A metamodel for PCLake

The level of detail in PCLake is reflected in relatively long execution times. The objective of this study was to develop a metamodel for PCLake - a model of the model PCLake - that generates approximately the same results in a considerably shorter time. The operational question in this study was to describe the effects of eight environmental and management factors on the chlorophyll content of the lake, as simulated by PCLake, with help of a metamodel. The factors were the depth and area of the lake, the inflow rate of water, the concentrations of phosphorus and inorganic matter in the inflowing water, the ratio between nitrogen and phosphorus concentrations in the inflowing water, the fishing rate, and the area of marsh along the lake.

Three metamodelling techniques were applied:

1. regression tree
2. radial basis function network
3. interpolation

Comparison of the techniques showed that interpolation gave the most accurate estimation of output values simulated by PCLake. The correspondence between PCLake and the most accurate metamodel, applied to a random sample of 80,000 points in input space, was characterised by R2 = 0.965. The duration of one calculation by all metamodels ranged from 1 - 2 milliseconds, compared to 9 seconds for PCLake. In combination with the broad ranges of input variables that the metamodel was developed for, this implies that the metamodel may be used to substitute PCLake in scenario studies where predictions for future conditions are made. Apart from a comparison of modelling techniques, the report also contains practical instructions for the application of the techniques that were studied.