Probabilistic forecasting for spatio-temporal raster data

We have a time series gridded/ratser panel dataset (spatio-temporal). The dataset is in 3D, where each ((x, y, t), where x and y ranges from 1-25 while t ranges from 1-1800 though we’re trying to predict just the next time step) coordinate has a numeric value (such as the sea temperature at that location and at that specific point in time). So we can think of it as a matrix with a temporal component. The dataset is similar to this but with just one channel:


We’re trying to predict/forecast the nth time step values for the whole region (i.e., all x, y coordinates in the dataset) given the values for the n-1 time steps and the uncertainty.

Can you all suggest any model/architecture/approach for the same? Is it possible to tackle this with multiple kernels with separate kernels for the spatial covariance and separate for the temporal covariance?


It really depends on the spatial-temporal resolution. You mentioned that you have temperature as the target variable, it is usually very smooth and seasonal. I had success with StateSpaceModels.jl, it is very robust and explainable, which is usually something you would like to have in climate/weather studies.

You might be interesting in trying TemporalGPs.jl, it is specifically designed to work on this kind of problem.