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For each dam, Source performs a water simulation based on the water balance between inflows, rainfall, evaporation, seepage, water usage and overflow components in each time step. Assumptions and detailed calculations for each element are described as follows.
Data requirements
For details of the input data requirements, parameter settings and descriptions, and output data, please see the Farm Dam Node chapter in the Source User Guide.
Water surface area
The water surface area in the farm dam (A) is used to convert a depth added (e.g., rainfall) or subtracted (e.g., evaporation or seepage) at each time step to a volume which can then be added to/subtracted from the current storage volume at that time step. The area is estimated as a function of storage volume and other parameters, with three possible options:
Option 1: Assumes a constant surface area at each time step, as defined by the Max dam surface area input at the farm dam UI (Equation 1)
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Where:
At - The surface water area at time step t
C – a constant defined by the input parameter Max. Dam Surface Area
Option 2: Allows a variable surface area per time step calculated as a non-linear function of storage volume at that time step using default coefficients according to a regression relationship as defined by McMurray (2004) 1 (Equation 2):
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Where:
At - The surface water area at time step t
Vt-1 - The surface storage volume at the previous time step. If t is 1 (i.e., the first modelled time step), the initial water volume at the farm dam is used as defined by the Initial Storage Percentage
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Option 3: Allows a variable surface area per time step calculated as a non-linear function of storage volume at that time step using user-defined coefficients according to a regression relationship as defined by McMurray (2004) 1
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Where:
At- The surface water area at time step t
a and b are user-inputted regression coefficients, as defined by McMurray (2004)1
Upstream flow
The total collected flow at an Onstream Farm Dam node consists of two parts:
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ActISFlowt - contributing Interstation Flow
Total upstream flow is split in two directions: (i) flows diverted into the dam, and (ii) flows bypassed directly to the downstream of the farm dam. The Actual Diverted flow is defined by Equation 6 below, and the remainder of the total upstream flow will be accounted in the downstream flow (Equation 23).
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Where:
ActDivFlowt - The actual diverted flows into the farm dam at time step t
DivFract - The percentage or proportion of total upstream flow will be involved in the water balance calculation in the edited farm dam
However, the actual inflow into the farm dam is related to the dam bypass capacity. As defined in the original plugin, if the bypass flow capacity for the farm dam is larger than or equal to the estimated actual diverted flow ActDivFlowt, all flow will bypass and no flows will be diverted into the farm dam, and actual bypass flow and actual inflow are estimated as in Equation 7. Else, they are estimated by Equation 8:
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Where:
ByPassFlowCap - The farm dam’s bypass flow capacity, an inputted parameter
ActByPassFlowt - The actual bypass flow at time step t, controlled by the bypass flow capacity and actual diverted flows ActDivFlowt
ActInFlowt - The actual inflow to the farm dam at time step t, also controlled by the bypass flow capacity and actual diverted flows
Rainfall
The Rainfall volume to the farm dam is estimated by Equation 9:
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Where:
ACTRainVolt - The actual rainfall volume to the farm dam at time step t
Raint - The inputted rainfall timeseries parameter at time step t
At- The surface water area at time step t
The intermediate storage volume at the farm dam is then estimated by Equation 10:
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Where:
Vt – The intermediate storage volume at time step t
ActInFlowt - The actual inflow to the farm dam at time step t
ACTRainVolt - The actual rainfall volume to the farm dam at time step t
Losses
The seepage volume from the farm dam at time step t is estimated by Equation 11:
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If ActSeepageVolt is greater than the available water Vt, the estimation is then continued by Equation 12, else by Equation 13:
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Where:
ActSeepageVolt - The actual seepage volume from the farm dam at time step t
SeepageTSt - The inputted parameter of seepage at time step t
Vt- The intermediate storage volume at time step t from Equation 10
The evaporation volume from the farm dam at time step t is calculated by Equation 14:
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If ActEvapVolt is greater than the available water Vt, the estimation is as in Equation 15, else by Equation 16.
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Where:
ActEvapVolt – The actual evaporation volume from the farm dam at time step t
Evapt - The inputted evaporation timeseries parameter at time step t
Vt- The intermediate storage volume at time step t from Equation 12 or 13
Available water, Demand and Releases
The available water for an onstream farm dam can then be calculated by Equation 17 as:
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Where:
AvailableWatert – The available water for the demand and release in the farm dam at time step t
DeadStorageVolt – The dead storage volume required in the farm dam at time step t
Vt- The intermediate storage volume at time step t from Equation 15 or 16
If AvailableWatert at time step t is less than or equal to zero, there is no water available to meet demands and releases at this time step and demand and release volumes are set to 0, as shown in Equation 18:
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If AvailableWatert at time step t is greater than zero, the model will calculate the water supplied for demands and releases as outlined in Equation 19 to Equation 25:
The average annual water demand for a farm dam is calculated by Equation 19:
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Where:
AvgYearDemand - The average annual demand volume from the daily reference demand data
DemandTSi- The user input demand timeseries at time step i,
and the total number of time steps in the demand time series is n
The actual water demand from a farm dam at time step t is estimated by equation 20 if AvgYearDemand from Equation 19 is not zero. Else, theactual water demand ActDemandVolt is zero.
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Where:
ActDemandVolt – The actual water demand volume requested from the farm dam at time step t
DemandTSt - The user input demand timeseries at time step t
DemandFactor - User input Demand Factor to convert the actual water demand from the referenced water demand timeseries
DamCap - User input farm dam capacity
If the ActDemandVolt is greater than the AvailableWatert calculated in Equation 17 above, Demand and Available Water are calculated according to Equation 21. Else Equation 22 is used.
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Where:
SupplyDemandVolt – The water to supply the actual demand volume from the farm dam at time step t
Vt- The storage volume at time step t according to Equation 15 or Equation 16
AvailableWatert – Water available for release at time step t from Equation 21 or Equation 22
If available water from Equation 21 or Equation 22 is zero, there is no Release at this time step, as shown in Equation 23. Else, Release is calculated as in Equation 24 and Equation 25.
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If the required ReleaseVolt is greater than AvailableWatert as calculated in Equation 22 above, the model continues the estimation according to Equation 24, else Equation 25 is used:
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Where:
ReleaseVolt – The Release Volume requested at time step t
ActReleaseVolt – The actual water volume released from the farm dam for Release Volume request at time step t
Vt- The storage volume (i.e., the available water) at time step t from Equation 21 or Equation 22
Spill
Spill occurs if the storage volume Vt as calculated by Equation 25 is greater than Dam Capacity and Storage volume and Spill volume are calculated according to Equation 26. Else according to Equation 27:
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Where:
SpillVolt – The actual spill volume from the farm dam at time step t
Vt - Final storage volume at time step t
Downstream Flow
Finally, flow directly downstream from the farm dam is calculated by Equation 28:
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Where:
DSFlowt – The actual water volume downstream of the farm dam at time step t
The Source simulation of onstream farm dams is based on a generalised water balance, and the final flow output downstream of the farm dam takes into account all components such as actual Interstation flow, actual diverted flows, actual inflow volume, actual bypassed flows, actual rainfall volume, actual evaporation volume, actual seepage, storage volume and downstream flow.
References
1 McMurray, D, 2004. Farm Dam Volume Estimations from Simple Geometric Relationships. Department of Water, Land and Biodiversity Conservation. South Australia. Report No. DWLBC 2004/48.