If I understand correctly, Universal Kriging will first compute the residuals between the drift and the variable to be predicted. Then the variogram has to be computed using these residuals, and kriging is performed on these residuals, using the variogram. The kriged values are then added back to the drift.
Now, I am wondering how to know when to remove the trend in the drift and/or the target variable.

Regarding the image above (values for x-axis are not illustrated, to keep the graph simple), would it be necessary to remove one or two trends?
For example, when we would remove the trend from the target variable, we could get something like the following:

My data contains the following trends:

Does someone has any steps on how to approach this problem? And how I can ensure that the necessary assumptions for UK are met?