In 1979, a study was conducted n England on the Bedford Ouse River using a Monte-Carlo simulation. At the time there were poorly defined nature of water resource systems coupled with poor sampling and measurement errors regarding water quality. Researchers wished to establish a statistical methodology that would be able to assess and forecast water quality of the river. By establishing a proper statistical based procedure to assess for the uncertainty regarding water resource systems. This would allow an analyst to reasonably asses their own uncertainty regarding their forecasts, and allow them to keep that in mind when making a forecast. This is similar to assessing a margin of error. To flush out the answer to this question the researchers used a Monte-Carlo simulation.
A Monte-Carlo simulation boils down to four basic elements:
1) Identifying the mathematical model of the activity you want to explore
2) Define parameters for each factor in your model
3) Create random data for those parameters
4) Simulate and analyze the output of your process
The researchers defined the mathematical model they wished to use as a black box model was chosen. This was due to its being the best model to adhere to both the model structure that is determined by the field data collection, or water samples. This model reflects a single input single output, or a stochastic difference equation to help account for a time series of events.
The researchers created parameters of both water quality and multi-reach flow and quality model. With established parameters for oxygen absorption volumetric flow rate in the stream, volumetric holdup in the reach, input from the precessing stream, saturation and concentration, turbulence, and sunlight dependent (for algae growth). All of these parameters were controlled for time series event to measure their effect on the overall water resource system over the course of the experiment.
The model was populated using upstream readings to be used as downstream forecasts. The deviation of this sample would be generate from the Monte-Carlo simulation but the forecasting data would be projected through the multiple iterations of the data within the parameters.
The Monte-Carlo simulation was able to predict the amount of dissolved oxygen within the water within .3% of expectations within the model. However the results were determined with some degree of uncertainty.