Model of lake dynamics

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

This is an introductory model that presents key concepts in the management of lakes subject to nutrient inputs from human activity.
The annual nutrient inputs into a lake arise mainly from the farms, towns, and factories in its catchment. For example, these could come from fertiliser being washed into a lake or even the urine from livestock entering a lake.
The quantity of nutrients in a lake in any given year depends on the quantity there at the beginning of the year plus any annual inputs. The amount there at the start of the year is what has been added to the lake in previous years minus losses.
Some nutrients are lost from the lake system. Fencing a lake protects the capacity of lakes to cause some of the nitrogen to be lost as a gas. A key difficulty in lake management is that phosphorus is a key driver of algal blooms, but is not lost to the atmosphere. It is assumed here that such losses are 1 tonne a year.

Nutrients can be lost from a lake through outflows from any lake outlets, for example these leakages could be into the surrounding groundwater. Many Northland lakes do not have defined outlets, so only small amounts of nutrients leave these lakes in this way.
This leakage represents a loss of nutrients from the lake.

In this example, we look at a lake in a natural state that has nutrient inflows of 2 tonnes and annual losses, including leakage and losses to the atmosphere, of 2 tonnes. Assume that the stock (quantity) of nutrient in the lake is 10 tonnes at the start of the simulation.

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 losses 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 inflows are greater than losses, then the stock of nutrients in the lake will increase. In our example below, nutrient inputs are increased to 6 tonnes per year, but outflows are only 2 tonnes per year. In this case, the level of nutrients in the lake will reach 50 tonnes after 10 years. At this level of nutrient load, the condition of the lake will change to a poor (degraded) state.

Even if we reduce the nutrient inflows, this will probably not improve the condition of a degraded lake. This is shown in the simulation below, where annual inputs have been reduced to 1 tonne per year but the lake begins the study period from a degraded state. The majority of nutrients stored in a lake will generally remain there, due to low losses through outflows and to the atmosphere. 

So, effective restoration of a lake with high nutrient levels will usually require a reduction in the inflow of nutrients (the external load), and removal of some of the nutrients already present there (the internal load).

View the model in Insight Maker