**2. General characteristics of modeling systems**

The generalized river/reservoir system management models explored in this chapter are based on volume-balance accounting procedures for tracking the movement of water through a system of reservoirs and river reaches. The model computes reservoir storage contents, water supply withdrawals, hydroelectric energy generation, and river flows for specified water demands, system operating rules, and input sequences of stream inflows and net reservoir surface evaporation rates.

From the perspective of the water management modeling systems addressed in this chapter, the spatial configuration of a river/reservoir system is represented by a set of model control points connecting river reaches as illustrated in Figure 1. Control points represent the sites of reservoirs, hydroelectric power plants, water supply diversions and return flows, environmental instream flow requirements, conveyance canals and pipelines, stream confluences, river basin outlets, and other system components. Stream inflows at control points are provided as input. Reservoir storage and stream flows are allocated between water users based on rules specified in the model. The models described in this chapter have been applied to river systems ranging in complexity from a single reservoir or run-of-river water supply diversion to river basins containing many hundreds of reservoirs and water supply diversion sites with operations governed by complex multiple-purpose reservoir system operating rules and institutional water allocation mechanisms.

The models of this chapter combine a specified scenario of water resources development, control, allocation, management, and use with a specified condition of river basin hydrology

This state-of-the-art assessment begins with a brief overview of the extensive literature and then focuses on the four modeling systems listed in Table 1. ResSim, MODSIM, WRAP, and RiverWare were developed and are extensively applied in the United States, are also applied in other countries, provide a broad range of analysis capabilities, and are representative of the state-of-the-art from the perspective of practical applications dealing with complex river systems. The four alternative modeling systems reflect a broad spectrum

> U.S. Army Corps of Engineers (USACE) Hydrologic Engineering Center (HEC) http://www.hec.usace.army.mil/

Colorado State University (CSU) and U.S. Bureau of Reclamation (USBR) http://modsim.engr.colostate.edu/

http://riverware.org/

The generalized river/reservoir system management models explored in this chapter are based on volume-balance accounting procedures for tracking the movement of water through a system of reservoirs and river reaches. The model computes reservoir storage contents, water supply withdrawals, hydroelectric energy generation, and river flows for specified water demands, system operating rules, and input sequences of stream inflows

From the perspective of the water management modeling systems addressed in this chapter, the spatial configuration of a river/reservoir system is represented by a set of model control points connecting river reaches as illustrated in Figure 1. Control points represent the sites of reservoirs, hydroelectric power plants, water supply diversions and return flows, environmental instream flow requirements, conveyance canals and pipelines, stream confluences, river basin outlets, and other system components. Stream inflows at control points are provided as input. Reservoir storage and stream flows are allocated between water users based on rules specified in the model. The models described in this chapter have been applied to river systems ranging in complexity from a single reservoir or run-of-river water supply diversion to river basins containing many hundreds of reservoirs and water supply diversion sites with operations governed by complex multiple-purpose reservoir

The models of this chapter combine a specified scenario of water resources development, control, allocation, management, and use with a specified condition of river basin hydrology

Texas Water Resources Institute (TWRI) and Texas Commission on Environmental Quality http://ceprofs.tamu.edu/rwurbs/wrap.htm

University of Colorado CADSWES and USBR

of computational methods, modeling environments, and analysis capabilities.

Short Name Descriptive Name Model Development Organization

ResSim Reservoir System

Simulation

MODSIM River Basin Management

WRAP Water Rights Analysis Package

RiverWare River and Reservoir Operations

and net reservoir surface evaporation rates.

Decision Support System

Table 1. Selected representative generalized modeling systems

system operating rules and institutional water allocation mechanisms.

**2. General characteristics of modeling systems** 

which is most often historical hydrology representing natural unregulated conditions. River basin hydrology is represented by stream flow inflows and net reservoir surface evaporation-precipitation rates for each time step of a hydrologic period-of-analysis.

Fig. 1. Illustrative schematic of a river system as viewed from a modeling perspective

The hydrologic simulation period and computational time step and may vary greatly depending on the application. Storage and flow hydrograph ordinates for a flood event occurring over a few days may be determined at intervals of an hour or less. Water supply capabilities may be modeled with a monthly time step and many-year hydrologic period-ofanalysis reflecting a full range of fluctuating wet and dry periods including extended multiple-year drought.

A river/reservoir system model simulates a physical and institutional water management system with specified conditions of water demand for each sequential time step of a hydrologic period-of-analysis. Post-simulation stream flow and reservoir storage frequency analysis and supply reliability analysis capabilities are typically included in the modeling systems addressed by this chapter. Reservoir storage and stream flow frequency statistics and water supply reliability metrics are developed for alternative river/reservoir system management strategies and practices.

Other auxiliary modeling features are also, in some cases, incorporated in the river/ reservoir management models. Some models include features for economic evaluation of system performance based on cost and benefit functions expressed as a function of flow and storage. Stream inflows are usually generated outside of the reservoir/river system management model and provided as input to the model. However, reservoir/river system models may also include capabilities for simulating precipitation-runoff processes to generate inflows. Though hydraulics issues may be pertinent to reservoir operations, separate models of river hydraulics are applied to determine flow depths and velocities.

Generalized Models of River System Development and Management 7

maximize an objective function subject to constraints. Optimization is covered by water resources systems books (Karamouz et al., 2003; Jain & Singh, 2003; Simonovic, 2009) as well as numerous operations research and mathematics books. Thousands of journal and conference papers have been published since the 1960's on applying variations of linear programming, dynamic programming, gradient search algorithms, evolutionary search methods such as genetic algorithms, and other optimization techniques to reservoir system analysis problems. Various probabilistic methods for incorporating the stochastic nature of stream flows and other variables in the optimization models have been proposed

This chapter focuses on generalized simulation models. A simulation model is a representation of a system used to predict its behavior under a given set of conditions. Alternative executions of a simulation model are made to analyze the performance of the system under varying conditions, such as for alternative operating plans. Although optimization and simulation are two alternative modeling approaches with different characteristics, the distinction is obscured by the fact that models often contain elements of both. An optimization procedure may involve automated iterative executions of a simulation model. Optimization algorithms may be embedded within simulation models either to perform certain periphery computations or to provide the fundamental

Of the many mathematical programming methods available, linear programming (LP), particularly network flow LP, has been the method most often adopted in practical modeling applications in support of actual water management activities. The general LP formulation described in many mathematics and systems engineering textbooks is as

subject to ij j <sup>i</sup> ∑ax b ≤ for i = 1,…,m and j=1,…,n (2)

A LP solution algorithm finds values for the n decision variables xj that optimize an objective function subject to m constraints. The cj in the objective function equation and aij

A number of generalized reservoir system simulation models including several discussed later in this chapter are based on network flow programming, which is a computationally efficient form of LP. Network flow programming is applied to problems that can be formulated in a specified format representing a system as a network of nodes and arcs

n

Minimize or Maximize ij ij ∑∑c q for all arcs (4)

j j j=1

<sup>j</sup> x 0 ≥ for j = 1,…,n (3)

Z = c x ∑ (1)

Minimize or Maximize

having certain characteristics. The general form of the formulation is as follows.

(Labadie2004).

follows.

computational framework for the simulation model.

and bi in the constraint inequalities are constants.

**3.2 Network flow linear programming** 

Some reservoir/river system management models simulate water quality constituents along with water quantities. However, generalized water quality models, not covered in this chapter, are designed specifically for particular types of river and/or reservoir system water quality analyses. The typically relatively simple water quality features of the models explored in this chapter are secondary to their primary function of detailed modeling of water development, regulation, allocation, and management.

Modeling applications often involve a system of several models, utility software products, and databases used in combination. A reservoir/river system management model is itself a modeling system, which often serves as a component of a larger modeling system that may include watershed hydrology and river hydraulics models, water quality models, economic evaluation tools, statistical analysis methods, databases and various software tools for managing time series, spatial, and other types of data.

The models discussed here are used for various purposes in a variety of settings. Planning studies may involve proposed construction projects or reallocations of storage capacity or other operational modifications at existing projects. Reservoir operating policies may be reevaluated periodically to assure responsiveness to current conditions and objectives. Studies may be motivated by drought conditions, major floods, water quality problems, or environmental losses. Operating plans for the next year or next season may be updated routinely based on a modeling system. Models support the administration of treaties, agreements, water right systems, and other water allocation mechanisms. Real-time modeling applications may involve decision-support for water management and use curtailment actions during droughts. Likewise, real-time flood control operations represent another type of application.
