Soil water depletion by oak trees and the influence of root water uptake on the moisture content spatial statistics

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Abstract
The space‐time statistical structure of soil water uptake by oak trees was investigated in a 3.1‐m‐diameter closed top chamber using a three‐dimensional measurement grid of soil moisture and pressure, and measurements of tree transpiration. Using the time domain reflectometery (TDR) measured moisture content, resistance block measured soil water pressure, and a compact constant head permeameter measured saturated hydraulic conductivity, the soil hydraulic properties for the chamber were first estimated. Then, dimensionless statistical measures that utilize the soil water pressure were proposed and used to assess the relative importance of lateral to vertical flow. On the basis of the measured statistical properties of the soil‐water pressure, it was found that the vertical flow is at least an order of magnitude larger than the lateral flow, and thus a one‐dimensional flow approximation to continuity was utilized. Using continuity and a first‐order Taylor series expansion of the Buckingham‐Darcy vertical flux about the spatial mean moisture content state, an approximate relation for the time variation of the spatial mean moisture content was derived and tested with the TDR measurements. Despite a large spatial coefficient of variation in the TDR measured moisture content (which was also shown to be comparable to reported values from larger‐scale field experiments), good agreement between mean moisture content predictions and measurements were found for two separate drying cycles. The approximate Taylor series flux expansion was utilized for deriving an analogous relation for the time variation of the spatial moisture content variance. The resultant variance budget was used to assess the role of root water uptake on the spatial variability of moisture content. It was found that the root uptake component, which resulted from a covariance between the root water uptake and moisture content spatial perturbations, is comparable to the contribution from soil hydraulic properties and soil water redistribution. One of the main findings in this study is that root water uptake is central to the moisture content spatial variance dissipation especially for dry soil moisture conditions. These results were further investigated using Monte‐Carlo simulations.