Projecting Ice-Affected Streamflow
by Extended Kalman Filtering
DAVID J. HOLTSCHLAG, CHARLES T. PARKER,
AND MOHINDER S. GREWAL
INTRODUCTION
The U.S. Army Corps of Engineers is responsible for mitigating flood damage and maintaining
navigable conditions in rivers throughout the U.S. Decisions affecting the day-to-day operation of
Corps dams are based on real-time streamflow data obtained by telemetry from streamflow-gaging
stations typically operated by the U.S. Geological Survey (USGS). Ice effects--variable blockage of
the channel by ice and increased flow resistance--reduce the accuracy of real-time streamflow data.
To improve the controllability of flow during ice-affected periods, CRREL supported this effort to
improve real-time estimates of ice-affected streamflow.
USGS operates a network of more than 7200 continuous-record streamflow-gaging stations
nationwide (Condes de la Torre 1994). Direct measurements of flow and stage (water-surface elevation
in the waterway) are routinely obtained about every 6 weeks. The average relationship between stage
and flow during open-water (no ice cover) conditions--the stagestreamflow rating--monotoni-
cally increases. The flow indicated by the rating for a particular stage is the apparent streamflow.
Deviations in the average relationship between stage and streamflow, which are interpreted from
individual direct measurements of them, are described by shifts in the rating. Together with hourly
or more frequent measurements of stage, the rating and its shifts are used to compute streamflow
records for annual publication, following a comprehensive analysis of streams in a network of
gaging stations.
During open-water conditions, uncertainty associated with shifts in the rating usually is small,
and doesn't much affect dam operations. Thus, real-time estimates of flow, traditionally deter-
mined directly from the rating and in some cases on the basis of a shift in the rating defined from the
most recent direct measurement, provide sufficient accuracy. However, during ice-affected periods,
the accuracy of real-time streamflow estimates is compromised by rapidly varying ice-backwater
conditions and large time-varying shifts. In these conditions, the ratio of the true to the apparent
streamflow, called the streamflow ratio, can vary from 1 during open-water conditions to a value
near 0. These shifts create enough uncertainty in traditional real-time flow estimates that dam oper-
ations can be hindered.
Previous work
Melcher and Walker (1992) evaluated and compared 17 methods for estimating ice-affected
streamflow that have traditionally been or could potentially be used in the nationwide streamflow-
gaging station network maintained by USGS. The methods were divided into two general cate-
gories, subjective and analytical, depending on whether or not judgment was necessary for method
application. They identified two subjective methods that were more accurate than other subjective
methods analyzed, and approximately as accurate as the best analytical method. Holtschlag (1996)
developed a dynamical-systems approach for computing ice-affected streamflow. This approach
ranked higher than the 11 analytical methods investigated by Melcher and Walker (1992) on the
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