A Network Model for Stemflow Solute Transport

Abstract:

While the role of stemflow in directing and concentrating water and nutrients into the rooting system is not in dispute, its mathematical representation remains a subject of inquiry and active research. We propose a network model to estimate stemflow solute concentration and leaching with the goal of unpacking the 'black box' that is solute transfer along tree trunks. The model utilizes the physico-chemical properties of individual furrows embedded in the tree bark as well as their interconnections. The equations for water and solute transport for a single furrow were first developed and then up-scaled to a rough-barked network topology. The single-furrow equations identify 5 dimensionless numbers most pertinent to momentum and scalar transport: a Reynolds number, a Froude number, a Damköhler number, and two Péclet numbers (for axial and vertical movement). The model parameters are calibrated using field measurements of tree bark; laboratory experiments on bark leaching for potassium, magnesium, and calcium; and published data on stemflow rates. These parameterizations provide plausibility constraints. Network complexity, including asymmetry in the subpaths connecting network nodes, was analyzed to determine outflow concentration. It was determined that an effective 'channel-flow' analogy may be used to represent solute concentration at the outflow when the network is symmetric. When asymmetry is introduced into the subpath lengths, the network has decreased efficiency in solute transport with the same rainfall input onto the stem. This mathematical model is a step towards developing further hypotheses about connections between network properties and the physico-chemical properties of bark. Using this study of networks can lead to advances in linking rainfall to stemflow and solute transport in a variety of different tree species with differing bark microrelief configurations.

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Publication note: This presentation is based on: Tucker et al. (2020). A network model for stemflow solute transport. Applied Mathematical Modelling 88: 266-282. [DOI: 10.1016/j.apm.2020.06.047]