I have a basic question regarding Geo data: is the normal assumption mandatory?
Given a dataset I identified outliers and inliers (using Moran local and plot test) so I excluded them from the original data. I checked normality in this new dataset, however it does not fit a normal distribution.
What is the effect of this non-normality in the variogram and krigging?
Normality of what? Your measurement values? As long as they aren't small counts or 0/1 or strictly positive then how "Normal" they look is not relevant. "Normality" is the distribution of the response given the explanatory variables (in a linear model).
Consider a linear model where the X values are integers 1 to 1000 and the Y values are twice that - 2 to 2000 in steps of 2, with a tiny bit of noise. X and Y will both look identical to Uniform distributions. That's okay. What is assumed to be normally distributed in a linear model is the noise.
In spatial sampling data, a skew distribution for a response or explanatory variable means maybe you took a lot of samples in places where the value was high. This doesn't affect the validity of the formulation of the model, but it might affect the uncertainty estimates in low value regions where you've not done as much sampling. The inference from the model predictions are still valid.
The normality assumptions are broken if response data could not reasonably have come from a Normal distribution because its not continuous or have possible range -Inf to +Inf - for example if it is discrete small counts, in which case you may need a Poisson model, or if its presence/absence (Binomial model) or continuous but strictly positive (Gamma model).
Note that some of these can be usefully approximated by a Normal model which simplifies things immensely. You might have discrete counts as your data, but large enough that a normal approximation is good enough (the shape of a Poisson distribution with large rate looks very like a Normal distribution because it doesn't "clip" at zero).
