Inserting Timesteps to Account for Spillway Flows
Model Description
This model employs a simple reservoir to demonstrate how event triggers are used to insert time slices for a more accurate accounting of spillway flows in a model with large timesteps. Compare the model titled, "single_pool_reservoir_monthly" to a similar model without the event triggers, where the spillway flow is not accurately accounted for. Compare this model to the one called, "single_pool_reservoir_monthly_noTS".
This is how timesteps are inserted into the model for spillway calculations:
1. Calculate the rate of change of reservoir pool elevation.
dHdT = (Qin - Qout) / A
Where
A is the reservoir pool surface area at the current timestep
Qi is the inflow to the reservoir
Qout is the current outflow from the reservoir
dHdT is the rate of change of reservoir pool elevation
2. Calculate the time it will take for the reservoir pool elevation to reach the spillway crest (if dHdT is a positive value, meaning its rising). It is likely the time to crest value is found to be less than the currently scheduled timestep length.
Tc = (Hs - Hr) / dHdT
Where
Hs is the elevation of the spillway crest
Hr is the reservoir pool elevation
dHdT is the rate of change previously calculated
Tc is the time to crest
3. Calculate the time it will take for the reservoir pool elevation to move by a known increment after the spillway crest has been exceeded. This is calculated only if the spillway crest is exceeded.
Ts = dH/ (abs(dHdT) + 1e-6 m/day), 1000 day)
Where
dH is an increment of change in reservoir pool elevation (distance)
dHdT is the rate of change previously calculated
Ts is the time until the reservoir pool elevation changes by the increment (dH)
The terms Ts and Tc are used to trigger a timed event using GoldSim TimedEvent elements, which will stop the internal clock and place an event, causing the model calculations to update and therefore, calculate a more accurate spillway flow.
Model Files
Screen Captures
Spillway calculations:
Inserted timesteps between scheduled, monthly timesteps:
Comparison of the spillway flow and reservoir pool elevation with and without inserted timesteps:
See Also
