Investigating Soil Moisture Spatial Scaling using Reduced Order Models and Analysis of Fractal Temporal Evolution Patterns

Wednesday, May 14, 2014 - 07:00
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It is well known that hydrologic models suffer from uncertainties rooted in their scale dependence. Soil moisture is the key variable that controls evapotranspiration (ET), infiltration, runoff, and recharge, and is known to exhibit statistical scale-invariance, or fractal relationships. To better understand spatial scaling patterns and possibly construct coarse models that resolve subgrid variability, we investigated fields from hyper-resolution simulations using a physically-based hydrologic-land surface model (PAWS+CLM). We employed two approaches: (a) Reduced Order Models (ROM) using relationships synthesized from fine-resolution simulations and (b) analysis of the temporal evolution pattern of the soil moisture statistical multi-fractal (SMSMF) in response to climate forcings. With approach (a), we developed simple, relatively accurate (R2 ~ 0.7 ~ 0.8) ROMs for the relationship between mean and higher-order moments during the non-frozen periods over five years. We tested sixteen system attributes hypothesized to explain the negative relationship between  mean and variance toward the wetter end of the distribution, and found that, in the model, 59% of the variance of this relationship can be explained by the elevation gradient convolved with the mean evapotranspiration flux. With approach (b), the SMSMF scaling exponents display complex hysteresis and are not simple functions of mean moisture. During non-frozen days in both basins, SMSMF is found to relate positively to basin water storage, producing a dominant seasonal mode and a more organized pattern in wetter seasons. Small-to-medium storm events induce hysteretic excursion loops which can be divided into three phases: (a) wetting, (b) re-organization-dominated, and (c) dry-down-dominated. Our initial results suggests that Approach (a) appears quite simple and practical. Approach (b) might be somewhat challenging due to the very complex nature of the fractal evolution. However, both approaches warrant further investigation.

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