Not all the phosphorus that enters a lake passes through it. The Dillon–Rigler retention model and the Reckhow nutrient-budget relationships quantify how much of the incoming load settles to the sediment versus how much is exported downstream — the retention coefficient that determines how a lake responds to any change in load.
Retention is the term that balances inputs against outputs. Quantifying it tells us how much phosphorus the lake is accumulating in its sediment — the store that becomes tomorrow’s internal load — and how quickly the lake will respond once the external load is cut.
Explore Our ProcessRetention is governed by how fast phosphorus settles relative to how fast water flushes through the basin.
R = 1 − (Pout/Pin) is the fraction of the incoming phosphorus that does not leave at the outlet. A lake with R = 0.8 retains four-fifths of its load in the sediment — building a large internal store — while a fast-flushing lake exports most of what enters.
The Dillon–Rigler form expresses retention through an apparent settling velocity vs against the areal hydraulic load: R = vs/(vs + qs). Deep, slow lakes settle more and retain more; shallow, fast lakes flush phosphorus before it can sediment.
Reckhow’s regression models predict in-lake phosphorus and retention from load and morphometry across large lake datasets, giving an independent cross-check on the mechanistic estimate and a confidence range for the budget.
The Dillon–Rigler mass balance closes the [P] = L(1 − R) / (z·ρ), where L is the areal phosphorus load, R the retention coefficient, z the mean depth and ρ the flushing rate (1/τ). Only the exported fraction (1 − R) of the load expresses itself in the water column; the retained fraction R is buried — or stored at the sediment surface, poised for release. Retention can be written through an apparent settling velocity as R = vs/(vs + qs), which makes the competition explicit: settling (vs) against hydraulic flushing (qs). This matters twice over. First, it sets how much the in-lake concentration will fall for a given load cut. Second, the cumulative retained mass is the inventory that drives internal loading once the sediment turns anoxic — which is why a lake with a long history of high retention may stay eutrophic for years after its external load is controlled.
It sets both the achievable target and the recovery timescale
The retention coefficient fixes how far in-lake phosphorus will drop for a planned load reduction — preventing over-promised outcomes.
A large retained sediment inventory means a delayed response; we forecast the lag so expectations and monitoring are set realistically.
Mechanistic and empirical (Reckhow) estimates are compared to bound the uncertainty in the phosphorus budget.
Reynolds & Bauhm quantifies the retention coefficient, closes the phosphorus budget and forecasts the recovery timescale — so the restoration target and programme are realistic from the outset.
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