F.3.2 Shift and Backwater Corrections
A shift is defined as an alteration in the s-d relation caused by a change in the stream control. The stage-discharge relation is not permanent at most stations but varies gradually or abruptly because of changes in the physical features of the control. If the change in the rating persists, this is an indication that a new rating curve should be prepared for this period of time. If the change is of short duration and is easily reversible (e.g., an obstacle hung up on the control), the original rating curve is still effective but, during this period, shifts or adjustments must be applied to the recorded stage before determining the corresponding discharge. Frequent discharge measurements must be made during any period to define the magnitude of the shift(s) when the condition is not correctable. For most gauging stations the stage-discharge curve represents the best-fit or average line and may not necessarily pass through all plotted points. That is, the stage-discharge relation is usually subject to minor random fluctuations.
Backwater is defined as a temporary rise in stage produced by an obstruction in the stream channel downstream of the gauge caused by ice, weeds, control structure, etc. The difference between the observed stage for a certain discharge and the stage as indicated by the stage-discharge relation for the same discharge is reported as the backwater at the station.
The computation of shift and backwater corrections is as follows, (adapted from the Manual of Hydrometric Data Computation and Publication Procedures, published by Environment Canada 1980):
(a) For many stations, a shift in the station control or a backwater condition may occur at certain times during the year as a result of weed effect, beaver action or ice conditions. During such periods, shift or backwater corrections are determined from available discharge measurements. These corrections are entered on Form AQU-05 and used subsequently to compute daily corrections, which are applied in the determination of the daily discharges.
(b) However, apart from these measurements which plot off the curve for reasons indicated above, most of the measurements will plot somewhat off the curve as a result of normal scatter. For these, no correction is computed; however, it is normally found useful for purposes of expressing mathematically the degree of scatter to indicate for each measurement the percentage difference between measured discharge and the discharge indicated by the stage-discharge relation. These percentage differences are entered in the "Diff." column on Form AQU-05. If desired, these differences may be expressed in cubic metres per second instead of percentage for discharges less than about 0.005 m³/s.
(c) A discharge measurement made during the computation period may plot substantially off the stage-discharge curve. It is recommended that discharge measurements be computed and plotted on site and redone if it plots off the curve. This can often determine if it is a bad measurement or if a shift has occurred. However, sometimes the second measurement can not be done, or sometimes it is done and the departure can not be explained. If, after careful analysis and review, no satisfactory cause of its departure from the stage-discharge curve can be determined, the measurement should be eliminated from use in the computation. In this instance, do not enter any figure in the "Shift" or "Diff." columns, but enter an explanatory note in the "Remarks" column on Form AQU-05, as well as on Station Analysis Form AQU-07. This should be a rare occurrence for good hydrometric stations and experienced technicians.
Several methods of distributing shifts may be used. Two of the more common methods are linear distribution by time and stage-shifting. These techniques will be briefly discussed here. A more comprehensive treatment of shifts may be found in Rantz et al. (1982), pages 354-360.
If the date on which the change occurred is not known, assume that the change occurred uniformly and distribute the correction in accordance with one of the two following methods:
Divide the change in the correction by the number of days to find the "change per day". For example: Suppose the correction was found to be +0.005 on March 20 and +0.009 on March 30. The number of days involved is 10 and the change in correction is 0.004. The change per day is 0.0004. The corrections to be applied are shown to the nearest thousandth of a metre.
When the change is small and the number of days is large, the preferable method is to divide the number of days by the change in correction. For example:
A correction of +0.003 is applicable on May 25, but on October 15 is 0.006, a period of 144 days.
Solution: Three 0.001 m increments are applied at intervals of 48 days as follows:
No change in correction will be applied during the first one-half interval of 24 days, i.e., the correction +0.003 will be continued from May 25 to June 17; an increase of 0.001 in the correction will be applied during each of the next two intervals of 48 days, i.e., a correction of +0.004 from June 18 to August 4 and +0.005 from August 5 to September 21.
The remaining 0.001 change will be applied during the remaining one-half interval, i.e., the final correction of +0.006 will be applied from September 22 to October 15.
Stage-shifting is normally done because of a temporary, or short-term condition at a gauging station. For example, perhaps a minor peak has occurred at a station, and discharge measurements indicate a significant change to the stage-discharge curve at higher stages. A short time later, a major flood drastically alters the stage-discharge relationship, requiring an entirely new stage-discharge curve. Instead of drawing two new curves with accompanying rating tables, the minor peak may be stage-shifted, and a new curve can be drawn for conditions following the major flood.