Soil moisture is an important component of the water, energy, and biogeochemical cycle [1
], and is of great significance to related research on water resources management, agricultural production, and climate change [4
]. Soil moisture monitoring can be divided into three categories based on data acquisition methods: site measurement, simulation and assimilation, and soil moisture inversions based on remote sensing data [3
]. Among them, the precision of soil moisture observed by stations is high, but because of the discrete characteristics of observation stations, the soil moisture observed by stations cannot reflect the temporal and spatial continuous variation characteristics of soil moisture at a regional scale. The soil moisture data simulated by assimilation models have continuity in space and time, but the accuracy of simulation largely depends on the selection of parameterization schemes and parameterization process. Besides, assimilation models require a large number of input parameters, reducing their practicability. Remote sensing has the remarkable advantage of large-scale synchronous observation and reflects the continuous change information of the earth’s surface in time and space [6
], which makes it an important data source for soil moisture inversion research.
Research into soil moisture retrieval based on remote sensing began in the 1960s [3
]. In early investigations of soil moisture inversions, researchers used single factors to establish inversion models, such as optical reflectance [7
], thermal infrared [10
], and microwave-based methods [11
]. Researchers directly established models of the relationship between a single factor (such as reflectance, brightness temperature, thermal inertia, or backscattering coefficient) and soil moisture [14
] or used a single factor to construct an index to indirectly reflect soil moisture. For example, the normalized difference vegetation index (NDVI) [15
], vegetation condition index (VCI) [16
], normalized difference water index (NDWI) [21
], global vegetation moisture index (GVMI) [22
], land surface water index (LSWI) [23
], visible and shortwave infrared drought index (VSDI) [24
], and normalized multi-band drought index (NMDI) [25
] are calculated using optical reflectance, while the land surface temperature (LST) [26
], normalized difference temperature index (NDTI) [28
], and temperature condition index (TCI) [16
] are calculated using thermal infrared bands. The indices mentioned above are often used to monitor surface drought and soil moisture.
Recently, researchers have used multiple factors, such as the combination of visible and thermal infrared bands or visible and microwave bands, to establish inversion models [29
] or construct comprehensive indexes to monitor soil moisture [31
]. For example, Goward et al. found that when the vegetation coverage in the study area changed widely, the surface temperature and NDVI formed triangular or trapezoidal shapes on the scatter plot; therefore, they put forward the concept of soil moisture contours [32
]. Gillies and Carlson constructed a universal triangle method for evaluation of surface soil moisture content [33
]. Satellite-derived surface radiant temperature and a vegetation index were associated in an inverse modeling scheme and found to fit the observed data well. Subsequently, Sandholt et al. constructed a temperature vegetation drought index (TVDI) based on the characteristic space, which takes into account the thermal infrared characteristics on the basis of optical characteristics and can better characterize the soil moisture status [9
]. D. Zhang et al. proposed a new soil moisture index, the temperature rising rate vegetation dryness index (TRRVDI) based on the surface temperature-vegetation index triangle method, in which the instantaneous temperature was replaced with the mid-morning land surface temperature rising rate [34
]. This index had better coefficient of determination at 19 meteorological stations in Spain than the one-time LST and vegetation index and reduced the uncertainty associated with the data; however, it requires substantial ground data and is complex to calculate [3
]. Amani et al. synthesized vegetation and soil characteristics to construct a temperature-vegetation-soil moisture dryness index (TVMDI) based on the perpendicular vegetation index (PVI), LST, and soil moisture (SM) [35
]. In this model, SM and PVI were calculated based on the red-near infrared feature space, after which, the LST was added to construct the three-dimensional (3D) feature space and the TVMDI was obtained according to the relationship of the body diagonals. The correlation coefficient between the TVMDI and measured soil moisture was 0.65. In addition to the combination of soil and vegetation features, there are soil moisture indices that have been proposed by combining visible and microwave bands. For example, X. Zhang et al. presented a synthesis method that divided soil moisture into a baseline and change value, in which the baseline was the lowest state of soil moisture in the observation period and the change value depended on the influence of meteorological elements, such as precipitation and evapotranspiration [36
]. This model accurately estimated the daily soil moisture content of 1 km resolution in the Xinjiang province with a mean square error of the model inversion results and ground measured values of 3.99%, indicating it can be used for high-precision soil moisture retrieval. It is important to note that the meteorological elements in this study only participated in the construction of soil water model as auxiliary variables in the form of rainfall correction factors, which means few studies have investigated the synthesis of soil, vegetation, and meteorological conditions.
Soil moisture content is influenced by many factors, including soil characteristics, vegetation coverage, and meteorological conditions, which results in it having high spatial heterogeneity. In the existing multi-factor soil moisture inversion research, two elements of vegetation, soil and meteorological elements, are usually considered comprehensively, but three elements are not considered at the same time. In theory, considering the meteorological, soil, and vegetation systems synthetically can improve the accuracy of soil moisture inversion. Therefore, this study was conducted to build a comprehensive inversion model of soil moisture by integrating meteorological, soil, and vegetation systems to indicate the soil moisture status. Specifically, this research proposes a cuboid model for soil moisture assessment, which is referred to as the cuboid soil moisture index (CSMI) in this paper. The main purpose of this paper is to introduce the model and construction process of the CSMI. Researchers can follow the methodology of this work to calculate the CSMI for their own study area by customizing the parameters and the length coefficients of the three edges of the cuboid model according to the meteorological, soil, and vegetation characteristics of their study area.
4.1. Impacts of Edge Length Coefficient on CSMI
The absolution values of correlation coefficients between three CSMIs and soil moisture at a depth of 10 cm with those of the three selected parameters and soil moisture at a depth of 10 cm were compared (Figure 6
). Overall, the correlation between CSMI and soil moisture was higher than that between single parameter and soil moisture. The correlation between CSMI and soil moisture was highest in April followed by May, while it was lowest in March. The edge length coefficients of CSMI-1, CSMI-2, and CSMI-3 were 2/1/2, 3/2/5, and 3/1/6, respectively; therefore, the ranking of the edge length coefficients of the three individual parameters was AP = ΔLST > LSWI in CSMI-1 and AP > ΔLST > LSWI in both CSMI-2 and CSMI-3. The ranking of correlation coefficients of the three individual parameters and soil moisture was ΔLST > AP > LSWI in March, AP ≈ ΔLST > LSWI in April, and AP > ΔLST ≈ LSWI in May, respectively. In CSMI-1, the ranking of the edge length coefficient of the three individual parameters was highly consistent with the ranking of correlation coefficients of the three individual parameters and soil moisture. Moreover, the ranking of correlation coefficients of the three individual parameters and soil moisture in CSMI-1 was the same as the ranking of the edge length coefficient of the three individual parameters in April. These findings explain why CSMI-1 was more closely related to soil moisture than CSMI-2 and CSMI-3 and why CSMI-1 had best relationship with soil moisture in April.
Based on the above analyses, the three edge length coefficients in the model had a great influence on the results of the CSMI calculation. In this study, the three edge length coefficients from March to May were the same, but the effects of climate, soil, and vegetation on soil moisture varied among different months. According to the influence of climate, soil, and vegetation on soil moisture in different months, the accuracy of CSMI can be improved by dynamically adjusting the coefficients of the three parameters monthly.
4.2. Impacts of Surface Temperature Difference, Crop Growth, and Accumulated Precipitation on CSMI
To analyze the effects of surface temperature differences, crop growth, and accumulated precipitation on the accuracy of the CSMI model, we divided the ΔLST into five grades with 5 °C, 10 °C, 15 °C, and 20 °C as break points, NDVI into five grades with 0.1, 0.3, 0.5, and 0.7 as break points, and AP into four grades with 10, 25, and 50 cm/ten days as break points. The correlation coefficients between CSMI-1 and soil moisture at different levels of ΔLST, NDVI, and AP were then calculated. As shown in Figure 7
, the correlation coefficients between CSMI-1 and soil moisture varied among different levels of ΔLST, NDVI, and AP. Under most cases, CSMI-1 had the best correlation with soil moisture at 10 cm, followed by 20 cm and 50 cm. In other words, the correlation coefficient between CSMI-1 and soil moisture generally decreased as soil depth increased, which is consistent with the findings in Table 5
. The correlation coefficients of CSMI-1 and soil moisture showed no obvious trend with the change of ΔLST (Figure 7
a). Regardless of the NDVI and AP levels, the correlation between CSMI-1 and soil moisture at different depths was greatest when ΔLST was 10–15 °C. When NDVI was lower than 0.7, CSMI-1 was highly correlated with soil moisture at a significance of 0.01, which indicated that CSMI had good applicability to the evaluation of soil moisture under different vegetation coverage (Figure 7
b). When NDVI was larger than 0.7, the correlation coefficients between CSMI-1 and soil moisture at different depths were below 0.4 and did not pass the significance test. One possible reason for this was that the stations we used in this study were agrometeorological stations, and there were few observation data for stations with NDVI values higher than 0.7. AP and soil moisture at different depths were highly correlated at a statistical significance level of α = 0.05 (Figure 7
c). Regardless of the NDVI and ΔLST levels, the correlation between CSMI-1 and soil moisture at different depths was greatest when AP was 25–50 cm.
4.3. Limitations and Potential Improvement of This Study
Firstly, in this paper, for selection of feature parameters of the CSMI model, only the correlation between candidate characteristic parameters and soil moisture was considered, and the correlation between parameters was not considered. We found that correlation among the three parameters varied with time (Figure 8
). The three parameters had the highest correlation in April, followed by March, and finally, May. The correlation between ΔLST and AP was the highest in April and May, and the correlation between LSWI and ΔLST was the highest in June. It may affect the setting of weights to some extent. In future studies, we will consider selecting characteristic parameters with high correlation with soil moisture and low correlation among variables to calculate CSMI index.
Second, this study is limited in that the spatial and temporal heterogeneity of soil moisture is not considered when determining the edge length coefficients of the three axes of the CSMI model. However, different land cover types, such as bare soil and vegetation, may have different soil moisture. The same type of land use, such as vegetation, also differs in soil moisture at different growth stages. When determining the edge length coefficient, the condition of the underlying surface can be fully considered, and the edge length coefficient can be adjusted dynamically, according to changes in the underlying surface to ensure that the coordinate axes of the cuboid model can play an effective role and further improve the accuracy of the model. If the edge length coefficient of any of the three parameters in the cuboid model is set to 0, the three-dimensional cuboid model will be transformed into a two-dimensional model. For example, when the coefficient of crop parameter is set to 0, the effect of vegetation cover on soil moisture is not considered, and the model is suitable for soil moisture inversion in bare soil. When the coefficient of soil parameter is set to 0, the effect of bare surface on soil moisture is not considered, and the model is suitable for the inversion of surface moisture in the case of dense vegetation coverage.
Another limitation is that, although precipitation can indicate soil water recharge, the changes in soil moisture caused by factors such as irrigation by human activities are not considered in this study. If irrigation information can be considered as artificial recharge precipitation added in the Z axis of CSMI, the accuracy of the model can be further improved. However, detailed irrigation information (such as irrigation location, time, and intensity) is very scarce, especially in large-scale research areas [45
]. Therefore, in theory, the current CSMI model without considering irrigation information has better applicability in rain-fed areas.
Finally, in this study, we constructed and validated the CSMI model based on the data of 58 agrometeorological stations in the Huang-Huai-Hai Plain in 2010. Larger regional validations, as well as those for other vegetation types (such as forests and grasslands) in other years have not yet been conducted. Among the many remote sensing parameters that have been developed to describe soil moisture, there are no accepted optimal parameters [3
]. The performance of the same parameter differs among regions [46
]. The main purpose of this article is to propose a model and construction process of the CSMI. Researchers can follow the methodology of this work, select the parameters of the three edges of the cuboid model suitable for their study area, and determine the length coefficients of the three edges according to the meteorological, soil and vegetation characteristics of their study area.
4.4. Significance of This Study
The importance of this study lies in two aspects:
Firstly, our study results indicate that integrating soil, vegetation, and meteorological feature parameters can improve the accuracy of soil moisture inversion. The relationship between feature parameters (such as AP, ΔLST, and LSWI) and soil moisture varies with time and soil depth. It may be a development direction in the future to build an adaptive soil moisture inversion model in which the weights of the three axes in CSMI varies with time. In general, the correlation coefficient between CSMI with soil moisture decreases with the increase of soil depth. Thus, it is more difficult to improve the precision of deep soil moisture inversion than to improve the precision of shallow soil moisture inversion by using the optical remote sensing data. It is a better choice to use radar image to retrieve deep soil moisture.
Second, the calculation steps of the CSMI model are clear and simple. Firstly, building the alternative soil, vegetation, and meteorological feature parameters set, secondly, selecting a soil feature parameter, a vegetation feature parameter, and a meteorological feature parameter which have the highest correlation with soil moisture from a parameter set. Thirdly, normalizing the selected feature parameters to 0–1 and making them positively correlated with soil moisture, fourthly, determining weight (the cuboid length coefficient) of each parameter based on the correlation between parameters and soil moisture, and lastly, calculating CSMI according to Formula 1. Following the above steps, researchers can select the weights of the feature parameters and parameters involved in the calculation and construct a CSMI model suitable for their own study area. Moreover, the three-dimensional CSMI model can be easily converted to a two-dimensional model to adapt to different surface conditions (as long as the weight coefficient of one parameter is set to 0). For example, one can set the weight of the vegetation feature parameter to 0 for the bare soil surface.
Overall, on the one hand, this study has some implications for the future research direction, on the other hand, it provides a reference method for soil moisture inversion using optical remote sensing images by integrating soil, vegetation, and meteorological feature parameters.
In this study, a cuboid model of soil moisture inversion was constructed. Three parameters related to soil moisture in the soil-vegetation-meteorological system were placed in the three-dimensional space. The X axis represents the soil system, the Y axis represents the vegetation system, and the Z axis represents the meteorological system. All parameters were positively correlated with soil moisture. The length of the cuboid diagonal reflects the soil moisture level and is named the cuboid soil moisture index (CSMI).
Taking the Huang-Huai-Hai Plain as the experimental area and the soil moisture data obtained from the agrometeorological stations as the reference, we screened ΔLST, LSWI, and AP as soil, vegetation, and meteorological system parameters respectively, for use in the CSMI calculation. The three edge length coefficients in the model had a great influence on the results of the CSMI calculation. Three sets of weight coefficients (2/1/2, 3/2/5, and 3/1/6) were considered, and the results showed that CSMI-1, with a cuboid length coefficient of 2/1/2, had the best correlation with observed soil moisture. The correlation of CSMI-1 with observed soil moisture was 0.64, 0.60, and 0.52 for depths of 10 cm, 20 cm, and 50 cm, respectively. When the NDVI was lower than 0.7, CSMI-1 was highly correlated with soil moisture at a significance of 0.01. Testing results successfully indicated that CSMI had a certain potential for assessing soil moisture.
The calculation steps of the CSMI model are clear and simple, researchers can follow our study to construct a CSMI model suitable for their own study area. Besides, our results indicate that building an adaptive soil moisture inversion model may be a development direction in the future since the relationship between feature parameters (such as AP, ΔLST, and LSWI) and soil moisture varies with time. The correlation coefficient between feature parameters derived from optical remote sensing images and soil depth decreases with the increase of soil depth. Radar image might be helpful to improve the retrieval accuracy of deep soil moisture.