1.Soil moisture patterns are important to predicting water quality of the runoff generated. Much attention in hydrology is paid to soil moisture as a risk indicator of surface runoff generation e.g. \cite{pearce1986storm, bronstert1997modelling, meyles2003runoff}. Surface runoff quickly transports water to streams causing pulses of high flow that increase flooding potential, impact wildlife habitat, and transport sediment and dissolved contaminants from the land surface. The ability to predict where and when runoff is likely to be generated guides the planning and implementation of management practices that reduce these negative impacts.
Traditionally, the temporal and spatial variability of soil moisture patterns is identified through two approaches. Complex, distributed hydrologic models such as the Soil Moisture Routing model \cite{frankenberger1999gis} predict patterns fairly well, but require climate and landscape data at fine resolutions to be reliable. In contrast, indices that draw on watershed-level hydrologic drivers such as terrain and soil properties can provide fast, simple estimates of soil moisture patterns. These topographic indices, originally developed by \cite{Beven_1979}, can be used to quickly estimate patterns in regions where soil moisture spatial variability is driven by topographic changes and shallow soil depths. In the Northeastern United States, topographic indices have been shown to work well to predict soil moisture patterns \cite{Buchanan2013}.
Soil moisture measurements can be collected rapidly and easily in the field, however due to signfiicant spatial and temporal variability, achieving a coverage for watersheds is a time-intensive endevor. Remote sensing techniques are in development, but the resolution of their predicitions is too coarse for meaningful guidance in management practices \cite{wagner2007operational}. In this project we are interested in using geostatistics and the topographic index models to extroplate soil moisture measurements for comparison with patterns predicted by a more complicated, uncalibrated hydrologic model. To do this, we use a geostatistical tool for characterizing spatial patterns, the semivariogram model. Semivariograms quantify the change in variance between two points in a field based on their distance. The sill represents the distance at very large distances (large being relative to the data). The distance at which the sill is stable is considered the range. At this distance, spatial correlation no longer exists. The variance in repeated measurements at the same location is given as the nugget of the semivariogram.
Kriging is a geostatistical technique that makes use of the semivariogram for interpolating data where it does not exist. Kriging with additional information, such as the output of the topographic index models, can be used to influence the spatial pattern. This is particularly useful where linear distance is not the only important correlation for a spatial pattern. In the case of soil moisture, a location in a stream may be continually saturated to a similar degree as a location far downstream that is also along a high accumalting flowpath. A location much closer in spatial distance to the saturated area may be significantly drier, perhaps because of a steep slope that transmits water away quickly. For this reason, straight kriging with the soil moisture data will present limited spatial results. In some variograms the range will occur at very close distances or spatial correlation will not be apparent. In this project we investigate the locations and dates where good spatial correlation is evident and use topographic index information to improve kriging predictions.