A physical analysis of sap flow dynamics in trees

The aim of this thesis was to analyze the water dynamics of trees by using a dynamic modeling approach. The work is of cross-disciplinary nature: tree water issues which is a subject of whole plant physiology is examined by means of physics. From physical principles five different models were derived. First, to study the sap flow and the water pressure dynamics in the xylem of tree stem, the effect of embolism on the sap flow, and the recovery of embolized conduits; and second, to analyze a sap flow measuring system based on the heat balance method. Sap flow and water pressure dynamics are analyzed with two models that are based on the relation between xylem water tension and changes in the diameter of sapwood. This new approach is advantageous because it offers a way to compare the model predictions with the easily measured diameter changes in intact trees. The model results give new insight into the water dynamics in the stem, stating that pressure propagation is fast, but time lags of a few minutes do exist. These time lags are related to the dimensions and radial elasticity of the stem, and to the sapwood permeability. The results are in agreement with the cohesion-tension theory but partly contradict the pipe model theory of a plant form. The embolism recovery model presents a quantitative analysis of the processes that have been suggested to recover embolized conduits while the water in surrounding conduits is under negative pressure. The model analysis reveals that under normal physiological circumstances, e.g., normal xylem water tension, osmotic pressure of living cells, or diffusion distances, the refilling process is possible if the two sides of the same living cell have different transport properties for solutes. The model for analyzing the performance of a sap flow measuring system reveals that the method, that assumes homogenous temperature field inside the stem, is not appropriate for stems with a diameter larger than a few centimeters. This study has shown that relatively simple models, based on physical principles, are useful in increasing our understanding of the processes and behavior of natural objects. Furthermore, model analysis leading to better understanding of dynamic systems, can guide forthcoming research and enhance the development of new instrumentation.