Thomas M. Over

A space‐time theory of mesoscale rainfall using random cascades

Following a brief review of relevant theoretical and empirical spatial results, a theory of space-time rainfall, applicable to fields advecting without deformation of the coordinates, is presented and tested. In this theory, spatial rainfall fields are constructed from discrete multiplicative cascades of independent and identically distributed (iid) random variables called generators. An extension to space-time assumes that these generators are iid stochastic processes indexed by time. This construction preserves the spatial structure of the cascades, while enabling it to evolve in response to a nonstationary large-scale forcing, which is specified externally. The construction causes the time and space dimensions to have fundamentally different stochastic structures. The time dimension of the process has an evolutionary behavior that distinguishes between past and future, while the spatial dimensions have an isotropic stochastic structure. This anisotropy between time and space leads to the prediction of the breakdown of G. I. Taylors hypothesis of fluid turbulence after a short time, as is observed empirically. General, nonparametric, predictions of the theory regarding the spatial scaling properties of two-point temporal cross moments are developed and applied to a tracked rainfall field in a case study. These include the prediction of the empirically observed increase of correlation times as resolution decreases and the scaling of temporal cross moments, a new finding suggested by this theory.

Statistical Analysis of Mesoscale Rainfall: Dependence of a Random Cascade Generator on Large-Scale Forcing

Abstract Under the theory of independent and identically distributed random cascades, the probability distribution of the cascade generator determines the spatial and the ensemble properties of spatial rainfall. Three sets of radar-derived rainfall data in space and time are analyzed to estimate the probability distribution of the generator. A detailed comparison between instantaneous scans of spatial rainfall and simulated cascades using the scaling properties of the marginal moments is carried out. This comparison highlights important similarities and differences between the data and the random cascade theory. Differences are quantified and measured for the three datasets. Evidence is presented to show that the scaling properties of the rainfall can be captured to the first order by a random cascade with a single parameter. The dependence of this parameter on forcing by the large-scale meteorological conditions, as measured by the large-scale spatial average rain rate, is investigated for these three da...

GEOtop: A Distributed Hydrological Model with Coupled Water and Energy Budgets

Abstract This paper describes a new distributed hydrological model, called GEOtop. The model accommodates very complex topography and, besides the water balance, unlike most other hydrological models, integrates all the terms in the surface energy balance equation. GEOtop uses a discretization of the landscape based on digital elevation data. These digital elevation data are preprocessed to allow modeling of the effect of topography on the radiation incident on the surface, both shortwave (including shadowing) and longwave (accounting for the sky view factor). For saturated and unsaturated subsurface flow, GEOtop makes use of a numerical solution of the 3D Richards’ equation in order to properly model, besides the lateral flow, the vertical structure of water content and the suction dynamics. These characteristics are deemed necessary for consistently modeling hillslope processes, initiation of landslides, snowmelt processes, and ecohydrological phenomena as well as discharges during floods and interstorm...

On scaling exponents of spatial peak flows from rainfall and river network geometry

Abstract The hypothesis of statistical self-similarity, or scaling invariance, in the spatial variability of rainfall, channel network structures and floods has been supported by recent advances in data analyses. This hypothesis is used here to calculate the statistical scaling exponents of peak river flows using a random cascade model of spatial rainfall intensities and the Peano basin as an idealized model of a river basin. The ‘maximum contributing set’ approximately determines the magnitudes of peak flows in a self-similar manner in different subbasins of the Peano basin. For an instantaneously applied random, spatially uniform rainfall, the Hausdorff dimension of the maximum contributing set appear, as the statistical simple scaling exponent of peak flows. This result is generalized to an instantaneously applied cascade rainfall, and it is shown to give rise to statistical multiscaling in peak flows. The multiscaling exponent of peak flows is computed and interpreted as a Hausdorff dimension of a fractal set supporting rainfall intensity on the maximum contributing set of the Peano basin. Potential implications of this interpretation are illustrated using the regional food frequency analysis of the Appalachian flood data in the United States and a rainfall data set from the tropical Atlantic ocean. It is argued that the hypothesis of self-similarity identifies a powerful theoretical framework which can unify a statistical theory of regional flood frequency with important empirical features of topographic, rainfall and flood data sets and distributed rainfall-landform-runoff relationships.

On the effect of air humidity on soil susceptibility to wind erosion: The case of air-dry soils

[1] Wind erosion is a widespread process in drylands, and contributes to loss of soil fertility, alteration of atmospheric radiation, and air pollution. Erosion occurs when wind speed exceeds a certain threshold, which depends on a number of factors, including surface soil moisture. It is shown that in air-dry soils surface moisture and threshold wind speed depend significantly on air humidity. Thus, in arid regions variations in surface soil moisture can be significantly affected by changes in atmospheric humidity, with an important effect on wind erosion potential. Wind tunnel tests were conducted to investigate this dependence of threshold velocity on air humidity in air-dry soils. It was found that at these moisture levels, the threshold velocity decreases with an increase in air humidity. This result is explained by the effect of hygroscopic forces and by their dependence on soil matric potential in dry soils. INDEX TERMS: 1815 Hydrology: Erosion and sedimentation; 1866 Hydrology: Soil moisture; 1809 Hydrology: Desertification. Citation: Ravi, S., P. D’Odorico, T. M. Over, and T. M. Zobeck (2004), On the effect of air humidity on soil susceptibility to wind erosion: The case of air-dry soils, Geophys. Res. Lett., 31, L09501, doi:10.1029/2004GL019485.

An Analysis of the Soil Moisture Feedback on Convective and Stratiform Precipitation

Abstract Land–atmosphere interactions in midlatitude continental regions are particularly active during the warm season. It is still unclear whether and under what circumstances these interactions may involve positive or negative feedbacks between soil moisture conditions and rainfall occurrence. Assessing such feedbacks is crucially important to a better understanding of the role of land surface conditions on the regional dynamics of the water cycle. This work investigates the relationship between soil moisture and subsequent precipitation at the daily time scale in a midlatitude continental region. Sounding data from 16 locations across the midwestern United States are used to calculate two indices of atmospheric instability—namely, the convective available potential energy (CAPE) and the convective inhibition (CIN). These indices are used to classify rainfall as convective or stratiform. Correlation analyses and uniformity tests are then carried out separately for these two rainfall categories, to asse...

Impact of Watershed Geomorphic Characteristics on the Energy and Water Budgets

The GEOtop model makes it possible to analyze the short- and long-term effects of geomorphic variation on the partitioning of the lateral surface and subsurface water and surface energy fluxes. The topography of the Little Washita basin (Oklahoma) and of the Serraia basin (Trentino, Italy) have been used as base topographies from which virtual topographies with altered slopes and elevations have been created with corresponding modifications of the soil thickness and the extension of the channel network, according to applicable geomorphological theories, in order to quantify the contribution of these topographic features to the spatial and temporal variability of energy and water fluxes. Simulation results show that both a more extended channel network and more accentuated slopes cause an increase in the discharge balanced by a diminution of the evapotranspiration. The diminution of the latent heat flux is balanced by the increase in the sensible heat flux. Net radiation shows a minor sensitivity to topography. Evaporative fraction, on the contrary, is shown to be strongly dependent on geomorphic characteristics. The results confirm the importance of including an adequate treatment of topography in large-scale land surface models.

River flow mass exponents with fractal channel networks and rainfall

An important problem in hydrologic science is understanding how river flow is influenced by rainfall properties and drainage basin characteristics. In this paper we consider one approach, the use of mass exponents, in examining the relation of river flow to rainfall and the channel network, which provides the primary conduit for transport of water to the outlet in a large basin. Mass exponents, which characterize the power-law behavior of moments as a function of scale, are ideally suited for defining scaling behavior of processes that exhibit a high degree of variability or intermittency. The main result in this paper is an expression relating the mass exponent of flow resulting from an instantaneous burst of rainfall to the mass exponents of spatial rainfall and that of the network width function. Spatial rainfall is modeled as a random multiplicative cascade and the channel network as a recursive replacement tree; these fractal models reproduce certain types of self-similar behavior seen in actual rainfall and networks. It is shown that under these modeling assumptions the scaling behavior of flow mirrors that of rainfall if rainfall is highly variable in space, and on the other hand flow mirrors the structure of the network if rainfall is not so highly variable.

An Assessment of ENSO-Induced Patterns of Rainfall Erosivity in the Southwestern United States

Abstract Microerosion processes due to the impact of raindrops on the soil (rainsplash) represent an important mechanism of detachment and removal of soil parcels. The annual and interannual patterns of rainsplash erosion are controlled by the variability of rainfall, vegetation cover, and land-use practice. This paper presents a study of the interannual variability of rainfall erosivity (which is an indicator of the erosive power of rainfall) due to winter precipitation in the southwestern United States and its connection to the El Nino–Southern Oscillation (ENSO). A remarkable degree of dependence was found between the values of winter erosivity and the Southern Oscillation index (SOI) in the months proceeding and during each winter. In general, it was observed that the erosive power of rainfall is stronger during El Nino years and weaker during the La Nina phase in the U.S. southwest, as is the rainfall itself. It was also observed that the erosivity and SOI are nonlinearly related. This dependence of ...

Accelerating advances in continental domain hydrologic modeling

In the past, hydrologic modeling of surface water resources has mainly focused on simulating the hydrologic cycle at local to regional catchment modeling domains. There now exists a level of maturity among the catchment, global water security, and land surface modeling communities such that these communities are converging toward continental domain hydrologic models. This commentary, written from a catchment hydrology community perspective, provides a review of progress in each community toward this achievement, identifies common challenges the communities face, and details immediate and specific areas in which these communities can mutually benefit one another from the convergence of their research perspectives. Those include: (1) creating new incentives and infrastructure to report and share model inputs, outputs, and parameters in data services and open access, machine-independent formats for model replication or reanalysis; (2) ensuring that hydrologic models have: sufficient complexity to represent the dominant physical processes and adequate representation of anthropogenic impacts on the terrestrial water cycle, a process-based approach to model parameter estimation, and appropriate parameterizations to represent large-scale fluxes and scaling behavior; (3) maintaining a balance between model complexity and data availability as well as uncertainties; and (4) quantifying and communicating significant advancements toward these modeling goals.