State-Space Model for River Ice Forecasting

摘要

Each winter ice forms on rivers streams, and navigable waterways, causing many problems through its effects on the operation of hydraulic control structures, locks and dams, hydropower plants, and water intakes. Ice covers increase river stages by presenting an additional rough boundary, which increases the channel wetted perimeter, reduces the channel hydraulic radius, and typically increases overall effective channel roughness. The increase in stage can result in flooding, especially during severe ice conditions or in low- lying areas. This situation is particularly critical downstream of hydroelectric power plants because the risk of ice-induced flooding may require operators of such plants to curtail power production and provide more expensive replacement power. This study presents a state space model for forecasting ice conditions and the resulting stages in rivers. The model incorporates a hydraulic component, a thermal and ice transport component, and an ice-cover progression component. The Kalman filter procedure is used to update the model with observed stages and observed positions of the upstream leading edge of the ice cover. The model thereby arrives at an efficient and optimal estimate of the river ice and hydraulic conditions. The state space model can also recursively estimate the effective channel roughness using the augmented Kalman filter procedure to account for changes in the channel roughness produced by the river ice cover and other effects. By way of an example the state space model is applied to the Missouri River downstream of Oahe Dam, located in Pierre, South Dakota, USA. Outflow from the dam, which is used for peaking power production, can vary between 0 and 55,000 cfs in a matter of minutes to meet the demands of the electric power grid it supplies. The system noise covariance of the model was adjusted to produce the optimal results based on least-squares criteria.