FINAL REPORT - International Joint Commission

ANNEX 3
Candidate Regulation Plan Descriptions
Plan A +
Plan B +
Plan D +
Plan A + : Balanced Economics
Plan A + development took place in two phases. First, an optimization model was used to generate a family
of rule curves for determining the release based on the current Lake Ontario level. Applying these rule
curves alone produced some undesirable results, so the plan was modified by the addition of adjustments
and limits based on forecasts and other conditions in the system.
Phase I: Optimization
The optimization model minimized expected deviations from target levels for Lake Ontario, Lac St. Louis,
Montreal Harbor, and Sorel, and from target flows for the release. All of these targets varied through the
year and were derived from relevant performance indicators or other similar sources. A graph of each set
of targets appears at the end of this document.
The optimization minimized the likely deviation from these desired targets given uncertain future inflows.
The model used a probabilistic approach to account for the uncertainty of these future inflows. Historical
Lake Ontario inflows (net total supply (NTS) from 1900 to 2000) were divided evenly into five categories
(very dry to very wet), according to total annual inflows. It is assumed that those inflows would be closely
correlated with annual precipitation, hence a good indication of wet/dry years.
For each flow range, a representative year was chosen: the year in which total inflows were the closest to
the average total annual inflows for that category. All the inflows and ice factors that are associated with
this flow range then come from the chosen representative year: very dry – 1933, dry – 1937, moderate –
1903, wet – 1954, very wet – 1993.
A transition matrix was built to define the probability of being in any particular flow category (e.g., wet,
very wet, etc.) for the upcoming year, given the flow category over the previous year. These transition
probabilities were determined using the 101 years of historical inflow data and are shown in Table B-2 below.
Table B-2: Transition matrix of probability of occurrence of specific weather conditions
These probabilities represent the probabilities of occurrence of a specific weather condition (very dry,
dry, moderate, etc.) for one year following a year characterized by the same or another specific weather
condition. For instance, if 2004 was a very wet year, there is a high probability (63% chance) that 2005
will turn out to be very wet as well, but only a 21% chance that 2005 will turn out to be a moderate year.
178 Options for Managing Lake Ontario and St. Lawrence River Water Levels and Flows