Beyond the semivariogram: Patterns, scale, and hydrology in a semi-arid landscape

As an alternative to geostatistical modeling, we characterized the hydrology of a semi-arid landscape in southeastern Washington state, USA, by coupling spatial patterns identified in the distributions of relative relief and vegetation with the influence each has on soil moisture storage and evapotranspiration at the appropriate scale. Gauging precipitation, soil moisture, and evapotranspiration over a two-year period while concurrently mapping relative relief and vegetation distributions at three scales ranging from centimeters to 90 m, we determined that soil moisture and soil moisture storage are significantly greater in topographic concavities than in convexities at the microrelief (20–50 cm) scale but are not significantly different in relief features at larger scales. A generalized microrelief surface produced using a two-dimensional Fourier transformation provided a good representation of the distribution of soil moisture within microrelief when scaled to soil moisture values. Applying a spatial point process analysis we determined that big sage are randomly distributed across the landscape at all scales, suggesting that lysimeter-derived sage evapotranspiration rates also be distributed randomly across the landscape. Where sage were not present, we applied an autoregressive moving-average model conditioned on grass lysimeter measurements to derive evapotranspiration rates. Combining these hydrologic spatial patterns derived from distributions in relief and vegetation with measured precipitation inputs and evapotranspiration outputs, we created a spatially distributed model of soil moisture which we tested against measured values over an eight-week period. The model provides accurate characterization of soil moisture, allows estimates of soil moisture between measurement points, permits extrapolation of soil moisture distributions outside the gauged area, and maintains small-scale variability when aggregating soil moisture to successively larger scales.