(383h) Predictive Control of Lake Levels and Estimation of Stream Flows for the Adaptive      Management Complex Natural Watersheds. Part 1. Estimation

This paper presents an overview of potential role of predictive control and estimation in the adaptive management of lake levels and river flows in a complex watershed. The study area comprises the Rainy River watershed straddling the Canada/United States border between Minnesota and Ontario. This 70,225 sq. km watershed is managed by the International Joint Commission as a component of the Lake of the Woods basin. The Rainy River basin includes wilderness areas and national parks on both sides of the borders, ultimately provides drinking water for 750,000 people, and is a source of electricity generation, recreation, and tourism. This watershed is a part of the Canadian Shield - a large landmass in North America that comprises 20% of the world’s fresh water.

Outflow from the two largest lake systems within the watershed, Rainy Lake and the Namakan Reservoir, are regulated by dams operated by commercial entities. Under terms of a treaty between the Canada and USA encompassing all transboundary waters, when feasible dam operators are required to manage lake levels to remain with 'rule curves' that establish desired upper and lower bounds on lake levels as a function of calendar date. From time to time the rule curves are reviewed and updated, the most recent changes occurring in 1970 and a 2000. Rule curves incorporate complex tradeoffs among stakeholders in the region with profound consequences for the region's ecological well-being. A review of the rule curves is currently underway for the purpose of proposing changes to take effect within the next few years.

This project was initiated following a series of high water events following the rule curve revision of 2000, including major flooding events in 2002 and 2014. The initial work used historical data for the period from 1948 to 2015 to establish that qualitative change in lake level control has occurred in recent decades.

The project now encompasses three main efforts:

• Development of a tracking filter to estimate net inflows to the major reservoirs in the watershed using available lake level gauges and limited stream flow measurements.

• Development of multivariable predictive control strategy for the integrated control of the two major dams in the watershed. Constraints on dam operation include management of emergency high water and low water events, hydrological conveyance constraints upstream of the dams, ecological and property considerations, and constraints on river bank erosion downstream of the dams.

• Development of a revised rule curve order for the adaptive management of the water levels and flows that is feasible, can accommodate more variable seasonal flows resulting from the effects of climate change, and that accommodate the biological requirements of key sentinel species representative of the regional ecology.

For the purpose of estimating the net inflow to Rainy Lake, a novel Kalman tracking filter has been developed that uses available level gauges and incomplete stream flow data to estimate inflows. The serendipitous occurrence of redundant lake measurements in the historical database provided a statistical model for the level measurement errors. The error model was used to tune the tracking filter to produce maximum likelihood estimates of inflows to Rainy Lake. The inflow estimates show a clear change in inflows between the periods 1970-2000 and 2000-2015

The statistical significance of this change was verified using an empirical stage­-frequency diagram for the flow on upper Rainy River. The K­S Kolmogorov–Smirnov) statistic verifies the statistical significance of this change. Local precipitation data for the same periods are not substantially different by the same statistic. This provides strong empirical evidence for the proposition that the change in seasonal flows caused by the 2000 rule curve change induced high water events on Rainy Lake due to the unique discharge characteristics of upper Rainy River.