Of course, multiple regression can be used to estimate monthly groundwater parameters. Your first step will be to decide on the variables that influence the parameter you wish to estimate. The second step will be to determine the level of influence of each variable on the parameter. One possible method for this may be Principal Component Analysis. This can be followed by thinking about which variables to be included in the regression analysis.
Such statistical analysis can be carried out using software such as SAS, Matlab, SPSS, MAPLE, etc. provided one is reasonably good at using the concerned software.
If this is about time series and 'future prediction', then it is domain of time series analysis. There are well established models, like ARIMA or ETS, that are used for that purpose. I think that a study of results of the query 'time series analysis' would give a quick answer, whether this is a proper tool set for the problem at hand. Maybe this textbook https://otexts.com/fpp2/dynamic.html can be of help.
Estimating time series models is, of course, kind of regression. But time series have an important property of directionality; i.e., we can safely assume that past values affect future, but not the other way around. Because of that and their overall importance, their theory is 'a separate field'.