressions are omitted in this equation.

atm_i ↑ τi εi (1−εi )(Ratm_i ↓+Rsatm_i ↓)+ρbi Rsi − εi

Bi−1

(3)

where B −1 is the inverse of the Planck function. The atmo↑ s s ↓, Ratm_i , Ratm_i ↑, Ris) spheric parameters (τi, Ratm_i ↓, Ratm_i can be calculated from atmospheric radiative transfer models, such as Moderate Resolution Atmospheric Transmittance and Radiance Code (MODTRAN, http://www.modtran5.com) [31] or Operational Release for Automatized Atmospheric Absorption Atlas (4A/OP, http://4aop.noveltis.com/) [32], if the atmospheric profile is available from either conventional radiosoundings or satellite soundings. To estimate LST from (3), both the surface bidirectional reflectivity ρbi and the directional emissivity εi must be known. B. Determination of the Bidirectional Reflectivity Based on the difference in the solar reflection in two adjacent MODIS MIR channels 22 (centered at 3.97 μm) and 23 (centered at 4.06 μm), Tang and Li [33] assumed that the surface bidirectional reflectivities were equal in channels 22 and 23 and that the ground brightness temperatures in those two adjacent channels were the same if the contribution of the direct solar radiation was not considered. They developed a new method to retrieve the bidirectional reflectivity in the MIR channel from MODIS channels 22 and 23 using 0 B22 (Tg_22 ) − B22 Tg_22 ρb_22 = (4) s R22 where the subscript 22 represents MODIS channel 22. ρb_22 is the bidirectional reflectivity of MODIS channel 22. Tg_22 is the daytime ground-based brightness temperature for channel 22, s and R22 is the solar irradiance at ground level in MODIS 0 channel 22. Tg_22 is the MIR ground brightness temperature without the contribution of the solar direct beam and can be estimated from the ground brightness temperatures Tg_22 and Tg_23 in channels 22 and 23 using 0 = Tg_22 +a1 +a2 (Tg_22 −Tg_23 )+a3 (Tg_22 −Tg_23 )2 (5) Tg_22

where Tg_23 is the daytime ground-based brightness temperature of MODIS channel 23. The coefficients a1 −a3 are only dependent on the solar zenith angle (SZA). More details concerning the development of this method can be found in [33]. C. Determination of the Directional Emissivity Based on Kirchhoff’s law, for an opaque medium in thermal equilibrium, the directional emissivity ε(θv , ϕv ) is related to the hemispherical directional reflectance ρh (θv , ϕv ) by ε(θv , ϕv ) = 1 − ρh (θv , ϕv )

(6)

with π

2π2 ρh (θv , ϕv ) =

ρb (θv , ϕv , θs , ϕs ) cos θs sin θs dθs dϕs 0

(7)

0

where θv is the viewing zenith angle (VZA), ϕv is the viewing azimuth angle, θs is the incident SZA, and ϕs is the solar azimuth angle.


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Assuming that the shapes of the BRDF in the MIR spectral region are the same as those in the visible and near-infrared regions [34], a kernel-driven BRDF model, i.e., RossThickLiSparse-R, can be used to describe the non-Lambertian reflective behavior of land surface [35]–[37] as ρb (θv , θs , ϕ) = kiso + kvol fvol (θv , θs , ϕ) + kgeo fgeo (θv , θs , ϕ) (8) where ϕ is the relative azimuth angle between the observation and incidence directions. kiso is the isotropic scattering term, kvol is the coefficient of Roujean’s volumetric kernel fvol , and kgeo is the coefficient of the LiSparse-R geometric kernel fgeo . It should be noted that the bidirectional reflectivity in the azimuthal direction is assumed in this model to be dependent on the value of ϕ regardless of the respective value of ϕv and ϕs , i.e., ρb (θv , ϕv , θs , ϕs ) = ρb (θv , θs , ϕ). Consequently, according to (6)–(8), the directional emissivity in the MIR channel can then be written as ε(θv ) = 1 − πkiso − kvol Ifvol (θv ) − kgeo Ifgeo (θv )

(9)

with π

2π2 Ifx (θv ) =

fx (θv , θs , ϕ) cos(θs ) sin(θs )dθs dϕ 0

(10)

0

where the subscript x represents the subscripts vol or geo. As the integrals of Ifvol (θv ) and Ifgeo (θv ) over the incident angle θs and the relative azimuth angle ϕ are complicated mathematical expressions and cannot be analytically derived, Tang et al. [38] proposed parameterization expressions to approximately calculate the integrals of Roujean’s volumetric kernel fvol and the reciprocal LiSparse geometric kernel fgeo as θv Ifvol (θv ) = −0.0299+0.0128 exp (11) 21.4382 θv −90.9545 2 . (12) Ifgeo (θv ) = −2.0112−0.3410 exp −2 68.8171 The parameters kiso , kvol , and kgeo in (8) can be fitted using a least square method, if there are more than three bidirectional reflectances ρb available with different angular configurations. The directional emissivity ε(θv ) in the MIR channel can then be calculated using (9)–(12). Subsequently, the LST can be estimated according to (3). IV. R ESULTS AND VALIDATIONS A. Application to Actual MODIS Daytime MIR Data 1) Data Preprocessing: Based on the clear-sky confidence level (i.e., clear, probably clear, uncertain, and cloudy) assigned to each IFOV in the MODIS cloud mask product MOD35_L2, the cloudy pixels were first screened out of the MODIS level_1B data. s ↓, To obtain the atmospheric quantities (τi , Ratm_i ↓, Ratm_i ↑ s s Ratm_i , Ratm_i ↑, Ri ) involved in (3), the latest radiative transfer model, i.e., MODTRAN 5, was used with the MODIS MYD07_L2 atmospheric profile product and the DEM data.

Fig. 3. Flowchart to retrieve LST from MODIS daytime MIR data in channels 22 and 23.

Fig. 4. Map of the LST estimated from MODIS MIR data for the Baotou study area observed at 06:05 UTC on May 27, 2014.

Because of the difference in the spatial resolutions between the MYD021KM data (1 km) and MYD07_L2 data (5 km), the atmospheric quantities need to be interpolated to match the MYD021KM data. A simple bilinear interpolation method proposed by Tang and Li [33] was adopted to perform the angular, altitudinal, and spatial interpolations in this study. 2) Estimation of LST: The objective of this study is to estimate the LST from daytime MIR data. Fig. 3 gives a flowchart of the proposed method to retrieve LST from the actual MODIS MIR data in channels 22 and 23. Fig. 4 shows an example of the estimation of LST for the Baotou study area on May 27 (DOY 147), 2014, at 06:05 Coordinated Universal Time (UTC). The model inputs

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Fig. 5. (a) Retrieved bidirectional reflectivity versus view zenith angle. (b) Sun and satellite zenith and azimuth angles in polar representation for grassland, barren land, and open shrubland, for the four days.

are the TOA MIR radiances of channels 22 and 23 from MYD021KM; geodetic latitude, longitude, solar zenith and azimuth angles, satellite zenith and azimuth angles from MYD03, cloud mask from MYD35_L2; temperature and moisture profiles from MYD07_L2 and the DEM data for the study area. Symbols A and B, which are located in the red and yellow colored areas in Fig. 4, represent the LSTs of barren or sparse grassland, and open shrubland, respectively. As shown in Fig. 4, the estimated LSTs on the southern side are lower than those on the northern side. This is because the elevation of the southern side is, on average, approximately 400 m higher than that of the northern side. B. Validation Using the MODIS LST Product MYD11_L2 To validate the proposed LST retrieval method, an intercomparison method was used with the MODIS LST V5 product MYD11_L2 retrieved using a generalized split-window algorithm [13] from the MODIS TIR data. Because both of the estimated LSTs are derived from MODIS level-1B data, geographic coordinate matching, temporal matching, and VZA matching for the intercomparison data do not need to be taken into account. As parameters kiso , kvol , and kgeo in (8) need at least three bidirectional reflectances ρb with different angular configurations on consecutive cloud-free days to be obtained, the MODIS data observed on Julian days 145, 147, 149, and 151, in 2014, for the Baotou field experimental site were selected. The bidirectional reflectivities ρb were retrieved from the MODIS MIR data using MODTRAN and the atmospheric profiles for this area in MYD07_L2, for images of the four days. Then, the corresponding directional emissivities ε in the MIR channels were calculated, and the LSTs were estimated according to (3). Fig. 5(a) shows, as an example, the bidirectional reflectivities retrieved for grassland, open shrubland, and barren land versus the VZA. Fig. 5(b) illustrates the observation geometry of the sun and satellite zenith and azimuth angles in polar representation for the four days. It should be noted that many more

observations with different angular configurations will generate better fitting results in the kernel-driven model. Consequently, combining Terra and Aqua MIR data on some consecutive cloud-free days will robust the inversion. Since most of the Terra data observed on Julian days 145–151, in 2014, for the Baotou field experimental site were contaminated by clouds or partial clouds, only Aqua data sets were used in this work. Fig. 6 shows a comparison of the LSTs retrieved with the proposed method from the MODIS daytime MIR data and the values extracted from the MYD11_L2 LST product for the Baotou experimental site for the four days. The LSTs derived from the MODIS MIR cloud-free data on the four days varied from 287 to 327 K. This is because the satellite overpass times for each day are different, and the satellite observation angles of the same pixel for different days are also different. For Julian day 145, the overpass time was 06:15 UTC. It was 06:05 UTC for Julian day 147, 05:50 UTC for day 149, and 05:40 UTC for day 151. Compared to the MYD11_L2 LSTs, the bias and rootmean-square error (RMSE) were −0.68 and 1.69 K for Julian day 145, −0.41 and 1.34 K for Julian day 147, 0.42 and 1.31 K for Julian day 149, and 0.81 and 1.55 K for Julian day 151, respectively. The results show that the maximum RMSE is 1.69 K and the minimum RMSE is 1.31 K, for the comparisons. The RMSEs could be different for the four days because the MYD11_L2 LSTs were derived with a generalized splitwindow algorithm [13], whereas the LSEs were determined via the classification-based method [39], without taking into account the directional effect of the LSE, which may lead to large errors in the LST retrieval for different observation angles. Fig. 7 shows the corresponding histograms of the differences between the LST estimated with the MODIS MIR data and those from the MYD11_L2 product. Although the maximum LST error in the comparison is approximately −4.5 K, we can see that 60.5% of the pixels have LST absolute differences below 1.5 K for Julian day 151 [see Fig. 7(d)]. This proportion is 65.6% for Julian day 145 and increases to 73.9% for day 147 and 77.4% for day 149. This finding implies that the proposed method can be used to estimate the LST from MODIS daytime MIR data.


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Fig. 6. Comparison of the LSTs estimated from MODIS daytime MIR data to those extracted from the MYD11_L2 LST product for the Baotou study area, on four continuous days 145, 147, 149, and 151, in 2014.

Fig. 7. Difference histograms between the LSTs estimated from MODIS daytime MIR data and those extracted from the MYD11_L2 LST product for the Baotou study area, on four continuous days 145, 147, 149, and 151, in 2014.

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are −0.17 K and 1.42 K, respectively, which indicate that the proposed method can accurately retrieve LST from MODIS daytime MIR data. V. C ONCLUSION

Fig. 8. Comparison of the LSTs estimated from MODIS daytime MIR data and those calculated using in situ measurements, at the time of the MODIS overpasses, at the Hailar study site.

C. Validation Using In Situ Measurements The in situ measurements observed by the infrared radiometer are ground-based radiances coupled to the LST, LSE, and downwelling atmospheric radiance; therefore, LST can be retrieved from

1 ↓ Lground,λ − (1 − ελ )Ratm,λ LST = Bλ−1 (13) ελ where B −1 is the inversion of the Planck function; Lground,λ is the ground-based radiance emitted from the surface; ελ is ↓ is the downwelling radiance from the sky, the LSE; and Ratm,λ which is obtained from measurements by the additional SI-111 infrared radiometer directed toward the sky at the study site. Determining parameters kiso , kvol , and kgeo in (8) from the MODIS MIR data requires at least three approximately cloud-free images of continuous days, as mentioned earlier. Therefore, five days of cloud-free MODIS images in November 2013, five days in March 2014, four days in April 2014, and six days in August 2014 were chosen. The land cover of the Hailar field site was dry grass from October 22 to November 5, 2013. From November 6, 2013, to March 25, 2014, the site was covered by snow. From April to May, the snow melted, and the site was again covered by dry grass. From June to September, the land cover at the site was green grass. Consequently, the value of ελ was assigned a constant value of 0.940 for dry grass, 0.983 for green grass, and 0.988 for snow cover, as calculated by combining the spectral response function of the SI-111 with the dry grass spectra, green grass spectra, and snow spectra provided by the MODIS University of California at Santa Barbara (UCSB) emissivity library of the MODIS LST Group (http://www.icess.ucsb.edu/modis/EMIS/html/em.html). Fig. 8 compares the LSTs retrieved from MODIS MIR data using the proposed method and those calculated using (13) from the in situ measurements, for all days with cloudfree conditions, at the time of the MODIS overpasses. Threeminute means of the ground-based observations were used. Fig. 8 shows that the bias and RMSE of the LSTs between the two measurements (ground-based and satellite-based methods)

This paper has developed a physics-based method to retrieve LST from the MODIS daytime MIR data in channels 22 (centered at 3.97 μm) and 23 (centered at 4.06 μm). On the basis of radiative transfer theory in the MIR region, a bidirectional reflectivity retrieval method proposed by Tang and Li [33] was used to separate the reflected solar direct irradiance and the radiances emitted by the surface and atmosphere. A kernel-driven BRDF model, i.e., RossThick-LiSparse-R, was proposed to describe the non-Lambertian reflective behavior of the land surface and to accordingly determine the directional emissivity if there were more than three bidirectional reflectances available with different angular configurations on several consecutive days. The MODIS LST/E product MYD11_L2, with LST retrieved using a generalized split-window algorithm at 1-km spatial resolution, was used to validate the proposed method. Comparisons of the LSTs estimated with the proposed method from the MODIS daytime MIR data and the values extracted from the MYD11_L2 LST product for the Baotou experimental site in Urad Qianqi, Inner Mongolia, China, on Julian days 145, 147, 149, and 151, in 2014, indicated a maximum RMSE of 1.69 K and a minimum RMSE of 1.31 K. To further demonstrate the proposed method, in situ LSTs measured at the Hailar field site in northeastern Inner Mongolia, China, were also used to validate the proposed method. The results showed that the bias and RMSE between the LSTs retrieved from MODIS daytime MIR data and those calculated using in situ measurements, at the time of the MODIS overpasses, were −0.17 K and 1.42 K, respectively, which implies that the proposed method could be used to accurately retrieve LST from MODIS daytime MIR data. R EFERENCES [1] H. Mannstein, “Surface energy budget, surface temperature, and thermal inertia,” in Remote Sensing Applications in Meteorology and Climatology, vol. 201, ser. NATO ASI Series, Series C: Mathematical and Physical Sciences, R. A. Vaughan and D. Reidel, Eds. Dordrecht, The Netherlands: Springer-Verlag, 1987. [2] P. J. Sellers, F. G. Hall, G. Asrar, D. E. Strebel, and R. E. Murphy, “The first ISLSCP field experiment (FIFE),” Bull. Amer. Meteorol. Soc., vol. 69, no. 1, pp. 22–27, Jan. 1988. [3] B.-H. Tang, Z.-L. Li, and R. Zhang, “A direct method for estimating net surface shortwave radiation from MODIS data,” Remote Sens. Environ., vol. 103, no. 1, pp. 115–126, Jul. 2006. [4] B.-H. Tang and Z.-L. Li, “Estimation of instantaneous net surface longwave radiation from MODIS cloud-free data,” Remote Sens. Environ., vol. 112, no. 9, pp. 3482–3492, Sep. 2008. [5] Z.-L. Li et al., “A review of current methodologies for regional evapotranspiration estimation from remotely sensed data,” Sensors, vol. 9, no. 5, pp. 3801–3853, May 2009. [6] J. Hansen, R. Ruedy, M. Sato, and K. Lo, “Global surface temperature change,” Rev. Geophys., vol. 48, no. 4, Dec. 2010, Art. no. RG4004. [7] F. N. Kogan, “Operational space technology for global vegetation assessment,” Bull. Amer. Meteorol. Soc., vol. 82, no. 9, pp. 1949–1964, Sep. 2001. [8] W. Kustas and M. Anderson, “Advances in thermal infrared remote sensing for land surface modeling,” Agric. Forest Meteorol., vol. 149, no. 12, pp. 2071–2081, Dec. 2009.


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