Climate, soil, and vegetation: 1. Introduction to water balance dynamics

A statistical dynamic formulation of the vertical water budget at a land‐atmosphere interface is outlined. Physically based dynamic and conservation equations express the infiltration, exfiltration, transpiration, percolation to groundwater and capillary rise from the water table during rainstorms and interstorm periods in terms of independent variables representing the precipitation, potential evapotranspiration, soil and vegetal properties, and water table elevation. Uncertainty is introduced into these equations through the probability density functions of the independent climatic variables and yields derived probability distributions of the dependent water balance elements: surface runoff, evapotranspiration, and groundwater runoff. The mean values of these quantities give a long‐term average water balance which, to the first order, defines the annual water yield and water loss in terms of the annual precipitation and potential evapotranspiration and in terms of physical parameters of the soil, vegetation, climate, and water table. This analytical framework provides physical insight into the dynamic coupling of climate‐soil‐vegetation systems. Details are presented in a series of subsequent papers.