Spatial analysis of soil moisture at the catchment scale with applications for estimation and interpolation - Perry, Mark A., author; Niemann, Jeffrey D., advisor; Green, Timothy R., committee member; Smith, Freeman M., committee member (Colorado State University. Libraries, 2006)
The spatial distribution of soil moisture is important to numerous applications in hydrology, agriculture, ecology and climatology. Soil moisture is a state variable for many physical processes in these fields such as infiltration and transpiration. Because these processes often have non-linear relationships with soil moisture, they depend on the spatial variation of soil moisture. The spatial variation of soil moisture can be complex because it can change through time. The goal of this thesis is to characterize the time varying properties of soil moisture patterns, from which to develop improved soil moisture estimation and interpolation methods. Here, soil moisture patterns are studied using Empirical Orthogonal Function (EOF) analysis. EOF analysis decomposes space-time variability into a series of time-invariant spatial patterns (EOFs) and spatially-invariant time series called expansion coefficients (ECs). This method is applied to soi l moisture data from the 10.5 ha Tarrawarra catchment in Australia. High-resolution soil moisture patterns are available for 13 days, spanning 14 months. The analysis shows that three EOFs explain 70% of the dataset variation. Connections are drawn between these EOFs and hydrologic processes that affect soil moisture. In particular, the most important EOF (EOF1) is most highly correlated with the topographic wetness index, which is conceptually related to steady lateral flow. The second most important EOF (EOF2) is most highly correlated with the potential solar radiation index, which is related to evapotranspiration. The third most important (EOF3) is most highly correlated to elevation and is related to the seasonal wetting-up and drying-down of the catchment. The EOFs and ECs are used for the purposes of estimation and interpolation. In the estimation problem, an estimate of the soil moisture pattern is desired for a time when only the spatial average soil moisture is known. It is assumed that the site's EOFs can be derived from fine resolution soil moisture data collected in a previous, short field campaign. The EC values are estimated from empirical relationships with the average soil moisture. Here, only ECs 1 and 2 are considered to be predictable through time, but this may be due to the limited temporal size of the dataset. An estimated soil moisture pattern is constructed form the average soil moisture, the observed EOFs 1 and 2, and the estimated ECs 1 and 2. This EOF-based estimation method is shown to outperform other available methods. Likewise in the interpolation problem, soi l moisture patterns are observed only at a coarse scale and a high resolution pattern is desired. In this case, the ECs from the coarse data are used directly, and the EOFs from the coarse data are interpolated to a higher resolution using either a distance-based method or multiple linear regression with topographic attributes. For spatial interpolation the number of useful EOFs is shown to vary with the coarse data spacing, but up to 4 EOFs are useful here. The EOF-based soil moisture interpolation provides better estimates of the fine-scale soil moisture patterns than direct soil moisture interpolation because the EOFs exhibit more consistent spatial behavior than measured soil moisture. This study shows that EOFs exhibit stronger topographic dependence than soil moisture, because important variation at Tarrawarra is related to topography and is partitioned into low order EOFs. Less important sources of variation and random noise are partitioned into high order EOFs. Low order EOFs are shown to exhibit distinct and higher linear correlations with common topographic attributes than soil moisture itself. Likewise in a geostatistical analysis, low order EOFs are shown to exhibit distinct and more consistent va1iogram functions than soil moisture. Previous studies have noted the difficulty of quantifying the time-varying relationship between dynamic soil moisture patterns and static topography. This study shows that time-invariant EOF patterns exhibit time-stable relationships to topography. The time-varying nature of the soil moisture-topography relationship can be quantified by the associated ECs. Finally, this thesis presents opportunities for future research. The Tarrawarra catchment has a strong seasonal climate, as well as spatially uniform soils and vegetation. Future studies should apply similar EOF analysis to sites without seasonal variation, with non-uniform vegetation and with non-uniform soils. In addition, analysis of the temporal behavior of ECs was limited here due to the dataset' s small temporal dimension. Unfortunately, there is a scarcity of soil moisture datasets with large space and time dimensions. One possible solution is computer simulation of soil moisture data. Simulation of large amounts of soil moisture data could allow better characterization of ECs. Based on results here, it is anticipated that ECs will exhibit more certain temporal behavior than soil moisture. This should allow better soil moisture forecasting when time-series modeling is done on ECs instead of on soil moisture itself.
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Keywords: Soil moisture; Watersheds