Spatial analysis is the process of modeling and obtaining results through computer processing and then examining and interpreting the results of the model. Spatial analysis is useful for assessing suitability and capacity, for calculating and predicting, and for interpreting and understanding spatial phenomena (ESRI, 2016b).
A license from the Spatial Analyst extension is required to run the tools used in this section.
9.1. GIS Book: Interpolations
Tobler’s first geography law (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 as well”.
According to Gruver & Dutton (2014) interpolation is a process that uses measurements made on some phenomenon (precipitation, temperature, elevation) in certain places (samples or stations) to make a prediction for the same phenomenon in places where no measurements have been made.
There are many methods of interpolation, some of which have a greater presence in GIS because they are more adapted to the type of data handled. The usual application within a GIS is two-dimensional, since a raster layer is such an entity. We are therefore talking about spatial interpolation. However, these methods are not only restricted to a plane, but can be extended to a larger number of dimensions to reflect other variables such as depth (e. g., to construct a three-dimensional model of soil characteristics between two established depths and at a given interval), or time (Olaya, 2014).
The interpolation techniques mentioned by Childs (2004) are deterministic and geostatistical. The deterministic interpolation technique creates surfaces based on measured points or mathematical functions. Methods such as Inverse Distance Weighting (IDW) are based on the degree of similarity of cells, while methods such as Trend are adapted to a smooth surface determined by a mathematical function. The geostatistical interpolation technique, Kriging, is statistics based and is used for the most advanced prediction of surface modeling, which also includes some degree of prediction certainty or accuracy. There are different classifications of interpolation methods, some of which can be consulted in Olaya (2014).
Without going into more detail on the various methods of interpolation, all of these are available at the following address:
ArcToolbox > Spatial Analyst Tools > Interpolation
Table 3 contains precipitation data from weather stations located at different points. The central idea is to construct a raster surface with estimated precipitation values for places where there are no weather stations.
However, to interpolate the data it is necessary to have a shapefile or
vector layer of points. If the point layer does not exist, XY coordinates can
be imported and transformed into a shapefile. ArcGIS supports different table
formats such as Excel 97-2003 files, tab delimited text, DBF, and CSV.
Practice: Add XY coordinates and export them as shapefile.
In a new ArcMap window, from the menu bar go to File > Add Data > Add XY Data. In the pop-up window that appears, you should set up the fields as follows:
- Choose a table from the map or browse for another table: Select the table containing precipitation data. Information from Table 3 is stored as an XLS file (Excel Book 97-2003).
- X Field: Select the field containing the longitude values (UTM_X).
- Y Field: Select the field containing the latitude values (UTM_Y).
- Z Field: This is optional, but you can select the field containing the altitude values (UTM_Z).
- Coordinate System of Input Coordinates: With the Edit button, select the coordinate system, in this case Projected Coordinate Systems > UTM > WGS 1984 > Southern Hemisphere > WGS 1984 UTM Zone 17S.
This process generates an event layer; however, to store this layer on the hard disk in shapefile format, it is necessary to follow the following steps: Right click on the layer in the table of contents and go to Data > Export Data. A pop-up window opens where the address and name of the file to be saved must be selected. If you do not save the file in shapefile format, you must verify that the format type has been selected correctly (in Save as type). This step is necessary for the information to be stored in a shapefile.
Of the various interpolation options allowed by ArcGIS, the method used here to interpolate precipitation is Kriging, which is located at the following address:
ArcToolbox > Spatial Analyst Tools > Interpolation > Kriging
The speed of execution of the process depends on the number of points to be processed and the available system resources. The configuration pop-up window in all interpolation tools looks similar. An example of the parameters required by the tool, in this case Kriging (Figure 38), is described below:
- Input point features: Select the point layer containing the precipitation values (e. g. shapefile created from Table 3).
- Z value field: Select the field that stores the precipitation values.
- Output surface raster: Select a directory or geodatabase to store the output raster file.
- Semivariogram properties: Allows you to select the Kriging interpolation method with its respective semivariogram model.
- Output cell size: Sets the cell size (resolution of the resulting map).
- Search radius: Sets the radius of the entry points to interpolate each cell.
- Output variance of prediction raster: This is an optional raster containing the semivariance values.
Figure 39 shows the results of interpolation on a raster surface with estimated values. On the left, you can see the points where the weather stations are located (converted to shapefile format). On the right, you can see the map resulting from the interpolation as a raster image, including the estimated precipitation values for each cell. The same process can be repeated to obtain a temperature raster image using the values in Table 3.
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