2.2. Interpolating point data

Next, we will be interpolating our data. There are many different algorithms for doing this, from simple algorithms that take the value of the closest point (Nearest Neighbour), to complex spline or Kriging <https://en.wikipedia.org/wiki/Kriging> interpolation techniques. We will be exploring the nearest neighbour, Inverse Distance Weighting and several splines in this chapter. Finally, we will obtain our rainfall value from the Thin Plate Spline algorithm. It is recommended to first read /docs/gentle_gis_introduction/spatial_analysis_interpolation.

2.2.1. Nearest Neighbour

1. Find and open the Grid (Nearest Neighbour) algorithm.

2. Set Point Layer to Reprojected [EPSG:32637]

3. Set Advanced Parameters ► Z value from field [optional] to PRCP.

4. Run the algorithm. The output map should look like this:

   

   Fig. 2.1 Nearest neighbour interpolated precipitation

   Challenge

   It seems to be possible to Set cellsize and extent in a similar way, so that your grid is automatically clipped to Hadocha_dem.

2.2.2. Inverse Distance Weighting

Inverse distance weighting is an interpolation method in which the influence of a datapoint on the value of the interpolated raster decreases with distance.

1. Find and open the IDW interpolation tool

2. Set Vector layer to Reprojected

3. As Interpolation attribute select PRCP

4. Press the button to add the layer to the selection.

5. For Extent, select … ► Calculate from layer ► Reprojected.

6. As Pixel size X and Pixel size Y enter 1970. The Rows and Columns fields should adjust.

7. Run the algorithm. Your map should look like this:

   

   Fig. 2.2 IDW interpolated precipitation.

8. try to get similar results with algorithms from GDAL and GRASS

2.2.3. Spline interpolation

A spline is a piecewise defined polynomial. There are many different ways to generate a spline from a set of datapoints. We will be using a thin plate spline which creates a minimum curvature surface through all datapoints.

1. find and open the Thin plate spline tool You may encounter the following warning that you can safely ignore:

   Warning

   SAGA version <version> is not officially supported - algorithms may encounter issues

2. For Points select Reprojected [EPSG:32637].

3. Set Attribute to PRCP

4. Set search range to [1] global

5. Set Number of Points to [1] All points within search distance

6. Set Search direction to [0] all directions

7. for Cellsize enter 1970

8. And finally, set Fit to [1] cells

9. Run the algorithm. Your output should look like this:

   

   Fig. 2.3 Thin plate spline interpolation

   notice that the raster value extremes exceed the values of the datapoints. This is a characteristic of (thin plate) spline interpolation.

2.2.4. Final interpolation

Now we have looked at different algorithms and compared their characteristics, it is time to select one and obtain a precipitation raster. Normally, to choose an interpolation method, you would randomly sample points, perform an interpolation on them and compare the error between interpolated and data values. Due to the amount of datapoints, this is not possible, and we choose thin plate spline by means of expert opinion.

1. Open the Zonal statistics tool.

2. For Input layer select … ► Browse for Layer and select Hadocha_mask:

   

   Note

   Note that the filepath becomes: path/00_raw_input.gpkg|layername=Hadocha_mask The last part after | tells the algorithm which layer to select from the GeoPackage. This may be useful if you want to manually enter a path to a GeoPackage layer!

3. As Raster layer select Target Grid [EPSG:32637]

4. We only want the Mean to be calculated. Run the algorithm. This creates a vector layer with the average precipitation value for our catchment.

5. Open the attribute table and copy the precipitation value to your clipboard

6. If not loaded yet, load the DEM into the map

7. Run the Raster calculator tool with:

   • Expression: <your precipitation value>,

   • Reference layer(s) used for automated extent, cellsize and CRS:

     <DEM file>

8. To save the raster layer in our 01_input.gpkg database, right-click Export ► Save as… with:

   • Format: GeoPackage

   • File name <path_to>/01_input.gpkg

   • Layer name P

   • the rest default

Solution

The rainfall value is 1744