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.     

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.     

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.     

PULSED TRICKLING EFFECTS ON SOIL MOISTURE DISTRIBUTION1

ABSTRACT Laboratory experiments were conducted to study effects of trickle emitter discharge rate on the distribution of soil moisture in a silty-clay loam soil. Both pulsed and continuous irrigation treatments were studied. A simulation model was used to evaluate the results obtained in the laboratory. The agreement between the predicted and measured soil moisture distribution patterns was quite good. For both pulsed and continuous applications, increasing trickle discharge rate resulted in a decrease in the horizontal component and an increase in the vertical component of the wetted soil profile. Compared to the continuous treatments, pulsed applications resulted in significant reduction in water loss below the root zone. Pulsed applications rates can replace continuous small discharge rates to reduce irrigation water runoff problems on heavy soils and with restricted infiltration allow the use of larger emitter orifices to decrease potential clogging of the trickle system.     

USING SOIL TEXTURE TO ESTIMATE SATURATED HYDRAULIC CONDUCTIVITY AND THE IMPACT ON RAINFALL-RUNOFF SIMULATIONS1

ABSTRACT: In this paper a new set of soil texture data is used to estimate the spatial distribution of saturated hydraulic conductivity values for a small rangeland catchment. The estimates of conductivity are used to re-excite and re-evaluate a quasi-physically based rainfall-runoff model. The performance of the model is significantly reduced with conductivity estimates gleaned from soil texture data rather than the infiltration data used in our previous efforts.     

MEASUREMENT OF HYDRAULIC CONDUCTIVITY AND DIFFUSIVITY FOR PREDICTING THE PROCESS OF SOIL WATER INFILTRATION FROM A TRICKLE SOURCE1

ABSTRACT: Two soil water functions, hydraulic conductivity K(θ) and diffusivity D(θ), were estimated by two methods In one method D(θ) was estimated according to Bruce and Klute (1956), and K(θ) was calculated from D(θ) and the retention curve. In the second, K(θ) was obtained by field estimation, with D(θ) being calculated from K(θ) and the retention curve. The criterion of reliability for both methods was agreement between experimental and predicted distribution of soil water content. The prediction was made using the functions K(θ) and D(θ) as soil water parameters in both methods. Theoretical and experimental agreement was generally good. The first method, however, was found to be best for high soil water content and the second for low soil water content. In addition, the water content at the end of the monotonic increase of function D(θ) (estimated according to Bruce and Klute 1956) was found to be about the upper limit of field soil water content. It can be used as a boundary condition in the numerical solution of a cylindrical model of infiltration from a trickle source. It was concluded that the best agreement between theory and experiment can be found when the combined values of D(θ) and K(θ) from both methods of estimation are used.     

Using Landsat data to estimate evapotranspiration of winter wheat

An evapotranspiration (ET) model that accurately estimates daily water use and soil moisture on a regional basis is required for many agricultural and hydrological studies. The model should use meterological data that are readily available and crop information that is responsive to the changing vigor of the plants.We evaluated an ET model with a weighing lysimeter and then applied it to winter wheatfields at four Kansas locations. Model inputs are solar radiation, temperature, precipitation, and leaf area index (LAI); included in the outputs are estimates of transpiration, evaporation, and soil moisture. An equation was developed to estimate LAI from Landsat data. Because LAI can be estimated from satellites, the ET model can potentially be used on a regional basis.     

A HYBRID OPTIMIZATION APPROACH TO THE ESTIMATION OF DISTRIBUTED PARAMETERS IN TWO-DIMENSIONAL CONFINED AQUIFERS1

ABSTRACT: In using non-linear optimization techniques for estimation of parameters in a distributed ground water model, the initial values of the parameters and prior information about them play important roles. In this paper, the genetic algorithm (GA) is combined with the truncated-Newton search technique to estimate groundwater parameters for a confined steady-state ground water model. Use of prior information about the parameters is shown to be important in estimating correct or near-correct values of parameters on a regional scale. The amount of prior information needed for an accurate solution is estimated by evaluation of the sensitivity of the performance function to the parameters. For the example presented here, it is experimentally demonstrated that only one piece of prior information of the least sensitive parameter is sufficient to arrive at the global or near-global optimum solution. For hydraulic head data with measurement errors, the error in the estimation of parameters increases as the standard deviation of the errors increases. Results from our experiments show that, in general, the accuracy of the estimated parameters depends on the level of noise in the hydraulic head data and the initial values used in the truncated-Newton search technique.     

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 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.     

IMPROVED RAINFALL/RUNOFF ESTIMATES USING REMOTELY SENSED SOIL MOISTURE1

ABSTRACT: Remotely sensed soil moisture data measured during the Southern Great Plains 1997 (SGP97) experiment in Oklahoma were used to characterize antecedent soil moisture conditions for the Soil Conservation Service (SCS) curve number method. The precipitation‐adjusted curve number and the soil moisture were strongly related (r²= 0.70). Remotely sensed soil moisture fields were used to adjust the curve numbers and the runoff estimates for five watersheds, in the Little Washita watershed; the results ranged from 2.8 km² to 601.6 km². The soil moisture data were applied at two spatial scales, a finer one (800 m) measuring spatial resolution and a coarser one (28 km). The root mean square error (RMSE) and the mean absolute error (MAE) of the runoff estimated by the standard SCS method was reduced by nearly 50 percent when the 800 m soil moisture data were used to adjust the curve number. The coarser scale soil moisture data also significantly reduced the error in the runoff predictions with 41 percent and 28 percent reductions in MAE and RMSE, respectively. The results suggest that remote sensing of soil moisture, when combined with the SCS method, can improve rainfall runoff predictions at a range of spatial scales.     

APPLICATION OF THE GREEN-AMPT INFILTRATION EQUATION TO WATERSHED MODELING1

ABSTRACT: A computer model was developed, based on the Green-Ampt infiltration equation, to computed rainfall excess for a single precipitation event. The model requires an estimate of parameters related to hydraulic conductivity, wetting front section, and fillable porosity of the soil layers. Values of parameters were estimated from soil textural averages or regression equations based on percent sand, percent clay, and porosity. Average values of effective porosity and wetting front suction were largely acceptable due to the relatively low variability and low model sensitivity to the parameters. Hydraulic conductivity was the most erratic constituent of the loss rate computation due to the high variability and the high sensitivity of the computed infiltration to the parameter. The performance of the Green-Ampt infiltration model was tested through a comparison with the SCS curve number procedure. Seven watersheds and 23 storms with precipitation of one inch or greater were used in the comparison. For storms with less than one inch of rainfall excess, the SCS curve number procedure generally gave the best results; however, for six of the seven storms with precipitation excess greater than one inch, the Green-Ampt procedure delivered better results. In this comparison, both procedures used the same initial abstractions. The separation of rainfall losses into infiltration, interception, and surface retention is, in theory, an accurate method of estimating precipitation excess. In the second phase of the study using nine watersheds and 39 storms, interception and surface retention losses were computed by the Horton equations. Green-Ampt and interception parameters were estimated from value sin the literature, while the surface retention parameter was calibrated so that the computed runoff volumes matched observed volumes. A relationship was found between the surface retention storage capacity and the 15-day antecedent precipitation index, month of year, and precipitation amount.     

DEFINING WATERSHED-SCALE EVAPORATION USING A NORMALIZED DIFFERENCE VEGETATION INDEX1

Monthly composites of the Normalized Difference Vegetation Indices (NDVI), derived from the National Oceanic and Atmospheric Administration's (NOAA) Advanced Very High Resolution Radiometer (AVILRR), were transformed linearly into monthly evaporation rates and compared with detailed hydrologic-model simulation results for five watersheds across the United States. Model-simulated monthly evaporation values showed high correlations (mean R²= .77) with NDVI-derived evaporation estimates. These latter estimates, used in a classical water balance model, resulted in equally accurate simulations of monthly runoff than when the model was run to estimate monthly evaporation via soil moisture accounting. Comparison of NDVI-derived evaporation estimates with pan data showed promise for transforming NDVI values into evaporation estimates under both wet and water-limiting conditions without resorting to the application of any kind of calibrated hydrologic models.     

DYNAMIC MODELING OF STREAM QUALITY BY INVARIANT IMBEDDING1

ABSTRACT. The estimator equations obtained using invariant imbedding is used to estimate the parameters in river or stream pollution. By using these equations, the parameters can be estimated directly from differential equations representing the pollution model and from measured noisy data such as BOD and DO. Another advantage of this approach is that a sequential estimation scheme is obtained. By using this sequential scheme, only current data are needed to estimate current or future values of the unknown parameters. Consequently, a large amount of computer time and computer memory can be saved. Furthermore, not only the parameters but also the concentrations of pollutants can be estimated. Thus, it also forms an effective forecasting technique. The classical least squares criterion is used in the estimation. Several examples are solved to illustrate the technique. (KEY WORDS: dynamic modeling; water pollution; invariant imbedding; forecasting; least squares criterion; estimation)     

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.     

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.     

ASSESSMENT OF SAMPLING ERROR ASSOCIATED WITH SOIL MOISTURE ESTIMATION DESIGNS1

A spectral formalism was developed and applied to quantify the sampling errors due to spatial and/or temporal gaps in soil moisture measurements. A design filter was developed to compute the sampling errors for discrete measurements in space and time. This filter has as its advantage a general form applicable to various types of sampling design. The lack of temporal measurements of the two‐dimensional soil moisture field made it difficult to compute the spectra directly from observed records. Therefore, the wave number frequency spectra of soil moisture data derived from stochastic models of rainfall and soil moisture were used. Parameters for both models were estimated using data from the Southern Great Plains Hydrology Experiment (SGP97) and the Oklahoma Mesonet. The estimated sampling error of the spatial average soil moisture measurement by airborne L‐band microwave remote sensing during the SGP97 hydrology experiment is estimated to be 2.4 percent. Under the same climate conditions and soil properties as the SGP97 experiment, equally spaced ground probe networks at intervals of 25 and 50 km are expected to have about 16 percent and 27 percent sampling error, respectively. Satellite designs with temporal gaps of two and three days are expected to have about 6 percent and 9 percent sampling errors, respectively.     

ROOT DEPTH AS A SENSITIVE PARAMETER IN A DETERMINISTIC HYDROLOGIC MODEL1

ABSTRACT: Deterministic models of watershed hydrology require accurate a priori estimates of soil, vegetation, and watershed parameters. Physical fidelity of these values to those of the prototype natural watershed is essential. One vegetation parameter most neglected, perhaps because it is least understood, is plant root activity. Plant roots directly or indirectly affect many hydrologic processes, including evaporation, transpiration, soil moisture, and ground water. One of their more important functions is in opening surface-connected hydraulic pathways for rainfall penetration. This paper presents the results of a study in which available information on roots has been applied in hydrologic computations.     

Using nighttime light data to estimate water evaporation inside buildings in China's urban areas

Urbanization has a great impact on urban evapotranspiration. Water evaporation inside buildings is an important part of urban water vapor resources and a crucial core of urban hydrological processes. The systematic studies on building water evaporation (BWE) are mostly the method of experimental monitoring. This study proposed a new method to simulate and estimate water evaporation flux inside buildings in urban areas. Based on the nighttime light data and urban per capita gross domestic product (GDP), a new modeling system was built to simulate the total BWE. Building area was calculated using the nighttime light data. And the BWE coefficient D_f was estimated according to the important indicator of economic development per capita GDP value. Then the water evaporation inside urban buildings and the spatial distribution of water evaporation inside buildings in typical cities could be obtained. The results showed that the total amount of water evaporation inside buildings in China's urban areas was 24.5 billion m³. Among the 31 provincial capitals in China, Shanghai had the largest BWE of 1.08 billion m³. The minimum water evaporation of buildings in Lhasa was 20.0 million m³. Studies of BWE can assess urban water budgets, support on-demand allocation of water resources, and provide a fundamental understanding of the relationship between water resources and energy heat island effects in urban areas.     

Mechanistic Simulation of Tree Effects in an Urban Water Balance Model1

Abstract: A semidistributed, physical‐based Urban Forest Effects – Hydrology (UFORE‐Hydro) model was created to simulate and study tree effects on urban hydrology and guide management of urban runoff at the catchment scale. The model simulates hydrological processes of precipitation, interception, evaporation, infiltration, and runoff using data inputs of weather, elevation, and land cover along with nine channel, soil, and vegetation parameters. Weather data are pre‐processed by UFORE using Penman‐Monteith equations to provide potential evaporation terms for open water and vegetation. Canopy interception algorithms modified established routines to better account for variable density urban trees, short vegetation, and seasonal growth phenology. Actual evaporation algorithms allocate potential energy between leaf surface storage and transpiration from soil storage. Infiltration algorithms use a variable rain rate Green‐Ampt formulation and handle both infiltration excess and saturation excess ponding and runoff. Stream discharge is the sum of surface runoff and TOPMODEL‐based subsurface flow equations. Automated calibration routines that use observed discharge has been coupled to the model. Once calibrated, the model can examine how alternative tree management schemes impact urban runoff. UFORE‐Hydro model testing in the urban Dead Run catchment of Baltimore, Maryland, illustrated how trees significantly reduce runoff for low intensity and short duration precipitation events.