This project concerns an agricultural watershed in Central New York (Figure \ref{fig:FarmLocation}). Soil moisture measurements were taken in several fields owned and managed by a dairy farm. The fields are moderately sloping (% range TBD) with silty loam soils underlaid by a shallow restrictive layer, often called a frangipan (average depth TBD). The low permeability of this restrictive layer prevents water in the shallow subsurface from draining rapidly and sets up conditions for overland runoff by a saturation-excess process \cite{Walter2003,easton2008re}.
A total of 1,956 volumetric water content measurements at 81 locations were taken using a Time Domain Reflectrometry (TDR) probe across transects of agricultural fields. The sampling design was clustered in 9 fields. For this project, two individual fields were evaluated, as their clustering design more reliably showed spatial correlation. (Figure \ref{fig:FieldLoc}). At least three readings per location were taken. Their position was recorded using GPS units with horizontal accuracy to about 3 meters. Measurements were collected fall of 2012 and spring, summer, and fall of 2013. Measurements were made at least 24 hours after larger storm events (when precipitation exceeded 6 mm).
Terrain and soil characteristics were obtained from publicly available sources at United States Geological Survey (USGS) and United States Department of Agriculture Natural Resource Conservation Service (USDA-NRCS), respectively. 10-meter digital elevation maps (DEMs) from the National Elevation Dataset were processed to calculate local slope and area upslope contributing to shallow subsurface flow. Saturated hydraulic conductivity and soil depth to the restrictive layer were taken from the Soil Survey Geographic (SSURGO) database. The soil data was used to calculate the soil’s transmissivity properties.
The empirical variogram characterizes the spatial variability in the soil moisture data. A variogram for each sampling date (n=14) and each field cluster (n=9) were plotted and a spherical model fitted the variogram. The variograms by date are used in the kriging methods to define the measure of spatial correlation. Variogram parameters consist of a nugget (the variance of a repeated measurement in the same location), sill (the limit of the variance), and the range (the distance at which spatial correlation has a declining effect). Because of the clustered sampling procedure, the range of the variogram occurs much closer than the farthest distance between two points. Observations outside of the cluster are deemed to have very little effect on the local conditions.
Soil moisture was correlated to the original topographic index (TI) proposed by \cite{Beven_1979} and a regional variation of the soil topographic index (STI). This regional model removes the exponential decline with depth of saturated hydraulic conductivity. In the Northeast United States, the restrictive layer is shallow and saturated hydraulic conductivity can be assumed to be vertically uniform from the surface to this shallow layer. TI is described as a function of the upslope contributed area (\(\alpha\)) and slope (\(\beta\), m m-1):
\[TI = \ln \frac{\alpha}{\tan \beta}\]
The regional STI described by \citet{walter2002refined} and \citet{lyon2004using} includes the soil transmissivity properties (T, m2d-1) calculated from the product of saturated hydraulic conductivity and depth to the restrictive layer:
\[STI = \ln \frac{\alpha}{T \cdot \tan \beta}\]
By correlating soil moisture to these two simple models, we can use auxiliary information to make predictions about soil moisture conditions where we do not have observations.
Two kriging methods were used to predict soil moisture in unsampled locations. Ordinary kriging was completed with the soil moisture observations. With ordinary kriging we assume weak stationarity in the soil moisture observations. In other words, the mean and variance of the observations is relatively unchanged in the sampling cluster. In cokriging, additional information about the spatial autocorrelation can be introduced in addition to the sparse data. A cokriging approach was used with soil moisture observations as the primary variable and the TI or STI value as the secondary variable. The much more complete spatial grid of TI and STI allows for prediction of a larger spatial area.