Sources of Uncertainty in Canadian Low Flow Hydrometric Data

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Sources of Uncertainty in Canadian Low Flow Hydrometric Data Stuart Hamilton

Abstract: The uncertainty of estimated daily mean discharge is 5% at the 95% confidence interval (Herschy, 1999a). The use of this unique value requires acceptance of the assumption of uniformity of uncertainty within the hydrometric dataset. It is the implicit responsibility of each researcher to challenge this assumption with respect to any given hypothesis test. This paper evaluates this assumption of uniformity for a subset of the hydrometric dataset—low flow in Canada. Studies of low flow phenomena are becoming more prevalent with increasing recognition of the importance of low flows for viable ecosystems and sustainable economies and as a sentinel of change. Environmental and operational circumstances are identified that elevate the opportunity for error with respect to measurement of low flows. These factors are examined qualitatively and are found to exist throughout all steps of the data production process. The uncertainty of low flows in Canada is very likely different from the uncertainty of the global hydrometric dataset. The magnitude of low flow uncertainty remains undefined because no field experiments were conducted as part of this study. It is hoped that these findings will inspire the design of future research needed to overcome this deficiency. Résumé : L’incertitude liée au débit moyen quotidien estimatif est de 5 %, avec un intervalle de confiance à 95 % (Herschy, 1999a). Le recours à cette valeur unique implique l’acceptation du postulat d’uniformité de l’incertitude dans l’ensemble de données hydrométriques. Chaque chercheur a la responsabilité implicite de remettre en question ce postulat dans le contexte d’une vérification d’hypothèse. La présente communication évalue ce postulat d’uniformité pour un sous-ensemble de l’ensemble de données hydrométriques—basses eaux au Canada. Les études portant sur les phénomènes d’étiage (basses eaux) sont de plus en plus répandues étant donné la reconnaissance croissante de l’importance des basses eaux pour la viabilité des écosystèmes et la durabilité des économies, et aussi comme sentinelle du changement. Sont cernées les circonstances environnementales et opérationnelles qui élèvent les possibilités d’erreur relativement à la mesure des basses eaux. Ces facteurs sont examinés qualitativement et, selon les constatations, ils existent à tous les stades du processus de production de données. L’incertitude liée à l’étiage au Canada est fort probablement différente de l’incertitude liée à l’ensemble des données hydrométriques globales. L’ampleur de l’incertitude liée à l’étiage n’a toujours pas été définie car aucune expérience sur le terrain n’a été menée en tant que volet de l’étude. Ces résultats, espère-t-on, serviront d’inspiration pour l’élaboration d’une méthodologie de recherche future permettant de surmonter cette lacune. Stuart Hamilton1 1

Water Survey of Canada, Vancouver, BC V6C 3S5

Submitted January 2008; accepted February 2008. Written comments on this paper will be accepted until December 2008. Canadian Water Resources Journal Revue canadienne des ressources hydriques

Vol. 33(2): 125–136 (2008)

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Introduction Hydrometric data are one of the most consistent,reliable, inter-comparable, geographically comprehensive and spatially-integrative environmental datasets that span the last century. These features make hydrometric data attractive for disentangling and understanding natural dynamics and anthropogenic forces at work in the environment. This new use for hydrometric data, much of which have been collected for other very specific, pragmatic reasons, is welcome but may require a re-examination of the issue of hydrometric data uncertainty. Data analysts unfamiliar with hydrometric methods adopt a confidence in the data based on guidance such as ISO 8363 (1997), a source which implies uniformity in uncertainty within the global hydrometric dataset, and is based on the acceptance of assumptions known to be valid only under optimal measurement conditions. Sub-optimal conditions for hydrometric data collection can be encountered at the extremes of the measured range. Given the increasing recognition of the importance of low flows as a sentinel of change and as an index of ecosystem health it may be worthwhile to ask the question: Is the assumption of uniformity in hydrometric uncertainty valid for low flow conditions? This paper reviews the principle sources of uncertainty in hydrometric data with emphasis on low flows. A better understanding of the factors contributing to uncertainty is needed to discover, or adapt, theories, principles, methods, technologies and techniques of hydrometry to ensure that confidence in the data can be justified without site-specific knowledge. In addition to the use of the term low flow, small flow is used to describe the sub-set of low flows that are in, or perhaps below, the lowest range of applicability of conventional gauging equipment.

The Certainty of Hydrometric Uncertainty Uncertainty can be described as an envelope within which the true value of an observation may actually lie. Uncertainty is usually expressed as a range spanning 2 σ (95%) bounding the measurand when normality of the uncertainty distribution is assumed and is calculated as

U = (B 2 + P 2)1/2

(1)

where U is uncertainty, B is bias, P is precision and σ is the standard deviation of the random variable (ISO, 1995). Uncertainty can be measured in controlled conditions where the true value of the variable of interest is known. Standard operating procedures have been developed based on these studies to minimize the uncertainty of measurements made in the field. Uncertainty exists because of inexactness (i.e., low sensitivity) of equipment, observational errors (procedural or environmental in origin), or unrepresentative sampling (e.g., mis-location in time or space; inappropriate duration or extent; or insufficient sample size). Measures of uncertainty are useful because they allow an evaluation of whether variance in the data is due to variance in the variable being measured or due to variance in the measure. Uncertainty in the magnitude of the uncertainty prevails when field conditions deviate from the controlled conditions in which theoretical uncertainty was determined. The relative complexity of the process for production of a discharge time-series makes it very difficult, if not impossible, to explicitly characterize the uncertainty of discharge data unless it can be confirmed that field conditions are similar to the conditions used for controlled studies of uncertainty. Standard hydrometric measurements can be unbiased and precise under controlled conditions for singular determinations of discharge. Pelletier’s (1988) review of measurement uncertainty emphasizes that these studies do not adequately cover the stream or river types found in Canada. Pelletier specifically lists droughts, very low runoff and winter ice as conditions outside of the scope of existing measurement uncertainty studies. Standard operating procedures are used to control the potential for error in hydrometric data production. These operating standards may need to be relaxed to accommodate environmental constraints or limitations in technology, techniques or methods of measurement. Small flows, which are near the lower limit of validity for conventional hydrometric equipment, can serve as an example of how the need to relax standards for operational reasons can influence uncertainty. While the uncertainty of small flows cannot be explicitly quantified, it is possible to qualitatively examine some operational factors that can have a deleterious effect on uncertainty. A qualitative assessment of uncertainty is less than ideal from an engineering perspective but can © 2008 Canadian Water Resources Association

Hamilton

help ground analytical judgment and inform decisions pertaining to future needs for data investment.

Factors Related to Hydrological Processes An understanding of the hydrology of low flow is a prerequisite to an understanding of the uncertainties in low flow hydrometry. A more complete treatment of the hydrology of Canadian low flows can be found in Burn et al. (this issue) but selected phenomena are discussed to illustrate the connection between low flow hydrometry and hydrology.

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Occasionally, an understanding of biological processes can improve the explanation of low flow phenomena. The emergence of aquatic vegetation or the activity of beavers can result in flow regulation. In general, organic flow regulation conserves water in lake, wetland or channel storage, with a subsequent positive effect on water levels—thereby maximizing critical aquatic habitat as a biological adaptive strategy. Every effort is made to locate hydrometric stations away from such sources of variability because of the disruptive effect backwater has on hydrometric data quality. Winter Hydrology

Part of the value of hydrometric data is that hydrometric data are an integrative measure of everything that is happening upstream in the watershed. However, during episodes of low flow, hyporheic exchange flow (Anderson et al., 2005) may result in flow discontinuity along the length of a stream. In these conditions, surface discharge data may not represent the atmospheric and storage depletion processes controlling runoff at the scale of the watershed. There is no requirement for locating a hydrometric station to ensure that no significant hyporheic flow bypasses the gauge during low flow at that location. As a result, a station may provide data representative of low flow runoff or only provide data specific to the cross-section at the gauge. This, in itself, is not necessarily a critical short-coming of the gauging strategy but the fact that we don’t know which stations are affected by such conditions is of greater concern. Stream gauging for low flow could include procedures for longitudinal validation along the length of a stream to detect and document hyporheic exchange flow variations relative to the gauge location. As there is currently little demand for enhancing the value of the data in this way, it is up to each end user to carefully consider the implications this source of uncertainty could have on their decision-making.

Winter streamflow is generally dominated by depletion processes of groundwater, lake and wetland storage complexes and is additionally influenced by river ice and its effects on channel storage processes. Winter is a dominant force in the Canadian landscape and low flows often occur during the winter months (Burn et al., this issue). Understanding of the patterns and processes of winter hydrology is limited by the ability to obtain consistent and reliable winter discharge data. However, there are a number of examples of winter hydrological processes non-compliant with the assumption of monotonically declining storage release during the winter season. These include stage-up discharge depression (Hamilton, 2004; Moore et al., 2002), stream-aquifer interaction (Hamilton, 2004) lake outlet polynia effects (Hamilton, 2004), evolution of ice roughness effects (Hamilton, 2004), and river-ice hyporheic-exchange interaction (Hamilton and Saso, 2007). There is insufficient understanding of the controlling forces in winter streamflow on which to base an evaluation of the adequacy of winter data for determining what discharge is probable at any given time at any given station. For example, in one study the error in estimates of winter flow has been shown to be greatest during the early winter period (Hamilton et al., 2000), which is when Beltaos et al. (1993) suggest the annual low flow may occur in some rivers.

Hydroecology

Factors Related to the Monitoring of Stage

Low flows are generally controlled by storage depletion processes from groundwater and surface storage. In most cases, these processes are geophysical in nature.

Water levels at a gauging station are measured from a benchmark with a known reference elevation and datum and related to mechanical (e.g., float actuated

Hyporheic Exchange Flow

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chart recorders) or electronic (e.g., pressure transducers with dataloggers) recording devices by concurrent observations. Many Canadian hydrometric stations are necessarily located in cold regions on clay-silt soils. In this environment it can be very difficult to maintain a constant reference elevation. Frost action is inherently seasonal in nature, but the action of frost on any given benchmark can also be progressive. To mitigate this, several benchmarks are tied together in level circuits and the most stable of these is selected for use as the ‘control’ benchmark. At some northern Canadian stations the magnitude of relative change in benchmark elevations can exceed several centimetres between successive station visits. There is no guarantee that the ‘control’ is actually stable introducing a source of uncertainty into the water level data. An error less than a few centimetres may have little relative effect on the estimation of discharge at high stage but at low flow the same magnitude of error can introduce substantial uncertainty. The accuracy of equipment used for recording variations in stage is usually expressed as a percentage of full scale of the sensor (Freeman et al., 2004). The scale of the measurement is therefore irrespective of the scale of the measurand, hence the relative error of a measurement increases as the measurand approaches zero. The error band of any given sensor, relative to the depth of water, can be a substantial source of uncertainty during low flow conditions. Elevated uncertainty in low flow data can result from conditions more favourable for biofilm production, which can foul submerged equipment. There is also an increased risk of data loss due to stranding of intakes or bubbler orifices. Discharge estimated when stage data are not available is flagged with an ‘E’. The actual uncertainty of flagged data is incalculable. The occurrence of ‘E’s in low flow statistics is about 50% more frequent than the general occurrence of ‘E’s in the daily mean data, reflecting these higher risk factors for data loss.

Factors Related to the Measurement of Discharge Expert judgment is required to select the best possible discharge measurement method for any given circumstance. There are relative advantages of each method with respect to local conditions and the correct

choice is the one which minimizes uncertainty.However, operational considerations (such as availability of the necessary equipment and/or training) usually prevail in making this choice. In Canada, such operational considerations within the Water Survey of Canada usually result in the use of the area-velocity method using Price model 622 (Frazier, 1967) current meters. The potential uncertainties of alternate methods are also discussed for comparison and contrast with the area velocity method. Volumetric Methods

An accurate estimate of discharge can be obtained at small flow by diverting the flow into a reservoir of known volume and recording the time to fill the reservoir. This method is most accurate for very small flows with free-fall, such as at the outfall of a culvert. Sources of uncertainty include the calibration of the reservoir, operator reaction time to start the measurement exactly when the reservoir starts to fill and stop when it is full, and losses to spillage or by-pass. This technique is generally considered to be unbiased but imprecise; so many replicate samples will reduce uncertainty. Volumetric measurements become more reliable as the streamflow approaches zero. The method is dependent on gravity-driven diversion of flow requiring a vertical difference in the stream greater than the height of the calibrated reservoir. For this reason, the technique, though interesting, is useful mainly for small, constrained flows in steep gradient streams. Tracer Methods

Tracer methods are primarily recommended for small, turbulent streams under open-water conditions where the assumption of complete mixing can be assessed. Discharge measurements using tracers require the injection of a known mass (or concentration) of a tracer into the stream, either as a slug or at a constant rate, and then measuring the dilution of that tracer at a location downstream of the mixing zone (Kilpatrick and Cobb, 1985). Any tracer that is conservative, water soluble, easily detectable, and environmentally benign can be used. Salts and flourometric dyes are tracers that generally satisfy these criteria. © 2008 Canadian Water Resources Association

Hamilton

Three issues are known to be problematic in the use of tracer methods during low flows. First, the requirement that the tracer must be conservative means that salt should not be used for under-ice conditions because of the potential for interaction between the salt and the ice. Second, the requirement for complete mixing can be particularly problematic during low flow. At low velocities the stream may lack sufficient turbulence to achieve complete mixing over a time- or distance-scale that is operationally feasible. Third, during low flow conditions there is a relative increase in channel storage elements that are occupied by water that is not contributing to flow as compared to median- or high-flow conditions. The tracer from a slug injection can be partially captured in these storage elements and diffuse back into active flow at a very slow rate thereby increasing analytical uncertainty in integrating the tracer wave. Though this latter problem can be circumvented by the use of a constant-rate injection technique, the logistics of applying this technique require circumstances that are more favourable than are generally realized in an operational setting. Rated Structure Methods

Rated structures such as weirs and flumes are best suited for small streams in hydrological regimes with low range of discharge and mild winters. In Canada, three and even four orders of magnitude in seasonal discharge variability are common and it takes a very robust structure to provide both good low flow data and survive peak flows. Winter ice jams can frequently destroy gauging structures (Rahn and Giddings, 1967, referred to in Church and Kellerhals, 1970) and frost action in cold climates frequently results in bypass flow and leaks. The reliability of data from rated structures is a function of the frequency of inspection, cleaning and upkeep, while the remoteness of many Canadian stations makes high frequency inspections and maintenance impractical and prohibitively expensive. Construction of in-stream structures that could impede fish passage requires a potentially expensive permitting process. There are relatively few rated gauging structures in the Canadian hydrometric network as a result of these factors. Low flow uncertainty is primarily a function of structural design as well as the maintenance and integrity

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of the designed structure. The risk of contamination of the weir crest by ice, debris, or organic material is greatest on the falling limb of the hydrograph or during low flow when there is insufficient volume to provide a flushing action. Any leakage or seepage by-pass can introduce a relatively larger percentage error into low flow data. Rated structures that do exist in Canada usually must be field calibrated using conventional measurements; hence these structures are subject to the uncertainty of conventional measurements. Zero Flow Methods

Confirmation of zero flow may be a simple ‘windshield’ survey from the seat of a truck or a rigorous search for any sign of flowing water. If tranquil water is continuous along the thalweg with no detectable velocity (i.e., approaching, or less than, the response speed of the meter) an arbitrary nominal velocity may be assigned to calculate non-zero flow. The discrimination between zero flow and negligible flow is based on personal judgment. Uncertainty in the duration of low flows can result from monitoring methods that are insufficiently sensitive to accurately capture the timing of the start and end of zero flow episodes. Winter Discharge Estimation Methods

Thirty-five percent of all low flow statistics in Canada are flagged with a ‘B’, indicating ice conditions (Environment Canada, 2007). This flag means that discharge was estimated, without the benefit of a valid stage-discharge relation, using one of many discharge estimation methods. Melcher and Walker (1991) evaluated 17 different methods for estimating winter streamflow in a controlled study on three rivers in Iowa during one winter and documented a wide range of discharge estimates. Of the resultant 51 trials, 20 were statistically different from the baseline data and none of the methods were consistently able to keep the daily discharge error under 100%. In general, winter streamflow estimation methods attempt to use some independent variable(s) to temporally distribute discharge between infrequent field measurements of discharge. Rather than address each method individually, a more efficient strategy is to examine the relative merits of the most commonly © 2008 Canadian Water Resources Association

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used predictor variables. The predictors used in the methods described by Melcher and Walker (1991) are given in Table 1, along with an assessment [positive (+), negative (–), or unknown (?)] of the validity of one or more underlying assumptions based on field studies. There are few reports examining the validity of the underlying assumptions of these predictors with respect to the conditions identified by Pelletier (1990) (e.g., reduction and/or blockage of the cross-section due to ice growth and/or frazil ice; changes in roughness of ice from thermal processes; ice break-up, jams, and releases as determined by ice flow channel characteristics). There is also insufficient operational experience with emerging winter streamflow estimation methods (e.g., Chokmani et al., 2008; Hicks and Healy, 2003; Holtschlag and Grewal, 1998) to evaluate the effect these methods may have on winter streamflow uncertainty.

While the actual uncertainty of any of the methods for estimating winter streamflow is not known, the minimum attainable uncertainty is bounded by the uncertainty of the discharge measurements on which the methods all depend. In addition to all of the sources of uncertainty of open water field work, Pelletier (1990) lists several that are specific to winter streamflow measurements (Table 2). The severity of the effect of these sources of uncertainty generally varies as a function of the relative area of ice to flowing water, which is generally greatest in small flows in cold climates. The environmental and procedural sources of uncertainty identified by Pelletier vary from stream to stream, from winter to winter, and from measurement to measurement, thereby challenging the ability to make broad generalizations about the uncertainty of winter streamflow.

Table 1. Predictor variables in use for winter streamflow estimation. Predictor

Assumption

Validity

References Relevant to Validity of Assumption

Water Level

Stage is highly correlated with discharge and the slope of the relation is always positive Stage data are reliable

-

Hamilton, 2004

-

Hamilton, 2003

Air Temperature

Air temperature is highly correlated with discharge

+ -

Chin, 1966 Hamilton and Moore, 1996

Precipitation

Precipitation is highly correlated with discharge

?

Time

Discharge variability is monotonic

-

Hamilton and Moore, 1996; Melcher and Walker, 1991; Chin, 1966

Discharge Comparison

Response characteristics are independent of local conditions

-

Hamilton, 2004

Fall

Stage is highly correlated with cross-sectional area available for flow

?

Index Velocity

Stage is highly correlated with cross-sectional area available for flow

?

Specific Conductance

Dilution of solutes is highly correlated with streamflow

-

Hamilton and Moore, 1996

© 2008 Canadian Water Resources Association

Hamilton

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Table 2. Sources of uncertainty in winter streamflow measurements. Additional Sources of Uncertainty Specific to Winter Conditions (from

Component of Standard Uncertainty Affected

Pelletier, 1990)

(from Equation 2)

Presence of ice in the river, either covering the surface, attached to the bottom or banks in the form of anchor ice, or floating throughout the cross-section as frazil ice

Sm Sbi Sdi Sei Spi

Inability of the cup type meter to accurately measure low velocities (less than 0.3 m/s) as is often encountered during the ice period

Sci

Freezing of the meter while the technician is passing it from one measuring point to another, or making necessary repairs

Sci

Accumulation of frazil ice in the cups of the current meter, resulting in under-estimation of the mean velocity

Sci

Inability of the hydrometric technician to detect under surface eddies or other conditions that disturb the distribution of flow, and the tendency to measure velocity at too few points

Sm Spi

Impossibility of measuring the effective cross-section as accurately under ice cover as in open water, especially when frazil ice is present

Sbi Sdi

Hurry in the work, due to physical discomfort of the technician making the discharge measurement

Sm Sbi Sdi Sei Spi

Possibility of the stream having a different velocity profile that (sic) the standard assumed for winter measurements

Spi

Presence of thin or moving ice or overflow, making the physical access to the flow cross-section unsafe or simply impractical

Sm Sbi Sdi Sei Spi

Area-Velocity Method

Herschy (1999a) provides an equation for the estimation of uncertainty in a single measurement of discharge uc(q) =

[

〈(b d v ) (s + s + s + s s +Σ (Σb d v ) 2 m

i i i

2

2 bi

2 di

i i i

2 ei

2 pi

+ sci2

)〉

]

1/2

(2)

where uc(q) is the combined standard uncertainty in discharge (%), sm the standard uncertainty in the number of verticals used, sbi the standard uncertainty in width

measurement (%), sdi the standard uncertainty in depth measurement (%), sei the standard uncertainty due to pulsations in flow (%), spi the standard uncertainty due to the restricted number of points taken in the vertical (%), sci the standard uncertainty in current meter rating (%), bi, di and vi are the width, depth and velocity of vertical i and m the number of verticals. Small flows create sub-optimal measurement conditions.Terzi (1981) recommends minimum criteria for measurements made using conventional metering equipment such as: 20 verticals; 0.15 m spacing; 0.15 m depth; and 0.045 m/s velocity. Therefore any conventional measurement made with a Price current meter that is less than 0.02 m3/s must be non-compliant © 2008 Canadian Water Resources Association

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with one or more of these recommendations (i.e., 20 × 0.15 × 0.15 × 0.045). The fact that 20% (18,638 out of 90,416) of annual minimum daily discharge data published by the Water Survey of Canada in 2007 (Environment Canada, 2007) are less than 0.02 m3/s illustrates the extent to which such small flows contribute to our knowledge of low flows. In order to follow the recommendation that verticals should not be spaced closer than 0.15 m when using the Price No. 622 meter (Terzi, 1981) the stream must have sufficient depth to correctly position the meter over a width of 3 m, or more, in order to achieve the recommended minimum number of 20 verticals. In a sample of 1730 WSC measurements, 92 had a total width of less than 3 m. This necessitated a decrease in the number of verticals to an average of 11.3 with an average of 20.7% of total flow captured in the largest vertical. Herschy (1999b) suggests a doubling of uncertainty to 10% for a measurement with ten verticals. Measurements of width are generally considered to be more accurate during low- and small flow conditions as compared to median- or high-flow conditions. Tapes calibrated to the millimetre are often used for small flow width measurements compared to the markings on cableways and taglines (used for bridge measurements) which are usually marked to the nearest metre. Measurements of depth have a scale of observation that is independent of scale of measurement resulting in greater relative imprecision at shallow depths. Wading rods used for small flow depth measurements are marked in two centimetre intervals and increments of one centimetre are easily interpolated. At a depth of 1.0 m the sensitivity of the measurement is therefore one in 100, whereas at 0.2 m depth the sensitivity of the measurement is one in 20, or a five-fold relative difference. Standard protocols specify a measurement resolution of three significant figures (1 in 1000); hence the attainable resolution of small flow depth measurements can be substantially less than the reported resolution of the measurement. Dickinson (1967) provides a review of flow pulsations that does not indicate any particular concerns with respect to flow pulsations during low flow. Dickinson does not specifically address pulse duration as a function of velocity but does note studies showing that pulse duration increases both as a function of nearness to bed and as a function of bed roughness. Elevated uncertainty at low flow would result if the

duration of flow pulsations in shallow depths exceeds the duration of the velocity measurement as a result of these factors. Standard procedures for velocity measurement are independent of considerations of flow depth or bed roughness. The number of points in the vertical is limited to one in most small flow measurements and Herschy (1999b) gives an uncertainty of 15% for measurements with a single point in the vertical. Uncertainty is likely higher than this estimate at small flows because of positioning error in the vertical. In very shallow water it is often not possible to position the meter at the recommended 0.6 of the depth with the meter buckets fully submerged and without interference from streambed roughness. Current meter rating uncertainties are not linear with velocity. Current meters have increased bias at low velocities. For example, Whalley et al. (2001) found that meter performance at lower velocities varies as a function of meter maintenance. Current meters also have decreased precision at low velocities. Whalley notes that at very low velocities there appears to be a greater range in meter performance with a range of positive and negative deviations. Current meters are routinely rated in a tow tank where an empirically determined linear equation is established. In a sample of 30 WSC rating equations the average offset in this equation (i.e., the minimum response speed) was 0.005 m/s with a range from 0 to 0.01 m/s. The implication being that the average meter would measure 0.005 m/s of velocity at zero revolutions per second of the bucket wheel. The minimum response speed of a meter is likely a factor in judgments of the discrimination between zero flow and negligible flow. Methods Using Emerging Technologies

Acoustic Velocity Meters (AVM) and Acoustic Doppler Current Profilers (ADCP) represent examples of technologies that are rapidly evolving. The relative uncertainty of low flow measurements will not be known until the technological advances stabilize and more experience is gained in the full range of field conditions. As with conventional technology, this equipment is likely used outside of the range of the assumptions implicit in the standard operating procedures. New sources of uncertainty include factors such as the ratio of blanking distance to depth of flow— © 2008 Canadian Water Resources Association

Hamilton

a factor that reaches a maximum at the shallowest depths and hence lowest flows. Methods of uncertainty estimation dependent on development of standard operating procedures will always lag behind the adoption of emerging technologies. The sources of uncertainty are initially unknown when applying new technologies in an operational setting and can, potentially, be quite different from the uncertainties measured in controlled studies.

Factors Related to the Use of a StageDischarge Relation The stage-discharge relation is the keystone of conventional hydrometric data production and also contributes to hydrometric uncertainty. Uncertainty can arise from use of a stage-discharge relation in violation of one or more of the assumptions of: stable control feature; steady, uniform flow and no complicating sources of local stage variability (e.g., weeds, bed movement, debris entrapment, ice). The latter assumption, especially, is more likely to be false under low flow conditions. A well-conceived stage-discharge relation will integrate the information from a number of independent measurements to average out imprecision and accurately identify the most probable value of the ‘true’ discharge at any given stage. However, a stage discharge relation can be compromised by errors in influential observations (i.e., measurements in poorly sampled regions of the curve) resulting in the estimation of discharge data that have little similarity with reality. The uncertainty of an empirically determined stage discharge relation is greatest in the zones of extrapolation at both extremes, and certainly at the low end. In the absence of a strong physical constraint on the shape of the curve, the uncertainty in the lowest discharge measurement will likely be exaggerated by extrapolation from this lowest discharge value to the lowest gauged stage. The most common method for determining stagedischarge relations in Canada is empirical. There are two categories of techniques for the empirical method of determining stage-discharge relations—subjective and analytical. Most objective functions in use with contemporary analytical techniques are dependent on the assumption of uniformity of error in the

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discharge measurements. Techniques that account for heteroscedasticity (Petersen-Overleir, 2004) have not yet been widely adopted. One might reasonably infer from the previous discussion on factors related to the measurement of discharge in the previous section that the assumption of homoscedasticity is not valid for fitting the low end of rating curves, resulting in adoption of an invalid model. The ease and convenience of simplistic methods of segmenting curves can result in over- or under-fitting, which tends to enhance uncertainty at the low end of the curve in one of the zones of extrapolation. Techniques for objective segmentation of compound rating curves (PetersenOverleir and Reitan, 2005) have only recently been developed but may provide some benefit in the future. Given the many sources of uncertainty with respect to analytical techniques for curve fitting, it may be fortunate that most curves used by the Water Survey of Canada are still determined by subjective techniques. Subjective curve fitting has one substantial advantage in that the uncertainty of the discharge measurements is not assumed to be constant. Field technologists have the local-scale knowledge to judge which measurements should be trusted with the highest confidence and they use this judgment in fitting a smooth line amongst the scatter of points. Scrutiny of many historic curves shows that skilled hydrographers are capable of drawing curves, often based on relatively few measurements, which stand the test of time very well. There are also many examples showing that, over a period of time, many different curves are fit to the data as measurements accrue, when a posteriori analysis would indicate that a single curve would have sufficed for the entire period of time. Subjectively drawn curves have unquantifiable uncertainty because differences in individual skill and site-specific experience are inherently unquantifiable. Regardless of the method or technique of curvefitting the use of any curve requires the acceptance of the assumptions that stage varies uniquely as a result of discharge and that the controlling geometry of the stream channel is stable over time. Known violations of these assumptions are compensated for by the use of shift corrections. Shifts are based on the concept of a change in elevation of a critical-flow device (Freeman and Bolster, 1910, referred to in Schmidt, 2004) Shift corrections are applied to the data on a timelinear or stage-linear interpolation between discharge measurements. © 2008 Canadian Water Resources Association

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Shifts are more likely to be applied at the bottom end of the stage discharge curve, elevating the uncertainty of low flow data. Considerable skill, good judgment and experience are required to use shift corrections correctly. It is, nonetheless, easy to use shift corrections to generate a hydrograph that is in exact agreement with the discharge measurements. This is a fundamental problem in hydrometry—all information is consumed in fitting the stage-discharge model with no information left over for independent validation.

agencies. These standards have stood the test of time remarkably well and are all the more remarkable given the relatively high incremental costs of operating a high quality gauging network. Consistently justifying these standards over the past century could not have been easy given that the demand for data quality varies according to perceived data importance and that funding agencies’ perception of the importance of hydrometric data, and especially low flow data, varies through time.

Discussion

Conclusions

In this paper, the hypothesis that the uncertainty of low flow data differs from the uncertainty of any other flow regime was not rigorously tested because: 1) there is not ready access to all of the documentation required to discriminate between compliant and noncompliant data; and 2) the uncertainty in hydrometric data acquired in circumstances that are non-compliant with the assumptions underlying the theoretical uncertainty cannot be quantified. However, some of the factors that increase hydrometric uncertainty in low flow hydrometric data were qualitatively described. The factors presented in this paper are illustrative, not exhaustive, of sources that influence the uncertainty of low flow hydrometric data. This qualitative assessment suggests that Canadian low flow uncertainty is different, and likely greater, than theoretical uncertainty as is generally assumed for the global hydrometric data set. The evidence presented in this paper supports the notion that the uncertainty in estimating hydrometric data could be decreased by investments in hydrometric science, particularly by improving the methods, technologies and techniques for low flow and winter streamflow monitoring. Acknowledging that there is still room for improvement, Canadian hydrometric data are, nonetheless, very good considering the environmental conditions prevailing at locations where data are needed. The data are good, just not quite good enough to meet the needs of researchers. Though the uncertainty of hydrometric data may not be uniform, the quality of Canadian hydrometric data has always been very high and may be improving, though methods for consideration of uncertainty as a time-series would be required to test for improvement. We are fortunate that the pioneers of hydrometry demanded stringent rigor from nascent monitoring

The assumption of uniformity of hydrometric uncertainty is challenged in this paper with the question ‘is the assumption of uniformity in hydrometric uncertainty valid for low flow conditions?’ The answer to this question is no, but a quantitative description of the distribution of uncertainty as a function of stage will require field studies. Further development of the principles and methods of quantifying the uncertainty of hydrometric measurements and estimation is needed to reduce our dependence on compliance with standard procedures that are impractical in field conditions. Once we can explicitly and exactly quantify the uncertainty that actually bounds our data we will be able to examine uncertainty as a time series and be better able to focus hydrometric research and development on reducing the most significant sources of uncertainty. The question of non-stationarity in uncertainty has not been addressed and deserves further clarification to examine the effect of evolving measurement technologies on uncertainty when viewed as a time-series. The prudent data analyst recognizes that uncertainty can conceal or reveal patterns in the data that can lead to spurious conclusions. If a given hypothesis test is particularly sensitive to the assumptions of stationarity and/or uniformity in data uncertainty, a conversation with the data provider about the site-specific circumstances that could affect the confidence with which the data can be used for that specific purpose is warranted. A little known, but equally true, corollary of the truism that ‘we manage what we measure’ is that ‘we mismanage what we mis-measure’. If it is true that low flows are a limiting factor for healthy ecosystems and robust economies and that we value sustainability, then one might reasonably infer that we should value good © 2008 Canadian Water Resources Association

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measures of low flow. Achieving this value will require an investment in hydrometrology to improve our methods, techniques and technologies for measurement and monitoring of small flow and winter streamflow and in accurately quantifying the uncertainty associated with hydrometric data estimation.

Artificial Neural Networks and Multiple Regression Techniques.” Journal of Hydrology, 349: 383-396.

Acknowledgements

Dickinson, W.T. 1967. “Accuracy of Discharge Determinations.” Hydrology Paper No. 20. Colorado State University, Fort Collins, Colorado.

I am very grateful to Greg MacCulloch and Paul Doyle for guidance and direction resulting in substantial improvements from the earliest drafts. I am also very grateful to two anonymous reviewers who provided extremely insightful and helpful comments and to Chris Spence and Paul Whitfield for their insistence that I complete this work.

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