  The use of weather index insurances is subject to spatial basis risk, which
arises from the fact that the location of the user's risk exposure is not the
same as the location of any of the weather stations where an index can be
measured. To gauge the effectiveness of weather index insurances, spatial
interpolation techniques such as kriging can be adopted to estimate the
relevant weather index from observations taken at nearby locations. In this
paper, we study the performance of various statistical methods, ranging from
simple nearest neighbor to more advanced trans-Gaussian kriging, in spatial
interpolations of daily precipitations with data obtained from the US National
Oceanic and Atmospheric Administration. We also investigate how spatial
interpolations should be implemented in practice when the insurance is linked
to popular weather indexes including annual consecutive dry days ($CDD$) and
maximum five-day precipitation in one month ($MFP$). It is found that although
spatially interpolating the raw weather variables on a daily basis is more
sophisticated and computationally demanding, it does not necessarily yield
superior results compared to direct interpolations of $CDD$/$MFP$ on a
yearly/monthly basis. This intriguing outcome can be explained by the
statistical properties of the weather indexes and the underlying weather
variables.
