# Mass Balance Calculation in Reservoirs

Dear EFDC Development Team,

I have a question about the mass balance calculation for the reservoir. I have known discharge and known elevation at the outlet dam and the elevation and discharge at upstream dam. The downstream dam doesn’t have the good stage discharge relation that can be represented by a equation. A traditional rating curve will have 1 stage value to equal 1 discharge value. But in my case, I have 1 stage value equal more than 1 discharge value, and vice-versa. I have a difficulty doing the exact mass balance calculation. I know all the inflows, and outflows but I don’t know how to find the volume change at each time step. Since, we don’t have the proper relation between the stage and discharge at the downstream dam, I don’t know how can I find the volume difference from the know elevations at the downstream dam. I can find out the initial volume in the system by multiply dx, dy and depth on each cell. But so far I haven’t found good approach to find the volume change in each time step.

I have here a sample discharge and elevation data at dam.

Julian Day Discharge Elevation
200.4402778 0 77.67828
200.4409722 0 77.681328
200.4416667 0 77.67828
200.4423611 0 77.67828
200.4430556 0 77.681328
200.44375 0 77.67828
200.4444444 0 77.67828
200.4451389 0 77.67828
200.4458333 0 77.67828
200.4465278 0 77.6478
200.4472222 224.7340761 77.653896
200.4479167 298.8036128 77.61732
200.4486111 285.4323978 77.623416
200.4493056 284.4704745 77.629512
200.45 288.0488744 77.626464
200.4506944 287.7883594 77.623416
200.4513889 287.2571354 77.63256
200.4520833 287.0841195 77.626464
200.4527778 287.0841195 77.626464
200.4534722 286.2943626 77.638656
200.4541667 288.7630253 77.623416
200.4548611 289.2064671 77.635608
200.4555556 288.4589024 77.629512
200.45625 288.8584531 77.63256
200.4569444 235.3410572 77.635608
200.4576389 0 77.705712
200.4583333 0 77.684376
200.4590278 0 77.67828
200.4597222 0 77.675232
200.4604167 0 77.67828
200.4611111 0 77.66304
200.4618056 0 77.666088
200.4625 0 77.66304
200.4631944 0 77.659992
200.4638889 0 77.672184
200.4645833 0 77.669136
200.4652778 0 77.669136
200.4659722 0 77.672184
200.4666667 0 77.669136

Would you please give me some suggestions on how can I proceed for the mass balance calculations ? Thank you so much.

John

Hi John, this is really a reservoir management issue. The key to this is to create a good conceptual model of the reservoir, with flows, seepage, evaporation etc. The EFDC model will always maintain mass balance. Our recommendation is that you create the model with high resolution and with good data to support your model.

Dear EFDC Development Team,

Thank you so much for your reply. I have created a high resolution grid and I also have high resolution bathymetry data as well. The problem is that there seems to be some leakage at the Lock and Dam. What is the best way to calculate the leakage in the dam ? As you said earlier, we can’t use water surface elevation at the downstream because it doesn’t accurately represent the scenario. So, when I use the outflow it seems like my water surface elevation is continuously increasing. Would you please give me some suggestions on how can I use mass balance output to calculate the missing outflow / leakage ? Thank you.

John.

Hi John,

This is not really an issue with the model – it depends mainly on the hydraulics of the system. You need to calculate the mass balance correctly as the model is indicating the mass balance is not yet correct. It would seem your inputs and loss terms are not yet properly accounted for. You may to make an estimate of the leakage of the lock f this is where the losses are. However, without looking at the model and the overall system we can’t really help you much on this. We could provide a solution if you would like to set up a support contract.