Tobler’s first law of geography (1970) states, “Everything is related to everything else, but near things are more related than distant things.” For example, if it rains on one side of a street, it is highly likely to rain on the other side of the street, but less likely to rain on a street on the other side of the city.
Gruver and Dutton (2014) define interpolation as using specific location measurements to predict phenomena where no measurements exist. This is useful for understanding and predicting spatial patterns in variables like precipitation, temperature, or elevation. Various interpolation methods exist, with the choice depending on the data or variable type.
The most common GIS application is two-dimensional (2D) spatial interpolation, appropriate for raster layers. However, interpolation can also extend to more dimensions, incorporating variables like depth or time.
Interpolation techniques are categorized into deterministic and geostatistical (Childs, 2004). Deterministic interpolation, like Inverse Weighted Distance (IDW), relies on similarity measures, while methods like “Trend” use mathematical functions for surface creation. Geostatistical interpolation, such as Kriging, employs statistics for advanced surface modeling and prediction accuracy. Various geostatistical methods are detailed in Olaya (2020).
Interpolation methods in ArcGIS Pro are accessible via:
Geoprocessing > Toolboxes > Spatial Analyst Tools > Interpolation
Geoprocessing > Toolboxes > Geostatistical Analyst Tools > Interpolation
As an example, precipitation data recorded at weather stations will be used to create a raster surface with estimated values for areas lacking direct measurements.
Monthly precipitation and temperature data from a network of weather stations.
To interpolate data, a point vector layer or shapefile is needed. If it does not exist, XY coordinates can be imported and converted into a shapefile. ArcGIS Pro supports Excel files, tab-delimited text (.txt), DBF, CSV, and more.
Importing a Table of XY Coordinates (Taken with a GPS)
Working with Excel files typically requires Microsoft .NET Desktop Runtime 6.0.5 – Windows x64. The appropriate driver should be selected based on the ArcGIS Pro version. After installation, it is advisable to restart the computer.
To import the table and create an events layer, go to Map > Add Data > XY Point Data and configure the fields:
- Input Table: Select the data table in xlsx, xls, csv, or txt format.
- X Field: Select the field with UTM_X values.
- Y Field: Select the field with UTM_Y values.
- Z Field (optional): Use for UTM_Z values.
- Coordinate System: Projected Coordinate Systems > UTM > WGS 1984 > Southern Hemisphere > WGS 1984 UTM Zone 17S.
Importing a table with UTM coordinates in ArcGIS Pro.
Once completed, an events layer will be generated. To store this layer as a shapefile, right-click on the layer in the Contents panel and select Data > Export Features. Choose a folder (not a geodatabase) as the destination to ensure the file is saved as a shapefile.
Interpolating Data with Kriging
Among the interpolation options available in ArcGIS Pro, the “Kriging” method is suitable for interpolating both precipitation and temperature data.
Path to access the tool:
Geoprocessing > Toolboxes > Spatial Analyst Tools > Interpolation > Kriging
Tool configuration includes:
- Input point features: Select the shapefile with weather data.
- Z value field: Select the field with precipitation or temperature values. If it is not selectable, ensure the decimal separator is correctly set in the system settings.
- Output surface raster: Choose a directory or geodatabase. Avoid spaces in file paths.
- Semivariogram properties: Choose the desired Kriging method and semivariogram.
- Output cell size: Set the desired resolution.
- Search radius: Define the number of points used for interpolation.
- Output variance of prediction raster: Optional raster showing variance values.
Configuration of the Kriging tool parameters.
The resulting raster surface will display estimated precipitation or temperature values across the area of interest. The same process can be repeated for other variables such as temperature using the corresponding data fields.
Precipitation Interpolation. Weather station points (left) and interpolated prediction surface (right).
