Hi,

I suggest to use a regression function. Use x, y coordinates AND height as depending variables and the rainfall as independent variable. Based on the regression function, you may calculate for each raster cell the interpolated rainfall value.

I've got some good results with this method, as it will really consider the height dependancy of the rainfall.

Have a nice day

Dietrich

Hi Dietrich,

thank you, seems a really good method. 

I have two more questions:

1) Which interpolation method is the best? QGIS allows:

0 — [0] Nearest Neighbor

1 — [1] Bilinear Interpolation

2 — [2] Inverse Distance Interpolation

3 — [3] Bicubic Spline Interpolation

4 — [4] B-Spline Interpolation

2) Do you have any reference for that?

Best

Giulio

There is no general answer to this question, this depends always on your data and the terrain characteristics.My sugessted solution is not using any of them, but using a different approach which really considers the height dependency explicitely modelled.

Anyway, if you want to use one of the above methods for your data, I would suggest Neraest Neighbor, as it will consider the high variability of your data best.

What about the regression function? It is maybe through that that I can making the relationship explicit.

QGIS Regression analysis allows to choose both the Interpolation method and the function which is considered for the regression.

I am currently working on Rainfall = Height * a + b (linear) with Nearest Neighbor interpolation

https://docs.qgis.org/2.6/en/docs/user_manual/processing_algs/saga/geostatistics/regressionanalysis.html

To be honest, I've mainly worked up to now with ArcGIS.

There I used a function like rainfall = a*Height + b * X + c * Y with X and Y the coordinates of the stations. There no interpolation is needed, because after calulated a,b,c I used the values to calculate the grid. Unfortunely, in the link you gave I don't see any explanation how the algorithm works in QGIS. But I suppose the steps are all included in the method offered in QGIS?!

Hi Giulio

As Dietrich said, there is no specific method for  interpolation. If I were you, I would divide my data to two parts, calibration and validation (training and test), then several methods will be applied for interpolation by using calibration data, in this stage you have some errors in estimation. the next step is comparing the calculated data with validation data, as well as previous step you have some errors in this stage so you could make a decision which model is the best.

If you want to use DEM, it is better to suppose mean elevation of the DEM as a base height and then interpolate data with X and Y by several method like what I said before. finally by using  RASTER CALCULATOR (in Arc GIS) correct the data with regards to  its elevation in each pixel by following procedure:

1- calculating Delta Z  (Elevation_in pixel i - Mean elevation)

2- Interpolated data* elevation coefficient  * Delta Z 

elevation coefficient : could be calculate by linear regression between two points with low and high elevation

Dear Giulio,

in addition to DEM data, you may also use rainfall patterns from satellite data as explanatory variable. However, you should always check for your specific study area, if there is a significant relationship with the co-variate.

I have tested some methods in a study area in India. In this case, regression kriging worked best. I am attaching the paper below for your information.

Kind regards,

Paul

Article Comparison and evaluation of spatial interpolation schemes f...

Use different co-kriging method where you can use elevation as an auxiliary variable. For example, you can use, collocated ordinary cokriging (OCK), kriging with external drift (KED), regression kriging (RK), Simple kriging with local means (SKlm), Universal ordinary cokriging (UCK) etc. These all are applicable in mountainous areas to interpolate rainfall by taking elevation as a secondary variable. These would give you better results than the univariate interpolation methods.