Many lakes can exist in two regimes, one characterized by clear water and the other one turbid. The turbid, or eutrophic, condition is caused by excessive fertilization with nutrients. By fitting nonlinear time series models to data from Lake Mendota, NTL researchers have estimated that the probability of the turbid regime is about 75%. Furthermore, the probability of irreversible turbidity (sustained by recycling from sediments) is about 25%. We have also estimated the effects of changes in phosphorus loading on the regime, and used spatial models to study the effects of farming practices on the phosphorus loading.

NTL interdisciplinary studies have calculated the net economic value of water quality, based on the economics of farming, value of housing near the lake, and the recreational economy derived from boating, fishing and so forth. These analyses suggest that the economically optimal loading (which maximizes net costs and benefits to society as a whole) is around one-third of the current loading rate to the lake.

The long-term data also suggest that even the economically-optimal phosphorus loads may incur a high risk of shifting the lake into an irreversible eutrophic state. This risk is related to the high variability in loading caused by variable climate. It also depends on the proportion of the watershed used for phosphorus-intensive agriculture such as dairy or meat production.

If climate variability is ignored, economic value appears to peak when phosphorus -intensive farming covers about 75% of the watershed (red line in Fig. 1A). If climate variability is accounted for, economic value is maximum when phosphorus-intensive farms cover about half the watershed (blue line in Fig 1A). When phosphorus-intensive farms cover a bit more than 80% of the watershed, the irreversibly turbid regime occurs. Mathematically, this corresponds to disappearance of the stable attractor for the clear water state ( blue line in Fig. 1B). However, large inputs caused by unusually wet years can also tip the lake into the turbid regime. Variability of the loads increases with the proportion of land used for phosphorus-intensive farming (yellow line in Fig. 1B). Near the economic optimum where about half the land is used for phosphorus-intensive farming, the standard deviation of loading is large enough to shift the lake into the turbid regime about one year in ten.

NTL long-term data have shown, therefore, that economically optimal phosphorus loads are considerably lower than would be expected from models that ignore climate variation. Even when climate variation is accounted for, the probability of shifting to the turbid state is surprisingly high.

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