S. E. A. T. M. van der Zee

Stochastic modeling of soil salinity

A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The long term probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equation to a single stochastic differential equation driven by multiplicative Poisson noise. The novel analytical solutions provide insight on the interplay of the main soil, plant and climate parameters responsible for long‐term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in longterm soil salinization trends, with significant consequences e.g. for climate change impacts on rain‐fed agriculture

Quantifying catchment-scale mixing and its effect on time-varying travel time distributions

Travel time distributions are often used to characterize catchment discharge behavior, catchment vulnerability to pollution and pollutant loads from catchments to downstream waters. However, these distributions vary with time because they are a function of rainfall and evapotranspiration. It is important to account for these variations when the time scale of interest is smaller than the typical time-scale over which average travel time distributions can be derived. Recent studies have suggested that subsurface mixing controls how rainfall and evapotranspiration affect the variability in travel time distributions of discharge. To quantify this relation between subsurface mixing and dynamics of travel time distributions, we propose a new transformation of travel time that yields transformed travel time distributions, which we call Storage Outflow Probability (STOP) functions. STOP functions quantify the probability for water parcels in storage to leave a catchment via discharge or evapotranspiration. We show that this is equal to quantifying mixing within a catchment. Compared to the similar Age function introduced by Botter et al. (2011), we show that STOP functions are more constant in time, have a clearer physical meaning and are easier to parameterize. Catchment-scale STOP functions can be approximated by a two-parameter beta distribution. One parameter quantifies the catchment preference for discharging young water; the other parameter quantifies the preference for discharging old water from storage. Because of this simple parameterization, the STOP function is an innovative tool to explore the effects of catchment mixing behavior, seasonality and climate change on travel time distributions and the related catchment vulnerability to pollution spreading.

Influence of soil structure and root water uptake strategy on unsaturated flow in heterogeneous media

[1]xa0We analyze the combined effects of the spatial variability of soil hydraulic properties and the water uptake by plant roots on unsaturated water flow. For this analysis, we use a simplified macroscopic root water uptake model which is usually applied only for homogeneous or layered soil and therefore we also determine whether it is applicable for multidimensional heterogeneous media. Analytical solutions for mean and variance of pressure head (first-order second-moment approximations) in layered media and numerical solutions of two-dimensional (2-D) autocorrelated multi-Gaussian and non multi-Gaussian parameter fields are analyzed for steady state and transient flow conditions. For non-Gaussian topological features, that have little influence on the mean and the variance of the pressure field if root water uptake is ignored, we test whether the influence is significant if root water uptake is accounted for. The results reveal that, in field structures with large patches of coarse material, local regions with pressure head values at the wilting point develop; these are surrounded by wet material. Without a compensation mechanism for local stress, the global transpiration demand is not met if local wilting occurs. Various compensation mechanisms are tested that depend, respectively, on the saturation, the relative conductivity or a strategy where the deficit in the global uptake rate is equally distributed to unstressed locations. The strategies lead to a global actual transpiration rate at the potential value and attenuate the formation of locally wilted areas. Wilted regions can, however, still occur, and may be an artifact of the simplified model concept as root-soil interactions are neglected. Therefore simplified macroscopic models for root water uptake should be used with caution in heterogeneous media.

Stochastic modeling of salt accumulation in the root zone due to capillary flux from brackish groundwater

[1] Groundwater can be a source of both water and salts in semiarid areas, and therefore, capillary pressure-induced upward water flow may cause root zone salinization. To identify which conditions result in hazardous salt concentrations in the root zone, we combined the mass balance equations for salt and water, further assuming a Poisson-distributed daily rainfall and brackish groundwater quality. For the water fluxes (leaching, capillary upflow, and evapotranspiration), we account for osmotic effects of the dissolved salt mass using Vant Hoffs law. Root zone salinity depends on salt transport via capillary flux and on evapotranspiration, which concentrates salt in the root zone. Both a wet climate and shallow groundwater lead to wetter root zone conditions, which in combination with periodic rainfall enhances salt removal by leaching. For wet climates, root zone salinity (concentrations) increases as groundwater is more shallow (larger groundwater influence). For dry climates, salinity increases as groundwater is deeper because of a drier root zone and less leaching. For intermediate climates, opposing effects can push the salt balance either way. Root zone salinity increases almost linearly with groundwater salinity. With a simple analytical approximation, maximum concentrations can be related to the mean capillary flow rate, leaching rate, water

Low-Resolution Modeling of Dense Drainage Networks in Confining Layers

Groundwater-surface water (GW-SW) interaction in numerical groundwater flow models is generally simulated using a Cauchy boundary condition, which relates the flow between the surface water and the groundwater to the product of the head difference between the node and the surface water level, and a coefficient, often referred to as the conductance. Previous studies have shown that in models with a low grid resolution, the resistance to GW-SW interaction below the surface water bed should often be accounted for in the parameterization of the conductance, in addition to the resistance across the surface water bed. Three conductance expressions that take this resistance into account were investigated: two that were presented by Mehl and Hill (2010) and the one that was presented by De Lange (1999). Their accuracy in low-resolution models regarding salt and water fluxes to a dense drainage network in a confined aquifer system was determined. For a wide range of hydrogeological conditions, the influence of (1) variable groundwater density; (2) vertical grid discretization; and (3) simulation of both ditches and tile drains in a single model cell was investigated. The results indicate that the conductance expression of De Lange (1999) should be used in similar hydrogeological conditions as considered in this paper, as it is better taking into account the resistance to flow below the surface water bed. For the cases that were considered, the influence of variable groundwater density and vertical grid discretization on the accuracy of the conductance expression of De Lange (1999) is small.