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

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

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

Cellular Models for River Networks

A cellular model introduced for the evolution of the fluvial landscape is revisited using extensive numerical and scaling analyses. The basic network shapes and their recurrence especially in the aggregation structure are then addressed. The roles of boundary and initial conditions are carefully analyzed as well as the key effect of quenched disorder embedded in random pinning of the landscape surface. It is found that the above features strongly affect the scaling behavior of key morphological quantities. In particular, we conclude that randomly pinned regions (whose structural disorder bears much physical meaning mimicking uneven landscape-forming rainfall events, geological diversity or heterogeneity in surficial properties like vegetation, soil cover or type) play a key role for the robust emergence of aggregation patterns bearing much resemblance to real river networks.Comment: 7 pages, revtex style, 14 figure

Spatial characteristics of observed precipitation fields: A catalog of summer storms in Arizona, Volume 2

The parameters of the conceptual model are evaluated from the analysis of eight years of summer rainstorm data from the dense raingage network in the Walnut Gulch catchment near Tucson, Arizona. The occurrence of measurable rain at any one of the 93 gages during a noon to noon day defined a storm. The total rainfall at each of the gages during a storm day constituted the data set for a single storm. The data are interpolated onto a fine grid and analyzed to obtain: an isohyetal plot at 2 mm intervals, the first three moments of point storm depth, the spatial correlation function, the spatial variance function, and the spatial distribution of the total storm depth. The description of the data analysis and the computer programs necessary to read the associated data tapes are presented

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

Modeling urban street patterns

Urban streets patterns form planar networks whose empirical properties cannot be accounted for by simple models such as regular grids or Voronoi tesselations. Striking statistical regularities across different cities have been recently empirically found, suggesting that a general and details-independent mechanism may be in action. We propose a simple model based on a local optimization process combined with ideas previously proposed in studies of leaf pattern formation. The statistical properties of this model are in good agreement with the observed empirical patterns. Our results thus suggests that in the absence of a global design strategy, the evolution of many different transportation networks indeed follow a simple universal mechanism.Comment: 4 pages, 5 figures, final version published in PR

Local minimal energy landscapes in river networks

The existence and stability of the universality class associated to local minimal energy landscapes is investigated. Using extensive numerical simulations, we first study the dependence on a parameter $\gamma$ of a partial differential equation which was proposed to describe the evolution of a rugged landscape toward a local minimum of the dissipated energy. We then compare the results with those obtained by an evolution scheme based on a variational principle (the optimal channel networks). It is found that both models yield qualitatively similar river patterns and similar dependence on $\gamma$. The aggregation mechanism is however strongly dependent on the value of $\gamma$. A careful analysis suggests that scaling behaviors may weakly depend both on $\gamma$ and on initial condition, but in all cases it is within observational data predictions. Consequences of our resultsComment: 12 pages, 13 figures, revtex+epsfig style, to appear in Phys. Rev. E (Nov. 2000

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