Following is a description of the available algorithms.

The Bisection algorithm is the most basic and most robust algorithm implemented. All other algorithms fall back to the bisection if the individual run does not succeed. In Bisection, the minimum and maximum yield is tried first. Then the min and max are averaged or bisected to find the intermediate yield and a run is made with that value. After the third run, the algorithm decides if the yield is too high or too low and modifies the upper or lower bound as appropriates and bisects again. This procedure continues until the solution is found. It is robust as the min and max yields are tried first to bound the solution. No additional information on the reservoirs or physical processes are used, so it is often the simplest to get working. It can be slow as it uses a brute force approach; no information on the processes are used to estimate the next yield to try.

In Heuristic A, first the minimum, then the maximum yields are tried. Then the average of those two yields is tried. If this third and subsequent yield estimate is too high, meaning the minimum level difference is negative, the bisection method will be used as described above. If the minimum level difference is positive the following approach will be taken to compute the next yield.

Assume that we have completed a simulation with a yield which resulted in a positive minimum level difference, i.e. the reservoir is above the bottom of conservation pool throughout the run. In this case, we have underestimated the yield. Examining the results from the simulation, we can find the dates of the drawdown period defined as the last date when the reservoir was full (at the top of the conservation pool) to the date of the minimum level difference. If we had guessed the correct yield then the drawdown period would have ended in a minimum level difference of zero, but we know that we underestimated the diversion because there is water remaining in the conservation pool at the end of the drawdown period. To exactly drain the conservation pool during the drawdown period, we would have needed to divert additional storage equal to the volume of the conservation pool at the minimum level difference date as well as enough to compensate for the reduced evaporation which would result from lower elevations over the drawdown period.

Figure 5.7 shows a plot of storage versus time for this situation. In this figure, the curve Sr is the storage produced from the previous run. Additional water must be released to lower the pool to the bottom of conservation pool. The shaded area is the volume of water that must be released to scale the solid black curve to reach the bottom of conservation pool. This would produce a curve similar to the dotted blue curve.

This analysis motivates Equation 5.1 for using the results from one run to choose a yield which will lead to a minimum level difference of zero in the next run.

Then we can use this along with the method for computing evaporation as a function of storage, Evap(S(t)), to compute the total estimated evaporation over the drawdown period using Equation 5.3.

In Heuristic B, the minimum and maximum yields are computed to bound the solution, but no runs are made with the values. Instead the average of them is used on the first run (If the Reservoir Data for Bisection.Initial Yield to Try is not specified). Then after each successful run, regardless of whether the minimum level difference is positive or negative, the is computed using Equation 5.1 and used on the next run. On unsuccessful runs, a bisection is used.

Table 5.1 summarizes the strengths and weaknesses of each algorithm. This is particularly important for long model runs where any extra runs means hours of computations. own.