In an area of 125 square kilometers with about 2000 sampling points distributed at a density between 10 to 500 meters, if high resolution is not a primary concern, you can generalize or simplify information to facilitate administration of this process what you can be done using a set of tools ArcGIS (similar in QGIS or gvSIG process), such as interpolation, creating a homogeneous mesh points and extract the values of a raster from a point layer.
This example is intended to generalize the points at a density of 1000 x 1000 meters, the first step is to interpolate the data with the aim of creating a raster image information to simplify the method of inverse distance interpolation IDW, conforms to variable (monthly precipitation) in the exercise, also be used Kriging, Spline, Natural Neighbor, among others.
ArcToolbox > Spatial Analyst Tools > Interpolation
ArcToolbox > Data Management Tools > Feature Class
Report an output directory in a geodatabase in Template Extent select the point layer (or interpolated raster) to get the same extension, cell size drop spacing in meters in width and high, check the Create Label Point box, leaving the remaining fields by default.
The last process is to extract the values of the interpolated raster IDW and transfer the values to the point layer obtained with the Create Fishnet tool, to do this use the Extract Values to Points tool (activate the Interpolate values at the point locations box) located at:
ArcToolbox > Spatial Analyst Tools > Extraction
The layer contains general points estimated based on the interpolated data from the initial information values. Another option would create a Spatial Join between the mesh points (created with fishnet) and the centroids of the initial layer of points.
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