Evaluation of the Airborne CASI / TASI TsVI Space Method for Estimating Near-Surface Soil Moisture

High spatial resolution airborne data with little sub-pixel heterogeneity were used to evaluate the suitability of the temperature/vegetation (Ts/VI) space method developed from satellite observations, and were explored to improve the performance of the Ts/VI space method for estimating soil moisture (SM). An evaluation of the airborne ∆T /Fr space (incorporated with air temperature) revealed that normalized difference vegetation index (NDVI) saturation and disturbed pixels were hindering the appropriate construction of the space. The non-disturbed ∆T /Fr space, which was modified by adjusting the NDVI saturation and eliminating the disturbed pixels, was clearly correlated with the measured SM. The SM estimations of the non-disturbed ∆T /Fr space using the evaporative fraction (EF) and temperature vegetation dryness index (TVDI) were validated by using the SM measured OPEN ACCESS Remote Sens. 2015, 7 3115 at a depth of 4 cm, which was determined according to the land surface types. The validation results show that the EF approach provides superior estimates with a lower RMSE (0.023 m3·m−3) value and a higher correlation coefficient (0.68) than the TVDI. The application of the airborne ∆T /Fr space shows that the two modifications proposed in this study strengthen the link between the ∆T /Fr space and SM, which is important for improving the precision of the remote sensing Ts/VI space method for monitoring SM.


Introduction
Improving soil moisture (SM) evaluation processes is important for understanding the land-atmosphere exchange process in which the SM content controls evaporation from areas of bare soil and transpiration from vegetated areas [1,2].Various remote sensing approaches to SM observations have been developed in the last two decades.With the launch of the Soil Moisture and Ocean Salinity (SMOS) satellite [3], a near-surface SM remote sensing method could help study the spatial heterogeneity and temporal dynamics of SM at global or regional scales.The surface reflectance/temperature in the optical domain and the microwave brightness temperature are the main remote sensing measurements used to infer near-surface SM contents and are consistent with in situ SM measurements [4][5][6][7][8].The passive microwave brightness temperature (T ) is highly sensitive to SM at spatial scales of 25 to 150 km [9].The spatial scales depend on the antenna size and the altitudes of the low-orbit satellites [10], such as the National Airborne Field Experiment (NAFE) [11], SMOS [3], Aquarius [12] and the future Soil Moisture Active Passive (SMAP) satellites [13].However, the spatial resolutions of the passive microwave data currently used for retrieving SM are coarse, which are useful in large-scale land surface hydrological processes but lead to insufficient representations of SM spatial-temporal dynamics/variations and uncertainties at small scales.Optical remote sensing satellites offer an improved method for monitoring the spatial characteristics of SM at small scales because they provide 10-to 200-times greater spatial resolutions than microwave satellite platforms.The spatial resolutions of optical satellite instruments for estimating SM can reach 1 km (e.g., MODIS) [14] or 90 m (e.g., ASTER) [15].
Investigations of optical high-spatial-resolution SM show that the four following core algorithms are currently in use: (1) the disaggregation algorithm, which optically provides detailed supplementary data combined with microwave data to produce high-resolution SM maps [16][17][18]; (2) the empirical relation between vegetation indices(VI)/land surface temperature (Ts) and SM [19]; (3) the apparent thermal inertia (ATI) method [20]; and (4) the SM dryness indices of the Ts/VI space [21].In these methods, the Ts/VI space is widely used in remote sensing satellites that measure reflectance and thermal radiation to predict SM [22][23][24][25] due to its definite physical meaning, convenient calculation without a substantial amount of auxiliary data and its high estimation accuracy for areas of bare soil and vegetation [8,26].The successful use of the Ts/VI space for estimating SM mainly depends on the correct choice of the dry and wet edges in the Ts/VI space.However, it is challenging to implement appropriate extraction of the dry and wet edges of the Ts/VI space when two inherent defects of the Ts/VI space are non-negligible.One defect is the saturation of the NDVI, which asymptotically approaches saturation after reaching a certain leaf area index (LAI) [27].Although NDVI saturation also occurs in optical remote sensing data with coarse spatial resolutions, it is more obvious in higher spatial resolution data (e.g., LANDSAT and ASTER) [8,[28][29][30][31].Another defect is the presence of disturbed pixels, which hinders the construction of the Ts/VI space.An ideal Ts/VI space is constructed using three types of pixels: bare soil pixels, vegetation-covered pixels, and mixed pixels with bare soil and vegetation components [21].Disturbed pixels, such as shadow and building pixels, fail to depict SM status due to their deviations from the ideal Ts/VI space in terms of their incident radiation, albedo and thermal inertia [8].It is necessary to analyze the defects and uncertainties of the Ts/VI space by using higher spatial resolution remote sensing data with less sub-pixel variability.Such high spatial resolution data can be obtained from aircraft measurements, which are better than satellite data because satellite data average the sub-pixel variability and mask the underlying sub-pixel heterogeneity of SM contents and landscapes [10].
With the implementation of the Heihe Watershed Allied Telemetry Experimental Research project (HiWATER) in 2012 [32], visible/near-infrared reflectance (1 m spatial resolution) and thermal temperature (3 m spatial resolution) measurements based on an airborne platform were collected to understand the applicability of Ts/VI space to the retrieval of SM at higher spatial resolutions and improve the remote sensing performance of the Ts/VI space algorithm.Moreover, aircraft data can cover several satellite footprints each day, allowing the satellite pixels to be simulated to test and improve remote sensing algorithms before applying real satellite platforms [33].
The objectives of this paper are to evaluate the applicability of the Ts/VI space in an SM-estimation method based on the airborne data from the Compact Airborne Spectral Imager (CASI) and the Thermal Airborne Spectrographic Imager (TASI) and to improve the capabilities of the Ts/VI space for monitoring SM.This study is presented as follows.First, the airborne HiWATER experiment and in situ measurements are illustrated.Then, we present the Ts/VI space algorithm and propose its reformulation for CASI/TASI SM estimations.Finally, we evaluate the improved airborne Ts/VI space method and the airborne-based SM estimations.

Study Area and Field Campaign
The study area (Figure 1) was located in an artificial oasis-riparian ecosystem-wetland-desert area in the middle reaches of the Heihe River Basin (HRB) in northwestern China (38.87°N, 100.40°E),where field SM data, meteorological data and airborne remote sensing data were obtained from the HiWATER experiment.The annual precipitation in the artificial oasis is 117 mm, with a high potential evaporation of 1200-1800 mm.Irrigation is the main source of water, and the main crops include maize, wheat and vegetables.HiWATER is an ongoing, watershed-scale, eco-hydrological experiment that is designed from an interdisciplinary perspective to address various problems, such as heterogeneity, scaling, uncertainty and the closed water cycle at the watershed scale [32].
As part of HiWATER, an eco-hydrological wireless sensor network (EHWSN) was installed in a foci experiment area.The EHWSN design is explained in [34,35].In addition, 48 WATERNET nodes of the EHWSN measured SM, and soil temperature data were obtained for two layers (4 cm and 10 cm).The SM measurements were based on the frequency-domain reflectometry method using Hydro Probe II (HP-II) sensors.In addition, 10 automatic weather stations (AWSs) in the foci experiment area generated observational data, including air temperature (Ta), vapor pressure, wind speed, and SM for seven layers (2 cm, 4 cm, 10 cm, 20 cm, 40 cm, 60 cm, and 100 cm).All nodes selected in this study were located in the cornfield, and the statistics of their fractional vegetation cover based on their airborne footprint (3 m) are listed in Table 1.We chose an area of approximately 4.5 km × 5.0 km that was covered by WATERNET and AWSs as the validation area (Figure 1).Next, 10 AWS SM observations were selected to analyze the relationships between the dryness indices and SM at different SM depths in Section 5.2.In addition, 58 measured SM contents at a depth of 4 cm (10 AWSs and 48 WATERNET nodes) were selected to retrieve and validate the SM.Using a systematic sampling method, 29 nodes were sampled to establish the coefficients of the algorithms presented in Section 3 (the training subsample), and the other 29 nodes were used as validation subsamples in Section 5.3.The distribution of subsamples is displayed in Figure 1.

Airborne Hyperspectral Measurements
The airborne hyperspectral datasets of CASI and TASI were simultaneously acquired on 10 July 2012, between 12:00 and 12:30 (local time) at an altitude of 2500 m to improve the remote sensing methods used for observing key eco-hydrological processes [32].Table 2 displays the basic specifications of these two sensors.
CASI1500 is a visible and near-infrared pushbroom hyperspectral sensor with 48 bands that cover 380-1050 nm with a ground spatial resolution of 1 m.The raw data were acquired as 14-bit digital values and converted into 16-bit radiances.Geometric corrections were applied using a digital elevation model and ground control points.Atmospheric corrections were applied to produce a reflectivity profile at the pixel level using the ModTRAN model [36].The processed CASI 1500 data were resampled at a spatial resolution of 3 m to fit the TASI 600 grid.
The TASI 600 sensor is a thermal pushbroom hyperspectral sensor that has a spectral range of 8 to 11.5 μm (32 bands) and a spatial resolution of 3 m.The TASI 600 data were processed using radiometric calibration, geometric correction and atmospheric correction [37].Atmospheric correction was performed using an atmospheric profile extracted from NCEP data, which was modified by the local meteorological data and ModTRAN5.0[38].Land surface temperatures were produced using a modified temperature and emissivity separation (TES) algorithm with an RMSE of less than 1.5 K [39].

Theory of Ts/VI Space
The scatter plot of Ts and VI exhibits a triangular-trapezoidal shape when the study area contains a wide range of fractional vegetation cover and SM.The conceptual Ts/VI space is shown in Figure 2, where VI is plotted on the x-axis and Ts is plotted on they-axis.The dry edge (AB) represents minimum SM or evapotranspiration, with low SM in the root zone under the full range of fractional vegetation cover conditions.Along the dry edge, the maximum values of Ts decrease as the fractional vegetation cover increases.The horizontal wet edge (BC) represents the maximum soil wetness conditions and potential evapotranspiration.The left edge represents bare soil, which ranges from dry to wet and from maximum to minimum Ts.The Ts/VI space method has been widely used to estimate evapotranspiration and SM [7,21,40,41].Soil moisture and evapotranspiration mechanisms mainly determine the locations of pixels in the Ts/VI space [8,21].The fractional vegetation cover can be represented by VI, which determines the proportion of bare soil and vegetation visible to a sensor.Differences in radiative temperatures between the soil and canopy affect the spatially integrated Ts, which is largely controlled by evapotranspiration (ET, also denoted as LE) and is used to determine the surface energy balance as follows: where R , LE, H, G are the net radiation, evapotranspiration, sensible heat flux and soil heat flux, respectively, and the units of all fluxes are W•m −2 .In addition, the LE and H are partly influenced by the stomatal resistance to transpiration, which is partly controlled by the availability of SM [42].Furthermore, Ts is partly affected by thermal inertia, which controls the heat flow into G, and the thermal inertiais related to the SM content.The available energy incident at the surface (Rn-G) affects Ts [15].The radiative control of Ts indicates that the surface exhibits a higher temperature with a higher net shortwave radiation balance, such as a low albedo, which is a function of the SM content, soil type and fractional vegetation cover.In addition, the Rn-G is a driving force for ET.Thus, the interactions between ET and Ts are controlled by R , H, and G, which are all influenced by SM availability.Thus, ET is allowed to predict SM availability in the Ts/VI space.
Based on the Ts/VI space, a number of evapotranspiration indices and soil dryness indices have been proposed for assessing ET and SM [7,8,43].The evaporative fraction (EF) was introduced as an evapotranspiration index for parameterizing ET.In addition, the EF was generally more stable during the day than ET and was regarded as a more suitable indicator of SM relative to ET [44].Furthermore, the EF can be calculated using ancillary data combined with the Ts/VI space.Soil dryness indices were also proposed by simplifying the ET models.The most widely applied soil dryness index, the temperature vegetation dryness index (TVDI), was proposed by simplifying the evapotranspiration rate [14,24,25,44].The TVDI can be obtained by using the Ts/VI space.
One inherent assumption of the Ts/VI space is that the air temperature (Ta) is considered constant for the selected study area, which results in errors for larger areas.The Ta incorporated in the Ts/VI space was used to correct the error by replacing Ts with the Ts-Ta term (∆T ) [23,45].The ∆T value is calculated as the difference between the surface temperature and the air temperature, and represents the energy exchange at the earth's surface.In addition, VI (such as NDVI) is a greenness variable that characterizes the degree of vegetation cover and can be replaced by the fractional vegetation cover (Fr), which presents the relative abundance of vegetation within a pixel [46].Furthermore, Fr is calculated from NDVI by using the following equation [47]: where is the NDVI of full vegetation (Fr = 1), which can be calculated from the maximum NDVI in the study area, and is the NDVI of the bare soil (Fr = 0), which can be obtained from the minimum NDVI in the study area, excluding the NDVI in the water bodies [31].Therefore, Fr and ∆T were used to construct the ∆T /Fr space in thisresearch.

SM Estimation from EF
EF is defined as the ratio of ET to the available energy (Rn-G), where ET and Rn-G imply a strong relationship with the SM contents mentioned above.An algorithm proposed by Jiang [48] is used to estimate the EF and ET values because it obtains satisfactory accuracy with a few input variables, where EF is estimated as a function of the Priestley-Taylor parameter as follows [48]: where ∅ is the so-called Priestley-Taylor parameter, ∆ is the slope of the saturated vapor pressure and Ta (hPa•K −1 ), and is the psychometric constant (hPa•K −1 ).Furthermore, ∆ and were calculated using the relationships given by [49] and the Ta, vapor pressure and wind speed.In Jiang's model [48], the Priestley-Taylor parameter ∅ is estimated by using a two-step linear interpolation scheme and the Ts/VI space, as shown in Figure 2 [23].The dry edge is defined by the maximum ∆T T , and the wet edge is defined by the minimum ∆T (T .In addition, the ∅ value varies from ∅ = 0 (along the dry edge line) to ∅ = 1.26 (along the wet edge line).Point A represents Fr = 0 and T , and point B represents Fr = 1 and T .For ∅ at point E, the length of AE represents ∅ ∅, while the length of AD is ∅ ∅ .Thus, considering the similarity between EFD and ADC, the ∅ value for any point in the Ts/VI space can be estimated as follows: where ∆T represents Ts-Ta, and Ta is the observed air temperature from the AWSs.As shown in Figure 2, the wet edge (BC) for a given Fr is calculated by averaging a group of points in the lower limits of the ∆T /Fr space.The dry edge is modeled using a linear empirical fit to Fr.The ∅ value is constant and equal to 1.26 at the wet edge, and ∅ is denoted as follows: Next, EF is converted to SM using the Lee model, which has took into account the water transport from the inner soil pores to the soil surface and the soil hydraulic conductivity [45,50].The Lee model can be expressed as follows: where SM is the remotely sensed volumetric SM content that represents a soil layer of several centimeters in depth [50,51] and is the volumetric SM content at field capacity.The soil in the study area has a silt loam texture, and a of 0.35 m 3 •m −3 .
In the EF estimation model, the dry and wet edges are assumed to represent the minimum and maximum ET values, respectively.The Ts varies from a minimum (T , ∅ ), with the strongest evaporative cooling, to a maximum (T , ∅ ), with the weakest evaporative cooling.Therefore, the dry edge represents the minimum EF, and the wet edge represents the maximum EF.The model is valid when the minimum and maximum ET values can both be observed within the boundaries of the study area.One important assumption is that these variations largely result from differences in SM availability.Assuming that the soils in the study area should have some of the same fixed soil-water characteristics [50], the Lee model for estimating SM was proposed by studying the quantitative relations between the field EF and in situ SM measurements.

SM Estimations from the TVDI
The TVDI was proposed by simplifying the evapotranspiration rate, which is important for the ET estimation model.The TVDI depends on an empirical parameterization of the Ts/VI space that is completely based on remote sensing data.As shown in Figure 3, it was assumed that the dry edge represents the driest surface soil conditions when TVDI = 0, and the wet edge represents the wettest soil conditions when TVDI = 1.If the SM varies linearly from the dry edge to the wet edge of the Ts/VI space, the TVDI is formulated as follows: where the definitions of ∆T , T , and T are the same as those described for Equation (4).The isolines of the TVDI in Figure 3 represent the equal availability of surface moisture and take on values between the maximum SM (SM ) and minimum SM (SM ) contents.By obtaining SM at the surface along the wet edge and SM along the dry edge, the TVDI can be converted to near-surface SM by using the following formula [15,52]: where SM can be set as equal to the field capacity in most cases, and SM is equal to the permanent wilting point [53].In this study, the coefficients of least square regression between the in situ SM and the remotely sensed TVDIs were used to derive SM and SM throughout the study region.In this study, the applicability of airborne ∆T /Fr space to assessing the surface SM was evaluated and proposed to improve the precision of the Ts/Fr space for monitoring SM. Figure 4 shows a flowchart in which the ∆T /Fr space incorporating T was built using CASI, TASI and AWS data.Next, the ∆T /Fr space was adapted using NDVI de-saturation and by eliminating disturbed pixels with land use and land cover change data (LUCC).At the airborne level, a reasonable construction of the Ts/Fr space could be interfered with by the disturbed pixels and the saturation of Fr caused by the saturation of the NDVI at high LAIs.These characteristics could affect the EF and TVDI when estimating the SM content.We attempted to use the airborne Ts/VI space to accurately estimate the EF and TVDI and further improve their performances in the SM estimation process.Then, based on the improved ∆T /Fr space, the TVDI and EF were calculated to obtain the airborne SM.Finally, the resulting SM estimates were validated using WSN to determine the effectiveness of using the improved airborne Ts/VI space for monitoring SM.

The Adaption of Airborne Ts/VI Space
As shown in Figure 5, the raw ∆T /Fr space (green scatter plot) from the CASI and TASI data forms an irregular trapezoid, indicating that the non-linear downward trend at Fr is greater than 0.8.Considering the calculation of Fr from Equation (1) based on the NDVI, the non-linear trend may result from NDVI saturation.This trend could result in extraction errors at the dry edge at high Fr values and affect the accuracy of the SM estimation.Thus, the de-saturated ∆T /Fr space (∆T /Fr ) was proposed for describing the actual Fr conditions for the areas with high vegetation coverage.In the de-saturated ∆T /Fr space, the NDVI saturation effect is reduced based on the different sensitivities of the ratio vegetation index (RVI) and NDVI to the LAI [15].The NDVI is more sensitive to moderate and low LAIs (where NDVI < 0.78), and the RVI is more sensitive to high LAIs (where the NDVI > 0.78).In addition, the NDVI and RVI exhibit similar sensitivities to LAI when the NDVI is between 0.75 and 0.85.As shown by the regression analysis of the relationship between the RVI and NDVI when the NDVI is between 0.75 and 0.85 (Figure 6), Equation ( 9) was used to predict the de-saturated NDVI when the raw NDVI was greater than 0.78 (where the NDVI is less sensitive to the corn field LAI [30]).The de-saturated ∆T /Fr space is shown in Figure 5 (blue scatter plot).

NDVI
RVI 0.016 0.65 (9) where NDVI is the desaturated NDVI.The RVI can be calculated using the ratio between the near-infrared reflectance and the visible red reflectance.An ideal ∆T /Fr space is composed of pixels from three main land types: bare soil, full-cover vegetation, and a mixture of bare soil and vegetation.Coarse satellite data can include some mixed pixels, in which other types of land only contributes lightly to the final radiation of the pixels.However, in the airborne data with a 3-m spatial resolution, many pixels are dominated by other land cover types, which make it difficult to estimate the SM content.These pixels, such as houses, roads, shaded roads and shaded trees, are defined as "disturbed pixels" (Figure 7).Artificial facilities, such as greenhouses, buildings and roads (pathways) may also result in the overestimation of the dry edge because the land surface temperature is higher than that of the bare soil.Shadowed pixels have lower incident radiation than sunlit pixels for the same surface types, which affects the Fr and Ts.Thus, the Fr and Ts of shadowed pixels are lower than those of sunlit pixels, resulting in the underestimation of dry and wet edges.A complete tree crown is composed of a sunlit side and a shaded side in the airborne data, which indicates that a single pixel in the ∆T /Fr space cannot reflect the SM content in the root zone of a tree.Although the Fr saturation is solved in the ∆T /Fr space, these disturbed pixels will affect the construction of the ∆T /Fr space, resulting in uncertainty and errors in the observed dry and wet edges.Therefore, disturbed pixels should be eliminated to improve the SM estimations from remotely sensing data.The approach used for removing the disturbed pixels is described as follows: (1) Artificial facility pixels.The building and road pixels were recognized by LUCC data based on the same CASI data provided by HiWATER [54].Many pathway pixels between farmlands were too shallow to display in LUCC data and were removed in step ( 4).(2) Shadowed pixels.The shadowed pixels were identified when their pixel reflectance values in the 554-nm CASI band were less than 0.027 [54].(3) Tree pixels.Woods were extracted when the areas were >20 m 2 and when the reflectance variance in the CASI 554-nm band was >0.025.Green belts were identified when the ratio of the girth to the area was >0.38 and when the height was >15 m by using the vegetation height product with a spatial resolution of 1-m from the digital surface model [55].(4) Pathway, greenhouse, and outlier pixels.The common characteristics of these pixels were that they were all distributed in farmland.The pixels' T were much greater than the neighboring farmland pixels, and their NDVI values were much lower.Based on these characteristics, belt transect pixels covering areas of 1 km × 1 km were used to calculate the variance of T (D ), and the NDVI variance ( D ) of each pixel.Combined with ground surveys and visual interpretations, the pixels with D values less than 0.15 or D values greater than 20 K 2 were defined as disturbed pixels.Then, the pathway, greenhouse, and outlier pixels were removed from the study region using a 1 km × 1 km window size and thresholds of D and D .The red scatter plot in Figure 5 shows the non-disturbed ∆T /Fr space (∆T /Fr ) after removing the disturbed pixels.The non-disturbed dry edge was lower than the raw dry edge, and the non-disturbed wet edge was greater than the raw wet edge.The non-disturbed lower dry edge could be attributed to the removal of artificial facility pixels.Under conditions of similar fractional vegetation cover, the noon-Ts values of the cement buildings, greenhouses and asphalt/concrete roads were higher than those of the bare soil due to evaporative control [15].This result occurred because the bare soil is cooled by SM through evaporation [15], while the buildings, greenhouses and asphalt/concrete roads are impervious surfaces from which evaporative cooling is scarce [56,57].Furthermore, the building and road pixels, which are mixed with forest and grassland components, have higher noon-Ts than the mixed pixels that include bare soil and vegetation at the same Fr [56].

Analysis of ∆ /Fr Space
Figure 5 shows the raw, de-saturated and non-disturbed ∆T /Fr space.The raw ∆T /Fr space (green scatter plot) exhibits an irregular trapezoid shape and Fr saturation when Fr > 0.8, and the corresponding dry and wet edges exhibit the worst fits with the lowest r 2 < 0.38 (Table 3).Thus, the raw ∆T /Fr space fails to describe the SM content when Fr > 0.8.The de-saturated ∆T /Fr space (blue scatter plot) shows the Fr saturation effect of the dense vegetation canopies being removed.The dry and wet edges are a better fit compared with the raw ∆T /Fr space (with a higher r 2 , as shown in Table 3).After eliminating the disturbed pixels based on the de-saturated ∆T /Fr space, the non-disturbed ∆T /Fr space (red scatter plot) results in the best extraction of the dry and wet edges and the highest r 2 , particularly in terms of the non-disturbed dry edge (r 2 = 0.96, Table 3).We conclude that after the NDVI desaturation and the elimination of the disturbed pixels, the non-disturbed ∆T /Fr space can be constructed reasonably, which contributes to the accuracy of the TVDI and EF estimations.
In addition, a narrower divergence in the non-disturbed ∆T /Fr space was observed relative to the other two spaces (Figure 5).The lower dry edge may result from the elimination of disturbed pixels with high Ts, such as roads, greenhouses, and green belts.The rising wet edges may result from the removal of disturbed pixels with low Ts, such as shadows.

The Relationships between Dryness Indices and SM Contents at Different Depths
One important prerequisite for the SM estimation process is the choice of the measured SM depth for validating the dryness index estimates.In this study, the validated SM depth was determined by conducting a correlation analysis between the dryness indices from the three ∆T /Fr spaces and the in situ measurements of SM from 10 AWSs at different depths.
The correlation analysis results are displayed in Table 4, and the correlations were evaluated using the linear model for the TVDI and the Lee model for the EF.Table 4 shows that the TVDI and EF exhibit relationships with the measured SM at a depth of 4 cm and a weak relationship at a depth of 2 cm.These findings may result from AWSs located at the mixed land surfaces of the bare soil and vegetation due to the Fr of the AWS pixels between 0.21 and 0.62 (Table 1).At the mixed land surface, the dryness indices reflect the soil water contents that were determined by the vegetated root zone (0-20 cm) and the top (0-5 cm) or thin layer (~1 mm) of the bare soil [58].Therefore, in situ measurements at a depth of 4 cm were selected from 10 AWSs and 48 WATERNET nodes to retrieve and validate the SM content in Section 5.3 by considering the AWSs and WATERNET nodes with similar surface conditions (Table 1).The details of the sampling strategy were introduced in Section 2.1 and are displayed in Figure 1.A similar SM depth was used by other researchers to validate the EF and TVDI estimates [10,15,23].Notes: Values less than 0.1 were defined as null.r 2 is the coefficient of determination.TVDI and EF were obtained from the raw∆T /Fr space, TVDI and EF were obtained from the∆T /Fr space, and TVDI and EF were obtained fromthe ∆T /Fr space.
In addition, no relationship between the dryness indices and the field SM contents at depths of more than 20 cm can be attributed to the fact that SM contents at depths of 0-20 cm were the main water source during the maize maturation stage when 80% of the maize roots were distributed within the upper 0-20 cm of the soil [59].
The results of the correlations at a depth of 4 cm are presented in Figure 8.No significant relationship was found between the in situ measurements and the dryness indices from the raw ∆T /Fr space.However, the de-saturated EF and TVDI values were obviously related to the in situ measurements (the r 2 values of the TVDI and EF were 0.43 and 0.45, respectively).Thus, adjusting the NDVI saturation enhances the sensitivity of the ∆T /Fr space to the SM content, particularly in vegetation-covered areas.Furthermore, the TVDI and EF values from the non-disturbed ∆T /Fr space exhibit higher correlations with the in situ measurements, with r 2 values of 0.53 and 0.6 for the TVDI and EF, respectively.This finding demonstrates that eliminating the disturbed pixels further improves the correlation by removing their influences on the observed dry and wet edges.In conclusion, adjusting the NDVI saturation and eliminating the disturbed pixels can improve EF and TVDI performance when estimating SM.Therefore, the non-disturbed TVDI and EF can be used as better proxies for SM relative to raw and de-saturated dryness indices.The SM estimates from the non-disturbed dryness indices are shown in the next section.
In addition, as shown in Figure 8, the linear relationship between SM and the TVDI was negative, and the relationship between SM and EF was explained by a cosine function.These results correspond with the observations presented in other studies [45,50].Therefore, the negative linear model was used for the TVDI and the cosine model (Lee model) was used for the EF to obtain the SM contents.

Validation and Evaluation of the Estimated SM
The SM was estimated at a spatial resolution of 3 m using the TVDI and EF generated from the non-disturbed ∆T /Fr space from the CASI and TASI data.The results are displayed in Figure 9, and the corresponding statistics are shown in Table 5.Overall, the results show that the spatial distribution of the TVDI estimates is similar to that of the EF estimates.For example, the Gobi is located at an area with low SM, and the crops are located in areas with high SM.In addition, the crops exhibit different SM patterns due to differing irrigation patterns.The estimates in the validation area show the similarly spatial distribution pattern in Figure 10.However, as observed in Table 5, a greater dynamic range of the EF estimates (0.002-0.35 m 3 •m −3 ) with a larger standard deviation (0.092 m 3 •m −3 ) is found relative to the range (0.01-0.336 m 3 •m −3 ) and standard deviation (0.075 m 3 •m −3 ) of the TVDI estimates.Similarly, the EF estimates in the validation area exhibit a wider range and higher standard deviation for SM when compared with the TVDI estimates.In addition, some null pixel outputs can be observed in Figures 9 and 10 due to the removal of disturbed pixels and noise pixels in Section 3.3.
For validation, Figure 11 shows a comparison of the non-disturbed EF and TVDI estimates with the SM contents measured in situ.In addition, the error statistics (bias, mean absolute error (MAE), root mean square error (RMSE) and correlation coefficient (r)) are summarized in Figure 11.Compared with the TVDI, smaller errors were obtained for the SM estimates from the EF regarding the MAE (0.019 m 3 •m −3 ), RMSE (0.023 m 3 •m −3 ) and a high correlation coefficient (r) of 0.67.These validation results suggest that the EF performs better for estimating SM in the study area and that the EF estimates provide sufficient accuracy that is comparable to other international studies using airborne and satellite data [53].

Discussion
The proposed adaption of airborne ∆T /Fr space in this study is valuable for improving the remote sensing Ts/VI space algorithm for precise SM products.This work proposed that NDVI saturation resulted in the inappropriate extraction of dry edges, which exist in low-to-medium spatial resolution satellite data (e.g., AVHRR and MODIS) from dense vegetation canopies and more evidently in satellite data with a high spatial resolution (e.g., ASTER and LANDSAT).Therefore, the remotely sensed NDVI data are likely desaturated for the appearance of NDVI saturation before constructing the Ts/VI space.However, our implicit assumption is that the saturated ranges of NDVI for different vegetation types are the same.Possible future research would be to further ascertain the range for each vegetation type and select the referenced de-saturated method.
The accurate SM estimate from the non-disturbed ∆T /Fr space implies that the disturbed pixels should be identified and removed using similar or higher spatial resolution LUCC data to build a reasonable Ts/VI space.Similar spatial resolution LUCC data can be used to identify and remove disturbed pixels.If LUCC data are available with a higher resolution and for more land use types and detailed land use classifications, it could be more beneficial to remove some mixed pixels containing buildings or other disturbed types of land.
Incorporating Ta into the ∆T /Fr space could enhance the sensitivity of dryness indices for SM.The Ts/Fr space (without considering Ta) assumes that Ta is constant for the window selected for constructing the space.However, this assumption ignores the heterogeneity of Ta and increases the errors in the TVDI and EF estimations [5].However, incorporating Ta into the ∆T /Fr triangle space addresses this inconsistency by retrieving the evaporation and transpiration statuses.The Ts-Ta gradient on the y-axis of the ∆T /Fr space is physically more accurate because it forces the scatter plot of the data to resemble that described in [7,23].
It was also indicated that EF outperformed TVDI in terms of estimating the SM.Note that the excellent performance of the EF depends on the accuracy of the remotely sensed EF estimation from the ∆T /Fr space and on the appropriate model used to obtain the SM.The remotely sensed EF values rely on the accurate extraction of wet and dry edges, because the accurate extraction is beneficial for estimating extreme SM values over a wide range of Fr.The dry and wet edges were accurately extracted in this study after adjusting the NDVI saturation and eliminating the disturbed pixels.Furthermore, quantitative relationships between ground-measured EF and SM values have been studied and properly described using various models.For example, Lee's model was developed for SM estimations at soil depths of more than 2 cm and produced satisfactory estimates [50].Although the θ value impacts the SM estimation of EF in Lee's model, this estimation can be improved by collecting a number of field SM measurements during extremely dry and wet conditions.Therefore, the EF has better potential as an index than the TVDI for monitoring dry conditions and SM at regional or global scales when supported by weather stations data.However, the remotely sensed EF algorithm is based on the assumption that differences in surface temperature primarily result from evaporation for a given net radiation and atmospheric condition [50].To apply the algorithm over large areas, it is preferential to use normalized forms of Ts and VI to minimize the effects of heterogeneous net radiation and the complex near-surface atmosphere [50].
It should be noted that no clearly quantitative relationship exists between the TVDI and SM because the true TVDI values are immeasurable.Although the TVDI has been widely used to estimate SM, the relationship between the TVDI and SM was estimated using empirical functions at the satellite scale [21].Therefore, no fixed relationship exists between the TVDI and SM.This relationship is also influenced by the spatial resolution [57], window size [60], vegetation type and topography [58].Therefore, this relationship may be unsuitable for airborne data with a spatial resolution of 3 m.In addition, it could be an unreasonable assumption that the dry edge represents the minimum SM and the wet edge represents the maximum SM for the TVDI.The Ts is an indicator of surface energy flux rather than SM [40].Thus, the dry edge more likely represents the limiting values of surface evaporation rather than a purely dry soil surface [48].
The uncertainties in the ∆T /Fr space method for remotely sensed SM estimations should be emphasized.First, the representative dryness index of the ∆T /Fr space requires a full range of vegetation cover and SM availability.However, these conditions are difficult to achieve in most situations, particularly in small study areas.Second, uncertainties still exist in the validation of SM depth.Although a depth of 4 cm for the SM was indicated as suitable for validating the dryness index estimates in Section 5.2, the depth was determined from only 10 AWS measurements.The accuracy of the depth could be improved by using a greater number of field SM measurements at different layers.The depth used for the SM derived from the ∆T /Fr space also varies from thin to deeper layers as the fractional vegetation cover increases.This trend could result in errors when measurements taken at the same depth are used for validation.Third, the ∆T /Fr space method is ineffective in fully vegetated areas.Specifically, one assumption involving the development of the Ts/VI space is that the canopy temperature is insensitive to variations in SM in the surface and deep layers [61].However, airborne CASI/TASI SM estimations could be improved under a range of vegetation covers with help of microwave data, which are affected by canopies in only a limited fashion.

Conclusions
This study attempted to improve the performance of Ts/VI space on retrieving SM based on airborne CASI/TASI data with high spatial resolution to provide a fundamental basis for advancing the precision of SM estimations from optical satellite platforms based on the Ts/VI space algorithm.SM observations are important for promoting eco-hydrological research, improving runoff simulations and developing predictions in cold and arid regions.The ∆T /Fr space (incorporated with Ta) in airborne data revealed that the NDVI saturation and disturbed pixels interfere with the appropriate construction of the airborne ∆T /Fr space, which influences the accuracy of airborne SM estimations.As a result, the dry and wet edges were poorly extracted from the raw airborne ∆T /Fr space, as shown in Table 3.No significant relationships were found between the SM and raw dryness indices (TVDI and EF), with r 2 < 0.24.However, after adaptation of the ∆T /Fr space by adjusting the NDVI saturation and eliminating disturbed pixels, we observed that the accuracies of the extracted dry and wet edges were improved and the SM content was strongly correlated with the dryness indices from the non-disturbed ∆T /Fr space (r 2 > 0.53).Therefore, the adapted airborne ∆T /Fr space exhibited an improved performance for estimating SM.
The EF and TVDI estimates from the non-disturbed ∆T /Fr space were validated using the measured SM at a depth of 4 cm, which was determined by mixed land surfaces composed of bare soil and vegetated areas.The validation results showed that the EF approach outperformed the TVDI because it was better correlated with the measured SM (RMSE = 0.023 m 3 •m −3 and r 2 = 0.67).
This work indicates that airborne data with less sub-pixel heterogeneity can be used to assess the Ts/VI space algorithm developed from satellite observations.In addition, this assessment reveals that NDVI saturation in dense vegetation canopies and disturbed pixels should be evaluated and adapted when the Ts/VI algorithm is applied for estimating the SM from remote sensing data.By using LUCC data with similar or higher spatial resolutions and more detailed land use classification information, the coarse spatial resolution's disturbed pixels and the mixed pixels containing the disturbed land cover types can be discriminated and removed.This method may improve SM estimations based on optical satellite platforms and using the Ts/VI space algorithm.
The airborne results show that the EF could be used as an index for monitoring SM and dryness conditions due to its high sensitivity to SM.However, additional work is required to improve the accuracy of SM estimations under various vegetation covers, especially areas with high vegetative cover in which microwave data should be used.Moreover, the fine spatial details of airborne SM estimation enhance the scale consistency between the in situ measurements and the remotely sensed SM, which provide a promising method for validating coarse-scale microwave SM products and developing a SM downscaling algorithm.

Figure 1 .
Figure 1.Land classification map of the study area with in situ SM measurement points (the WATERNET_TS and AWS_TS nodes are used as the training subsample, and the WATERNET_VS and AWS_VS nodes are used as the validation subsample).

Figure 2 .
Figure 2. A theoretical diagram of the surface temperature/vegetation index space.

Figure 3 .
Figure 3. Conceptual diagram of the Ts-VI triangle for determining the TVDI.

Figure 4 .
Figure 4. Algorithm flowchart for this research.

Figure 5 .
Figure 5.The initial and improved ∆T /Fr space.

Figure 6 .
Figure 6.The result of the desaturated NDVI by the RVI.

Figure 7 .
Figure 7.The distribution of disturbed pixels from the CASI data (red band: 855 nm, green band: 645 nm, and blue band: 552 nm).

Figure 8 .
Figure 8. Correlation between the dryness indices and the SM measured at a depth of 4 cm.

Figure 9 .
Figure 9. SM estimations in the study area.(a) The SM estimation from EF based on ∆T /Fr space.(b) The SM estimation fromTVDI based on the ∆T /Fr space.

Figure 10 .
Figure 10.SM estimation in the validation area.

Table 1 .
Summary of the WSN data used in the study.

Table 3 .
The statistics of the dry and wet edges.

Table 4 .
The correlation analysis of the dryness indices with different SM depths.

Table 5 .
Statistical analysis of the SM content from TVDI and EF .