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 (>150 mm), but new TDR waveguides tend to use short probes (<40 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