دانلود رایگان مقاله ترمودینامیک Megascale در یک حوزه محافظه کار

Abstract

In a series of earlier papers the authors have proposed a unique approach for watershed modelling, which is based on developing watershed-scale balance equations for mass, momentum, energy and entropy by averaging the point-scale (microscale) equations over appropriate averaging regions or control volumes (megascale). The regions are referred to as Representative Elementary Watersheds (REWs), as they are considered to be invariant with respect to the spatial scale. Here, the REW-approach is generalized by developing balance equations and constitutive relationships for sub-REW units, referred to as Elements. Similar to an REW, Elements are divided into a series of zones to accommodate typical flow processes. The subdivision of an REW into Elements supports sub-REW-scale process representation. The proposed procedure yields exchange terms for mass, forces and thermal energy across phase and Element boundaries. These terms constitute unknowns and require a systematic closure. The closure is addressed within a thermodynamic approach, in which the Clausius–Duhem inequality formulated for a watershed serves as a mathematical and physical constraint. The present paper represents a clear extension of earlier work, as it includes non-isothermal processes in presence of the conservative gravitational field. The subdivision of an REW into Elements also provides means for including sub-REW variability due to landuse, geology or presence of infrastructure in the watershed. The paper also shows how an REW Element-scale unsaturated flow equation and non-linear reservoir equations for overland and channel flow can be consistently derived within the thermodynamic theory framework.

12. Discussion and conclusions

This paper is an extension of the original work by the authors (Reggiani et al., 1999, 1998). The concept of Representative Elementary Watersheds introduced earlier has been revised and extended to include novel features. First we recall that an REW effectively is a “mixture” of zero-dimensional contiguous phases filling separate portions of space. Following the definitions by Gray et al. (1993) we adopt a “megascopic” perspective of the system. Through spatial and temporal averaging and zero-dimensional representation, the state variables and physical properties for an entity remain only time-dependent. This leads to a system of coupled ordinary differential governing equations (ODEs), which are computationally cheaper to solve than conventional distributed models (Abbott et al., 1986a,b). This can be a major advantage in probabilistic applications that require multiple consecutive model executions, as in real-time or long-term climate forecasting. To extend earlier work, we now accommodate a more flexible modelling of watersheds by allowing for a subdivision of an REW into Elements, for which we provide conservation equations and constitutive relationships. The sub-division of REWs can be dictated by either topographic features or geological formations, by landcover or landuse patterns, or by anthropic factors such as urbanization, all of which influence flow behaviour