1. Reservoir Convergence Algorithms
Convergence Algorithm Previously Used
Current Convergence Algorithm

2. General
Convergence algorithm used in functions that require the simultaneous solving of a set of 2 equations
Bisection algorithm used in all reservoir types in
getMaxOutflowGivenInflow
getMaxReleaseGivenInflow
getMinSpillGivenInflowRelease
solveMB_givenInflowRelease

3. Example - getMaxOutflowGivenInflow
fMAX(stor,Q)
QMAX,MB
fMB(stor,Q)
storMAX,MB
storage

4. 1. Simple Convergence Algorithm
Iterates by updating the dependent variable (outflow) based on the changing of the
independent variable (storage)
outflow
outflow
fMAX(stor,Q)
fMAX(stor,Q)
These functions started out using this simple convergence algorithm. The first step in an iteration is to calculate the outflow based on the storage of the previous iteration, using the max outflow function.
Using that outflow, a storage is determined using the mass balance function.
Again, the max outflow function determines an outflow based on this storage value.
When these values for outflow converge, the method is exited.
This becomes problematic when an area of zero slope is present in one of the curves. Convergence can never be obtained under this scenario using this algorithm.
fMB(stor,Q)
fMB(stor,Q)
storage
storage
Ideal
Problematic

5. Bisection Algorithm
Incremental search method where the interval is divided in half at each iteration
outflow
outflow
QMBave
fMAX(Q,stor)
fMAX(Q,stor)
QMAXave
QMBave
To fix that problem an algorithm based on the bisection method was implemented.
This is an incremental search method that divides the search interval in half at each iteration
QMAXave
fMB(Q,stor)
fMB(Q,stor)
stor_low
stor_ave
stor_high
storage
stor_low
stor_ave
stor_high
storage
stor_low
stor_ave

6. 2. Bisection Replaces Simple Algorithm
The simple algorithm was replaced with the bisection algorithm. This approach also
proved to be problematic.
outflow
outflow
fMAX(Q,stor)
fMAX(Q,stor)
QMBave
QMAXave
fMB(Q,stor)
fMB(Q,stor)
stor_low
stor_ave
stor_high
stor_low
stor_high
storage
storage
stor_low
stor_ave
Ideal
Problematic

7. 3. Current Algorithm - Combination of Simple & Bisection
If the simple convergence routine fails, the bisection routine is employed.
The last 4 points of the simple routine become the bisection routine’s starting points.
outflow
outflow
fMAX(Q,stor)
fMAX(Q,stor)
QMBave
QMAXave
fMB(Q,stor)
fMB(Q,stor)
stor_low
stor_ave
stor_high
storage
storage
Simple
Bisection