A mathematical model linking tree sap flow dynamics to daily stem diameter fluctuations and radial stem growth

To date, models for simulating sap flow dynamics in individual trees with a direct link to stem diameter variation include only the diameter fluctuation driven by a change in stem water storage. This paper reports results obtained with a comprehensive flow and storage model using whole-tree leaf transpiration as the only input variable. The model includes radial stem growth based on Lockhart's equation for irreversible cell expansion. It was demonstrated that including growth is essential to obtaining good simulation results. To model sap flow dynamics, capacitance of storage tissues was assumed either constant (i.e., electrical analogue approach) or variable and dependent on the water content of the respective storage tissue (i.e., hydraulic system approach). These approaches resulted in different shapes for the desorption curve used to calculate the capacitance of storage tissues. Comparison of these methods allowed detection of specific differences in model simulation of sap flow at the stem base (F(stein)) and stem diameter variation (D). Sensitivity analysis was performed to select a limited subset of identifiable parameters driving most of the variability in model predictions of F(stein) and D. Both the electrical analogue and the hydraulic system approach for the flow and storage model were successfully calibrated and validated for the case of a young beech tree (Fagus sylvatica L.). Use of an objective model selection criterion revealed that the flow and storage model based on the electrical analogue approach yielded better predictions.