Surface Temperature Retrieval From Gaofen-5 Observation and its Validation

Surface temperature (ST) plays a great role in urban heat island effect, environment monitoring, earth resources monitoring, and water balance at local and global scales. The Chinese Gaofen-5 (GF5) satellite can capture Earth’s thermal infrared information for use in national high-resolution Earth observations. In this article, the nonlinear split-window algorithm and the refined generalized split-window method are used to retrieve sea surface temperature (SST) and land surface temperature (LST) from GF5 observations. For different atmospheric and surface conditions, the algorithm coefficients are calculated using a statistical regression method from the numerical values simulated with the atmospheric radiative transfer model MODTRAN 5.0. The simulation results show that the root mean square error (RMSE) for SST and LST retrieval ranges from 0.09 K to 0.46 K and 0.19 K to 0.69 K, respectively, with increasing water vapor content (WVC). To validate the retrieved STs, Moderate Resolution Imaging Spectroradiometer (MODIS) STs extracted from the MYD11A1 product are used. Note that the RMSEs of both the LST and SST are less than 3.3 K. The RMSE for SST retrieval varies from 1.2 K to 1.45 K, with a mean value of 1.33 K; the RMSE for LST retrieval ranges from 1.57 K to 3.3 K, with a mean value of 2.41 K.

The associate editor coordinating the review of this manuscript and approving it for publication was Stefania Bonafoni . have provided us with a reliable data source to obtain ST over the entire globe.
To date, a large number of methods have been proposed to retrieve LST and SST from thermal infrared (TIR) remotely sensed data. McMillin first proposed a split-window (SW) algorithm to retrieve SST from two satellite TIR channels without atmospheric profile information [24]. Subsequently, many algorithms were developed to successfully obtain SST. Additionally, with the development of remote sensing applications, scientists have proposed many methods to retrieve LST based on the approximation and hypothesis of the atmospheric radiation transfer model. Some scientists extended the SW algorithm to LST retrieval with the knowledge of land surface emissivity (LSE), such as the linear SW algorithm and nonlinear SW algorithm. Wan et al. proposed a generalized split-window (GSW) method that is widely used to retrieve LST based on the differential water vapor absorption in two adjacent TIR channels [25].
Over the past two years, some methods have been proposed to retrieve LST or SST from simulated GF5 data. For example, Chen et al. used the semiempirical quadratic SW equation to retrieve SST from simulated GF5 data, and a bias of −0.05 K and a root mean square error (RMSE) of 0.53 K were obtained [28]. Tang developed nonlinear SW algorithms to estimate LST and SST from simulated Chinese GF5 satellite data, and the results showed that the methods are appropriate, with an RMSE of 0.7 K for LST retrieval and an RMSE of 0.3 K for SST retrieval [33]. Ye et al. proposed a four-channel method to retrieve LST from GF5 data simulated from Thermal Airborne Spectrographic Imager (TASI) data with an RMSE less than 1 K [34]. Ren et al. used a hybrid algorithm to retrieve LST and LSE with simulated GF5 data, and the results showed that this method can obtain an RMSE less than 1 K and 0.015, respectively [35]. Meng et al. used the real GF5 data to obtain LST and SST, the retrieval results were relatively ideal cross-validated by Moderate-resolution Imaging Spectroradiometer (MODIS) LST/SST, Visible infrared Imaging Radiometer (VIIRS) LST/SST, and Advanced Himawari Imager (AHI) SST products [26]. However, LST and SST retrieved from the simulated data can obtain acceptable results, but these retrieval methods used on the real GF5 data still need to be further verified with sufficient images. The objective of this article is to evaluate the LST and SST retrieval approaches applied to real GF5 TIR observations based on different test sites.
This article is organized as follows: Section 2 describes the methodology for the LST and SST retrieval methods. In Section 3, the retrieval algorithms are applied GF5 data, and the results are validated with MODIS LST products. The conclusions are presented in Section 4.

II. METHODOLOGY AND SIMULATION DATASETS A. THERMAL RADIATIVE TRANSFER EQUATION
From the radiative transfer theory, for a cloud-free atmosphere under local thermodynamic equilibrium, the radiative transfer equation (RTE) in the TIR channel can be written as [36] (1) in which B i (T ) is the radiance of the blackbody at temperature T, T i is the brightness temperature for channel i, ε i and T s are surface emissivity in channel i and the surface temperature, respectively, τ i is the transmittance in channel i, and R ↑ atm_i and R ↓ atm_i are the upwelling and downwelling atmospheric thermal radiance in channel i, respectively. To obtain ST from (1), the atmospheric effect and LSE must be known or removed in advance. According to the SW algorithm, the atmospheric effect can be removed based on the differential water vapor absorption in the two adjacent TIR channels.

B. SST RETRIEVAL ALGORITHM
The linear SW algorithm for SST retrieval was first proposed by McMillin in the 1970s. To improve the accuracy of SST retrieval, a nonlinear SW algorithm was developed from satellite TIR data as [28] where SST is the sea surface temperature, T i and T j are the TOA brightness temperatures in TIR channels i and j, respectively, and a 0 ∼ a 5 are fitting coefficients.

C. LST RETRIEVAL ALGORITHM
Wan et al. first used a GSW algorithm to retrieve LST based on the differential water vapor absorption in two adjacent TIR channels. Then they refined this method by adding a quadratic term of the difference between two TIR brightness temperatures to improve the accuracy. Therefore, in this study, the widely used GSW algorithm is selected, this algorithm can be written as [37] where ε i and ε j are the LSEs in channels i and j, respectively, ε is the averaged emissivity, ε is the emissivity difference between the two TIR channels, and b i (i = 0∼7) is the unknown coefficient that can be derived from simulated data.

D. LSE ESTIMATION
LSE is a crucial factor in the retrieval of LST. It can be seen from (1) that LSE must be corrected before LST retrieval. However, LST and LSE are coupled together through the RTE, and it is quite difficult to separate the two parameters. Tang et al. used an improved normalized difference vegetation index (NDVI)-based threshold method to retrieve LSE [38]. In this method, the pixels are divided into three kinds: bare soil pixels, dense vegetation pixels, and soil/vegetation mixed pixels. For the bare soil pixels, LSE is estimated from the relationship between the visible/nearinfrared channel reflectances and TIR emissivities (see (4)).
For the dense vegetation pixels, LSE is calculated by the relationship between the TIR emissivities and NDVI for dense vegetation (NDVI v ) (see (5)). For the soil/vegetation mixed pixels, LSE is calculated according to the proportion of bare soil to vegetation (see (6)). LSE can be calculated as: where ε si represents emissivity of bare soil in the pixel for TIR channel i, a i0 and a ij are the regression coefficients for TIR channel i, ρ j is visible/near-infrared reflectance in channel j, and n means that there are n visible/near-infrared channels. The value ε vi represents the emissivity of dense vegetation in the pixel for TIR channel i, b i0 is the regression coefficient for TIR channel i, and ε i is the emissivity of the soil/vegetation mixed pixel for TIR channel i. P v is the vegetation proportion, and it can be calculated from: where NDVI v and NDVI s are the values for full vegetation and bare soil pixels, respectively. In this part, NDVI v and NDVI s are set to be 0.86 and 0.2, respectively. This means that if the NDVI value is less than 0.2, the pixel is regarded as a bare soil pixel, while the full vegetation pixel is determined with an NDVI larger than 0.86. NDVI can be calculated from the red and near-infrared reflectance. The term C i in (6) includes the effect of geometrical distribution on natural surfaces and internal reflections, expressed as where F is a shape factor ranging from 0 to 1, and normally to be set as a mean value of 0.55.

E. DATA SIMULATION
The MODTRAN 5.0 radiative transfer code is used to predict the brightness temperatures at TOA to obtain the coefficients in (2) and (3)    at nadir, the view zenith angle (VZA) is set to be 0 • in MODTRAN 5.0. Fig. 1 shows the RMSEs of SST and LST retrieval using the coefficients of (2) and (3) obtained from simulation data (see Table 1 and Table 2). The accuracies of SST retrieval are better than those of LST retrieval in all WVC subranges. The RMSEs increase with increasing WVC for both SST and LST retrieval. The minimum RMSE for SST (LST) retrieval is 0.09 K (0.19 K) and appears in the subrange of WVC ∈ [0-1.5 g/cm 2 ], while the maximum RMSE for SST (LST) retrieval is 0.46 K (0.69 K) appears in the subrange of WVC ∈ [4-5.5 g/cm 2 ]. VOLUME 9, 2021 F. SENSITIVITY ANALYSIS The LST and SST retrieval accuracies are mainly affected by the instrument noise equivalent difference temperature (NE T), and the uncertainties of LSEs and WVCs. In this section, the uncertainties of NE T, LSE, and WVC for ST retrieval are investigated.   The errors caused by the uncertainties of LSE and WVC are shown in Fig. 3. The results demonstrate that an uncertainty of 1% in the LSEs causes an error ranges from 0.37 K to 0.73 K for LST retrieval; an uncertainty of 10% in the WVCs can produce errors ranging from 0.19 K to 0.69 K (0.09 K to 0.46 K) for LST (SST) retrieval, respectively. Both errors increase with increasing WVCs.
Considering the instrument noises (δ(LST NE T )), the uncertainties of LSEs (δ(LST ε )) and WVCs (δ(LST WVC )), and the accuracy of the algorithm (δ(LST r )), the overall error on the ST (δ(ST )) can be described as follows: Fig. 4 shows the overall errors in LST and SST retrieval. It can be seen from Fig. 4(a) that the maximum RMSE is approximately 2.5 K for the uncertainties of NE T: 0.5 K, LSE: 1%, and WVC: 10%; the minimum RMSE is approximately 0.46 K for the uncertainties of NE T: 0.1 K, LSE: 1%, and WVC: 10%. Fig. 4(b) shows the overall errors in SST retrieval without LSE error. The figure demonstrates that the maximum RMSE is approximately 1.9 K for the uncertainties of NE T: 0.5 K and WVC: 10%; the minimum RMSE is approximately 0.21 K for the uncertainties of NE T: 0.1 K and WVC: 10%. Because the uncertainty of WVC has relatively little influence on SST retrieval, the overall error is mostly caused by NE T.

III. PRELIMINARY APPLICATION TO GF5 DATA A. CROSS-CALIBRATION
To obtain the LST and SST information, radiometric calibration is the first and most important step. Because of the unserviceable official calibration coefficients for GF5 images, the VIIRS TIR images are used for cross-calibration because of the high calibration accuracy. Fig. 5 displays the spectralresponse functions of VIIRS TIR (bands 15 and 16) and GF5 TIR (bands 9, 10, 11, and 12). GF5 bands 11 and 12 are selected as the ST retrieval bands due to the similarity between GF5 bands 11 and 12 and VIIRS bands 15 and 16. Because of the difference between the spectral response functions of VIIRS and GF5, 70 different emissivities and atmospheric profiles with WVC ∈ [0-1.5 g/cm 2 ] are used to calculate the spectral matching factor. Fig. 6 shows the spectral matching factors for VIIRS bands 15 and 16. We can see that for VIIRS band 15 (16), the slope is 0.98435 (0.98897) and the intercept is 0.09177 (0.04396). Therefore, the GF5 TIR radiances can be obtained using the two empirical relationships below from VIIRS TIR images.
where R G 11 and R G 12 are the radiances of GF5 TIR data and R V 15 and R V 16 are the radiances of VIIRS TIR data. For GF5 TIR channel i, the relationship between the TOA radiance and the image digital number (DN) can be written as: where DN j is the DN value in pixel j and the value of Offset is assumed to be 0 in this article, R G i is the TIR radiance in channel i of GF5. To derive the cross-calibration coefficient Gain, a common calibration area is selected. In this article, only 7 clear-sky  GF5 TIR images are available for retrieving STs: three images of the Qinghai Lake (see Fig. 7) for SST retrieval, and four images of Dalat, Dunhung, and Geermu (see Fig. 8) for LST retrieval. First, the spatial resolution of GF5 and VIIRS TIR images should be matched. Then calibration sites including 6 × 6 pixels covered by soil (for LST retrieval) and sea water (for SST retrieval) are selected to calculate the coefficients. Based on the mean value of DNs for GF5 and radiances obtained from VIIRS radiances using (10) and (11) in the calibration sites, the calibration coefficient (Gain) can be derived from (12). From the results, it can be found that the calibration coefficients are not the same for different days (see Table 3); therefore, radiometric calibration should be carried out for each GF5 image.

B. RESULTS AND VALIDATION
After data processing, the SSTs and LSTs can be derived using (2) and (3) from the real GF5 TIR data, respectively. The coefficients of the two retrieval algorithms are both determined by the WVC. In this part, the MODIS WVC product is used to obtain information on the water vapor content. VOLUME 9, 2021 The MODIS level-2 atmospheric precipitable water product consists of total atmospheric column water vapor amounts over clear land and oceanic areas of the globe, and the short name for this level-2 MODIS total precipitable water vapor product is MYD05 [39]. Based on MYD05, the coefficients can be selected.   9 shows the SST and LST retrieval results for different underlying surfaces. It is obvious that for the same day, the temperature of water is lower than that of soil and rock. The temperature of the soil is higher than that of vegetation. A possible reason is the specific heat capacity of water is higher than those of vegetation and soil. Water can absorb or release a large quantity of heat energy with little change in temperature. Thus, under the same radiation conditions, the temperature of the water body is lower than the other two kinds of underlying surface temperatures.
Because of the lack of in situ measurements, MODIS LST products (short name: MYD11A1) are used to cross-validate the STs retrieved from GF5 TIR data. The MYD11A1 Version 6 product provides daily per-pixel land surface temperature and emissivity (LST&E) with 1 kilometer (km) spatial resolution in a 1,200 by 1,200 km grid [37], [40]. The MODIS reprojection tool (MRT) was used to transform the sinusoidal projection (which is used in the LST products) onto a geographic projection (which is used in the GF5 images). For the MYD11A1 product, the scientific data sets of the daytime LSTs and quality control (QC) are selected.
Due to the spatial resolution difference between the retrieved STs and MODIS LST products, equation (13) is used to make them to the same resolution.
where ST is the aggregated target pixel value, N is the total pixel number in the target pixel, ω j is the weight of pixel j, S j,p is the partial area of pixel j overlapping with the target pixel, S j is the total area of pixel j, and ST j is the temperature information of the pixel j. Additionally, the QC value of MODIS LST product is used to decide whether the aggregated retrieved ST is selected. The aggregated pixel is recognized as useful when QC equals 0 in this study. Fig. 10 and 11 show the RMSEs of MODIS STs minus retrieved STs. From Fig. 10, it can be found that the RMSE for  SST retrieval ranges from 1.2 K to 1.45 K with a mean value of 1.33 K. The figures in Fig. 11 demonstrate that the RMSE for LST retrieval ranges from 1.57 K to 3.3 K with a mean value of 2.41 K. We can see that there are some differences between MODIS STs and the retrieved STs, which may be due to the following: 1) the difference on imaging times of MODIS and GF5 is approximately 30 minutes, which can lead to different radiation for the two TIR images; or 2) there is a large difference in spatial resolution for the two datasets, which may produce some errors during the process of upscaling. Furthermore, it is obvious that the accuracy of SST retrieval is better than that of LST retrieval. The possible reason for this result is that water emissivity is higher than the emissivity of soil and rock, and the SST can also be retrieved by assuming the water emissivity as a constant value, while the LSE must be known in advance for LST retrieval. Therefore, the effect of emissivity uncertainty for SST retrieval is less than that for LST retrieval.

IV. CONCLUSION
In this study, the nonlinear SW algorithm and the refined GSW method are used to retrieve SST and LST, respectively, for real GF5 TIR images. The coefficients of the two algorithms are calculated using a statistical regression method from the numerical values simulated with the atmospheric radiative transfer model MODTRAN 5.0 under different atmospheric and surface conditions. From the simulation results, it can be seen that the RMSEs for SST (LST) retrieval range from 0.09 K(0.19 K) to 0.46 K (0.69 K) as the WVC increases. In addition, the sensitivity analysis is performed in terms of NE T, the uncertainty of the LSE and WVC. The results show that when WVC ranges from 0 g/cm 2 to 1.5 g/cm 2 , an NE T of 0.1 K, 0.2 K, and 0.5 K can produce 0.32 K (0.21 K), 0.41 K (0.29 K), and 0.57 K (0.48 K) for LST (SST) retrieval; an uncertainty of 10% in the WVCs will result in an error of 0.20 K and 0.09 K for LST retrieval and SST retrieval, respectively; an uncertainty of 1% in the LSEs carries an error ranging from 0.37 K to 0.73 K for LST retrieval.
Finally, the two algorithms are applied to the real GF5 TIR images covered by water and soil. Due to the unserviceable official calibration coefficients for GF5 TIR images, GF5 images are cross-calibrated by VIIRS TIR images. Additionally, the TIR LSE is obtained with the help of GF5 visible images. Unfortunately, in situ measurements are unavailable, and the MODIS LST product MYD11A1 is used for crossvalidation. From the cross-validation results, it can be seen that both RMSEs of LST and SST are less than 3.3 K, which are caused by the difference on imaging times of MODIS and GF5, and the difference in spatial resolution for the two datasets. The RMSE for SST retrieval varies from 1.2 K to 1.45 K with a mean value of 1.33 K, and the RMSE for LST retrieval is from 1.57 K to 3.3 K with a mean value of 2.41 K. The results indicate that the two ST retrieval methods can be applied to real GF5 TIR observations, and the retrieval accuracy is less than 3.3 K. Notably, the calibration coefficients are unstable for the TIR images of different days; therefore, the radiometric calibration should be carried out for each GF5 image.
In the future, more GF5/MSI images would be used for LST retrieval using the Temperature Emissivity Separation (TES) algorithm, and the corresponding in situ measurements will be collected for validating the retrieved LST. Meanwhile, these factors related to RMSE for LST retrieval in each site would be quantitatively analyzed.