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Discussion papers | Copyright
https://doi.org/10.5194/hess-2018-32
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 13 Feb 2018

Research article | 13 Feb 2018

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

A new probability density function for spatial distribution of soil water storage capacity leads to SCS curve number method

Dingbao Wang Dingbao Wang
  • Department of Civil, Environmental, and Construction Engineering, University of Central Florida, Orlando, Florida, USA

Abstract. Following the Budyko framework, soil wetting ratio (the ratio between soil wetting and precipitation) as a function of soil storage index (the ratio between soil wetting capacity and precipitation) is derived from the SCS-CN method and the VIC type of model. For the SCS-CN method, soil wetting ratio approaches one when soil storage index approaches infinity, due to the limitation of the SCS-CN method in which the initial soil moisture condition is not explicitly represented. However, for the VIC type of model, soil wetting ratio equals soil storage index when soil storage index is lower than a certain value, due to the finite upper bound of the power distribution function of storage capacity. In this paper, a new distribution function, supported on a semi-infinite interval x[0, ∞), is proposed for describing the spatial distribution of storage capacity. From this new distribution function, an equation is derived for the relationship between soil wetting ratio and storage index. In the derived equation, soil wetting ratio approaches zero as storage index approaches zero; when storage index tends to infinity, soil wetting ratio approaches a certain value (≤1) depending on the initial storage. Moreover, the derived equation leads to the exact SCS-CN method when initial water storage is zero. Therefore, the new distribution function for soil water storage capacity explains the SCS-CN method as a saturation excess runoff model and unifies the surface runoff modeling of SCS-CN method and VIC type of model.

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Short summary
A novel distribution function is proposed for describing the spatial distribution of soil water storage capacity; and then the classical and empirical hydrologic model, SCS curve number method, is derived as when initial soil water storage is zero. This distribution function unifies SCS curve number method and saturation excess runoff model, and the unified model provides a better way for modeling surface runoff.
A novel distribution function is proposed for describing the spatial distribution of soil water...
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