Calculator
Example Data Table
| Scenario | V0 (m³) | C0 (mg/L) | Vin (m³) | Cin (mg/L) | Eff | k | t | Vout | Ve | Avg (mg/L) |
|---|---|---|---|---|---|---|---|---|---|---|
| Rainfall runoff pulse | 5000000 | 2.50 | 75000 | 18.00 | 1.00 | 0.00 | 0 | 0 | 0 | 2.7291 |
| Partial surface mixing | 1200000 | 0.80 | 30000 | 12.00 | 0.35 | 0.02 | 5 | 2000 | 500 | 0.9696 |
| Treatment dosing event | 800000 | 1.20 | 1200 | 450.00 | 0.60 | 0.10 | 2 | 0 | 0 | 1.5328 |
| High outflow week | 3500000 | 6.00 | 50000 | 9.00 | 0.75 | 0.03 | 7 | 90000 | 2000 | 4.8992 |
| Evaporation stress | 650000 | 3.30 | 5000 | 2.10 | 0.50 | 0.00 | 0 | 0 | 8000 | 3.3315 |
Formula Used
- Vmixed,0 = Eff × V0
- Vunmixed,0 = V0 − Vmixed,0
- Vmixed,pre = Vmixed,0 + Vin
- Mmixed,pre = C0·Vmixed,0 + Cin·Vin − Msed
- Volumes are converted from m³ to L.
- Mass units are handled consistently (mg and g).
- Mafter = Mbefore · exp(−k·t)
- k is in 1/day and t is in days.
- Applied to both mixed and unmixed compartments.
- Outflow removes water and solute at the current concentration.
- Evaporation removes water only (solute conserved).
- Cavg = Mtotal / Vtotal after updates.
How to Use This Calculator
- Enter the lake volume and the initial concentration.
- Add the inflow volume and its concentration.
- Set mixing efficiency based on how much water mixes.
- Use decay if the chemical breaks down over time.
- Add outflow and evaporation if they occur during the event.
- Press Submit to see results above the form.
- Download CSV or PDF for reporting and sharing.
Mixing efficiency and stratification
Mixing efficiency represents the fraction of lake volume that actively exchanges with incoming water during an event. A wind‑mixed surface layer may be 0.20–0.50 of total volume in summer, during seasonal changes, while turnover conditions can approach 1.00. If efficiency is 0.35 and the lake is 1,200,000 m³, the mixed compartment starts at 420,000 m³, so inflows shift surface concentrations more than deep water.
Mass balance in practical units
The calculator converts cubic meters to liters to keep concentrations in mg/L. Mixed mass is computed as C0·Vmixed,0 + Cin·Vin, with an optional subtraction for sedimentation removal. For example, with C0 = 0.8 mg/L, Vmixed,0 = 420,000 m³, Vin = 30,000 m³, and Cin = 12 mg/L, the mixed mass before decay is about 4.896×10^11 mg, producing a mixed concentration near 1.09 mg/L.
Decay and settling adjustments
First‑order decay models processes such as biodegradation or hydrolysis. The remaining fraction is exp(−k·t), so k = 0.02 1/day over t = 5 days retains about 0.905 of mass. Sedimentation removal is treated as a direct mass subtraction, useful for particle‑bound contaminants. Combining both adjustments keeps assumptions transparent and allows sensitivity checks by changing k, t, or removed grams.
Flow and evaporation impacts
Outflow is assumed to withdraw from the mixed layer first, removing both water and solute at the current concentration. This can lower total mass and reduce downstream exposure estimates. Evaporation removes only water from the surface layer, concentrating dissolved constituents when other losses are small. If 8,000 m³ evaporates from a 325,000 m³ mixed layer, concentration rises by roughly 2.5% if mass is conserved.
Interpreting results for decisions
Use the mixed‑layer concentration for near‑shore monitoring and short‑term exposure screening, and the whole‑lake average for longer‑term inventory tracking. A dilution factor above 1 indicates net dilution; below 1 indicates enrichment. When a guideline threshold is provided, compare it to the whole‑lake average and the mixed value to see whether exceedances are localized or system‑wide.
FAQs
What does mixing efficiency mean?
It is the fraction of lake water that exchanges with inflow during the event. Use 1.0 for full turnover, or smaller values to represent a mixed surface layer over deeper, stratified water.
Why does evaporation increase concentration?
Evaporation removes water but leaves dissolved mass behind. If no other loss occurs, the same solute mass is distributed in fewer liters, so concentration rises in the mixed layer and slightly in the lake average.
When should I use decay k and duration t?
Use them when the chemical degrades or transforms on the event timescale. Enter k in 1/day and t in days. If you do not know them, set k or t to zero for a conservative, no‑decay estimate.
How is outflow handled in the model?
Outflow is withdrawn from the mixed compartment first, then from unmixed volume if needed. The withdrawn water carries solute at the compartment concentration at that time, reducing remaining mass and influencing the final average.
What does the guideline check compare?
It compares your threshold to the final whole‑lake average concentration. Also review the mixed‑layer value, because localized exceedances can occur even when the average is below the limit.
Which result should I report to stakeholders?
Report both: mixed‑layer concentration for near‑surface sampling and immediate exposure, and whole‑lake average for inventory and longer‑term tracking. Always document assumed efficiency, inflow quality, and any decay or removals.