A Comparison of Predictive Phosphorus Load-Concentration Models for Lakes

Abstract

Lake models that predict phosphorus (P) concentrations from P-loading have provided important knowledge enabling successful restoration of many eutrophic lakes during the last decades. However, the first-generation (static) models were rather imprecise and some nutrient abatement programs have therefore produced disappointingly modest results. This study compares 12 first-generation models with three newer ones. These newer models are dynamic (time-dependent), and general in the sense that they work without any further calibration for lakes from a wide limnological domain. However, static models are more accessible to nonspecialists. Predictions of P concentrations were compared with empirical long-term data from a multi-lake survey, as well as to data from transient conditions in six lakes. Dynamic models were found to predict P concentrations with much higher certainty than static models. One general dynamic model, LakeMab, works for both deep and shallow lakes and can, in contrast to static models, predict P fluxes and particulate and dissolved P, both in surface waters and deep waters. PCLake, another general dynamic model, has advantages that resemble those of LakeMab, except that it needs three or four more input variables and is only valid for shallow lakes.

Predicting future effects from nutrient abatement and climate change on phosphorus concentrations in Lake Bourget, France

“…Although easy to use, these static models do not account for year-to-year variations in internal loading (nutrient transport from sediments to water through resuspension, bioturbation and diffusion) and may therefore comparatively poorly describe the recovery process of eutrophied lakes (Bryhn and Håkanson, 2007). One such well-known and widely used model that will be tested in this work is that of Vollenweider (1976), which calculates TP concentrations in lakes from two parameters; the TP concentration in the inflowing water and the water retention time.…”

“…A third model type also produces dynamic predictions, but is, in addition, general, meaning that the model has been developed to contain a unique set of equations and calibration constants, and the output data have subsequently been tested against empirical data on TP concentrations from several lakes (Aldenberg et al, 1995;Janse, 2005;Bryhn and Håkanson, 2007;Håkanson and Bryhn, 2008). Only easily accessible and measurable driving variables are used (e. g., lake area, mean and maximum depth and total P loading) and driving variable values should be site-specific for each lake.…”

“…LakeMab, which has been tested against TP data from deep and shallow lakes from northern Sweden to central Florida (Bryhn and Håkanson, 2007). However, neither of these models has been tested against data from meromictic lakes, which for long periods sustain three vertical water layers with limited exchange of water and P. PCLake simulates P masses and fluxes to and from a mixed water column (Janse, 2005) while LakeMab describes two communicating vertical water layers.…”

“…-The structure should be as simple as possible and should to the greatest extent possible replicate LakeMab, whose detailed test results (r 2 =0.96 for modelled TP concentrations against empirical data in a cross-systems comparison) have been reported in Bryhn and Håkanson (2007) and Håkanson and Bryhn (2008).…”

“…The number of possible calibration constant sets decreases drastically if the same model is tested for more than one system without re-calibration (Bryhn and Håkanson, 2007). Moreover, there are only five years (2004)(2005)(2006)(2007)(2008) for which both TP concentration data and reliable TP loading data are available for Lake Bourget.…”