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Thiessen Polygon Weighting <br />A Thiessen polygon weighting procedure can be used to assign weights associated with defined <br />point climate station locations. This procedure is straightforward in the standard GIS software <br />packages used in the SPDSS. The method works well for regions larger than the individual <br />Thiessen polygons. However, discontinuities can arise from this method when areas are <br />relatively small and near the boundaries of the computed polygons. The climate station weights <br />could differ enough to result in abrupt changes in the climate station data used to estimate <br />consumptive use (or evaporation, recharge, etc.) across a short distance. <br />Linear Interpolation of Climate Station Weights <br />An alternate method is to use varying weights based on the distance from each station, ranging <br />from 1.0 at the station itself to 0.0 at each adjacent station. A Triangular Irregular Network <br />(TIN) is created by joining the location of each climate station into a series of triangles that cover <br />the entire region of interest. The triangular network defined around each climate station can be <br />adjusted, if necessary, to reflect engineering judgment (elevation consideration, topographic <br />influences, extrapolation, etc.) At the selected climate station, each triangle vertex is assigned a <br />value of one while all other vertices are assigned a value of zero. <br />A grid is then created for each climate station as a linear interpolation of each triangle in the <br />TIN. This automated process is then repeated for each climate station. The final product is a <br />spline interpolation with linear basis functions. This assures that the sum of the weights at any <br />point equal one and that at a particular climate station, the weight for that climate station is equal <br />to one. It also assures that all weights are greater than zero, which is not always guaranteed in <br />the kriging method described below. By using ArcView's spatial analyst extension, the weights <br />are stored as separate grids and can be combined easily for a point location or summarized for <br />any polygon area. Note that weights can be automatically extended between the edge of the <br />study area and climate stations within the study area based on user-input criteria or climate <br />stations outside the study area (for instance climate stations in the Republican Basin). <br />Once the grids are created for each climate station, they can be used for weighting any region in <br />the study area from large areas such as water districts to small areas including ditch structures or <br />individual farm parcels. <br />Kriging <br />Kriging is another method for spatially interpolating point values to a continuous surface and is <br />available in the ArcView GIS program. A major disadvantage of the kriging method in existing <br />GIS software is that it is necessary to define the point or area at which the weights are being <br />determined before developing the weights as opposed to the Thiessen polygon or linear <br />interpolation method which defines a grid around each climate station. Another disadvantage is <br />that the kriging method does not ensure that all weights are greater than zero. <br />Results - GW Model and CU Model <br />After reviewing the Thiessen polygon weighting, linear interpolation, and kriging methods, it <br />was determined that the linear interpolation method was most appropriate for the SPDSS ground <br />water and consumptive use models. This method is data centered, compatible with the existing <br />Page 3 of 11 <br />