Correlation, regression and cross-correlation modelling of time series in hydrogeology

Correlation, regression and cross-correlation are one of the most commonly applied methods in modelling of time series in hydrogeology. Ground water levels in aquifer systems interact with inflows/outflows of the system i.e. ground water level oscillations strongly depend on boundary conditions of the aquifer system. Interaction of aquifer boundary conditions and ground water levels can be strong or weak, which points to importance i.e. the dominancy of a certain boundary condition and its impact on ground water level rise or fall. The strength of the relationship between boundary conditions and ground water levels can be determined using correlation analysis. Interaction between boundary conditions and ground water levels can also have functional dependence, which in turn enables prediction of ground water levels in aquifer, based solely on measurements of a certain boundary conditions. Functional relationship between boundary conditions and ground water levels can be determined using regression analysis. Likewise, interaction between boundary conditions and ground water levels can either be fast or slow, which in turn points to an impact of a certain boundary condition on ground water dynamics. In such an analysis, ground water pressure propagation can be determined using cross-correlation analysis. Aquifer boundary conditions like recharge from precipitation, recharge/drainage from rivers, lake or creeks, outflow from springs, pumping/injecting from or into the wells or inflow/outflow through aquifer outer boundaries, are designated as time series, just like ground water levels. Since processes in nature occur in cycles, which are in hydrogeology measured as one hydrologic year, time series generally contain several hundreds or even several thousands of measured data. Further, if we consider analysing national time series database, the number of data in time series can be significantly larger. In such cases we can speak about millions of measurements which need to be processed. Statistical analysis are therefore essential in studying processes in hydrogeology. Although the methods of correlation, regression and cross-correlation are well known and long present, Croatian terms related to those methods, primarily related to coefficients which numerically describe the results of correlation, regression and cross-correlation models, are often mixed. Therefore this paper also deals with Croatian statistical terms related to considered statistical method.