Simple model of lake dynamics

This is an introductory conceptual model that introduces key concepts in the management of lakes subject to nutrient inputs from human activity.

This is an introductory conceptual model that introduces key concepts in the management of lakes subject to nutrient inputs from human activity.
The annual nutrient inputs into a lake depend mainly on the land management and point sources that are present in its catchment. 

The stock of nutrient in a lake depends on the stock at the beginning of each year plus any annual inputs from land management and point sources.
Nutrients can be lost from a lake through its outflow. Loss of nutrients in outflows is minor in Northland lakes, particularly given the lack of defined outflows.

This leakage represents a loss of nutrients from the lake.
Lets focus on the natural state of the lake.
Assume that the annual delivery of nutrient is 1 tonne and the annual outflow of nutrient is 1 tonne.
Also, assume that the natural level of nutrient in the lake is 10 tonnes. 
Any value of nutrient above 50 tonnes in the following examples represents a degraded state.
This run of the simple model shows that in its natural state, the stock of nutrients in the lake remains at a constant level as outflows are equal to inflows.
Even if nutrient inputs are slightly greater than outflows, then the rate of increase will typically be minor and the lake will remain in a pristine state.
On the other hand, if nutrient inputs increase, then the capacity of outflows to limit the build-up of the stock in the lake is greatly impaired.
Thus, the lake load will increase over time to a point such that a level of 50 tonnes, the level of nutrient that represents a degraded state, is reached near the end of the time horizon that is considered. 
Reducing the inflows of a degraded lake will generally not reverse its degraded state.
This is shown in this simulation, where annual inputs have been reduced to 1 but the lake begins the study period from a degraded state.
The majority of nutrients stored in a lake will generally remain there within each year, due to low losses through outflows.
So, effective restoration of a lake with high nutrient levels will usually require a reduction in the inflow of nutrients (the external load), alongside attention being paid to reducing the nutrients already there (the internal load).

View the model in Insight Maker