Firstly, it would be nice to share an image showing how the stations are distributed in the area. Are they clustered or not? The distribution of your point has a significant impact on the interpolation.

Secondly, the temperature is correlated with the vegetation, this, I would suggest to use a vegetation product (e.g., EVI) along the topography, because I believe it will further assist the downscaling.

Thirdly, you check both regions for downscaling. Is it possible to add the 8 stations with the other 87?

Nikolaos Tziokas

thanks you for your help, I am going to upload an image ,also the smaller region is specified, please let me know (the region is in Italian alps )

There is a point outside your study area (located in the northern part), you should consider either removing it or correct its location. I believe you will have a better luck using the 87 stations.

As for the Kriging with External Drift (KED), it suffers from expensive computational cost, as it computes Kriging weights locally. As you can understand, the bigger the study area, the higher the computational time required for the interpolation. Compared with KED, area-to-point regression Kriging (ATPRK) is more efficient and you can incorporate multiple covariates. This is something you need to consider.

Nikolaos Tziokas thanks professor for the answer , I would do the interpolation on 87 stations (all the area ) but I am not very familiar with all the kriging methods (I used the KED )because I already have the scripts in R and in case if I want to avoid considering elevation , what can be the option to interpolate ? (like IDW , ordinary kriging , ....)

I thought you were working in QGIS, as you said in your question

Yes I am working with Qgis +r

but thanks a lot for the help it’s really really useful ;I hope one of these methods can give me acceptable results

best regards

Nikolaos Tziokas sorry I have another question, a professor was saying that we can’t use kriging when we have few points , I wanted to know this statement is true ? or I can use regression kriging or KED for the area that I specified before by having 8 stations

Very few points for Kriging. You should research online which interpolation methods are suitable for small samples

Mahsa Kheradmand INRE:"can’t use kriging when we have few points". Think deeply about the old saying 'you need three points to get a curve, and two of those points are useless because they are on the boundary'. The second thing to consider is the basic idea of 'sample size / sampling rate and intervals, in this case the spatial coordinate field of the points. What is happening is a surface is being generated that passes through the control points, the fewer the control points, possible surfaces approach infinity. For simple cases, these might be 1st, second, or 3rd degree polynomials, Kriging just increases the degree to get a better 'fit', it may not have any relationship to the actual phenomena under investigation. Further, there is an implicit assumption that there is some sort of consistent continuous field between the points - weather station data within orographic regions have no such thing - on only needs to look at a mountainside to see the ecological transitions from the valleys to the ridge lines, specializations occurring because of fundamental PV=nRT affecting water vapor, ie. the 'surface' is not a single data type like 'temperature', it could be a derivative of multiple facors. See "Assessment of High Resolution Air Temperature Fields at Rocky Mountain National Park by Combining Scarce Point Measurements with Elevation and Remote Sensing Data" at Article Assessment of High Resolution Air Temperature Fields at Rock...