RA is forecast to be at level 10.2, RB at 8.9, RC at 9.5. The key control point, CPY, assigned balance level 9.0 to reservoirs RA, RB and RC, and so its balance level for the current timestep is 9.0. The balance level set is { 9.0, 5.0 }. There are three passes, one at 9.0, one at 5.0 and a “final” pass at 5.0, in which certain constraints, described below, are removed. On the first pass, the algorithm proposes release schedules for RA and RC that will bring them down as close to operating level 9 as possible in 5 days, given empty space constraints at control points. It considers RA before RC because RA is forecast to be “fuller” (at a higher operating level). On the second pass, the algorithm proposes releases for RA, RC, and RB, to bring them down to operating level 5.0 while still respecting all the constraints of the first pass. On the final pass, all reservoirs are considered, with the goal of bringing them to level 5.0, with slightly different constraints, as described below.

If there were no routing coefficients at CPC for routing from RA to CPC, the flood control algorithm would stop checking constraints at CPA, even if control points downstream of CPC had routing coefficients for releases from RA. If the routing coefficients for RA to CPC were { 0,0,0,.5,.5 }, no releases after the 2nd day would be considered from CPC on downstream, because no water from such releases would reach CPC or beyond within the forecast period. Finally, if the Routed Release Tolerance were 0.000001 cms, and a release were to route to a control point but the arriving flow were to be less than 0.000001 cms, the flood control algorithm would stop at said control point. Thus, the Routed Release Tolerance can be used to tune the algorithm - to make it run faster, but with less precision.

Routing coefficients from RA to CPC could be {.5,.5} and from RA to CPY could be {.8,.2}, and RiverWare would not notice. It is entirely up to the modeler to see that the coefficients are consistent with each other and with the simulation routing methods.

The routing coefficients on the Reach between CPA and RC might be {.1,.2,.3,.4}, and all else as described in the reference subbasin. RiverWare would use the routing coefficients on the reach during simulation, and the routing coefficients on the control points for flood control. The fact that they don’t match would not be discovered by RiverWare. The Reaches might not use linear routing at all. RiverWare would have no way to tell if the linear routing used in flood control is an “acceptable” approximation of the (possibly non-linear) routing selected on the Reaches and used during simulation.

The key control point balancing method on CPY apportioned its empty space as follows: 60% to RA and 40% to RB. With three passes, at operating levels 9.0, 5.0 and 5.0, on the first two passes (9.0 and 5.0), RA releases can consume at most 60% of the empty space at CPY on any day of the forecast period, while RB can consume at most 40%. On the final pass, any unused space at CPY is available to both RA and RB. Empty space at CPC is available to RA and RB on all passes because CPC is not key.

We are proposing a release from RB. For the purpose of this example, let us assume that below CPX, no other constraints reduce a release, that is, this example considers only the effects of CPB and CPX. RB has volume of 150 units to release to bring it down to the goal balance level for the pass. RB has a Max Release Variation of 10 flow units per timestep. Empty space at CPB for the forecast period is { 50, 50, 50, 50, 50 }. For the first forecast day, the empty space at RB would permit a stepped-down release hydrograph of {50, 40, 30, 20, 10}, so it proposes a release of 50 units. For the second day, the remaining empty space at CPB would then be { 0, 50, 50, 50, 50 }, so it proposes a release of 50 units again. Now the proposed release schedule is { 50,50, 0, 0, 0 } and the proposed empty space at CPB is {0,0,50,50,50}. Thus, CPB will impose the same upper bound on each day’s release from RB.

Continuing the above example, we now consider the empty space at CPX, which is { 50, 60, 40, 50, 50 }. For the first day, the stepped-down hydrograph would be 55, 45, 35, 25, 15}, which, routed, yields {27.5,50,40,30,20}, limited by day 3. Since the release is already constrained to 50 units on each day, CPX does not impose any constraints on the RB release schedule for the first day. Assuming the release from RB for the first day is indeed 50 units (after considering all control points and all other constraints), arriving at CPX as {25,25,0,0,0), on the second day the resulting free space at CPX would be {25, 35, 40, 50, 50}. This empty space dictates a stepped-down hydrograph for day 2 of { 0, 45,35,25,15}, resulting in an arrival hydrograph of { 0, 22.5, 40, 30, 20 }, restricted by day 3. Thus, the upper bound of 45 is imposed on the release for day 2. Assuming that holds, we route it to CPX, and it arrives as {0,22.5,22.5,0,0}. This leaves empty space for day 3 at { 25,12.5,17.5,50,50}. This empty space dictates a stepped-down hydrograph for day 3 of {0,0,35,25,15}, which, routed to CPX gives an arrival hydrograph of {0,0,17.5,30,20}, being restricted by day 3. Thus, the upper bound of 35 is imposed on day 3, which we assume remains the release for day 3. Routed to CPX, it arrives as {0,0,17.5,17.5,0), which reduces the empty space to {25,12.5,0,32.5,50}. The day 4 hydrograph is then { 0,0,0,55,45}, routed to CPX arriving as 0,0,0,27.5,50}, being restricted by day 5. Thus, the day 4 upper bound is 55, and if it ends up being released, it routes to CPX as {0,0,0,,27.5,27.5}, leaving empty space of {25,12.5,0,5,22.5}. This empty space dictates a day 5 hydrograph of {0,0,0,0,45}, which gives the upper bound of 45 for day 5. Thus control point CPX imposes limits of {55, 45,35,55,45}, and the release schedule is {50,45,35,55,45}.

RA’s Allowable Rising Release Change (ARRC) is 20. Computing RA’s optimal release for the first day yields a release of 100. The total release (surcharge release plus flood control release) made on the prior simulation timestep was 75, so RA will not release more than 95 today (surcharge and flood control releases combined). After applying all other constraints, we end up with a release for today of 55. That means that the second forecast day’s release will not exceed 75, and so on throughout the forecast period.

RA’s Allowable Falling Release Change (AFRC) value is 10 flow units per timestep. RA is forecast to have150 units of flood pool volume at the end of the balance period, so 150 units is the release goal on a pass at balance level 5.0. The stepped-down hydrograph computed for 150 units volume for the first timestep is {50, 40, 30, 20, 10}, which releases all the volume in the forecast period. Thus, 50 is an upper bound on the first day’s release. Having ultimately released 40 on the first day, due to space restrictions downstream, we compute a new hydrograph for the second day, to release 110 units in the 4 remaining days. This hydrograph is {42.5, 32.5, 22.5, 12.5}.

The second hydrograph imposes an upper bound of 42.5, in addition to the upper bound of 50 on the release for the second day. Assuming we could ultimately release 41 units on day 2, we have for the third day 110-41=69 units to release. We compute a hydrograph for the third day: {33, 23, 13}. Thus the third day’s release is subjected to the upper bound of 50 and the upper bound of 33. If a downstream control point imposes a limit of 0 on the third and fourth day releases, we will still have 69 units to release on day 5. This will give us a stepped-down hydrograph of {69}, and the upper bounds of 69 and 50 will apply to day 5. Thus, the upper bounds for each of the days for this constraint will be: {50,42.5,33,39.5,50}.

RA can release 100 units, and RC cannot store any water (having stored plenty from RB). Routing 100 units from RA to RC, we get {50,50}, and we then apply the spillway constraint at RC, considering the 50 arriving as being in addition to any other inflows at RC, and considering any other proposed releases from RC. If the release from RA, upon flowing through RC, could exceed the spillway capacity of RC, RA’s release will be reduced accordingly.

Key control point CPY assigns to RA a maximum release of 40 units, and to RB a maximum release of 30 units. If we have three passes, at levels 9.0, 5.0 and 5.0, on the first two passes, RA will release no more than 40 units on any day of the forecast period. RB will not release more than 30 units on any day of the forecast period. Thus even though RA may be forecast to be significantly higher than RB, it may not be able use all the downstream channel space otherwise available to it. Only on the final pass will these limits be lifted, and RA will be free to consume all remaining channel space, subject to its other constraints. Assuming that the key control point allocates these maxima in proportion to the fullness of the reservoirs, using the maxima may have the effect of allowing each reservoir to release something each timestep, rather than allocating all channel space to RA today, leaving RB “fuller” tomorrow, allocating all channel space to RB tomorrow, leaving RA “fuller” the next day, and so on (causing undesirable oscillating behavior). Of course, the effect depends on the key control point balancing method selected.

RB is forecast to be at level 10.0 and RC is forecast to be at level 5.0 at the end of the balance period. The key control point balancing method assigns level 7.0 to all three reservoirs. On the first pass, at balance level 7.0, RC takes on 100 units from RB, released as { 40, 30, 20, 10}. Since the forecast period is 5 days long, the arrival hydrograph for this release schedule from RB is {4, 19, 30, 25, 15}, but because we consider only that water that arrives within the balance period, we account for only the 53 units arriving on days 1-3, leaving 47 units that arrive after the end of the balance period. Thus, in future calculations based on the forecast storage in RC, 53 units of volume will be added to RC’s forecast storage. RC will be free to release on day 1 an additional 4 units of volume, and on day 2 an additional 19 units of volume, and so on through the forecast period. If the Two-Reservoir Midpoint method is selected, the starting volume for RC will henceforth include 53 units of volume above its forecast volume at the end of the balance period.

There are four passes at balance levels 9.0, 8.7, 5.0 and 5.0. RC, subject to more than one key control point (not shown in the example subbasin), has been assigned a balance level of 8.7. On the first pass (9.0), RA may store water in RC to bring RC up to the larger of 9.0 (balance level of the pass) and 8.7 (balance level assigned RC). On the second pass, RC will accept water to bring it no higher than 8.7 again. On the last two passes, it will accept no water, unless it is forecast to be in the conservation pool at the end of the balance period, in which case, it will accept water to fill the conservation pool. If the Two-Reservoir Midpoint method is selected, RC will, in addition, agree to accept more water. Let us assume, as in a prior example, that RA is forecast to be at 10.2, RB at 8.9, and RC at 9.5. RC will accept, from RA, that volume of water that, if instantaneously moved from RA to RC, would put RC and RA a the same operating level. That level will be somewhere between 10.2 and 9.5. RC will not initially accept any water from RB because RB is forecast to be lower than RC. If, on the first pass, RC is able to release enough water to bring it below the ending operating level of RA at the conclusion of the pass, RC will accept water from RB.

This example applies only when Pass Behavior is Compute Compute Additional Release. On the first pass, RA releases 100 units of volume to be stored in RC, as follows: {50,30,20,0,0}. The key control point, CPY, has allocated to RA {30, 30, 30, 30, 30}, to RB {10, 10, 10, 10, 10} and to RC {20, 20, 20,2 0,20}. Having stored 100 units of RA’s water in RC, on a later pass we might be able to release some or all of that 100 units from RC, but because that water originated at RA, we transfer its ownership to RC. Routing the release hydrograph to CPY, we get {12,5, 32.5, 32.5, 17.5, 5}, so we transfer such units of water in CPY’s accounts. Now CPY has allocated to RA: {17.5, 0, 0, 12.5, 25}, and to RC: {32.5, 50, 50, 37.5, 25}.