Stochastic Transfer Function Model and Neural Networks to Estimate Soil Moisture1

Abstract: A practical methodology is proposed to estimate the three‐dimensional variability of soil moisture based on a stochastic transfer function model, which is an approximation of the Richard’s equation. Satellite, radar and in situ observations are the major sources of information to develop a model that represents the dynamic water content in the soil. The soil‐moisture observations were collected from 17 stations located in Puerto Rico (PR), and a sequential quadratic programming algorithm was used to estimate the parameters of the transfer function (TF) at each station. Soil texture information, terrain elevation, vegetation index, surface temperature, and accumulated rainfall for every grid cell were input into a self‐organized artificial neural network to identify similarities on terrain spatial variability and to determine the TF that best resembles the properties of a particular grid point. Soil moisture observed at 20 cm depth, soil texture, and cumulative rainfall were also used to train a feedforward artificial neural network to estimate soil moisture at 5, 10, 50, and 100 cm depth. A validation procedure was implemented to measure the horizontal and vertical estimation accuracy of soil moisture. Validation results from spatial and temporal variation of volumetric water content (vwc) showed that the proposed algorithm estimated soil moisture with a root mean squared error (RMSE) of 2.31% vwc, and the vertical profile shows a RMSE of 2.50% vwc. The algorithm estimates soil moisture in an hourly basis at 1 km spatial resolution, and up to 1 m depth, and was successfully applied under PR climate conditions.     

SOIL MOISTURE PREDICTION USING SUPPORT VECTOR MACHINES1

ABSTRACT: Herein, a recently developed methodology, Support Vector Machines (SVMs), is presented and applied to the challenge of soil moisture prediction. Support Vector Machines are derived from statistical learning theory and can be used to predict a quantity forward in time based on training that uses past data, hence providing a statistically sound approach to solving inverse problems. The principal strength of SVMs lies in the fact that they employ Structural Risk Minimization (SRM) instead of Empirical Risk Minimization (ERM). The SVMs formulate a quadratic optimization problem that ensures a global optimum, which makes them superior to traditional learning algorithms such as Artificial Neural Networks (ANNs). The resulting model is sparse and not characterized by the “curse of dimensionality.” Soil moisture distribution and variation is helpful in predicting and understanding various hydrologic processes, including weather changes, energy and moisture fluxes, drought, irrigation scheduling, and rainfall/runoff generation. Soil moisture and meteorological data are used to generate SVM predictions for four and seven days ahead. Predictions show good agreement with actual soil moisture measurements. Results from the SVM modeling are compared with predictions obtained from ANN models and show that SVM models performed better for soil moisture forecasting than ANN models.     

Enhancing the Ability of a Soil Moisture‐based Index for Agricultural Drought Monitoring by Incorporating Root Distribution

Agricultural drought differs from meteorological, hydrological, and socioeconomic drought, being closely related to soil water availability in the root zone, specifically for crop and crop growth stage. In previous studies, several soil moisture indices (e.g., the soil moisture index, soil water deficit index) based on soil water availability have been developed for agricultural drought monitoring. However, when developing these indices, it was generally assumed that soil water availability to crops was equal throughout the root zone, and the effects of root distribution and crop growth stage on soil water uptake were ignored. This article aims to incorporate root distribution into a soil moisture‐based index and to evaluate the performance of the improved soil moisture index for agricultural drought monitoring. The Huang‐Huai‐Hai Plain of China was used as the study area. Overall, soil moisture indices were significantly correlated with the crop moisture index (CMI), and the improved root‐weighted soil moisture index (RSMI) was more closely related to the CMI than averaged soil moisture indices. The RSMI correctly identified most of the observed drought events and performed well in the detection of drought levels. Furthermore, the RSMI had a better performance than averaged soil moisture indices when compared to crop yield. In conclusion, soil moisture indices could improve agricultural drought monitoring by incorporating root distribution.     

WATER LOSS EQUATIONS AND COEFFICIENTS TO ESTIMATE RUNOFF FROM RAINFALL1

Infiltration models are based on physical characteristics of the soil and initial soil moisture. For a given soil it is based on the initial soil moisture distribution. A computer simulation model for flood runoff systems (FH-Model) was used to analyze 39 sets of rainfall-runoff data on four small watersheds ranging in size from 17 to 342 square kilometers located in the Yamaska River basin in Quebec. From these analyses, parameters and coefficients have been determined for a water loss (infiltration) equation. A method for determining the loss parameters, using a nonlinear least square curve fitting technique, is presented. Expressions were made to relate the loss parameters to antecedent precipitation. The equations were tested on 11 storm rainfall and runoff events on a watershed located in the same region and close agreements were found.     

SPATIAL DISTRIBUTION OF POINT SOIL MOISTURE ESTIMATES USING LANDSAT TM DATA AND FUZZY-C CLASSIFICATION1

ABSTRACT: Many hydrologic models have input data requirements that are difficult to satisfy for all but a few well-instrumented, experimental watersheds. In this study, point soil moisture in a mountain watershed with various types of vegetative cover was modeled using a generalized regression model. Information on sur-ficial characteristics of the watershed was obtained by applying fuzzy set theory to a database consisting of only satellite and a digital elevation model (DEM). The fuzzy-c algorithm separated the watershed into distinguishable classes and provided regression coefficients for each ground pixel. The regression model used the coefficients to estimate distributed soil moisture over the entire watershed. A soil moisture accounting model was used to resolve temporal differences between measurements at prototypical measurement sites and validation sites. The results were reasonably accurate for all classes in the watershed. The spatial distribution of soil moisture estimates corresponded accurately with soil moisture measurements at validation sites on the watershed. It was concluded that use of the regression model to distribute soil moisture from a specified number of points can be combined with satellite and DEM information to provide a reasonable estimation of the spatial distribution of soil moisture for a watershed.     

Comparison of Field Performance of Multiple Soil Moisture Sensors in a Semi‐Arid Rangeland1

Abstract:  Automated electronic soil moisture sensors, such as time domain reflectometry (TDR) and capacitance probes are being used extensively to monitor and measure soil moisture in a variety of scientific and land management applications. These sensors are often used for a wide range of soil moisture applications such as drought forage prediction or validation of large‐scale remote sensing instruments. The convergence of three different research projects facilitated the evaluation and comparison of three commercially available electronic soil moisture probes under field application conditions. The sensors are all installed in shallow soil profiles in a well instrumented small semi‐arid shrub covered subwatershed in Southeastern Arizona. The sensors use either a TDR or a capacitance technique; both of which indirectly measure the soil dielectric constant to determine the soil moisture content. Sensors are evaluated over a range of conditions during three seasons comparing responses to natural wetting and drying sequences and using water balance and infiltration simulation models. Each of the sensors responded to the majority of precipitation events; however, they varied greatly in response time and magnitude from each other. Measured profile soil moisture storage compared better to water balance estimates when soil moisture in deeper layers was accounted for in the calculations. No distinct or consistent trend was detected when comparing the responses from the sensors or the infiltration model to individual precipitation events. The results underscore the need to understand how the sensors respond under field application and recognize the limitations of soil moisture sensors and the factors that can affect their accuracy in predicting soil moisture in situ.     

ESTIMATION OF SOIL MOISTURE WITH API ALGORITHMS AND MICROWAVE EMISSION1

Large area soil moisture estimations are required to describe input to cloud prediction models, rainfall distribution models, and global crop yield models. Satellite mounted microwave sensor systems that as yet can only detect moisture at the surface have been suggested as a means of acquiring large area estimates. Relations previously discovered between microwave emission at the 1.55 cm wavelength and surface moisture as represented by an antecedent precipitation index were used to provide a pseudo infiltration estimation. Infiltration estimates based on surface wetness on a daily basis were then used to calculate the soil moisture in the surface 0–23 cm of the soil by use of a modified antecedent precipitation index. Reasonably good results were obtained (R²= 0.7162) when predicted soil moisture for the surface 23 cm was compared to measured moisture. Where the technique was modified to use only an estimate of surface moisture each three days an R² value of 0.7116 resulted for the same data set. Correlations between predicted and actual soil moisture fall off rapidly for repeat observations more than three days apart. The algorithms developed in this study may be used over relatively flat agricultural lands to provide improved estimates of soil moisture to a depth greater than the depth of penetration for the sensor.     

APPLICATION OF AN INTEGRATED BASIN-SCALE HYDROLOGIC MODEL TO SIMULATE SURFACE-WATER AND GROUND-WATER INTERACTIONS1

ABSTRACT: Hydrologic models have become an indispensable tool for studying processes and water management in watersheds. A physically-based, distributed-parameter model, Basin-Scale Hydro-logic Model (BSIIM), has been developed to simulate the hydrologic response of large drainage basins. The model formulation is based on equations describing water movement both on the surface and in the subsurface. The model incorporates detailed information on climate, digital elevation, and soil moisture budget, as well as surface-water and ground-water systems. This model has been applied to the Big Darby Creek Watershed, Ohio in a 28-year simulation of rainfall-runoff processes. Unknown coefficients for controlling runoff, storativity, hydraulic conductivity, and streambed permeability are determined by a trial-and-error calibration. The performance of model calibration and predictive capability of the model was evaluated based on the correlation between simulated and observed daily stream discharges. Discrepancies between observed and simulated results exist because of limited precipitation data and simplifying assumptions related to soil, land use, and geology.     

On the Relationship Between Mean and Variance of Soil Moisture Fields1

Abstract: The objective of this work was to explain an apparent contradiction in the literature related to the relationship between mean and variance (or standard deviation) of soil moisture fields. Some studies found an increase in soil moisture variance with decreasing mean soil moisture, while others showed a decrease. The evidence of maximum variance in the mid‐range of mean soil moisture was also reported in the literature. In this paper, we focus on the effects of spatial variability of soil texture on the relationship between variance and mean of soil moisture during soil dry‐down processes. Soil texture influences soil moisture mean and variance through its direct effects on evaporation and drainage, which are two main factors controlling soil drying. A differential equation describing soil moisture dry down is proposed and studied. Our study shows that as mean soil moisture is greater than a threshold, variance increases with decreasing mean soil moisture. If mean soil moisture is less than the threshold, variance decreases with decreasing mean soil moisture. The threshold depends on soil texture and is between the field capacity and the wilting point. The soil moisture dry‐down equation is also applied to explain the apparent contradiction with regard to the relationship between mean and variance of soil moisture fields reported in the literature.     

PREPLANTING SOIL MOISTURE USING PASSIVE MICROWAVE SENSORS1

ABSTRACT: Accurate assessment of preplanting soil moisture conditions is necessary for good agricultural management, and can have a significant influence on crop yield in the Texas Panhandle region. The Texas High Plains Underground Water Conservation District invests considerable time and money in developing a soil moisture deficit map each year in the hopes of achieving optimal use of irrigation water. Microwave sensors are responsive to surface soil moisture and, if used in this application, can provide timely and detailed information on root zone soil moisture. For this reason, an experiment was conducted in 1984 to evaluate the potential of aircraft-mounted passive microwave sensors. Microwave radiometer data were collected over a 2700 km² area near Lubbock, Texas, with a processed resolution of 0.32 km². These data were ground registered and converted to estimates of soil moisture using an appropriate model and land cover and soil texture information. Analyses indicate that the system provides an efficient means for mapping variations in soil moisture over large areas.     

EVAPOTRANSPIRATION AND SOIL MOISTURE DYNAMICS ON A SEMIARID PONDEROSA PINE HILLSLOPE1

ABSTRACT: Detailed measurements of soil moisture and ET in semiarid forest environments have not been widely reported in the literature. In this study, soil moisture and water balance components were measured over a four‐year period on a semiarid ponderosa pine hillslope, with evapotranspiration (ET) determined as the residual of measured precipitation, runoff, and change in soil moisture storage. ET accounts for approximately 95 percent of the water budget and has a distinctly bimodal annual pattern, with peaks occurring after spring snowmelt and during the late summer monsoon season, periods that coincide with high soil moisture. Weekly growing season ET rates determined by the hillslope water balance are found to be invariably below calculated potential rates. Normalized ET rates are linearly correlated (r²= 0.62) with soil moisture; therefore, a simple linear relation is proposed. Growing season soil moisture dynamics were modeled based on this relation. Results are in fair agreement (r²= 0.63) with the observed soil moisture data over the four growing seasons; however, for two dry summers with little surface runoff, much better results (r² > 0.90) were obtained.     

Modeling the Spatially Varying Water Balance Processes in a Semiarid Mountainous Watershed of Idaho1

Stratton, Benjamin T., Venakataramana Sridhar, Molly M. Gribb, James P. McNamara, and Balaji Narasimhan, 2009. Modeling the Spatially Varying Water Balance Processes in a Semiarid Mountainous Watershed of Idaho. Journal of the American Water Resources Association (JAWRA) 45(6):1390‐1408. Abstract: The distributed Soil Water Assessment Tool (SWAT) hydrologic model was applied to a research watershed, the Dry Creek Experimental Watershed, near Boise Idaho to investigate its water balance components both temporally and spatially. Calibrating and validating SWAT is necessary to enable our understanding of the water balance components in this semiarid watershed. Daily streamflow data from four streamflow gages were used for calibration and validation of the model. Monthly estimates of streamflow during the calibration phase by SWAT produced satisfactory results with a Nash Sutcliffe coefficient of model efficiency 0.79. Since it is a continuous simulation model, as opposed to an event‐based model, it demonstrated the limited ability in capturing both streamflow and soil moisture for selected rain‐on‐snow (ROS) events during the validation period between 2005 and 2007. Especially, soil moisture was generally underestimated compared with observations from two monitoring pits. However, our implementation of SWAT showed that seasonal and annual water balance partitioning of precipitation into evapotranspiration, streamflow, soil moisture, and drainage was not only possible but closely followed the trends of a typical semiarid watershed in the intermountain west. This study highlights the necessity for better techniques to precisely identify and drive the model with commonly observed climatic inversion‐related snowmelt or ROS weather events. Estimation of key parameters pertaining to soil (e.g., available water content and saturated hydraulic conductivity), snow (e.g., lapse rates, melting), and vegetation (e.g., leaf area index and maximum canopy index) using additional field observations in the watershed is critical for better prediction.     

Reconstructions of Soil Moisture for the Upper Colorado River Basin Using Tree‐Ring Chronologies1

Anderson, SallyRose, Glenn Tootle, and Henri Grissino‐Mayer, 2012. Reconstructions of Soil Moisture for the Upper Colorado River Basin Using Tree‐Ring Chronologies. Journal of the American Water Resources Association (JAWRA) 48(4): 849‐858. DOI: 10.1111/j.1752‐1688.2012.00651.x Abstract: Soil moisture is an important factor in the global hydrologic cycle, but existing reconstructions of historic soil moisture are limited. We used tree‐ring chronologies to reconstruct annual soil moisture in the Upper Colorado River Basin (UCRB). Gridded soil moisture data were spatially regionalized using principal components analysis and k‐nearest neighbor techniques. We correlated moisture sensitive tree‐ring chronologies in and adjacent to the UCRB with regional soil moisture and tested the relationships for temporal stability. Chronologies that were positively correlated and stable for the calibration period were retained. We used stepwise linear regression to identify the best predictor combinations for each soil moisture region. The regressions explained 42‐78% of the variability in soil moisture data. We performed reconstructions for individual soil moisture grid cells to enhance understanding of the disparity in reconstructive skill across the regions. Reconstructions that used chronologies based on ponderosa pines (Pinus ponderosa) and pinyon pines (Pinus edulis) explained more variance in the datasets. Reconstructed soil moisture data was standardized and compared with standardized reconstructed streamflow and snow water equivalent data from the same region. Soil moisture and other hydrologic variables were highly correlated, indicating reconstructions of soil moisture in the UCRB using tree‐ring chronologies successfully represent hydrologic trends.     

Estimating Root Zone Soil Moisture at Continental Scale Using Neural Networks

This study investigates the feasibility of artificial neural networks (ANNs) to retrieve root zone soil moisture (RZSM) at the depths of 20 cm (SM20) and 50 cm (SM50) at a continental scale, using surface information. To train the ANNs to capture interactions between land surface and various climatic patterns, data of 557 stations over the continental United States were collected. A sensitivity analysis revealed that the ANNs were able to identify input variables that directly affect the water and energy balance in root zone. The data important for RZSM retrieval in a large area included soil texture, surface soil moisture, and the cumulative values of air temperature, surface soil temperature, rainfall, and snowfall. The results showed that the ANNs had high skill in retrieving SM20 with a correlation coefficient above 0.7 in most cases, but were less effective at estimating SM50. The comparison of the ANNs showed that using soil texture data improved the model performance, especially for the estimation of SM50. It was demonstrated that the ANNs had high flexibility for applications in different climatic regions. The method was used to generate RZSM in North America using Soil Moisture and Ocean Salinity (SMOS) soil moisture data, and achieved a spatial soil moisture pattern comparable to that of Global Land Data Assimilation System Noah model with comparable performance to the SMOS surface soil moisture retrievals. The models can be efficient alternatives to assimilate remote sensing soil moisture data for shallow RZSM retrieval.     

Water balance characterization of the early 21st century drought in the western United States

Monthly temperature and precipitation data for 923 United States Geological Survey 8-digit hydrologic units are used as inputs to a monthly water balance model to compute monthly actual evapotranspiration, soil moisture storage, and runoff across the western United States (U.S.) for the period 1900 through 2020. Time series of these water balance variables are examined to characterize and explain the dry conditions across the western U.S. since the year 2000. Results indicate that although precipitation deficits account for most of the changes in actual evapotranspiration and runoff, increases in temperature primarily explain decreases in soil moisture storage. Specifically, temperature has been particularly impactful on the magnitude of negative departures of soil moisture storage during the spring (April through June) and summer (July through September) seasons. These effects on soil moisture may be particularly detrimental to agriculture in regions already stressed by drought such as the western U.S.     

SOIL MOISTURE VARIATION PATTERNS OBSERVED IN HAND COUNTY,SOUTH DAKOTA1

ABSTRACT: Sail moisture data were taken during nine sampling events (1976-1978) at a test site in South Dakota as part of the ground truth used in NASA's aircraft experiments studying the microwave sensing of soil moisture. This portion of the study dealt only with the spatial variability observed with regard to the ground data. Samples were taken over three surface depths at each point, and the data reported as the mean field moisture content within each of three surface horizons. The results shed additional light on the relationship between ground sampling and remote sensing of soil moisture. First, it was found that it is best to partition data of well drained sites from poorly drained areas when attempting to characterize the surface moisture content throughout an area of varying soil and cover conditions. It was also found that the moisture coefficient of variation within a field decreased as the mean field soil moisture increased, and that the standard deviation was at a maximum in the mid-range of observed moisture conditions (15-25 percent). Within field sample variation also decreases as the sample is integrated over a greater surface depth. It was determined that a sampling intensity of 10 samples per kilometer was adequate to characterize the mean field soil moisture at all three depths along a transect in the areas of moderate to good drainage-.     

Soil Moisture Data Assimilation Using Support Vector Machines and Ensemble Kalman Filter1

Abstract: A hybrid data assimilation (DA) methodology that combines two state‐of‐the‐art techniques, support vector machines (SVMs) and ensemble Kalman filter (EnKF), is applied for soil moisture DA in this work. The SVM methodology provides a statistically sound and robust approach to solving the inverse problem, and thus to building statistical models. EnKF is an extension of the Kalman Filter (KF), a well‐known tool in prediction updating. In the present research, ground measurements were used to build a SVM‐type soil moisture predictor. Subsequent observations and their statistics were assimilated to update predictions from the SVM model by coupling it with EnKF. In this way, both model predictions and ground data, as well as their statistics, are fused thus minimizing the prediction error and making the predictions and observations statistically consistent. The results are shown for two approaches; one in which update is done at every time step and the other which assumes that data is only available at alternate time steps (in window of 10 time steps) and hence update is performed at those occasions. The SVM‐EnKF coupling is shown to improve soil moisture forecasts in an example using data from the Soil Climate Analysis Network site at Ames, Iowa.     

SIMULATING SOIL WATER RECESSION COEFFICIENTS FOR AGRICULTURAL WATERSHEDS1

ABSTRACT: The antecedent precipitation index (API) has been a useful indicator of soil moisture conditions for watershed runoff calculations, and recent attempts to correlate this index with spaceborne microwave observations have been fairly successful. The prognostic equation for soil moisture used in some of the atmospheric general circulation models (GCM) together with Thomthwaite-Mather parameterization of actual evapotranspiration leads to API equations. The recession coefficient for API is found to depend on climatic factors as contained in potential evapotranspiration and to depend on soil texture as reflected by field capacity and permanent wilting point. A recently developed model for global insolation is used with climatological data for Wisconsin to simulate the annual trend of the recession coefficient. Good quantitative agreement is shown with the observed trends at Fennimore and Colby watersheds in Wisconsin. This study suggests that API could be a unifying concept for watershed and atmospheric general circulation modeling.     

Spatial Dynamics of Soil Moisture in a Complex Terrain in the Semi‐Arid Loess Plateau Region,China1

Abstract: Soil moisture is an important hydrological variable in reforestation practices in a water‐limited region of the Loess Plateau of northwestern China. The objective of this study was to quantify the spatial dynamics of soil moisture on a complex terrain. During 2004‐2006, a total of 313 sample points in two kinds of grid (2 × 2 m and 20 × 20 m) were arranged for soil moisture measurements (two soil layers: 0‐30 and 30‐60 cm) with Time Domain Reflectometry. The geostatistical properties of soil moisture patterns, the variance and correlation structure of the soil moisture, and the effects of terrain factors on soil moisture were analyzed. The results suggested that our sampling grid captured the spatial variability of soil moisture distributions for this complex terrain. Principal Component Analysis and Cluster Analysis statistics showed that soil moisture decreased as slope gradient increased; that sunny aspects (112.5°‐292.5°) had relatively lower soil moisture than did shady aspects (292.5°‐112.5°); that soil moisture was lowest in the SWW direction and highest in the NWN direction; and that hillslope aspect was the main factor affecting soil moisture in the 0‐ to 30‐cm soil layer, whereas the main factor for the 30‐ to 60‐cm layer was slope gradient. It was found that the relative values of soil moisture for steep slopes (>36%) with shady aspect (292.5°‐112.5°), gentle slopes (<36%) with sunny aspect (112.5°‐292.5°), and steep slopes with sunny aspect were 99, 82, and 80, respectively – assuming a soil moisture value of 100 for gentle slopes with shady aspect. The results of this study are expected to be relevant to and useful for reforestation planning and design, parameterization of distributed hydrology models, and land productivity assessment in the study region.     

METHODOLOGY AND EMPIRICAL ESTIMATES OF THE RESPONSE FUNCTION OF SORGHUM TO IRRIGATION AND SOIL MOISTURE1

ABSTRACT: This paper presents a methodology for the estimation of response functions of crops to irrigation and soil moisture. A system analysis framework is applied to describe the relationships involved. Two subsystems are distinguished, with the first one involving the relationship between irrigation decision variables and soil state variables, and the second involving the relationship between soil state variables and crop yield. A method for tracing and predicting soil moisture profile variations over time and depth is presented, and empirical estimates of the response function of grain sorghum to soil moisture are derived. In the specification of the response function the concept of “critical days” is applied with a “critical day” being defined as one where the soil moisture is depleted below a certain critical level. The paper provides empirical evidence for the usefulness of the approach