The decisive lake-restoration question is not how much algae there is, but where the phosphorus comes from. The Vollenweider areal-loading relationship and the OECD eutrophication models link the external load, mean depth and residence time to the steady-state in-lake phosphorus — the analysis that tells us whether catchment control will work before a single intervention is chosen.
Run the mass balance before anything else and the result is unambiguous: if the model reproduces the observed phosphorus from the external load alone, the catchment is the problem and in-lake measures will disappoint. If the lake holds far more than the load explains, the sediment is releasing it internally — a different lever entirely.
Explore Our ProcessThree terms set the steady-state phosphorus concentration a lake will reach
The external phosphorus load is normalised to lake surface area as an areal loading rate L in g P/m²·yr. Expressing it per unit area lets lakes of different size be compared against the same critical-loading thresholds that separate oligotrophic from eutrophic outcomes.
The areal hydraulic load qs = z/τ (mean depth over residence time) is the rate at which water — and the phosphorus it carries — passes through. A deep lake or a short residence time dilutes the load; a shallow, slow lake concentrates it.
Water residence time governs how long phosphorus stays in contact with the sediment and biota, and so how much settles out. It enters the model through the √τ sedimentation term — longer residence means proportionally more retention.
At steady state the in-lake phosphorus concentration is [P] ≈ L / (qs(1 + √τ)), where L is the areal load, qs the areal hydraulic loading and τ the residence time in years. The (1 + √τ) denominator is the sedimentation term — it captures the fraction of phosphorus lost to the sediment as a function of how long the water lingers. The OECD eutrophication programme generalised this into probabilistic load–response relationships, giving the likelihood of a given trophic outcome for a measured loading. The practical test is direct: insert the measured external load and morphometry, compare the predicted [P] with the observed in-lake [P], and the gap between them is the signature of internal loading. A model that matches says “control the catchment”; a large under-prediction says “the sediment is the source” — the single most consequential branch in the whole assessment.
The model turns nutrient figures into a defensible strategy
We assemble the external load from catchment land use, point sources and atmospheric input, normalised to lake area for comparison against critical thresholds.
The Vollenweider prediction is set against measured in-lake phosphorus — the discrepancy quantifies the internal contribution that catchment control alone will miss.
We project the in-lake phosphorus under candidate load reductions, so the expected water-quality gain is known before capital is committed.
Reynolds & Bauhm builds the load budget, runs the Vollenweider and OECD models, and isolates the internal contribution — so the restoration targets the real source.
Our expertise spans multiple industries with sector-specific water treatment solutions.