Analysis of a hybrid numerical method – decomposing leaf hydraulic conductance

Abstract

We describe a hybrid numerical method to solve a boundary value problem where an unknown parameter of the model is chosen to satisfy an additional boundary condition. After the solution of the differential equation is approximated using a one-step method, a secant method is used to update the value of the unknown parameter. The model is a generalization of a model first used to describe water flow through roots, which was later used to describe water flow through the tank bromeliad Guzmania lingulata. In both cases, identification of the unknown parameter represents the decomposition of overall plant conductance into components in the radial and axial directions. We describe convergence of the one-step and secant portions of the method in a base case corresponding to previous applications of the model and in an intermediate case corresponding to a first approximation of the geometry of the leaf. We demonstrate that in the more general case, which better represents the geometry of G. lingulata, the one-step method also converges as expected. Finally, we discuss the implications of including a better description of the geometry of the leaf in context of radial conductance and show that our modeling of the leaf geometry increases the component of the overall leaf conductance in the radial direction by as much as 25%.