Scientific Investigations Report 2006–5060

U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2006–5060

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Appendix A. A New “Withdrawal Blending” Capability for CE-QUAL-W2

Modifications were made to CE-QUAL-W2 to enable it to blend withdrawals from more than one lake outlet, and set the depth of any adjustable-depth outlets, in order to meet a user-specified time series of target temperatures for water released from a reservoir. In this way, the model can be used to (1) assess whether certain downstream temperature targets can be met under various structural and operational scenarios, (2) assess the effects of using different types of outlets, either singly or in combination, and (3) assess the effects of specifying different temperature targets, among other things. Some of these objectives, such as using multiple fixed outlets to meet a downstream temperature target, could have been accomplished with the model previously, but only by running the model multiple times and iterating on the flow rates from each outlet. The changes added by the USGS modeling team allow these tasks to be accomplished in a single model run, because the necessary operational changes are done automatically.

Several additions were made to the model in order to implement this new ability to blend withdrawals from multiple outlets. The most important of these changes are listed below.

  1. Each withdrawal is now given a user-specified “bottom elevation limit,” corresponding to the lowest elevation from which that outlet can withdraw water. This simulates any physical limits of an outlet structure. If the water surface declines below this level, the outlet is dry and no water can be withdrawn from that outlet.
  2. Each withdrawal is now classified by the model user as either a fixed-elevation outlet, a “floating” outlet, or a sliding-gate outlet (fig. A1). Fixed-elevation outlets have an unchanging centerline outlet elevation. Floating outlets are hydraulic structures that may stretch the limits of modern engineering, but are nevertheless useful to imagine in a modeling exercise; in the model, their centerline outlet elevation is always set to 1.5 meters below the water surface, unless the water surface declines below the outlet’s bottom elevation limit. Sliding-gate outlets have a variable outlet elevation, adjusted by the model, that ranges between the outlet’s bottom elevation limit and the water surface.
  3. Each withdrawal is assigned to a “withdrawal group” for modeling purposes. A total withdrawal flow rate is assigned by the user to each group rather than to each individual withdrawal. Flows from the withdrawals in each group are adjusted by the model to match the total withdrawal flow rate for the group. If a group is assigned more than one withdrawal, or if one of the withdrawals is a sliding-gate outlet, then it is assumed that the user wishes to match a downstream temperature target. In that case, the group is assigned a user-specified time series of target water temperatures. The model then will attempt to blend water from the various outlets in that group and set the elevation of any variable-elevation outlets in that group to meet the target water temperature.
  4. To simulate a situation in which dam operators must make decisions about the blending of flows from different outlets, the model only adjusts the blending of flows a user-specified number of times per day. For example, in a model simulation in which water from two fixed-elevation outlets is blended to meet a specified temperature target, the total amount of water withdrawn from the two outlets is set by the user in the normal manner. The model determines how much of that total to withdraw from each of the two outlets, in an attempt to match the target temperature. The user, however, specifies how many times per day and at what time of day the model can make its blending adjustment. The model was set up this way to simulate the fact that these adjustments may be done manually and that practical reasons may preclude frequent adjustments. For the same reasons, the model also allows the user to give the dam operator the weekend off, in which case no blending adjustments are made on Saturday or Sunday. (A day-of-week function was added for this calculation.)
  5. No more than two outlets are used for blending at any one time. If more than two outlets are assigned to the same withdrawal group, and more than two of those outlets are below the water surface, then the model applies a set of rules to determine which two outlets to use. All other outlets in the group are turned off (zero flow). When more than two outlets are available, multiple solutions to the blending problem can be calculated; by using only two outlets, the solution becomes straightforward and is described below. The following rules are used to determine which outlets to use and which ones to close:
    1. The highest and lowest outlets that are “wet” generally are used. The rest of the rules are an attempt to enforce this rule and maintain a maximum amount of flexibility to access water through as much of the water column as possible.
    2. Sliding gates are preferred over floating outlets because they are more flexible in accessing water with different temperatures.
    3. Fixed outlets are preferred over floating outlets when a sliding-gate outlet is present.
    4. A floating or sliding-gate outlet is preferred over the highest of two fixed outlets.
    5. Only one floating outlet is ever necessary. Given any other type of outlet, only one floater will ever be considered for use.
    6. The lowest fixed outlet is preferred when the other outlet is either a floater or a slider.
    7. A sliding-gate outlet is preferred over another sliding-gate outlet if its bottom elevation limit is lower.
    8. When two sliding-gate outlets are present, a fixed outlet is preferred over the shorter slider only if the fixed outlet is lower than the bottom elevation limits of both sliders.
  6. The depth of the opening of a sliding-gate outlet is set by the model in response to a need to access water of a certain temperature. If a sliding gate is used by itself, the model will set the elevation of its opening at the point in the water column that best matches the target temperature. If a sliding-gate outlet is one of a pair of outlets being blended to meet a target temperature, the sliding gate is set either near the water surface (1.5 meters depth), or deep in the lake, 1 meter above its bottom elevation limit, depending on whether the target temperature is warmer or colder than the water available to the other outlet.

When flows from two outlets are blended to meet a target temperature, determining the flow from each outlet is a straightforward calculation. The total release rate from the withdrawal group is known because it was set by the user in the model’s withdrawal flow file. The target temperature also is known. If more than two outlets are available within a withdrawal group, the model’s rules, described above in item 5, are used to select the two active outlets. The depth of each outlet is known, and therefore the simulated water temperature in the lake at the depth of each outlet also is known. The flows in each outlet, then, are calculated using the following equations. Conservation of energy requires that:

Figure - refer to figure caption for alternative text description, (A1)

where

Figure - refer to figure caption for alternative text description

is

the total release rate,
Figure - refer to figure caption for alternative text description

is

the target temperature,
Figure - refer to figure caption for alternative text description

is

the flow in the first outlet,
Figure - refer to figure caption for alternative text description

is

the temperature associated with the first outlet,
Figure - refer to figure caption for alternative text description

is

the flow in the second outlet, and
Figure - refer to figure caption for alternative text description

is

the temperature associated with the second outlet.

Conservation of mass requires that:

Figure - refer to figure caption for alternative text description. (A2)

Determining the value of Figure - refer to figure caption for alternative text description, therefore, is a simple matter of substituting Figure - refer to figure caption for alternative text description with (Figure - refer to figure caption for alternative text description) and solving for Figure - refer to figure caption for alternative text description, which leaves:

Figure - refer to figure caption for alternative text description. (A3)

Once Figure - refer to figure caption for alternative text description is found, the value of Figure - refer to figure caption for alternative text description is determined through application of equation A2. Note that equation A3 applies only when the target temperature is between the temperatures at the two selected outlets; this is why the outlet selection rules outlined above were crafted to select the two outlets that can draw water from as high and as low in the water column as possible, thus maximizing the available temperature difference Figure - refer to figure caption for alternative text description.

If the target temperature is greater or less than both of the outlet temperatures, the model assigns all flow to the outlet having the temperature closest to the target temperature. If the two outlet temperatures are identical, then flow is split equally between the two outlets only if those temperatures also equal the target temperature; otherwise, a higher target temperature results in all flow being assigned to the higher outlet while a lower target temperature results in all flow being assigned to the lower outlet.

For more details on how the model implements this blending strategy, the ultimate source of information is the model’s source code, which is available online at the project website: http://or.water.usgs.gov/tualatin/hagg_lake/scenarios/. Note that the model code also implements a set of “avoidance” algorithms in which “avoidance rules” may be set by the user and consulted by the model when making decisions concerning which outlets to choose for blending. For example, the user could tell the model to avoid withdrawing any water where the dissolved oxygen is less than a certain concentration, and/or where the ammonia exceeds some concentration. No avoidance rules were used in the Hagg Lake model runs, though they may be used in future scenarios. At this point, the avoidance algorithms are fairly simple and could be improved in the future.

In addition to the algorithms that take care of the blending details, new output options were added to the model that aid in documenting how the blending was done. Such output includes the actual flow rate from each of the withdrawals involved in blending, their elevation, and the layers in the model from which the water ultimately was withdrawn.

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