# Introduction

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. (Pearce 1986, Bronstert 1997, Meyles 2003). 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 (Frankenberger 1999) 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 (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 (Buchanan 2013).

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 (Wagner 2007). 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.

# Methods

## Study area

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 (Walter 2003, Easton 2008).

## Field data

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).

## Source data

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.

## Variograms

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.

## TI & STI Calculation

Soil moisture was correlated to the original topographic index (TI) proposed by (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 Walter et al. (2002) and Lyon et al. (2004) 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.

## Kriging Method

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.