Showing RMSE and MAE results as percentage error I have the results of RMSE and MAE from different spatial interpolation methods as a monthly averages (See the figure below). As we know, the two metrics I used have units similar to my observed data units (mm rainfall per month in this case).
I want to compare the RMSE and MAE results with the monthly averages of the rainfall calculated from all available rainfall point stations used for the interpolation (the combination of test and validation sets).
Is it statistically logical to present the RMSE and MAE results as percentage error by calculating RMSE/MAE ratio to the monthly averages of the observed rainfall values (calculated from all available points) multiplied by 100?


There are relative metrics as discussed in How to interpret error measures? In the case of squared error you normalize by variance, while in the case of absolute error by mean absolute deviation. This makes the measures to be relative to the units of the predicted values. Another possibility is percentage errors like MAPE or RMSPE (see Hyndman and Koehler, 2005) but they are asymmetric which makes them tricky to interpret.
