A group of the Human Dimensions Program
Aquarius: A Modeling System for River Basin Water Allocation
Gustavo E. Diaz
Thomas C. Brown
**We have updated the software to version 10. We have not yet updated the documentation and the text of this website to reflect these changes.
Aquarius is a state-of-the-art computer model devoted to the temporal and spatial allocation of water among competing uses in a river basin. The model is driven by an economic efficiency operational criterion requiring the reallocation of stream flows until the net marginal return in all water uses is equal. This occurs by systematically examining, using a nonlinear optimization technique, the feasibility of reallocating unused or marginally valuable water storage and releases in favor of alternative uses. Because water-system components can be interpreted as objects of a flow network, the model considers each component as an equivalent node or structure in the programming environment as well. This is done using an object-oriented programming language (C++).
Aquarius Model Description
Aquarius is an analysis framework rather than a single dedicated model for water allocation. The model was implemented using an object-oriented programming (OOP) language (C++). Water systems are ideal candidates for modeling under an OOP framework, where each system component (e.g., reservoir, demand area, diversion point, river reach) is an object in the programming environment. Aquarius supports the following water uses (system components):
An economic efficiency criterion was adopted for determining water allocation because economic demands play a key role in water allocation decisions, and because of the greater accessibility of economic value estimates for nontraditional water uses such as instream and lake recreation. This decision criterion calls for reallocating streamflows until the marginal returns in all water uses are equal. Each traditional use and nontraditional use is, if possible, represented by a demand curve (i.e., a marginal benefit function) that is characterized by exponential, linear or constant price functions.
For a water use with a predetermined level of allocation but without a defined economic demand function, the analyst can either constrain the model to meet the specified allocation or experiment with surrogate demand curves until the required level of water allocation is reached. Indirectly, the latter approach indicates the level of economic subsidy required to provide the incremental increases of flow to sustain the use in open competition with other uses. The interactive nature of Aquarius facilitates such experimentation.
The water allocation problem solved by Aquarius requires a complex nonlinear objective function. The solution technique uses the special case of the general nonlinear programming problem that occurs when the objective function is reduced to a quadratic form and all the constraints are linear. The method approximates the original nonlinear objective function by a quadratic form using Taylor Series expansion and solves the problem using quadratic programming. A succession of these approximations is performed using sequential quadratic programming until the solution of the quadratic problem reaches the optimal solution.
The model's input data have been divided into physical and economic data. The physical data include the information associated with the dimensions and operational characteristics of the system components, such as maximum reservoir capacity, percent of return flow from an offstream demand area, and powerplant efficiency. The economic data consist mainly of the demand functions of the various water uses competing for water.
Although the present version of the model implements only a monthly time step, Aquarius was conceived to simulate the allocation of water using any time interval, including days, weeks, months, and time intervals of nonuniform lengths. Future versions of the model will support these other time steps.
Aquarius can be used in a fully deterministic optimization mode, for general planning purposes, or in a quasi-simulation mode, with restricted foresight capabilities. The model distinguishes between the period of analysis, used to specify the length of the whole segment of time for which the model will simulate system operation, and the optimization horizon, used to specify how far into the future the model should look to build the optimal operational policies. Setting the optimization horizon equal to the period of analysis produces a full-period optimization.
Formulating a water allocation problem entirely within the domain of the objective function allows the user to redirect the water allocation process in any direction in real time, directly from the screen, as the optimization progresses. This unique feature provides an expeditious and innovative mode of exploring "what if" scenarios.
How to Interact with the Model
The user interacts with the model through the network worksheet screen (NWS), which represents the water system of interest using the inherent capability of the object-oriented paradigm for graphical representation. In the NWS, each water system component corresponds to an object, a graphical node or link, of the flow network. These components are represented by icons, which are pictorial representations of the objects. By dragging and dropping these icons from the menu, the model creates instances of the objects on the screen. Components can be repositioned anywhere in the NWS or can be removed. Once nodes (e.g., reservoirs, demand areas) are placed, they are linked by river reaches and conveyance structures. This operation occurs by left-clicking on the outgoing terminal of a node and then on the incoming terminal of the receiving node. This procedure facilitates the assembly or alteration of water systems by connecting their system components in the NWS. The creation and alteration of flow networks is further facilitated by copying and inserting an object or whole portions of an existing network onto the same or a new NWS. Copy/paste creates new instances of the object(s) and duplicates their data structure, creating clones of the original objects.
Aquarius runs on a personal computer under most Microsoft Windows operating systems (95/98/NT/2000).
Actual versus Efficient Water Allocation
Under the dominant water allocation doctrine in the Western United States, the Prior Appropriation Doctrine, the water available for a new application is reduced by the sum of all prior established rights. A priority-based allocation in a heavily appropriated river can become inefficient as values change if institutional barriers or market failures impede voluntary transfers of rights from lower-valued to higher-valued uses. Because institutional barriers and market failures commonly affect Western water, actual water allocations may be different from the economically efficient allocations achieved using Aquarius.
It may be helpful to compare the "actual allocation" with an "efficient allocation". Such a comparison may indicate promising opportunities for private water trades or, where such trades are hampered or precluded by institutional barriers, may indicate areas where institutional reforms can allow for a more efficient water allocation. Where water developments are publicly financed, the comparison may indicate directions that the public entity should consider to increase the efficiency of the project. Aquarius facilitates such comparisons by characterizing an efficient allocation, subject to the analyst's ability to specify demand functions for the key water uses.