Development of phenomenologically-based distribution fitting procedures and spatial processes for mixed population soil properties

In the literature, two distinct flow phenomena, namely, flow through the main body of the soil, and flow through preferential flow paths, have been identified. Models which try to incorporate the effects of these two phenomena require either an explicit or an implicit knowledge of the probability distribution functions associated with the soil properties affecting flow. In keeping with the fact that these properties are influenced by two distinct phenomena, it is postulated that they should be represented by heterogeneous distribution functions. These distribution functions are, by design, suitable for representing mixed population data.

Procedures were developed for fitting heterogeneous distribution functions to data. These procedures are encoded in Microsoft QUICKBASIC with some additional FORTRAN routines. The fitting procedures do not utilize any moment above the second order, and are markedly different from the use of regression methods for fitting multiple parameter distributions. Procedures were developed for two types of mixtures. One type is suitable for instances where a measured quantity is the sum of values from two populations, while the other is applicable when a measured quantity may be from one population or from another, but not from both at the same time or location. The procedures were applied to several data sets, including flow data, infiltrability data, and pH data. In many instances, the use of heterogeneous distributions resulted in an improvement in fit quality as compared to the fit quality for homogeneous distributions. The most dramatic improvement are observed in the fit to extreme data values.

Procedures were also developed to incorporate heterogeneous distribution functions into three common processes in Soil and Water Engineering, namely, Monte Carlo simulation, stochastic field generation, and interpolation. In these procedures, data which are best represented by heterogeneous distributions are transformed to Gaussian space and existing Gaussian-based procedures are applied. In several validation efforts the modified processes were found to as good as, or better than, conventional procedures.

In the process of developing the modified spatial processes mentioned above, a robust trend surface procedure and a new matrix decomposition procedure were developed. These ancillary procedures were shown to be useful in other engineering applications.