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Rachel Blakers, Andrew Davidson
Version
Source v4.1
Availability/Conditions
The Exponential Decay model is automatically installed with Source. For Lumped constituent routing, it can be applied to constituents in:
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Trend Concentration and Percent Reduction%
This function allows to investigate the task decay concentration and then remove the certain percentage of the constituent flexibly. The basic formula is the equation 9.
Trend Concentration
It considers two conditions.:
(i): Trend Concentration < Concentration at the begging of time step:
Where:
M'(t+1) is the constituent mass after the process
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of Trend Concentration
A= V* TrendConcentration is the total mass for the task concentration
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(i): Trend Concentration < Concentration at the begging of time step:
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.
(ii): Trend Concentration > Concentration at the begging of time step
Percent Reduction%
The function will remove the input percent value directly from the processed constituent mass.
Where:
C’(t+1) is the constituent concentration at the storage after the process of Trend Concentration
M’’(t+1) is the sum of the constituent mass after the process of Trend Concentration and
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in the outflow
M(t+1) is the final constituent mass after the process of Trend Concentration and Percent Reduction.
Example
If the half-life is equal to the time step, then the constituent mass after one time step will be equal to one half of the previous mass (ignoring losses and gains from outflows and inflows). For example, consider a half-life of h = 1 day, a daily time step, zero inflows and zero outflows. Equation 9 tells us that, after 1 day, the constituent mass will be:
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Parameter | Description | Units | Default | Range |
Half-life | The half-life of the constituent | seconds | 86400 (equivalent to 1 day) | 0 to ∞ |
| Percent Reduction | A percent value that the user wish wishes to remove directly from the processed constituteconstituent | % | 0 | 0 to 100 |
| Trend Concentration | The designed task concentration what the user wish to investigateconcentration to trend down to | mg/L | 0 | 0 to ∞ |
Outputs
A time series of stored constituent mass.
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