Spatial analysis of storm depths from an Arizona raingage network

Eight years of summer rainstorm observations are analyzed by a dense network of 93 raingages operated by the U.S. Department of Agriculture, Agricultural Research Service, in the 150 km Walnut Gulch experimental catchment near Tucson, Arizona. Storms are defined by the total depths collected at each raingage during the noon-to-noon period for which there was depth recorded at any of the gages. For each of the resulting 428 storm days, the gage depths are interpolated onto a dense grid and the resulting random field analyzed to obtain moments, isohyetal plots, spatial correlation function, variance function, and the spatial distribution of storm depth

Space-time modeling of soil moisture: Stochastic rainfall forcing with heterogeneous vegetation

The present paper complements that of Isham et al. (2005), who introduced a space-time soil moisture model driven by stochastic space-time rainfall forcing with homogeneous vegetation and in the absence of topographical landscape effects. However, the spatial variability of vegetation may significantly modify the soil moisture dynamics with important implications for hydrological modeling. In the present paper, vegetation heterogeneity is incorporated through a two dimensional Poisson process representing the coexistence of two functionally different types of plants (e.g., trees and grasses). The space-time statistical structure of relative soil moisture is characterized through its covariance function which depends on soil, vegetation, and rainfall patterns. The statistical properties of the soil moisture process averaged in space and time are also investigated. These properties are especially important for any modeling that aggregates soil moisture characteristics over a range of spatial and temporal scales. It is found that particularly at small scales, vegetation heterogeneity has a significant impact on the averaged process as compared with the uniform vegetation case. Also, averaging in space considerably smoothes the soil moisture process, but in contrast, averaging in time up to 1 week leads to little change in the variance of the averaged process

A stronger topology for the Brownian web

We propose a metric space of coalescing pairs of paths on which we are able to prove (more or less) directly convergence of objects such as the persistence probability in the (one dimensional, nearest neighbor, symmetric) voter model or the diffusively rescaled weight distribution in a silo model (as well as the equivalent output distribution in a river basin model), interpreted in terms of (dual) diffusively rescaled coalescing random walks, to corresponding objects defined in terms of the Brownian web.Comment: 22 page

Stochastic description of waterlogging and hydroperiods in wetlands

Wetlands are found at the interface between aquatic and terrestrial ecosystems, where different hydrologic factors and ecosystem processes interact to generate unique characteristics and a delicate balance between biotic and abiotic factors. The main hydrologic driver of wetland ecosystems is the water level, whose position above or below the ground level, determines the submergence or non-submergence of soil. When the water level lies above the soil surface, soil is saturated and hypoxic conditions affect all biochemical processes, inducing anaerobic microorganism functioning, variation of redox potential, and anoxic stress in plants, that might lead to the death of non-adapted organisms. When the water level is below the soil surface, the soil water balance is similar to that of groundwater-dependent ecosystems, which allows for both oxygen and water supply to the plant roots. Therefore, the succession of the submerged-unsubmerged conditions plays a fundamental role on the ecosystem. Shallow or above-ground water level fluctuations, at the daily time scale, are driven by stochastic precipitation; using a simple process-based model for soil water balance, the dynamics of groundwater level is here described as a function of evapotranspiration, lateral flow to/from an external water body and random precipitation, modeled as a marked Poisson process. This simple model provides the analytical long-term probability distribution of water table depth and the crossing properties of water table dynamics, which are used to study the timing of waterlogging. The interval of time during which a wetland remains flooded, often called “hydroperiod”, is represented by the first passage time of water table in down-crossing the soil surface; here we calculate the mean hydroperiod as the Mean First Passage Time of the process, that is a function of the model parameters, and we verify this result with numerical simulations. Focusing on the statistical properties of hydroperiods, we also propose to describe their long term probability distribution with a parametric distribution, whose parameters are linked to the model parameters through simple analytical relations. Numerical simulations again confirm the validity of the approach, and its capability of describing the properties of hydroperiods as a function of the climatic, pedological, and ecological characteristics of wetlands

Soil nutrient cycles as a nonlinear dynamical system

International audienceAn analytical model for the soil carbon and nitrogen cycles is studied from the dynamical system point of view. Its main nonlinearities and feedbacks are analyzed by considering the steady state solution under deterministic hydro-climatic conditions. It is shown that, changing hydro-climatic conditions, the system undergoes dynamical bifurcations, shifting from a stable focus to a stable node and back to a stable focus when going from dry, to well-watered, and then to saturated conditions, respectively. An alternative degenerate solution is also found in cases when the system can not sustain decomposition under steady external conditions. Different basins of attraction for "normal" and "degenerate" solutions are investigated as a function of the system initial conditions. Although preliminary and limited to the specific form of the model, the present analysis points out the importance of nonlinear dynamics in the soil nutrient cycles and their possible complex response to hydro-climatic forcing

Stochastic water table dynamics in groundwater-dependent ecosystems

Humidlands are environments where the groundwater plays a key role on the ecosystem function. Contrary to water limited ecosystems, where water table is mostly out of reach for the vegetation, groundwater-dependent ecosystems exhibit important interactions between the water table and vegetation dynamics. We propose here an analytical model to study the interactions between rainfall, water table and vegetation in humidland ecosystems. The groundwater dynamics is studied as a random process, stochastically driven by a marked Poisson noise representing rainfall events. Infiltration, root water uptake, water flow to/from an external water body, and capillary rise are accounted for in a probabilistic description of water table fluctuations. We obtain analytical expressions for the steady-state probability distribution of water table depth, which allows us to investigate the long term behavior of water table dynamics, and their sensitivity to changes in climate, vegetation cover, and water managemen

Stochastic water table dynamics in groundwater-dependent ecosystems

Humidlands are environments where the groundwater plays a key role on the ecosystem function. Contrary to water limited ecosystems, where water table is mostly out of reach for the vegetation, groundwater-dependent ecosystems exhibit important interactions between the water table and vegetation dynamics. We propose here an analytical model to study the interactions between rainfall, water table and vegetation in humidland ecosystems. The groundwater dynamics is studied as a random process, stochastically driven by a marked Poisson noise representing rainfall events. Infiltration, root water uptake, water flow to/from an external water body, and capillary rise are accounted for in a probabilistic description of water table fluctuations. We obtain analytical expressions for the steady-state probability distribution of water table depth, which allows us to investigate the long term behavior of water table dynamics, and their sensitivity to changes in climate, vegetation cover, and water managemen

Ecohydrology of groundwater-dependent ecosystems: a stochastic framework for plant transpiration

Groundwater-dependent ecosystems are found in areas with a shallow water table, where the groundwater plays a key role on the ecosystem functions. In these areas, the water table depth, the capillary fluxes, and the soil moisture content exert a major control on most ecohydrologic processes, such as infiltration, surface runoff, aquifer recharge, land-atmosphere feedbacks, vegetation dynamics, nutrient cycling, and pollutant transport. Understanding and modeling the soil water balance and its relationships with climate, soil, and vegetation is therefore a crucial aspect for geosciences such as hydrology and ecology. The ecohydrology of groundwater-dependent ecosystems can be described with a modeling framework based on a stochastic process-based water balance. The model is driven by a compound marked Poisson noise representing the rainfall events and, under some simplifying, yet realistic, assumptions, it includes rainfall infiltration, root water uptake, capillary flux, and subsurface flow to/from an external water body. The framework provides the long-term probability distribution of water table depth and of soil moisture vertical profiles, enabling a quantitative study of the local hydrology with a limited number of parameters. We here apply this framework to investigate plant transpiration and root water uptake. The probability distributions of water uptake are derived from those of the soil water content and are investigated for different scenarios of climate, soil, and vegetation. The results of this approach allow for interesting speculations about the groundwater contribution to root uptake, the soil water available for plant transpiration, and the optimal strategies of root growth and plant competition. This information is useful to assess the impact of climate changes, vegetation modification, and water management operation