A dynamical model is devised for a hydrologic system where unsaturated and saturated storage serve as the principal control on rainfall‐runoff and where complex topography, drainage area, and variable depth of moisture penetration describe the flow geometry. The model is formed by direct integration of the local conservation equation with respect to the partial volumes occupied by unsaturated and saturated moisture storage, respectively. This yields an “integral‐balance” model in just two state variables. The relationship of the dynamical model to field data in complex terrain is found through a joint probability density for terrain features. This serves as a “volume” weighting function to construct conditional averages for the state variables and fluxes over a specified range of terrain features. The scale of averaging could range from hillslopes to river basins. Two examples of the joint probability of terrain features (altitude and aspect) are demonstrated for Valley, Ridge, and Appalachian Plateau digital elevation models. The strategy of a dynamical model formed by conditional averages of state variables with respect to terrain features is proposed as a way of simplifying the dynamics while preserving the natural spatial and temporal scales contributing to runoff response. The parametric form of the storage‐flux or constitutive relationships for the proposed model is determined from numerical experiments in a simple hillslope flow geometry. The results show that a competitive relation exists between unsaturated and saturated storage except for the lowest precipitation rates. Saturation overland flow is proposed to be a storage‐feedback relation. Solutions to the integral‐balance model are presented in terms of the phase portrait, which represents all possible solution trajectories in state‐space. The timing and magnitude of peaks in the runoff hydrograph from pulse‐type input events demonstrate quick flow from near‐stream saturated storage, saturation overland flow including rejected rainfall (storage‐feedback), and late‐time infiltration from upslope subsurface flow.
Water Resources Research – Wiley
Published: Aug 1, 1996
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera