Soil Moisture–Vegetation–Carbon Flux Relationship under Agricultural Drought Condition using Optical Multispectral Sensor

: Agricultural drought is triggered by a depletion of moisture content in the soil, which hinders photosynthesis and thus increases carbon dioxide (CO 2 ) concentrations in the atmosphere. The aim of this study is to analyze the relationship between soil moisture (SM) and vegetation activity toward quantifying CO 2 concentration in the atmosphere. To this end, the MODerate resolution imaging spectroradiometer (MODIS), an optical multispectral sensor, was used to evaluate two regions in South Korea for validation. Vegetation activity was analyzed through MOD13A1 vegetation indices products, and MODIS gross primary productivity (GPP) product was used to calculate the CO 2 ﬂux based on its relationship with respiration. In the case of SM, it was calculated through the method of applying apparent thermal inertia (ATI) in combination with land surface temperature and albedo. To validate the SM and CO 2 ﬂux, ﬂux tower data was used which are the observed measurement values for the extreme drought period of 2014 and 2015 in South Korea. These two variables were analyzed for temporal variation on ﬂux tower data as daily time scale, and the relationship with vegetation index (VI) was synthesized and analyzed on a monthly scale. The highest correlation between SM and VI (correlation coe ﬃ cient (r) = 0.82) was observed at a time lag of one month, and that between VI and CO 2 (r = 0.81) at half month. This regional study suggests a potential capability of MODIS-based SM, VI, and CO 2 ﬂux, which can be applied to an assessment of the global view of the agricultural drought by using available satellite remote sensing products.


Introduction
Several decades of recent climate change are mainly driven by anthropogenic influences in a global scale. Even with the significant societal impact of the drought, it still remains challenging to deciduous broadleaf forests (14%), woody savannas (6%), and urban and built-up areas (5%) [7,31]. Western South Korea is mostly composed of croplands, while the central and east parts are covered with mixed and deciduous broadleaf forests. To validate the estimated remote sensing-based CO 2 flux and SM, CO 2 flux and SM data of the Sulmacheon (hereafter SMC) and Cheongmicheon (hereafter CMC) flux tower were provided by the Korea Institute of Hydrological Survey. The SMC flux tower is in Jeokseong-myeon, Paju-si, Gyeonggi-do, and the area is a typical mountainous terrain located at an altitude of 293 m.a.s.l. The CMC flux tower is in Janghowon-eup, Icheon-si, Gyeonggi-do, and is composed of a rice paddy terrain (Table 1). Data in the flux tower is measured by the Eddy covariance method, and reliable data is provided by quality control [30]. Both the CO 2 flux and SM data used in this study were extracted every 30 min, and data from 2014 and 2015 were used to analyze the relationship between the variables during a period of extreme drought status in Korea.
land cover classification, the landmass of South Korea consists of mixed forests (40%), croplands (30%), deciduous broadleaf forests (14%), woody savannas (6%), and urban and built-up areas (5%) [7,31]. Western South Korea is mostly composed of croplands, while the central and east parts are covered with mixed and deciduous broadleaf forests. To validate the estimated remote sensing-based CO2 flux and SM, CO2 flux and SM data of the Sulmacheon (hereafter SMC) and Cheongmicheon (hereafter CMC) flux tower were provided by the Korea Institute of Hydrological Survey. The SMC flux tower is in Jeokseong-myeon, Paju-si, Gyeonggi-do, and the area is a typical mountainous terrain located at an altitude of 293 m.a.s.l. The CMC flux tower is in Janghowon-eup, Icheon-si, Gyeonggido, and is composed of a rice paddy terrain (Table 1). Data in the flux tower is measured by the Eddy covariance method, and reliable data is provided by quality control [30]. Both the CO2 flux and SM data used in this study were extracted every 30 min, and data from 2014 and 2015 were used to analyze the relationship between the variables during a period of extreme drought status in Korea.

Optical Multispectral Sensor Dataset
We used MODIS data to calculate SM, VI, and GPP (Table 2). First, SM was calculated using LST of MOD11A1 and land surface albedo of MCD43A3. The details are introduced in Section 2.4. For VI, we used the NDVI of MOD13A1 and analyzed the CO 2 generation according to vegetation activity through GPP of MOD17A2H. A method for CO 2 analysis using GPP is introduced in Section 2.3. All MODIS data used in this study had a spatial resolution of 0.5 km × 0.5 km. As for the temporal resolution, MOD11A1 and MCD43A3 data were provided daily; MOD17A2H eight days, and MOD13A1 16 days. Various MODIS land products have different temporal resolutions. As these products were combined to calculate the drought index, they must be unified using the same time frame. Temporal resolution is unified on a daily scale. For the eight-day product, the same value is matched for the remaining seven days from the starting point. Similarly, the 16-day product matches the same value for the remaining 15 days from the starting point. All MODIS data from 2001 to 2019 can be obtained from NASA Earthdata website [32]. For this study, the results were obtained for 2001 to 2015.

Calculation of CO 2 Flux
Since CO 2 cannot be mapped directly by satellite images, it is calculated through the relationship between CO 2 and GPP. In general, CO 2 in the atmosphere is generated through the following three processes. First, through vegetation activity, i.e., the process of absorbing CO 2 in the atmosphere and producing oxygen (photosynthesis). Second, the process of vegetation biomass maintenance. Third, respiration according to dependent nutrition. Plants have a bidirectional flux that absorbs CO 2 from the atmosphere through photosynthesis and recirculates part of it to the atmosphere through respiration. The total amount of organic matter produced by plants by absorbing CO 2 through photosynthesis, or the total amount of carbon generated through the CO 2 circulation in the atmosphere, which is called GPP. Amid these processes, the relationship between CO 2 and GPP can be expressed by the following equation.
where NEE, (net ecosystem exchange) is a measure of the net exchange of carbon between an ecosystem and the atmosphere and is a primary measurement of the ecosystem's carbon sink strength [33][34][35][36]. R e is the ecosystem respiration of plants. NEE is the CO 2 flux data measured in the flux tower applied in this study. The relationship between CO 2 flux and GPP can be calculated from the Re value. Re is calculated by the following Equation [37];

Measurement of Soil Moisture Content by Optical Multispectral Sensor
Previous studies have estimated SM using passive microwave sensors by observing the brightness temperature of a land surface through sensors and leveraging its relationship with temperature. Since SM is calculated according to the physical properties of the land surface, it is quite accurate. However, it has a coarser spatial resolution than the optical sensor. The total area of South Korea is 106,286 km 2 . Since the AMSR-based SM products have a spatial resolution of 25 km, the entire country could be represented in 170 pixels only. Because the 0.5-km-resolution product of the optical sensor can represent the area with approximately 425,000 pixels, the passive microwave sensor product faces limitations in analyzing physical properties for cases such as this study. To overcome the limitations, we applied a method for calculating volumetric SM using optical sensor products presented by Verstraeten et al. [24]. The optical sensor used in this study is MODIS. Specifically, MOD11A1 LST and MOD43A3 land surface albedo were used.
where ∆LST is the difference between LST daytime and LST nighttime, LST daytime is the land surface temperature during daytime, and LST nighttime is the temperature during nighttime. ATI, which stands for apparent thermal inertia, is a physical property of materials describing their impedance to temperature change. α is the land surface albedo and 1-α represents physically absorbance. Volumetric SM (m 3 m −3 ) can be calculated by normalizing the maximum and minimum ATI values.

Agricultural Drought Indices
For a period of drought, the relationship between soil moisture, vegetation activity, and carbon generation were analyzed by the drought indices vegetation condition index (VCI) and the standardized soil moisture index (SSMI).

Vegetation Condition Index (VCI)
VI was used to analyze agricultural drought. VCI was calculated by normalizing the NDVI provided by MOD13A1 of the MODIS sensor [8].
VCI compares the current NDVI to those observed during the same period in previous years. It is expressed in % and gives an estimate of the location of the observed value between the extrema (minimum and maximum values) in the previous years.

Standardized Soil Moisture Index (SSMI)
In order to analyze the agricultural drought condition, a standard normalization was performed on the volumetric SM introduced in Section 2.4, and the result was processed as an index. This index is named standardized soil moisture index (SSMI). The SSMI is calculated as follows.
where Z is the standardized normalization, SM max the maximum SM value, SM min the minimum SM value, and SM i the SM in the i-th time point.

Temporal Variations of Soil Moisture and Comparison with Ground Observation
As mentioned in Section 2.4, Verstraeten et al. [24] and Chang et al. [25] presented a method for soil moisture (SM) estimation using optical sensor products. In this study, SM was calculated based on this estimation method (hereinafter referred to as SM MODIS ) and compared with soil moisture (hereinafter referred to as SM fluxtower ) measured at the SMC and CMC validation points. Figure 2 shows the comparison of SM MODIS and SM fluxtower from 2014 to 2015 and compares them with the precipitation values observed in the same period. Because the entire country was under a period of extreme drought status, the occurrence of rainfall in that period was less than the average year. However, when rainfall occurred, the value of SM also increased. Both sites show relatively low values in the period of September to October 2014 and after July 2015.

Temporal Variations of Soil Moisture and Comparison with Ground Observation
As mentioned in Section 2.4, Verstraeten et al. [24] and Chang et al. [25] presented a method for soil moisture (SM) estimation using optical sensor products. In this study, SM was calculated based on this estimation method (hereinafter referred to as SMMODIS) and compared with soil moisture (hereinafter referred to as SMfluxtower) measured at the SMC and CMC validation points. Figure 2 shows the comparison of SMMODIS and SMfluxtower from 2014 to 2015 and compares them with the precipitation values observed in the same period. Because the entire country was under a period of extreme drought status, the occurrence of rainfall in that period was less than the average year. However, when rainfall occurred, the value of SM also increased. Both sites show relatively low values in the period of September to October 2014 and after July 2015. Cheongmicheon (CMC) site. Figure 3 and Table 3 show the statistical analysis results of SMMODIS and SMfluxtower at two validation points. Figure 3 illustrates a one on one plot of the two results, revealing a high correlation at both sites.  Table 3 show the statistical analysis results of SM MODIS and SM fluxtower at two validation points. Figure 3 illustrates a one on one plot of the two results, revealing a high correlation at both sites. Cheongmicheon (CMC) site. Figure 3 and Table 3 show the statistical analysis results of SMMODIS and SMfluxtower at two validation points. Figure 3 illustrates a one on one plot of the two results, revealing a high correlation at both sites.   Results of the bias and RMSE showed that SM MODIS results in CMC were better than in SMC, while the correlation in SMC was somewhat higher. Results from both sites were statistically significant (95% confidence interval). The reason that bias is relatively higher in SMC is its geographical properties. SMC is in the mixed forest area of a mountainous region, where the land surface albedo value is heterogeneous. This heterogeneity leads to bias when measured by remote sensing [31].

Temporal Variations of CO 2 Flux and Comparison with Ground Observation
According to the relationship between GPP and CO 2 presented in Section 2.3, CO 2 (hereinafter referred to as CO 2_MODIS ) was calculated from MODIS GPP and compared with the CO 2 (hereinafter CO 2_fluxtower ) observed in a flux tower. CO 2_MODIS and CO 2_fluxtower consist of eight-day products. Figure 4 compares CO 2_MODIS and CO 2_fluxtower from 2014 to 2015 and compared them with the precipitation values observed in the same period. A similar tendency as the SM results in the same period can be seen in this figure after a time lag in the rainfall. As this is related to photosynthesis that occurs after SM affects vegetation activity, so that a certain duration of lag time occurs [38]. Figure 5 and Table 4 show the statistical analysis results of CO 2_MODIS and CO 2_fluxtower at two validation points. Figure 5 illustrates a one on one plot of the two results, showing a high correlation in both sites. The result of CO 2 flux is somewhat different from that of the SM were all included within the 95% confidence interval, making them statistically significant. The bias, RMSE, gradient of one on one plot, and correlation coefficients were almost similar at both SMC and CMC points, and the SMC results were better due to dense vegetation. Vegetation density is an important factor for the generation of CO 2 flux by photosynthesis in the two points. This density can be determined by the leaf area index (LAI). For SMC, LAI shows a value between 6 and 8. For CMC, LAI shows a value between 1 and 2 ( Table 1). Although the difference in LAI is somewhat large, CMC is less sensitive to drought status as it is located in the rice paddy terrain where the irrigation system is built [7]. These characteristics narrowed the difference between the results of the statistical analyses of SMC and CMC [31]. referred to as CO2_MODIS) was calculated from MODIS GPP and compared with the CO2 (hereinafter CO2_fluxtower) observed in a flux tower. CO2_MODIS and CO2_fluxtower consist of eight-day products. Figure 4 compares CO2_MODIS and CO2_fluxtower from 2014 to 2015 and compared them with the precipitation values observed in the same period. A similar tendency as the SM results in the same period can be seen in this figure after a time lag in the rainfall. As this is related to photosynthesis that occurs after SM affects vegetation activity, so that a certain duration of lag time occurs [38].   Table 4 show the statistical analysis results of CO2_MODIS and CO2_fluxtower at two validation points. Figure 5 illustrates a one on one plot of the two results, showing a high correlation in both sites. The result of CO2 flux is somewhat different from that of the SM were all included within the 95% confidence interval, making them statistically significant. The bias, RMSE, gradient of one on one plot, and correlation coefficients were almost similar at both SMC and CMC points, and the SMC results were better due to dense vegetation. Vegetation density is an important factor for the generation of CO2 flux by photosynthesis in the two points. This density can be determined by the leaf area index (LAI). For SMC, LAI shows a value between 6 and 8. For CMC, LAI shows a value between 1 and 2 ( Table 1). Although the difference in LAI is somewhat large, CMC is less sensitive to drought status as it is located in the rice paddy terrain where the irrigation system is built [7]. These characteristics narrowed the difference between the results of the statistical analyses of SMC and CMC [31].   [5] analyzed droughts in Korea from 2013 to 2015. Particularly, in 2014, not only did the drought occur severely, but the recorded rainfall was less than 50% the normal.   [5,39,40]. Kwon et al. [39] and Kim et al. [5] analyzed droughts in Korea from 2013 to 2015. Particularly, in 2014, not only did the drought occur severely, but the recorded rainfall was less than 50% the normal. Additionally, in 2015, the region experienced only 873 mm of precipitation, which is 64% of the historical average of 1,366 mm. Variations in the monsoon climate had resulted in a dry rainy season with no precipitation [41]. Figure 6

Drought Analysis and Validation during Drought Period
For the selected drought period, we analyzed the temporal variations of SSMI and VCI at the study sites (Figure 7). The temporal patterns of the two indices show similar tendency, with the period of the most severe drought status being October 2014 to May 2015.

Drought Analysis and Validation during Drought Period
For the selected drought period, we analyzed the temporal variations of SSMI and VCI at the study sites (Figure 7). The temporal patterns of the two indices show similar tendency, with the period of the most severe drought status being October 2014 to May 2015.  Table 5 represented the applicability of the agricultural drought indices through error analysis at two validation area. An error analysis is a formed array that consists of drought or wet conditions as compared to the category of drought by the SMfluxtower data. The median (50%) of the standardized SM was set as the threshold for moderate drought, while the lower quantile (25%) was set as the threshold for severe drought. When the value of the standardized SM is less than the threshold, it is considered a drought condition. In the case of the samples, it is the counting of the drought indices with a value less than the threshold. The drought accuracy for SSMI and VCI at the study sites was approximately 60% to 80% (Table 5); SSMI showed relatively high accuracy for moderate drought and VCI for severe drought. SSMI is a drought index based on soil moisture that is sensitive to current soil moisture conditions and shows high accuracy under moderate drought conditions. VCI, on the other hand, is an index that detects weak vegetation activity due to lack of soil moisture, whose accuracy increases if the drought persists for a prolonged period (as the drought becomes more severe). These indices were suitable for determining the agricultural drought conditions. Each index can be used depending on how long the agricultural droughts continue.   Table 5 represented the applicability of the agricultural drought indices through error analysis at two validation area. An error analysis is a formed array that consists of drought or wet conditions as compared to the category of drought by the SM fluxtower data. The median (50%) of the standardized SM was set as the threshold for moderate drought, while the lower quantile (25%) was set as the threshold for severe drought. When the value of the standardized SM is less than the threshold, it is considered a drought condition. In the case of the samples, it is the counting of the drought indices with a value less than the threshold. The drought accuracy for SSMI and VCI at the study sites was approximately 60% to 80% (Table 5); SSMI showed relatively high accuracy for moderate drought and VCI for severe drought. SSMI is a drought index based on soil moisture that is sensitive to current soil moisture conditions and shows high accuracy under moderate drought conditions. VCI, on the other hand, is an index that detects weak vegetation activity due to lack of soil moisture, whose accuracy increases if the drought persists for a prolonged period (as the drought becomes more severe). These indices were suitable for determining the agricultural drought conditions. Each index can be used depending on how long the agricultural droughts continue.

Relationship between SM, Vegetation and CO 2 during Drought Periods
The results mentioned above confirm the close correlation between SM, VI, and CO 2 during the drought period. Since there was a time lag between the correlations of these factors, a lag correlation was performed (Figure 8 and Table 6). For homogeneous comparison of the factors, the standardized factors SM and NDVI were applied. The range of the CO 2 flux was also standardized from −1 to 1 through standardized normalization. The results mentioned above confirm the close correlation between SM, VI, and CO2 during the drought period. Since there was a time lag between the correlations of these factors, a lag correlation was performed (Figure 8 and Table 6). For homogeneous comparison of the factors, the standardized factors SM and NDVI were applied. The range of the CO2 flux was also standardized from -1 to 1 through standardized normalization.  Figure 8 shows the result obtained from the lag correlation. Based on SM, the result showed the highest correlation for both NDVI and CO2 after the time lag. In the case of NDVI, the highest correlation was found at a lag time of half to one month, and CO2 showed the highest correlation at   Figure 8 shows the result obtained from the lag correlation. Based on SM, the result showed the highest correlation for both NDVI and CO 2 after the time lag. In the case of NDVI, the highest correlation was found at a lag time of half to one month, and CO 2 showed the highest correlation at a lag time of one and a half month. When compared with the results of CO 2 correlation based on NDVI, the highest correlation was obtained at half month. Taken together, the two results reveal that the variation of SM started first followed by the variation in VI and CO 2 flux after a certain period of time.
Choi et al. [42] studied the temporal lag of precipitation, soil moisture, evapotranspiration, and vegetation index. In their paper, the lag between SM and NDVI was approximately 16 days. However, such a result is generalized as extreme weather conditions are not considered. Therefore, the results presented in this study differ from the previous ones because they were obtained as the agricultural drought condition progressed. In extreme climatic conditions such as drought, a time lag of approximately one month between SM and VI, and half month between vegetation activity and photosynthesis had occurred.

Conclusions
The inter-relationship between soil moisture (SM), vegetation activity, and atmospheric CO 2 concentration was analyzed using MODerate resolution imaging spectroradiometer (MODIS), an optical multispectral sensor. The SM was also estimated using MODIS. The calculated SM MODIS was compared with the SM fluxtower observed in a flux tower of the study area. As a result, both points showed high correlation (SMC: 0.75, CMC: 0.66). A relatively large bias was obtained in SMC due to the influence of heterogeneous land surface albedo in mixed forest areas. In the case of atmospheric CO 2 flux, MODIS gross primary productivity (GPP) product was used to leverage the flux's relationship with respiration in the calculation. Similarly, the calculated results were compared with the CO 2 flux results of SMC and CMC to confirm their applicability. The flux values proved the relatively high applicability of the SMC result, which is due to the effect of leaf area index (LAI). This implies SMC in a dense forest area has a high value of LAI.
Lastly, the relationship between each variable was identified by comparing SM, VI, and CO 2 under the extreme drought periods of 2014 and 2015 in South Korea. As a result, the highest correlation was obtained when there was a time lag of one month between SM and vegetation and half month between vegetation and CO 2 . This tendency was similar in both SMC and CMC. As such, these three variables have been proved to affect each other with time lag, and it was confirmed that the lag is longer than the normal season during the drought period. In the long term, however, changes in atmospheric CO 2 concentration may affect carbon reservoirs in the land and the subsurface. In the future, relationship studies between SM, VI, and CO 2 on the land and the subsurface during droughts should be followed by considering sources and depletions in carbon fluxes.