Evaluating the surface temperature and vegetation index (Ts/VI) method for estimating surface soil moisture in heterogeneous regions

Remote sensing has been used to determine surface turbulent energy fluxes and surface soil moisture (SSM) since the 1970s (Carlson 2007). The main advantage of remote sensing is that it provides spatially heterogeneous data because surface variables with spatial information are essential for several applications such as drought monitoring, scheduling irrigation, soil erosion mitigation, evaluating evapotranspiration, and forest management. Direct measurement is the most accurate method for estimating these variables, but this technique only provides point measurements. Thus, ground instruments are usually capable of only providing localized estimates of surface variables over large areas. Therefore, the in situ measurements obtained may not represent the spatial distribution of these variables at regional and global scales.

Many satellite-based techniques can be used for estimating the SSM. They can be classified as microwave and optical-thermal techniques. Passive microwave sensors have fine temporal resolution (1–1.5 passes per day) but coarse spatial resolution (∼30 km). Specific methods based on active and passive microwave remote sensing were described by Wagner et al. (1999). Previous soil moisture mapping missions have included SMOS (Kerr et al. 2001), TMI (Bindlish et al. 2003), AMSR-E (Njoku et al. 2003), and SSM/I (Wentz 1997). However, their low spatial resolution makes it difficult to study sub-pixel variations at small scales. Optical-thermal remote sensing data can provide information at finer spatial resolution and remotely sensed thermal inertia has been employed for mapping soil moisture. The relationship between soil thermal inertia and water content can be used to estimate soil moisture (Lu et al. 2009), but many measurements are required in this method. Therefore, it is more feasible to use the apparent thermal inertia (Stisen et al. 2008) based on the noon–night land surface temperature (LST) difference to estimate SSM. However, this technique has limitations due to variable cloud cover conditions during the day and night or in two different hours during the daytime. Also, this method is not very accurate or reliable when surface vegetation cover is large (Petropoulos et al. 2015).

The surface temperature and vegetation index (Ts/VI) method is a synergistic approach for estimating surface turbulent energy fluxes and SSM conditions, and as the name suggests, it is based on information derived from the ‘scatter plot’ relationships between the satellite-derived vegetation index (VI) and surface temperature (Ts) measurements (Petropoulos et al. 2015). This method has been used in various applications, such as estimating evapotranspiration, evaporative fraction, and SSM, using the Advanced Very High Resolution Radiometer, Landsat, or Moderate Resolution Imaging Spectroradiometer (MODIS) sensors. The Ts/VI method assumes that the SSM has a complex relationship with the Ts and vegetation. This relationship was employed initially to detect canopy water stress and crop evapotranspiration using aerial thermal scanners (Heilman et al. 1976). Subsequently, based on remote thermal sensing imagery, indices such as the crop water stress index (CWSI) were developed for use in irrigation management (Jackson et al. 1981). The application of the Ts/VI method for SSM estimation was proposed by Nemani et al. (1993), who found a strong negative relationship between Ts and the normalized difference vegetation index (NDVI) for all biome types studied. The authors noted a distinct change in the slope between dry and wet days. The method was developed further by Moran et al. (1994) and Jiang & Islam (2001), and it is also called the triangle method or trapezoid method. Previous studies have focused mainly on the direct estimation of the SSM based on the Ts/VI space.

The basic assumption of the Ts/VI method is that Ts, which is associated with surface turbulent energy fluxes, is highly dependent on the SSM; the method is based on an interpretation of the image distribution in the Ts/VI space. In general, the range of Ts decreases as the vegetation cover increases. For a given VI, Ts increases gradually due to water stress in the surface soil from the minimum value at the wet edge (also called the cold edge) to the maximum value at the dry edge (also called the warm edge). On the other hand, the soil moisture decreases from the wet edge to the dry edge. Sandholt et al. (2002) proposed a simplified land surface dryness index called the temperature vegetation dryness index (TVDI), which is based on an empirical parameterization of the Ts–VI space. The results indicate that the spatial pattern of the TVDI is closely related to the SSM simulated using the MIKE SHE model. The TVDI may be estimated easily for each pixel without any ancillary data, and thus, it has been used widely for monitoring soil moisture conditions (Mallick et al. 2009; Gao et al. 2011; Son et al. 2012; He et al. 2013; Holzman et al. 2014; Zhang et al. 2014). The results of these past studies indicate that the TVDI has acceptable correlations with the observed soil moisture data. Thus, the TVDI is a useful index for monitoring the soil surface moisture condition. In addition, Son et al. (2012) compared the TVDI with a commonly used drought index called the CWSI, and the results showed that the TVDI is more sensitive to soil moisture stress than the CWSI. Comprehensive reviews of the application of remote sensing methods to the estimation of surface evapotranspiration and SSM, including their principles, advantages, and constraints, were conducted by Moran et al. (2004), Carlson (2007), Sun et al. (2012), and Petropoulos et al. (2015).

When applying the Ts/VI method, it is assumed that soil moisture is the main source of variation in the surface soil temperature, but this is only true for regions with flat terrain. Therefore, the most severe limitation of this method is that it requires a flat surface (Carlson 2007). Rahimzadeh-Bajgiran et al. (2012) incorporated observed air temperature calibrated using a digital elevation model (DEM) to account for a lapse rate while calculating the TVDI. However, the surface soil temperature is also affected by the altitude in heterogeneous regions. Therefore, the effect of altitude on the surface soil temperature needs to be considered when using the Ts/VI method to estimate surface turbulent energy fluxes or the SSM. However, the effect of altitude on the surface soil temperature has rarely been considered in most applications of the Ts/VI method. Thus, the main objective of this study was to evaluate the applicability of the Ts/VI remote sensing-based method for estimating the SSM in heterogeneous regions.

First, a high mountain region was selected as the study area. The Ts data were then normalized to a certain altitude to consider the effect of the altitude on the Ts. Instead of the initial Ts data, the normalized Ts–NDVI scatter plot was used to detect the TVDI values. The TVDI values were obtained from remotely sensed land Ts and NDVI data. In addition, a semi-automated algorithm was developed for determining the dry and wet edges in the TVDI method. Finally, field observations of SSM data for a complete hydrological year were used to evaluate the performance of the TVDI method for SSM estimation.

The TVDI is an index for representing the SSM conditions. A simplified representation of the TVDI concept is presented in Figure 1. The NDVI and LST represent the vegetation and SSM conditions, respectively. The triangle is characterized by two physical limits, which denote the extreme conditions of SSM and evapotranspiration. The dry edge represents the limits of the SSM and evapotranspiration for different VI classes, and the lower horizontal wet edge indicates the maximum soil wetness and potential evapotranspiration (Sandholt et al. 2002).

Identifying the dry and wet edges is essential for the TVDI method. In this study, we propose a semi-automated algorithm for determining the dry and wet edges based on scatter plots of the Ts and NDVI. This algorithm is based on previous studies by Tang et al. (2010) and Tomás et al. (2014). An important feature of the algorithm presented in this study is that it can automatically filter outliers. The steps followed to identify the dry edge are listed below:

1. Images with sufficient pixel values for the Ts and NDVI are selected. In this study, the number of pixels used was ≥10,000.

2. The NDVI is binned based on its data range. The bin size used in this study was 0.01. Bins with sufficient pixel values (≥100) are then selected.

3. In each bin, the maximum/minimum five Ts values are extracted and recorded as mx₁, mx₂, … , mx₅. The difference in mx_i – mx_i+1 (i = 1, 2, … , 4) is recorded as D_i. If |2D_i| > |mx₁ – mx₅|, then the maximum values ≥mx_i (or the minimum values ≤mx_i) are deleted. The optimal maximum/minimum Ts for each bin in the NDVI is then extracted.

4. If an inflection point exists in the scatter plot of the maximum Ts and NDVI (Figure 2), it is identified visually. The scatter points located to the right-hand side of the inflection point are selected for estimating the dry edge using least squares regression; otherwise, the dry edge is estimated by a least squares regression of the maximum Ts in each bin.

The surface temperature axis shown in Figure 1 is a simplified term based on the difference between the surface temperature and air temperature (Ts − Ta). It represents the energy exchange at the Earth's surface (Jackson et al. 1981). In general, Ts − Ta is often replaced by Ts due to the lack of air temperature data, because grid Ta data are difficult to obtain over large areas, whereas grid Ts data can be obtained easily from remote sensing images. The surface temperature is considerably affected by the heterogeneity of the Earth's surface, especially the heterogeneous altitude, which is usually assumed to decrease in a linear manner with the elevation according to a lapse rate (rate of decrease in the surface temperature with elevation). Therefore, the effect of altitude on the LST (lapse rate) should be considered in a quantitative manner when using remotely sensed Ts data (Wan & Dozier 1996; Minder et al. 2010). Otherwise, the Ts/VI method is only suitable for small regions and regions with little topographic variation.

The study area is the source region of the Yangtze River (SRYR), which is located in the central–eastern part of the Qinghai–Tibetan Plateau, China (Figure 3). This region includes a major river basin located at a very high altitude. The natural environment and ecosystem are highly sensitive to the availability of water. The study area is located in a mountainous region, and thus the lapse rate of 4.6 °C/km for the Cascade Mountains recommended by Minder et al. (2010) was used in this study. The DEM employed was derived from the ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) GDEM2 (Global Digital Elevation Model Version 2), a product created by the Ministry of Economy, Trade, and Industry (METI) in Japan and the National Aeronautics and Space Administration (NASA) in the United States. Its spatial resolution is approximately 30 m. The data were resampled to 1,000 m to match the resolution of the MODIS products. The altitude ranged from 4,413 m above sea level (a.s.l.) to 6,571 m a.s.l., and the average altitude was 4,963 m a.s.l. Most of the pixels (98.4%) were located between 4,500 m a.s.l. and 5,500 m a.s.l.

In this study, the MODIS LST product MOD11A1 and NDVI product MOD13A2 were used for Ts and VI, respectively. These products were obtained from NASA's Earth Observing System Data and Information System (http://reverb.echo.nasa.gov/reverb). MOD11A1 is produced daily at a spatial resolution of 1 km, whereas MOD13A2 is generated every 16 days at a spatial resolution of 1 km. The MODIS products were originally stored as a sinusoidal projection with a nominal spatial resolution of 1 km. The MODIS Reprojection Tool was used to reproject the images onto geographic latitude/longitude coordinates (Datum WGS-84). The MOD11A1 Ts data were normalized by considering the effects of altitude. Thus, each pixel's Ts value was interpolated to the lowest altitude in the image using the DEM, where the assumed lapse rate was 4.6 °C/km. As mentioned above, we assumed that the surface soil temperature was affected mainly by SSM when we applied the Ts/VI method. As normalizing the Ts data can remove the effect of altitude on Ts that exists in heterogeneous regions, we used the normalized Ts data to estimate the TVDI values based on the normalized Ts–NDVI scatter plot.

A field survey was conducted to obtain SSM data from 15 June 2014 to 30 June 2015. This study period included a complete hydrological year with low, normal, and high SSM contents, thereby allowing us to test the method over a wide range of soil wetness conditions. Measurements were obtained at four sites, but the instrument at one site was eventually damaged by natural environmental conditions. Therefore, the observed SSM data were acquired from only three sites (Figure 3). At each site, the soil moisture content and temperature were determined at two depths (10 and 60 cm), and the data were recorded by an Onset soil moisture and temperature sensor. This soil moisture and temperature measurement device could determine the volumetric soil moisture content and temperature with accuracies of 1% and 0.2 °C, respectively. The observation time step was 1 hour. Finally, the TVDI values were compared with field observed SSM data.

The normalized Ts data were used to remove the effect of altitude on the surface temperature, thereby satisfying the assumption of the Ts/VI method. Daily normalized Ts–NDVI scatter plots were created from 15 June 2014 to 30 June 2015. The dry and wet edges were determined from each normalized Ts–NDVI scatter plot to obtain the TVDI. Figure 4 illustrates some examples of the scatter plots of the normalized Ts–NDVI space. The pixels in each plot form a triangle denoting the wide range of soil moisture contents in the study area. The observations were consistent with the suggestion of Sandholt et al. (2002), namely, that the Ts decreases as the NDVI increases. The dry edges were identified by least squares regression, as described in the section ‘Identification of the dry and wet edges’, and there were significant correlations (R² > 0.8) in all cases. However, it should be noted that the observed surface soil temperature at all three field sites was below 0 °C from 27 October 2014 to 12 April 2015 (Figure 5), that is, the surface soil was frozen during this period. As mentioned above, the theoretical basis of the Ts/VI method is that the surface soil temperature is highly dependent on SSM, but this theoretical basis is not suitable for frozen ground. Therefore, the normalized Ts–NDVI scatter plots obtained during this frozen period were not suitable for determining the TVDI values, as discussed later.

The dry edges are shown for each scatter plot in Figure 4. The large area (13.5 × 10⁴ km²) contained sufficient pixels to represent the soil moisture and vegetation cover, as required by the TVDI method. The wide ranges of the NDVI and Ts data are evident in all the scatter plots, where the maximum NDVI of 0.8 occurred in August (i.e., 14 August 2014, DOY226) and the maximum Ts of 45 °C occurred in July (i.e., 15 July 2014, DOY196). Thus, in the SRYR, the vegetation cover was highest in August, and the surface temperature was greatest in July, which is consistent with the local water conditions (SSM) and incoming solar radiation, respectively.

The different characteristics of the dry edge parameters can indicate the availability of soil water. The results showed that the LST had a relatively narrow dynamic range in the summer months, for example, on 1 July (DOY182), 15 July (DOY196), 31 July (DOY212), 14 August (DOY226), and 6 September (DOY249) in 2014, as shown by the relatively flat dry edge slope and low intercept in Figure 4. This figure indicates the high availability of soil moisture, elevated evapotranspiration, and relative homogeneity of the LST. In other months, the situation was reversed, indicating the low availability of soil moisture (e.g., on 16 June 2014 (DOY167), 25 October 2014 (DOY298), 20 April 2015 (DOY110), 6 May 2015 (DOY126), 27 May 2015 (DOY147), and 6 June 2015 (DOY157)). In addition, there was a low slope and the Ts increased near the bare soil with precipitation. In general, the dry edge parameters obtained from the normalized Ts–NDVI scatter plots clearly indicated the surface wetness, and the results were consistent with the findings of previous studies (Mallick et al. 2009; Son et al. 2012; Sun et al. 2012).

In general, there was a strong correlation between the slope of the dry edge and the availability of surface soil water. The temporal variations in the mean slope and observed SSM over 10 days during the observation period (from the middle of June 2014 to early July 2015) are shown in Figure 5. The hourly observed surface soil temperatures at the three field sites are also shown in this figure. The annual mean surface soil temperature in SRYR was 1.0 °C. The mean surface soil temperature was highest in July (12.7 °C) and lowest in January (−12.3 °C). The surface soil temperatures at the three field sites were lower than 0 °C between 27 October 2014 and 12 April 2015. The SSM observed at the three field sites ranged from 10% to 20%.

Figure 5(a) shows a strong correlation between the mean slope of the dry edge and the observed SSM over 10 days in SRYR. The correlation coefficient for the whole period was 0.568. However, the correlation between the mean slope and observed SSM was weak during the period from the middle of October 2014 until late May 2015, possibly because the surface soil could have been frozen in some regions. The surface soil temperatures at the three observation sites exceeded 0 °C. Thus, the temperature may have been below 0 °C in other regions of the SRYR because the topography and underlying surface are complex in this region. The theoretical basis of the Ts/VI method is invalid for a frozen soil surface as the surface soil temperature is not dependent on the SSM because of the effect of the frozen ground. The range of the NDVI was relatively narrow during this period (Figure 4), and it was used for the dry edge extraction, which might also explain these results. Therefore, the Ts–NDVI scatter plots produced during this period were not suitable for detecting the SSM. When this frozen period was not included, the correlation between the slope and SSM was stronger; the correlation coefficient between the mean slope and observed SSM over 10 days was 0.820.

The TVDI values were compared with the observed SSM values in order to determine their correlation. The Ts/VI method is affected to a large extent by the altitude and frozen soil. Thus, Figure 6 shows scatter plots of the TVDI and observed SSM in four conditions with or without consideration of the effects of altitude and frozen soil. According to the soil temperature determined at the three field sites, frozen soil was also identified based on the correlation between the mean slope of the dry edges and the observed SSM, as shown in Figure 5(a). As mentioned above, the surface soil may have been frozen between October 2014 and late May 2015. Thus, this period was identified as a ‘frozen soil period’. Figure 5 shows that the observed SSM ranged mainly between 10% and 20%, whereas the TVDI values were between 0.2 and 0.9. The TVDI had a weak correlation with the observed SSM when the effects of altitude and frozen soil were not considered (the R² value was only 0.167). However, the correlation between the TVDI and observed SSM was stronger when the effect of altitude or frozen soil was considered. Therefore, the effects of altitude and frozen soil should be taken into account when using the TVDI method. The correlation was stronger when considering the effect of altitude rather than that of frozen soil. Thus, the effect of altitude on the TVDI (R² = 0.474) was greater than that of frozen soil (R² = 0.343). The TVDI had a relatively strong correlation with the observed SSM when the effects of both altitude and frozen soil were considered; in this case, R² improved to 0.617.

The Ts/VI method is a remote sensing-based approach that is representative of field conditions. It is used widely for estimating the evapotranspiration, evaporative fraction, and SSM. It is assumed that the surface soil temperature is affected mainly by the SSM for a certain vegetation cover type, but this is only true over flat regions. The surface soil temperature is also influenced by altitude in heterogeneous regions, especially in areas with high mountains. This study considered the effect of altitude when using the Ts/VI method to estimate the SSM in a heterogeneous region, that is, the SRYR, which is located in a high mountainous region that is also home to one of the world's biggest river basins. The following conclusions can be made based on our results:

1. Identifying the dry and wet edges is essential when applying the TVDI method. Thus, in this study, we proposed a semi-automated algorithm for determining the dry and wet edges based on a scatter plot of the Ts and NDVI. This algorithm is simple, practical, and effective. It is capable of rejecting anomalous points that might have negative effects on the identification of the dry edge. These anomalous points would reduce the accuracy of dry edge identification.

2. In general, the Ts/VI method assumes that surface soil temperature is affected mainly by SSM and vegetation cover. However, the surface soil temperature is also influenced by the altitude over heterogeneous regions. Therefore, the effect of altitude on the surface soil temperature needs to be considered when using the Ts/VI method for estimating surface turbulent energy fluxes and the SSM. In this study, we evaluated the performance of the Ts/VI method (TVDI) in estimating the SSM based on field observed data obtained over the high mountain region of the SRYR. The Ts data were normalized to a specific altitude to consider the effect of altitude on the Ts. The normalized Ts–NDVI scatter plots were then used instead of the initial Ts data to detect the dry and wet edges. The results showed that the TVDI had a weak correlation with the observed SSM when the effects of altitude and frozen soil were not considered (R² was only 0.167). The correlation between TVDI and the observed SSM was stronger when the effect of altitude was considered (R² improved to 0.474). Thus, we conclude that the effect of altitude should be considered when using the TVDI method to estimate the SSM in heterogeneous regions.

3. The effect of frozen soil also needs to be considered when employing the TVDI method to estimate the SSM in high altitude regions. The results of this study showed that the TVDI method is not suitable for estimating the SSM under conditions with frozen soil. The correlation between the TVDI and observed SSM improved when the effect of frozen soil was considered; R² improved from 0.167 to 0.343. Most of the applications of the remote sensing method for estimating the SSM involve agricultural drought monitoring, which focuses on the soil moisture during unfrozen periods of the year (spring, summer, and autumn). However, it should be noted that the TVDI values during the frozen period (usually winter) need to be rejected before establishing the relationship between the TVDI and observed SSM. This is because the TVDI values during the frozen period would reduce the correlation between the TVDI and observed SSM, thereby negatively affecting SSM estimation.

4. The traditional TVDI method performed poorly at estimating the SSM conditions in the SRYR. The TVDI had only a weak correlation with the observed SSM (R² of only 0.167). However, the performance of the method improved considerably when the effects of both altitude and frozen soil were considered. In this case, the TVDI had a strong correlation with the observed SSM (R² improved to 0.617). Therefore, we conclude that the Ts/VI method is suitable for obtaining satisfactory results in regions with high mountains if the effects of both altitude and frozen soil are considered.

This study was supported and funded by the National Natural Science Foundation of China (Grant Nos 41571027, 41371058, and 41190080). We also thank Lei Wang and Liguang Jiang for assistance in the field.