Numerical methods in soil hydrology: TDR waveform analysis and water vapor diode simulation

Soil water content impacts all soil physical, chemical and biological properties. Soil water movement in shallow soil layers has critical importance for plant water use, foundation stability, energy transfer and chemical diffusion. Numerical analysis is one way to study soil water. New numerical methods are presented in this thesis to determine soil water content from time domain reflectometry (TDR) measurements and simulate soil water accumulation in selected soil layers. TDR enables nondestructive and continuous soil water content measurements. Traditional TDR waveguides have relatively long probes (\u3e150 mm), but new TDR waveguides tend to use short probes (\u3c40 mm) to enable the measurements of water content near the soil surface. However, analyzing TDR waveforms obtained with short TDR probes can be challenging for traditional numerical analysis methods. A new numerical method is needed for analyzing the short-probe TDR waveforms. Coupled heat and water movement can be used to describe the liquid water and water vapor fluxes under combined soil matric potential gradients and thermal gradients. Water vapor flux is the dominant means of soil water movements in relatively dry soil layers. If the naturally occurring water vapor fluxes can be controlled, it is possible to impact the water content distribution in soil profiles. A water vapor diode (WVD), acting as a check valve, allows water vapor flux to occur only in one direction but heat flux occurs in both directions. By installing a subsurface WVD, it is possible to impose direction-controlled vapor fluxes, and WVDs can be used to accumulate or remove water in particular soil layers. However, necessary properties of the WVDs should be clearly defined, and the performance of the WVD should be investigated. Thus, the objectives of this thesis are to (1) develop a new tangent line/second order bounded mean oscillation (TL-BMO) model for analyzing short-probe TDR waveforms to determine the soil water content, and compare TL-BMO with tradition models, such as tangent line (TL) and adaptive waveform interpretation with Gaussian filter (AWIGF); (2) introduce the concept of a WVD and use numerical simulations to analyze the influence of WVDs on soil water redistribution. The TL-BMO is evaluated with TDR waveforms obtained by short-probe sensors in Nicollet, Ida and Hanlon soil samples for a range of water contents to test its accuracy and stability. The root mean squared error of the TDR estimated water content and the gravimetric water content is \u3c2%. In order to compare TL-BMO with the traditional models, waveforms obtained with long- and short-probe TDR sensors in CaCl2 solutions for a range of electrical conductivities are used. The results indicate that the TL-BMO model is consistent with the traditional TDR waveform models for some of the waveforms, but the TL-BMO performs better than the traditional models on some challenging waveforms. Thus, TL-BMO can effectively analyze the waveforms from both long- and short-probe TDR sensors. Inspired by the methods used with TL-BMO, the AWIGF model was also revised with a newly designed corner-preserving filter. The performance of the revised AWIGF model on short-probe TDR waveforms was similar to that of the TL-BMO model. One dimensional numerical simulations of soil water redistribution with WVDs are conducted to illustrate the concept and properties of WVDs. Four WVD configurations are discussed to control soil water redistribution. Simulation results indicate that WVDs can increase the local water contents by at least 0.1 m3 m-3 in a silt loam, but the effects of WVDs varied with deployment depth and separation distance between two adjacent WVDs. Two dimensional numerical simulations are performed to evaluate the effects of two possible designs of the WVDs, i.e., an egg-carton design and a Tyvek design. The soil water content can be altered by 0.02 m3 m-3 with the WVDs in the numerical examples, and the unsaturated subsurface drainage can be increased due to the soil water accumulation induced by the WVDs. In conclusion, the TL-BMO model can provide stable and accurate analysis of short-probe TDR waveforms, and the TL-BMO model is flexible enough to be used on for both long- and short-probe TDR sensors. The WVD can effectively manipulate soil water redistribution of soil profile water due to the naturally occurring thermal gradients. WVDs can be deployed to cause water accumulation in specific soil layers, and to assist in unsaturated subsurface drainage of soil profile water