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Taken from the report "Options for Managing Lake Ontario and St. Lawrence River Water Levels and Flows" prepared by the International Lake Ontario-St. Lawrence River Study Board, March 2006.
When Plan 1958-D was designed and tested, its authors measured its performance using the water supplies that had been experienced from 1860 to 1954. Almost as soon as it went into effect, it became apparent that it would not perform well because the test had been too limited. Had Plan 1958-D been strictly adhered to during the drought of the early 1960s and the wet periods since, Lake Ontario levels would have been lower and higher than they would have been without regulation, and in the late 1980s, they would have destroyed many houses along the shoreline.
The Study Board asked for a stochastically generated hydrologic test series to avoid these problems. This large sample of possible future hydrologic conditions also proved necessary to properly estimate the time value of erosive losses. "Stochastically" generated here means that a computer model was developed to produce a 50,000-year sequence of supplies to each of the Great Lakes, the Ottawa River and other downstream tributary flows, based on the statistical characteristics of the twentieth century supplies. The stochastic hydrology model included the important probabilistic relationships between the supplies from one year to the next, their seasonal patterns and their quarter-month to quarter-month correlations. The stochastic model also preserved other important statistical properties of the system, such as the varying length of drought periods and high supply periods, and the cross-correlation of supplies among basins (i.e. the probability that wet or dry conditions would occur in the various drainage basins at the same time). Each of these characteristics of the hydrology has a natural random component. This randomness is also captured in the stochastic model so that the 50,000-year generated sample contains a distribution of possible hydrology composed of mostly typical supplies with the appropriate number of rare and extremely rare events needed to fully test the regulation plans. A more detailed description of the stochastic modeling can be found in the report "Special Characteristics of the Multivariate Model Developed For Generating Synthetic NBS and Flows for the Great Lakes – St. Lawrence River Basin". A full description of the stochastic modeling is presented in the report "Stochastic Modeling and Simulation of the Great Lakes–St. Lawrence River System" (Fagherazzi et al, 2005). Both reports are technical documents and are available in English only.
Once generated using the stochastic model, the 50,000-year series of supplies to each of the Great Lakes was then entered into the Coordinated Great Lakes Regulation and Routing Model (CCGLBHHD, 2004) to produce a series of Lake Erie outflows, which, combined with the supplies to the local Lake Ontario basin, make up the total supplies to the Lake Ontario basin.
The full stochastic evaluation of plans is best for comparing average annual benefits and for estimating the expected timing of coastal erosion damages. Our analyses showed that coastal erosion and damage to shore protection structures is inevitable (i.e., it happens under all regulation plans), so the only difference between plans is how fast the damage happens, and that is a function of both the plan and the future sequencing of wet and dry supplies. Since that sequence is unknown ahead of time, the Board calculated damages for 495 supply sequences, each 101 years long, then determined the average erosion likely in the first year of plan implementation by averaging the erosion caused in the first year of each of 495 trials, and so on for the second, third and each year beyond. Had the Board attempted the same simulation using only the historical supplies, it would have been a good estimator of the future only if the supplies of 1900 were similar to the supplies in 2007, 1901 the same as 2008, and so on. The odds of this happening are next to zero. The panel of economic experts approved this approach. This is the first time erosion damage around a lake has been calculated using this rigorous, correct method.
