An analytic solution for groundwater uptake by phreatophytes spanning spatial scales from plant to field to regional

Abstract

Phreatophytes are important to the overall hydrologic water budget, providing pathways from the uptake of groundwater with its nutrients and chemicals to subsequent discharge to the root zone through hydraulic lift and to the atmosphere through evapotranspiration. An analytic mathematical model is developed to model groundwater uptake by individual plants and fields of plant communities and the regional hydrology of communities of fields. This model incorporates new plant functions developed through aid of Wirtinger calculus. Existing methodology for area-sinks is extended to fields of phreatophytes, and Bell polynomials are employed to extend existing numerical methods to calculate regional coefficients for area-sinks. This model is used to develop capture zones for individual phreatophytes and it is shown that the functional form of groundwater uptake impacts capture zone topology, with groundwater being extracted from greater depths when root water uptake is focused about a taproot. While individual plants siphon groundwater from near the phreatic surface, it is shown that communities of phreatophytes may tap groundwater from greater depths and lateral extent as capture zones pass beneath those of upgradient phreatophytes. Thus, biogeochemical pathways moving chemical inputs from aquifer to ecosystems are influenced by both the distribution of groundwater root uptake and the proximity of neighboring phreatophytes. This provides a computational platform to guide hypothesis testing and field instrumentation and interpretation of their data and to understand the function of phreatophytes in water and nutrient uptake across plant to regional scales.