Spatial interpolation techniques play an important role in hydrology as many point observations need to be interpolated to create continuous surfaces. Despite the availability of several tools and methods for interpolating data, <a>not all of them work consistently for hydrologic applications</a><a>. One of the techniques, Laplace Equation, which is used in hydrology for creating flownets, has rarely been used for interpolating hydrology data</a>. The objective of this study is to examine the efficiency of Laplace formulation (LF) in interpolating hydrologic data and compare it wih other widely used methods such as the inverse distance weighting (IDW), natural neighbor, and kriging. Comparison is performed quantitatively for using root mean square error (RMSE), visually for creating reasonable surfaces and computationally for ease of operation and speed. Data related to surface elevation, river bathymetry, precipitation, temperature, and soil moisture data are used for different areas in the United States. RMSE results show that LF performs better than IDW and is comparable to other methods for accuracy. LF is easy to use as it requires fewer input parameters compared to IDW and Kriging. Computationally, LF is comparable to other methods in terms of speed when the datasets are not large. Overall, LF offers an robust alternative to existing methods for interpolating various hydrology data. Further work is required to improve its computational efficiency with large data size and find out the effects of different cell size.

Ground subsidence due to underground coal mining is a complex, narrowly-understood phenomenon. Due to the complicated physical processes involved and the lack of a complete knowledge of the characteristics of overlying strata, the reliability of current prediction techniques varies widely. Furthermore, the accuracy of any given prediction technique is largely dependent upon the accuracy of field measurements and surveys which provide input data for the technique. A valuable resource available for predicting and modeling subsidence is aerial survey technology. This technology produces yearly datasets with a high density of survey points. The following study introduces a method wherein these survey points are converted into elevation plots and subsidence plots using GIS. This study also presents a method, titled the Type-Xi Integration method (TXI method), which improves upon a previous subsidence prediction technique. This method differs from the previous technique in that it incorporates accurate surface topography and considers irregular mine geometry, as well as seam thickness and overburden variations in its predictions. The TXI method also involves comparing predicted subsidence directly to measured subsidence from subsidence plots. In summary, this study illustrates a method of combining data from aerial survey points and mine geometry with subsidence models in order to improve the accuracy of the models.

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