Wednesday, June 10, 2015

Water Supply Yield Analysis

This example will demonstrate a simple yield analysis computation in ResSim for a single reservoir. The model consists of a single stream with one reservoir.  The only inflow point is at the upstream junction.  The yield analysis is concerned with the minimum flow at the junction, "downstream compute point".  For ease of computation, null routing is used in the routing reaches.      



The elevation-storage table for the pool is shown below.  I have set the top of conservation pool at elevation 50 ft.  This gives us a storage value of 200,000 acre-ft.  I have set the top of the inactive pool at elevation 25 ft.  This gives us a storage value of 100,000 acre-ft.  So, the total conservation pool is 100,000 acre-ft.  




There is one rule governing operation of the reservoir.  This rule requires a minimum release of 20 cfs at the junction, "downstream compute point".





This is the inflow hydrograph that I developed for this example.  The flow varies from 500 cfs to 25 cfs.  So, this should inform us that the yield of the reservoir will be greater than 25 cfs since we have 25 cfs coming into the reservoir.  Note that I neglect evaporation and other losses in this example.  It should also inform us that the critical period will begin in 2011 and end in 2013.  



 In the alternative editor, I specify that I am performing a yield analysis.



I select the demand rule as the minimum flow at the downstream location.  Recall that it was set to 20 cfs.  This will be the initial estimate for ResSim.  The tolerance is set to 5 cfs.  This will be explained in the results.  The tolerance for the storage lower limit is 1000 acre-ft.  This will also be covered in the results discussion.  



For the yield analysis, I used the bisection method.  The trial factor for the first iteration is 1.  This means that it uses the value that is currently in the rule, which is 20 cfs.  The simulated minimum storage is 200,000 acre-ft since it never leaves the top of conservation.  There is enough inflow to hold top of conservation and supply the downstream demand.  Since it does not get below 101,000 acre-ft (bottom of conservation plus storage tolerance of 1,000 acre-ft), it fails the storage convergence test.

For the next trial, the initial estimate of 20 cfs is doubled.  We see that the simulated minimum storage is in the conservation pool since it is below 200,000 acre-ft.  However, it is greater than 101,000 acre-ft so it fails the storage convergence test.  We also notice that 80 cfs fails the storage convergence test, but it is much closer to the 101,000 storage convergence value.

ResSim then tries 160 cfs.  This time it passes the convergence test.  Notice, however, the date of the minimum storage value is 04April2012.  This reaches the minimum value before the critical period ends.  At this point, ResSim checks to see if it can meet the flow tolerance of 5 cfs for the remainder of the critical period.  Basically, can it meet at least 155 cfs for the rest of the critical period.  It is unable to do this so it fails the flow convergence test.

ResSim continues its test by using values between the previous test and 80 cfs since it knows that 80 cfs put the minimum pool above its storage target.  ResSim discovers that using 85 cfs gives a minimum pool elevation on 15July2013.  This is very close to the end of the critical period, however, it is unable to maintain 80 cfs for the remainder of the critical period.  Finally, it tries 82.5 cfs, which passes both the storage convergence and the flow convergence tests.