Abstract
In trees, the vascular system is dual in structure and function. Sap flows upwards in the xylem to hydrate tissues and refill reserves from transpiration loss, in the leaves, some of the water recirculates into the phloem and sap, loaded with photoassimilates, flows downwards to supply tissues with carbohydrates. Flow and counter-flow occur in physically separated but hydraulically connected pathways. Water exchanges take place all along them. Understanding the entire system and its subprocesses is essential to precisely quantify the carbon-water fluxes at the soil-atmosphere interface. That understanding is also key to predict the functional limits of vascular transport and if dysfunction occurs, how it will impact the vitality of plant communities in response to drought events and foliar pathogen outbreaks. Here we present an integrated, spatially explicit model of phloem-xylem transport. The model implements Münch’s osmo-regulated pressure flow hypothesis for phloem transport and cohesion-tension for xylem transport. The evolution of phloem pressure, carbohydrate concentration and xylem pressure are governed by three coupled nonlinear partial differential equations. Sap flow velocity, volume flow and the amount of shrinkage and swelling are calculated as derived variables. The model uses a special-purpose numerical scheme and can simulate response to dynamic forcing such as the diurnal patterns of phloem loading and transpiration. Unlike in other models, transport equations are solved for a surface and account for tangential movement of water and carbohydrates. Phloem and xylem are treated as elasto-porous media with distributed hydraulic and mechanical properties. We also present a semi-automated image processing method to calculate the theoretical hydraulic conductivity of phloem and xylem tissues based on their anatomy. Key hydraulic characteristics are given for the phloem of juvenile Pinus radiata D. Don.