Determination of cost coefficients of a priority-based water allocation linear programming model – a network flow approach

Abstract

Abstract. This paper presents a method to establish the objective function of a network flow programming model for simulating river-reservoir system operations and associated water allocation, with an emphasis on situations when the links other than demand or storage have to be assigned with nonzero cost coefficients. The method preserves the priorities defined by rule curves of reservoir, operational preferences for conveying water, allocation of storage among multiple reservoirs, and transbasin water diversions. Path enumeration analysis transforms these water allocation rules into linear constraints that can be solved to determine link cost coefficients. An approach to prune the original system into a reduced network is proposed to establish the precise constraints of nonzero cost coefficients, which can then be efficiently solved. The cost coefficients for the water allocation in the Feitsui and Shihmen reservoirs' joint operating system of northern Taiwan was adequately assigned by the proposed method. This case study demonstrates how practitioners can correctly utilize network-flow-based models to allocate water supply throughout complex systems that are subject to strict operating rules.

Drought Water Right Curtailment Analysis for California’s Eel River

“…Appropriative water right priorities can be represented through cost coefficients, with junior lower-priority rights having lower penalties for shortage. Israel and Lund (1999), Ferreira (2007), and Chou and Wu (2014) extend this approach with algorithms for determining cost coefficients accounting for return flows.…”

“…Water uses such as hydropower and flood irrigation have high return flows to surface water. Israel and Lund (1999), Ferreira (2007), and Chou and Wu (2014) present methods for developing priority-based penalty coefficients for network flow and linear programming models of water resources system with return flows and appropriative rights. These algorithms could serve as pre-processors to account for return flows while preserving water rights priorities, or net surface water diversions could be used, assuming local return flows.…”

“…Rights where return flows return to supply far from the point of diversion, such as interbasin transfers through hydropower, present a larger challenge, but might just be considered as fully consumptive from surface water availability. Several studies (Israel and Lund, 1999;Ferriera, 2004;Chou and Wu, 2014) present methods for adjusting penalty coefficients for appropriative users to address this problem, but the method may be too complex for large systems and data on return flow locations may be difficult to acquire.…”

Western Lake Erie Basin: Soft-data-constrained, NHDPlus resolution watershed modeling and exploration of applicable conservation scenarios

“…For the past two decades, complex watershed simulation models such as the Soil and Water Assessment Tool (SWAT, Arnold et al, 2012), Agricultural Policy/Environmental eXtender (APEX, Williams et al, 2012), and Hydrological Simulation Program-Fortran (HSPF, Bicknell et al, 1997) have been implemented for water resources assessment. These and similar advanced technologies enable modelers to investigate challenges associated with water supply, water quality, pollutant control, and other ecosystem services (Chou and Wu, 2014;Jha and Gassman, 2014;Gebremariam et al, 2014). Model outputs are used to inform land management decisionmaking and policy development at local to national scales (White et al, 2015a, b;Johnson et al, 2015).…”

Minimizing the impact of vacating instream storage of a multi-reservoir system: a tradeoff study of water supply and empty flushing

“…The monthly shortage ratio in July following the empty flushing operations in 1989 and 2009 both reach 0.41. However, the corresponding shortage increments are both 0; therefore, they did not violate the constraints of Eqs (12). and(13).…”