Commonly used hydrologic models do not consider uncertainty or spatial variability associated with model input parameters. A heterogeneous natural system is modeled as a simple homogeneous system and mean values of soil properties are used without consideration for the variability about the mean. This study will help in better understanding and simulating flow and nitrate transport processes in the unsaturated zone. A comprehensive modeling system based on stochastic and geostatistical theories, as well as GIS technology, in combination with physically based hydrological simulation methodology needs to be developed for modeling solute transport. The results of this study are expected to provide important information for farmers, agency personnel and decision making. The approach should provide more realistic results of agri-chemical movement through the root zone.
ARC/INFO will be used to develop GIS (Geographic Information System) files by mapping and digitizing field boundaries, agricultural management practices and soils information. An illustration, for a hypothetical case at the Ohio MSEA, of how soils, cropping, and tillage data are mapped and overlayed is shown in Figure 1. When overlaying soils and management practice information, an ensemble of independent modeling units are developed by assuming that lateral interactions between the units are negligible. Each modeling unit can be treated as a large soil column penetrating down to a user defined lower boundary (Figure 2). Within each modeling unit there will still be variability in soil properties. Of interest is solute transport, especially of nitrate, entering from the surface through the unsaturated zone to the lower boundary. Solute transport is a function of the physical parameters regarded as random and varying deterministically with time. Initially in this study soil porosity, saturated hydraulic conductivity, soil organic matter content, soil wilting point, and SCS curve number are assumed as a 5-dimensional multivariate (MVN) normal random vector.
The GLEAMS model will be used as the base solute transport model because it has sophisticated nitrate transport algorithms that can reasonably simulate physical and biochemical processes associated with one-dimensional vertical solute transport. Physical processes to be considered are precipitation, infiltration, runoff, water flow in the unsaturated zone, advection and diffusion of nitrate with the flow, and evapotranspiration. Chemical and biological processes include solute adsorption and desorption, ammonification, nitrogen volatilization, nitrification and denitrification, immobilization, and mineralization.
A geostatistical analysis has been conducted to determine the horizontal and vertical correlation lengths and the proposed distribution of the random variable, as well as the property of the space (isotropic or anisotropic, in which dimension, etc.). The integral/correlation lengths were then used in the stochastic analysis and a Monte Carlo simulation. Spatial variograms for the study area were established for experimental data at both surface and subsurface layer. The geostatistical analysis were performed with the program, GEO-EAS version 1.2.1. Based on the experimental data, the population correlation matrix and dispersion matrix of the MVN were derived and 100 data sets were generated for each modeling unit. The GLEAMS model will then be used, with each of the 100 data sets for each unit, to evaluate a five year (1989-1993) period at the Ohio MSEA.
Field data from the Ohio MSEA project will be used to examine the validity of the modeling system. The project database includes soil core chemistry and water content data, chemistry data from vacuum lysimeters, and chemistry data from ground-water wells for 1991 and 1992. The results will be statistically evaluated against actual observations. Typical model outputs are: 1) visual displays of vertical and horizontal layers of soil water and nitrate concentration; and 2) tabular output data.
Field boundaries, soils, and agricultural practices have been digitized and edited as digital computer files ready for use. Various overlays have been done and thematic maps including sampling maps and modeling unit maps have been created. Geostatistics have been used to determine: (a) nugget effects, sills, and range of variograms; and (b) the spatial structure of each random space function for sampling data of each soil texture and the pooled data, for each layer, have been obtained.
The experimental data from Salchow and Lal (this proceedings) were analyzed with several statistical approaches. Statistical moments and normality of each random variable were calculated and examined. Results show that most variables are log-normally distributed for both soil layers. Statistical moments of the variables from the two different layers were also compared. It was concluded that variances of variables for the two layers were not significantly different. Therefore we can assume the same correlation and dispersion matrices for different layers. However, results indicated that for about half the cases, statistical means of variables from the two soil layers were significantly different, with those from the sub-surface layer being generally smaller. This was consistent with reality. For example, organic matter content should decrease with depth.
User-friendly programs have been written to conduct 5-D random MVN generation. Programs have been written to convert climate data from different sources in different formats to files in standard GLEAMS formats. Other input information about erosion, hydrology, and nutrient were also obtained and collected from MSEA data base as well as expertise. GLEAMS has been run successfully with real input and reasonable results have been obtained.