The geostatistical methods of ordinary kriging, co-kriging, and Empirical Bayesian Kriging (EBK) is usually best to interpolate the rainfall point location averages and create rainfall surface maps. Software like In ArcGIS, there are several methods available for interpolation, spanning from deterministic (e.g. Inverse Distance Weighting---IDW) method and Stochastic (e.g. all sorts of kriging) methods.

Sometime splines also perform well, when your data are not densed. Also regression equations could be more relevant when you apply them in raster calculator .

Paper below on Kinging but for mapping groundwater quality it may help.

https://www.researchgate.net/publication/258225101_Geostatistical_analysis_using_GIS_for_mapping_groundwater_quality_case_study_in_the_recharge_area_of_Wadi_Usfan_western_Saudi_Arabia?ev=prf_pub

Dear Harjeet,

There is a variety of interpolation methods that are used throughout the literature, one should be cautious however, in order to find the one that is optimal for the variable in concern. The available methods are basically statistical models that apply different kinds of assumptions, some of which might me unsuitable for the variable you want to interpolate. In your case with precipitation being the variable of interest, I would suggest a multivariate geostatistical method that also incorporates information on factors that affect precipitation. Precipitation is highly spatially variables and a method that applies smoothing (such as splines) is perhaps not optimal. One example of mulivariate geostatistical kriging for rainfall is this [1]. A nice review paper on the available interpolation methods you can find here [2]. If you decide to go down the way of regression-kriging, here [3] you can find some very helpful resources for doing so in R.

[1] https://journals.ametsoc.org/doi/pdf/10.1175/1520-0450%282001%29040%3C1855%3AGMOPFR%3E2.0.CO%3B2

[2] https://journals.ametsoc.org/doi/pdf/10.1175/1520-0450%282001%29040%3C1855%3AGMOPFR%3E2.0.CO%3B2

[3] http://spatial-analyst.net/wiki/index.php?title=Regression-kriging_guide

I hope that helps,

Maria

Thanks for your valuable suggestion

Dear Harjeet,

You Can also used the Thiessen (Voronoi) polygons if you have more than one rain gauge station.

As mentioned, the Thiessen (Voronoi) polygons, as well as the geostatistical methods of ordinary kriging, co-kriging, and Empirical Bayesian Kriging (EBK) can be suitable methods.

But mentioning a point here is essential, the use of these methods depend on the availability of sufficient data, especially about hard topographic study area. The distribution of rainfall over hard surfaces, high altitude changes, can be estimated using the rainfall– altitude relation in Excel environment (using extrapolating from the different stations, a linear equation can be fitted to the available data). In this way, you have auxiliary data that has a rainfall amount for each altitude station. Use of DEM (Digital Elevation Model) can now help you get a good estimate of precipitation.