I have climate datasets consisting of tables where each row has four elements: latitude, longitude, rainfall, and timestamp. This dataset covers the entirety of the planet. However this dataset is incomplete in the following way: no data exists for the majority of the earth's surface at any timestamp (i.e. timestamps covering say UTC 12:00:00-13:00:00 have rows in the table for only longitudes and latitudes corresponding to a large part of Western Europe and North America, and some sparse data for South America and East Asia).
I want to reconstruct the rainfall data for the entire world in such a way that I should be able to cut out any part of the Earth's surface and fill in the missing values in a meaningful way. For example, suppose I have 3 hours of data for Austria. I don't have enough values to cover the entirety of Austria, but would like to fill in the neighboring values based on the already-present data. I know I can do this by using algorithms such as Natural Neighbors interpolation or cubic spline interpolation, but I'm not sure whether doing this will result in any meaningful or physically relevant results. Unfortunately, I am not able to check this against any physical data; otherwise I would've used any prebuilt interpolator that worked the best and moved ahead with it.
Do any prebuilt neural networks/algorithms exist that preserve spatial and temporal variation while interpolating sparse data? Any help would be appreciated.
