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It is assumed herein that the width function is representative of the catchment's hydrological response.
The width function ( tilde{t}mapsto {left({x}_i^left tilde{t}right -{x}_i^left tilde{t}right -{xht)}_i^left tilde{t}right and continuous.
And the width function ( tilde{t}mapsto {left({x}_i^left tilde{t}right -{x}_i^left tilde{t}right -{xht)}_i^left tilde{t}rightive (firightfficiency region).
The following proof by contradiction will show that the width function cannot become positive at a later moment, thereby proving the connectedness of the efficiency region.
The novel framework proposed (ddRWF) embeds this spatially variable runoff weight in the well-known Rescaled Width Function (RWF) framework, based on the more general geomorphological theory of the hydrologic response.
Vector- and TIN-based methods allow representing the higher drainage density of urban areas, and consequently reveal the impact of these areas on the width function, since the DEM method fails.
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Fig. 3 The width function-based geomorphologic instantaneous unit hydrograph (WFIUH) of a watershed equals the sum of the WFIUHs of representative elementary hillslopes A through G.
The integral of all width functions w j (x) for an REH equals the REH drainage area A j : Fig. 1 Leaf cover on agricultural hillslopes is very sparse, which enhances rainfall impact at the soil surface and results in the formation of a sealing layer that impedes the infiltration process.
This phenomenon can be understood by examining the spin-dependent line-width function.
But the current through the bridge between the leads, which is directly proportional to the inter-lead line-width function, will be drastically varied by the angle.
Then the line-width function in the case of p L = p R = 0 is Γ β ≡ 2πρ β |t βd |2 ≈ 0.01, which is accessible in a typical QD[41 43].
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