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Equation 9 forms the basis of the Exponential Decay model in Source. The solution becomes less accurate as the half-life becomes smaller (particularly if the half-life is smaller than the time step) and as the flushing rate (Qout /Vt+1) becomes larger. It also follows from Equation 9 that if Vt+1 = 0 then Mt+1 = 0.
Trend Concentration and Percent Reduction%
This function allows to investigate the task concentration and then remove the certain percentage of the constituent flexibly. The basic formula is the equation 9
Trend Concentration
It considers two conditions and M'(t+1) is the constituent mass after the process of Trend Concentration:
(i): Trend Concentration < Concentration at the begging of time step:
(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.
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 flow out
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 to remove directly from the processed constitute | % | 0 | 0 to 100 |
| Trend Concentration | The designed task concentration what the user wish to investigate | mg/L | 0 | 0 to ∞ |
Outputs
A time series of stored constituent mass.
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