Inverse distance weighting (IDW)would not be an appropriate interpolation technique because the distribution of rain stations that actually collected both normal and total rain fall was not dense enough to capture an accurate extent of precipitation across Los Angeles county. IDW becomes less accurate as the distance to data points increases so the precipitation map would be accurate at rain station locations and inaccurate for areas in between stations.
Kriging would be a more suitable interpolation technique because it takes into account the fact that precipitation may be spatially correlated. So this method of interpolation should provide a better estimate of the level of precipation across Los Angeles county.
Below is a map of precipitation in Los Angeles County based on IDW and kriging.

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