Temperature Vegetation Dryness Index-Based Soil Moisture Retrieval Algorithm Developed for Geo-KOMPSAT-2A

The Korea Meteorological Administration (KMA) has developed many product algorithms including that for soil moisture (SM) retrieval for the geostationary satellite Geo-Kompsat-2A (GK-2A) launched in December 2018. This was developed through a five-year research project owing to the significance of SM information for hydrological and meteorological applications. However, GK-2A’s visible and infrared sensors lack direct SM sensitivity. Therefore, in this study, we developed an SM algorithm based on the conversion relationships between SM and the temperature vegetation dryness index (TVDI) estimated for various land types in the full disk area using two of GK-2A’s level 2 products, land surface temperature (LST) and normalized difference vegetation index (NDVI), and the Global Land Data Assimilation System (GLDAS) SM data for calibration. Methodologically, various coefficients were obtained between TVDI and SM and used to estimate the GK-2A-based SM. The GK-2A SM algorithm was validated with GLDAS SM data during different periods. Our GK-2A SM product showed seasonal and spatial agreement with GLDAS SM data, indicating a dry-wet pattern variation. Quantitatively, the GK-2A SM showed annual validation results with a correlation coefficient (CC) >0.75, bias <0.1%, and root mean square error (RMSE) <4.2–4.7%. The monthly averaged CC values were higher than 0.7 in East Asia and 0.5 in Australia, whereas RMSE and unbiased RMSE values were <0.5% in East Asia and Australia. Discrepancies between GLDAS and GK-2A TVDI-based SMs often occurred in dry Australian regions during dry seasons due to the high LST sensitivity of GK-2A TVDI. We determined that relationships between TVDI and SM had positive or negative slopes depending on land cover types, which differs from the traditional negative slope observed between TVDI and SM. The KMA is currently operating this GK-2A SM algorithm.


Introduction
Soil moisture (SM) is a significant variable for understanding the hydrological cycle, agriculture, weather forecasting, and water management. Dry soil often provides favorable conditions for natural disasters such as wildfires and desertification [1][2][3], whereas wet soil information can be utilized for detecting floods or abnormal overflow of rivers. SM regulates the Earth's thermal energy balance through interactions between the soil and the atmosphere [4][5][6][7][8][9]. SM is also considered a fundamental parameter in climate change studies and atmospheric circulation [9][10][11].
Although providing point measurements within limited regions, ground observations are the most accurate and commonly used to obtain land variable data such as SM. Satellite remote sensing presents the advantage of providing global SM observations including for regions lacking ground measurements. Thus, satellites equipped with the visible (VIS), The study area included the entire GK-2A disk area, including Australia in the southern hemisphere and East Asia and the Korean Peninsula in the northern hemisphere, as observed by GK-2A located at 128.0 • E. The data from August 2019 to July 2020 were utilized because the GK-2A began to operate on 25 July 2019 [36]. The verification of the calculated GK-2A soil moisture was carried out on a different date from the one on which the soil moisture conversion coefficient was calculated. The ocean pixels in the full disk data were masked using the land/sea mask data of GK-2A. The pixels with the solar zenith angle of 70 • or higher were also masked due to inaccurate satellite observation. In addition, the water, permanent wet land, urban, built-up, snow, and ice regions were excluded using the GK-2A land cover data. Figure 1 shows the study area for estimating TVDI and soil moisture. For validation, we cropped East Asia to represent the northern hemisphere and Australia to represent the southern hemisphere from the full disk.
Remote Sens. 2021, 13, x FOR PEER REVIEW 3 of 22 rithm development and validation. The GK-2A SM was temporally and spatially compared with the GLDAS SM for different periods. In addition, this study confirmed the dependence of TVDI characteristics on land cover type.

Study Area
The study area included the entire GK-2A disk area, including Australia in the southern hemisphere and East Asia and the Korean Peninsula in the northern hemisphere, as observed by GK-2A located at 128.0° E. The data from August 2019 to July 2020 were utilized because the GK-2A began to operate on 25 July 2019 [36]. The verification of the calculated GK-2A soil moisture was carried out on a different date from the one on which the soil moisture conversion coefficient was calculated. The ocean pixels in the full disk data were masked using the land/sea mask data of GK-2A. The pixels with the solar zenith angle of 70° or higher were also masked due to inaccurate satellite observation. In addition, the water, permanent wet land, urban, built-up, snow, and ice regions were excluded using the GK-2A land cover data. Figure 1 shows the study area for estimating TVDI and soil moisture. For validation, we cropped East Asia to represent the northern hemisphere and Australia to represent the southern hemisphere from the full disk.

GK-2A/AMI Satellite
The GK-2A satellite, located at 128.0° E, covers East Asia, including the Korea peninsula, and Australia in the full disk every 10 min. The GK-2A/AMI sensor has 16 VIS and IR channels. A variety of GK-2A L2 products such as the LST and NDVI have been developed [37,38,58]. In this study, we used the GK-2A LST and NDVI L2 products for estimating the TVDI, and GLDAS SM data, which were provided by NMSC/KMA. Table 1 summarizes the full disk data information used in this study.

GK-2A/AMI Satellite
The GK-2A satellite, located at 128.0 • E, covers East Asia, including the Korea peninsula, and Australia in the full disk every 10 min. The GK-2A/AMI sensor has 16 VIS and IR channels. A variety of GK-2A L2 products such as the LST and NDVI have been developed [37,38,58]. In this study, we used the GK-2A LST and NDVI L2 products for estimating the TVDI, and GLDAS SM data, which were provided by NMSC/KMA. Table 1 summarizes the full disk data information used in this study.  Table 2 summarizes the land covers used in this study. Notably, land cover areas were fixed because of annual average values. This may have caused differences around the borders between two different land types.

GLDAS
GLDAS, including SM, soil condition, and canopy condition data [59], is one of the representative global modeling systems for the land environment provided by NASA. It has been available since 1948. GLDAS SM data have been widely used as verification data in various SM studies [5,[60][61][62]. The GLDAS products incorporate various modeling systems (Noah, CLM, VIC, and Mosaic) and various datasets based on ground observations. GLDAS has a spatial resolution of 0.25 • and 1.0 • , and a temporal resolution of 3 h and 1 month for monitoring daily and monthly variations. In particular, GLDAS SM data include many soil layers: 0-10 cm, 10-40 cm, 40-100 cm, and 100-200 cm.
This study used the GLDAS L4 SM data for the 0-10 cm layer with a 0.25 • spatial resolution and a 3 h temporal resolution for the development and validation of the GK-2A SM algorithm according to the KMA's requirements for algorithm development.

TVDI Calculation Using GK-2A LST and NDVI
In this study, TVDI is an intermediate parameter used to estimate the GK-2A SM. TVDI is determined in the LST/NDVI space as a function of LST max and LST min , which are obtained from the linear regressions of NDVI and LST [40,42]. Figure 2 shows a scatterplot between the NDVI and the LST and illustrates the characteristics of TVDI. The regression line with the top dashed line represents LST max , and the regression line with the bottom dashed line indicates LST min . LST max represents the dry edge, while LST min indicates the wet edge. In the dry edge, the TVDI value is 1, which mainly exists in the bare soil Two edge lines and in the LST/NDVI space are expressed as follows [33,40,42]: where , b, c, d are the coefficients determined for and using real LST and NDVI data. This study used the GK-2A L2 LST and NDVI products. Table 3 shows the coefficient values of and according to the land cover on 19 July 2020.  Two edge lines LST max and LST min in the LST/NDVI space are expressed as follows [33,40,42]: where a, b, c, d are the coefficients determined for LST max and LST min using real LST and NDVI data. This study used the GK-2A L2 LST and NDVI products. Table 3 shows the coefficient values of LST max and LST min according to the land cover on 19 July 2020. TVDI is calculated using LST max and LST min as follows: where LST s,obs is the observed LST at a specific pixel.

Conversion Relationship between TVDI and SM
In this study, we applied linear regression to convert TVDI into SM based on the existent linear relationships between TVDI and model SM [63] as follows: where SM is the GK-2A SM in units of volumetric ratio (m 3 /m 3 ). A and B are the intercept and the slope for converting TVDI into SM, respectively. In this step, we used the GLDAS SM and GK-2A-derived TVDI to obtain these slopes and intercepts for various land cover types. Table 4 summarizes the data periods in which we obtained the conversion coefficients between TVDI and SM and validated the GK-2A-derived SM.   Table 5 summarizes the daily-averaged slopes and intercepts for different land cover types in the northern and southern hemispheres on 9 July 2020. Our linear relationships between TVDI and GLDAS SM for 16 land types showed low correlation coefficient values ranging from −0.432 to 0.268 in the northern hemisphere, while we found high correlation coefficients ranging from −0.845 to 0.360 in the southern hemisphere. In particular, our study showed a relatively low correlation between TVDI and SM for forests and savannas in the northern hemisphere and showed variable correlations, including high correlations for open shrublands, savannas, and grasslands and low correlations for mixed forest and closed shrublands, in the southern hemisphere. Notably Chen et al. (2015) [53] showed a negative correlation between the TVDI using LANDSAT-5 Thematic Mapper data and the in situ measured SM (R 2 = 0.15-0.8 in the Laoshan forest, the largest forest in Nanjing, China) under different tree species. In this study, all the data were synthesized as 10-day average data as per another requirement of the NMSC/KMA for their use. Notably, the elevation-correction to the LST was not performed because the GK-2A LST data were already calibrated according to the elevation pressure [37,58]. The GK-2A and GLDAS collocated in terms of their respective latitude and longitude data based on the calculation of the latitude and longitude of the nearest distance. Figure 3

Statistical Factors
In this study, the GK-2A SMs were quantitatively validated with the GLDAS SM data using the statistical indices: correlation coefficient (CC), bias, the root mean square error (RMSE), and unbiased RMSE (ubRMSE) as follows [64,65]: where is the total number of pixels in the corresponding GK-2A and GLDAS data, is the index from 1 to N, , indicates the SM of the pixel in the GLDAS data, and

Statistical Factors
In this study, the GK-2A SMs were quantitatively validated with the GLDAS SM data using the statistical indices: correlation coefficient (CC), bias, the root mean square error (RMSE), and unbiased RMSE (ubRMSE) as follows [64,65]:  Figure 4 shows the scatterplots between NDVI and LST data of GK-2A for 13 different land cover types (evergreen needleleaf forest, evergreen broadleaf forest, deciduous needleleaf forest, deciduous broadleaf forest, mixed forest, closed shrublands, open shrublands, woody savannas, savannas, grasslands, croplands, cropland/natural vegetation mosaic, and barren or sparsely vegetated) in the northern hemisphere on 19 Figure 6 shows the temporal variation of the 10-day averaged slopes of for various land types in East Asia and Australia during winter, spring, summer, and autumn of one year [55]. Sandholt et al. (2002) [55] reported that the slope of the function in the NDVI/LST space can be an indicator for determining dry periods [55]; further, TVDI is particularly variable in dry regions or dry periods as compared to those in wet regions or periods [55].

TVDI
The slopes for both East Asia and Australia showed common sinusoidal seasonal variations, which decreased relatively quickly during the dry season, from winter to early summer, and increased during other seasons. The slope values fluctuated more severely during the dry period from winter to early summer than during the wet period from summer to early winter. Notably, the barren or sparsely vegetated area (land cover 16) showed the highest variation in the slope value. Furthermore, the comparison between East Asia and Australia showed increased slope variation for each land cover in Australia compared to those in East Asia due to the higher ratio of dry regions in Australia than those in East Asia. These results show agreement with those of a previous study [55].  Figure 6 shows the temporal variation of the 10-day averaged slopes of LST max for various land types in East Asia and Australia during winter, spring, summer, and autumn of one year [55]. Sandholt et al. (2002) [55] reported that the slope of the LST max function in the NDVI/LST space can be an indicator for determining dry periods [55]; further, TVDI is particularly variable in dry regions or dry periods as compared to those in wet regions or periods [55].
The slopes for both East Asia and Australia showed common sinusoidal seasonal variations, which decreased relatively quickly during the dry season, from winter to early summer, and increased during other seasons. The slope values fluctuated more severely during the dry period from winter to early summer than during the wet period from summer to early winter. Notably, the barren or sparsely vegetated area (land cover 16) showed the highest variation in the slope value. Furthermore, the comparison between East Asia and Australia showed increased slope variation for each land cover in Australia compared to those in East Asia due to the higher ratio of dry regions in Australia than those in East Asia. These results show agreement with those of a previous study [55]. Remote Sens. 2021, 13, x FOR PEER REVIEW 11 of 22  Figure 7 illustrates the 10-day-averaged TVDI values for various land cover types in East Asia and Australia. Notably, the amount of vegetation decreased and the heights of trees decreased as the amount of land cover increased. East Asia showed stable temporal variations in TVDI values in general land types except for bare soil in spring. Australia showed similar patterns to East Asia, and greater variation for bare soil (land cover 16) than in East Asia. We identified that TVDI values highly fluctuated during the dry periods from January 1 to May 10 in East Asia and from August 28 to May 1 in Australia. The TVDI values were sometimes >1, especially in Australia, which is in agreement with a previous finding that TVDI values often exceed 1 in regions where LST is rapidly increasing because TVDI is sensitive to the effects of LST [55]. Thus, we examined the distributions of LST in East Asia and Australia during winter and summer (Figure 8) because TVDI values varied more in Australia than they did in East Asia and were often >1.  Figure 7 illustrates the 10-day-averaged TVDI values for various land cover types in East Asia and Australia. Notably, the amount of vegetation decreased and the heights of trees decreased as the amount of land cover increased. East Asia showed stable temporal variations in TVDI values in general land types except for bare soil in spring. Australia showed similar patterns to East Asia, and greater variation for bare soil (land cover 16) than in East Asia. We identified that TVDI values highly fluctuated during the dry periods from January 1 to May 10 in East Asia and from August 28 to May 1 in Australia. The TVDI values were sometimes >1, especially in Australia, which is in agreement with a previous finding that TVDI values often exceed 1 in regions where LST is rapidly increasing because TVDI is sensitive to the effects of LST [55]. Thus, we examined the distributions of LST in East Asia and Australia during winter and summer (Figure 8) because TVDI values varied more in Australia than they did in East Asia and were often >1.     Figure 7. The LST values in Australia increased sharply because most regions in Australia were dry except for the outskirts. In addition, LST increased rapidly in the Gobi Desert compared to that in other regions in East Asia. Therefore, TVDI values are often >1.  Figure 9 shows the three-month-averaged GK-2A and GLDAS SM data for spring (March, April, and May), summer (June, July, and August), autumn (September, October, and November), and winter (December, January, and February). The GK-2A SM showed a similar pattern to that of GLDAS SM including dry-wet patterns, while GK-2A SM showed discontinuous SM patterns near the Gobi Desert in the northern hemisphere and inland Australia in the southern hemisphere due to the fixed land cover area.   Table 6 summarizes the statistical results of the previous scatterplots.    resolution and 3-day-average intervals over the global land area excluding regions of snow and ice, frozen ground, mountainous topography, open water, and urban areas (https://smap.jpl.nasa.gov/science/objectives, access on 11 May 2021) Further, the RMSE of our GK-2A SM results ranged within the analogous values of the error requirement of SMAP SM. Table 6 summarizes the statistical results of the previous scatterplots.   Figure 12 shows the different characteristics of GK-2A SM in the northern and southern hemispheres based on the temporal dynamics of the spatial CC and RMSE between GK-2A and GLDAS SM in East Asia and Australia during one year. Figure 12a shows good and consistent agreement of CC (>0.7) between GK-2A and GLDAS SM in East Asia. In Australia, the CC values from February to November were similar to those in East Asia, whereas the CC values decreased rapidly during January and December, i.e., summer in the southern hemisphere. This may be attributed to the rapid increase of the LST effect in the Australian summer, which was described with the TVDI values being >1 in this period. Notably, Figure 12b,c shows that RMSE and ubRMSE values in Australia were consistent and smaller (0.03 m 3 /m 3 to 0.04 m 3 /m 3 ) than those in East Asia (0.04 m 3 /m 3 to 0.05 m 3 /m 3 ). However, the CC values dropped in January and December, which is summer in the southern hemisphere.   Figure 12a shows good and consistent agreement of CC (>0.7) between GK-2A and GLDAS SM in East Asia. In Australia, the CC values from February to November were similar to those in East Asia, whereas the CC values decreased rapidly during January and December, i.e., summer in the southern hemisphere. This may be attributed to the rapid increase of the LST effect in the Australian summer, which was described with the TVDI values being >1 in this period. Notably, Figure 12b

Discussion
In this study, the conversion coefficients between TVDI and SM were obtained for each land cover. Previous TVDI studies indicated that TVDI was negatively correlated with the model and ground observations of SM. However, this study determined the existence of positive as well as negative correlations between TVDI and SM based on satellite

Discussion
In this study, the conversion coefficients between TVDI and SM were obtained for each land cover. Previous TVDI studies indicated that TVDI was negatively correlated with the model and ground observations of SM. However, this study determined the existence of positive as well as negative correlations between TVDI and SM based on satellite observations and GLDAS SM data. TVDI variations in dry regions and periods increased due to the slope of LST max , a function of NDVI and LST, which can undergo drastic changes [55]. Figure 13 shows the scatterplots with negative (Figure 13a,c) and positive slopes (Figure 13b,d) between TVDI and the SM for different land cover types from August 2019 to July 2020 in the full disk of the GK-2A. The results in Figure 13a,c showed agreement with previous studies [53,55], but Figure 13b,d indicated differing results. In terms of data frequency, different land cover types showed similar data pixels in the northern hemisphere, as shown in Figure 13a,b. However, data frequencies in the southern hemisphere were concentrated in small areas with high TVDI and low SM values in the TVDI and SM space, as shown in Figure 13c observations and GLDAS SM data. TVDI variations in dry regions and periods increased due to the slope of , a function of NDVI and LST, which can undergo drastic changes [55]. Figure 13 shows the scatterplots with negative (Figure 13a,c) and positive slopes (Figure 13b,d) between TVDI and the SM for different land cover types from August 2019 to July 2020 in the full disk of the GK-2A. The results in Figure 13a,c showed agreement with previous studies [53,55], but Figure 13b,d indicated differing results. In terms of data frequency, different land cover types showed similar data pixels in the northern hemisphere, as shown in Figure 13a,b. However, data frequencies in the southern hemisphere were concentrated in small areas with high TVDI and low SM values in the TVDI and SM space, as shown in Figure 13c,d. These results indicate the simple land types such as dry regions in most parts of Australia.  Figure 14 shows the positively correlated data distribution between TVDI and SM ( Figure 13) represented in the NDVI/LST space. In Figure 14, the green line shows wet soil regions with high vegetation, high LST, and high TVDI values. The red line indicates dry soil regions with low vegetation, low LST, and high TVDI values. The regions with high vegetation density and high LST values were related to wet soil due to a high vegetation canopy. Thus, high TVDI values can be calculated based on the high LST value in this region. The regions with low vegetation density and low LST were related to dry soil due to a low vegetation canopy. However, high TVDI can be calculated based on the low LST value in this region.  Figure 14 shows the positively correlated data distribution between TVDI and SM ( Figure 13) represented in the NDVI/LST space. In Figure 14, the green line shows wet soil regions with high vegetation, high LST, and high TVDI values. The red line indicates dry soil regions with low vegetation, low LST, and high TVDI values. The regions with high vegetation density and high LST values were related to wet soil due to a high vegetation canopy. Thus, high TVDI values can be calculated based on the high LST value in this region. The regions with low vegetation density and low LST were related to dry soil due to a low vegetation canopy. However, high TVDI can be calculated based on the low LST value in this region. The quality of microwave satellite-based SM values such as SMAP and SMOS is insufficient for surface conditions that include mountainous terrain and dense vegetation with high vegetation water content (VWC) [66] because of the dependence on the radiative transfer model; sensitivity of polarization to the surface SM; various and a priori ancillary data including physical temperature, vegetation, roughness, and soil texture [21]; or a relation between SM and VWC [12]. In particular, it is difficult to directly measure the VWC, while NDVI has a high sensitivity to abrupt environmental change, such as floods and droughts, without a priori information [67]. Thus, this study, based on the TVDI as a function of NDVI and LST, showed feasible results for the vegetated and mountainous topology in the Korean Peninsula in addition to providing SM information, including regions lacking ground measurements and SMAP and SMOS SM values, and supplementing low spatial and temporal resolutions of GLDAS SM in the Korean Peninsula.

Summary and Conclusions
This study presented the GK-2A SM algorithm using TVDI as a function of GK-2A LST and NDVI products. GLDAS SM data were used for GK-2A SM algorithm development and validation as a requirement of the KMA. We obtained the daily LST, NDVI, TVDI, and GLDAS SM data and then composited 10-day-averaged LST, NDVI, TVDI, and SM data for various land types. The conversion coefficients between TVDI and GLDAS SM for different land types were obtained and validated with GLDAS SM for different periods from August 2019 to July 2020. The results showed a high CC of >0.75 in East Asia and >0.5 in Australia for all seasons, low bias from −0.001 to 0.001 m 3 /m 3 , and low RMSE of <0.05 m 3 /m 3 . Notably, the RMSE results showed a low error rate of 0.05 m 3 /m 3 or less, which is close to the NASA's accuracy requirement for SM products for the SMAP mission. The GK-2A SM values were accurate except those for summer in Australia. The slope of , a function of NDVI and LST, can show drastic changes. Our results presented this characteristic in the drier southern hemisphere but not in the northern hemisphere. We also identified and explained the positive correlation between TVDI and SM due to the high sensitivity of TVDI to LST. Our GK-2A SM algorithm has an advantage of better spatial and temporal resolutions compared to those of the other algorithms implemented in geostationary weather satellites. It allows for the monitoring of more spatial structures that would not be identified by GLDAS, captures extreme events where the SM content can change very quickly, and shows an accuracy similar to that of SM products of polarorbiting microwave satellites. However, the algorithm is dependent on the accuracy of GK-2A LST and NDVI products. The KMA is currently operating the proposed SM retrieval algorithm. A future scope of study will be to improve the conversion coefficients between TVDI and SM in our algorithm using the long-term GK-2A observational data. The quality of microwave satellite-based SM values such as SMAP and SMOS is insufficient for surface conditions that include mountainous terrain and dense vegetation with high vegetation water content (VWC) [66] because of the dependence on the radiative transfer model; sensitivity of polarization to the surface SM; various and a priori ancillary data including physical temperature, vegetation, roughness, and soil texture [21]; or a relation between SM and VWC [12]. In particular, it is difficult to directly measure the VWC, while NDVI has a high sensitivity to abrupt environmental change, such as floods and droughts, without a priori information [67]. Thus, this study, based on the TVDI as a function of NDVI and LST, showed feasible results for the vegetated and mountainous topology in the Korean Peninsula in addition to providing SM information, including regions lacking ground measurements and SMAP and SMOS SM values, and supplementing low spatial and temporal resolutions of GLDAS SM in the Korean Peninsula.

Summary and Conclusions
This study presented the GK-2A SM algorithm using TVDI as a function of GK-2A LST and NDVI products. GLDAS SM data were used for GK-2A SM algorithm development and validation as a requirement of the KMA. We obtained the daily LST, NDVI, TVDI, and GLDAS SM data and then composited 10-day-averaged LST, NDVI, TVDI, and SM data for various land types. The conversion coefficients between TVDI and GLDAS SM for different land types were obtained and validated with GLDAS SM for different periods from August 2019 to July 2020. The results showed a high CC of >0.75 in East Asia and >0.5 in Australia for all seasons, low bias from −0.001 to 0.001 m 3 /m 3 , and low RMSE of <0.05 m 3 /m 3 . Notably, the RMSE results showed a low error rate of 0.05 m 3 /m 3 or less, which is close to the NASA's accuracy requirement for SM products for the SMAP mission. The GK-2A SM values were accurate except those for summer in Australia. The slope of LST max , a function of NDVI and LST, can show drastic changes. Our results presented this characteristic in the drier southern hemisphere but not in the northern hemisphere. We also identified and explained the positive correlation between TVDI and SM due to the high sensitivity of TVDI to LST. Our GK-2A SM algorithm has an advantage of better spatial and temporal resolutions compared to those of the other algorithms implemented in geostationary weather satellites. It allows for the monitoring of more spatial structures that would not be identified by GLDAS, captures extreme events where the SM content can change very quickly, and shows an accuracy similar to that of SM products of polar-orbiting microwave satellites. However, the algorithm is dependent on the accuracy of GK-2A LST and NDVI products. The KMA is currently operating the proposed SM retrieval algorithm. A future scope of study will be to improve the conversion coefficients between TVDI and SM in our algorithm using the long-term GK-2A observational data.