American Society of Civil Engineers

Evaluation of the Advection Scheme in the HSPF Model

by Sen Bai, P.E., (Environmental Engineer, Tetra Tech, Inc., 10306 Eaton Place, #340, Fairfax, VA 22030. E-mail:

Journal of Hydrologic Engineering, Vol. 15, No. 3, March 2010, pp. 191-199, (doi:

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Document type: Journal Paper
Abstract: This paper studied the mass conservation and constancy-preserving conditions of the advection scheme in the Hydrological Simulation Program-Fortran (HSPF) model. Equations were derived to examine the conditions for achieving both mass conservation and constancy-preserving properties. Case studies of simulating conservative materials, water temperature, and dissolved oxygen were conducted to show the impacts of the advection scheme on model applications. The mass conservative condition of HSPF can only be achieved weakly even though the advection equation is written in a mass conserved format for the current advection scheme. The constancy-preserving condition is strongly violated due to the inconsistency with continuity. The advection scheme was modified by the writer to use one single weighting factor for solving both water routing and material advection. Unrealistic results are removed and mass conservation and constancy-preserving conditions are achieved with the modified advection scheme.

ASCE Subject Headings:
Hydrologic models
Dissolved oxygen

Author Keywords:
Mass conservation
Constancy preserving