Estimation of the impact of short-term fluctuations in inputs on temporally aggregated outputs of process-oriented models

Process-oriented models driven by highly resolved meteorological inputs and comprising a short internal time step are sometimes used to predict substance fluxes in air, soil and water over fairly long periods of time. To ascertain whether regression-based input–output analyses in such cases can provide adequate parametric models of the impact of daily and monthly fluctuations in inputs on annual outputs, we studied the SOIL/SOILN model of vertical transport of heat, water and nitrogen through arable soils. Annual leaching of nitrate from the root zone was regarded as the response variable, and regressors were selected from among the set of all linear combinations of daily or monthly values of five different meteorological inputs. We found that, although several of the underlying processes described by the SOIL/SOILN model are non-linear, both ordinary and partial least squares regression (OLS and PLS) identified the subsets of input variables with the strongest influence on the model output, and the dominating time lags between model inputs and outputs. Furthermore, highly resolved explanatory variables were a prerequisite for good performance of linear predictors of temporally aggregated outputs and, to discern the full dynamic behaviour of the model, it was necessary to analyse the response to artificially generated daily meteorological data representing a very large number of different weather conditions. PLS had one advantage over OLS: a smooth pattern in the regression coefficients facilitated physical interpretation of the derived impulse–response weights.