5 BEST PRACTICES FOR BUILDING BETTERSTAGE-DISCHARGE RATING CURVES

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Stream discharge is, arguably, the single most valuable environmental variable required for the e�ective management of food supply, energy generation, industrial production, transportation, health, and for the protection of global ecosystems. It is also one of the most di�cult variables to measure and monitor on a continuous basis in natural streams and rivers.

The derivation of an empirical relation between stage (i.e. water level) and discharge (i.e. stream�ow) is fundamental to the production of almost all information about fresh water quantity. This relation can be explained from �rst principles.

Engineers have progressively simpli�ed the theory into equations: �rst to explain the relevant variables (e.g. the Bernoulli equation); then to collapse them into terms that explain the majority of the variance, assuming the physical properties of freshwater are constants (e.g. the Manning equation); and �nally to reduce the equation to a univariate form (the stage-discharge equation) valid for steady, uniform �ow conditions.

The best hydrographers are skilled at unveiling the truth from scatter plots of stage and discharge measurements. Armed with a set of working hypotheses that explain not only the underlying form, but also all deviations from that basic shape, highly e�ective hydrographers are able to build better rating curves. They are able to e�ciently perform, explain, and defend their work.

A true curve will hold its shape as the density of rating measurements increases and will predict accurately in extrapolated zones, such that new data outside the previously calibrated range is likely to also agree with the curve. Any residuals will make intuitive sense: for example, if a rating measurement is a�ected by backwater it will plot left of the curve, while a measurement during rapidly rising stage will plot to the right. Informative residuals are essential for accurate modeling of the dynamic processes governing �ow in a natural channel.

This whitepaper presents 5 best practices employed by expert hydrographers around the world to derive credible records of stream discharge.

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THE 5 BEST PRACTICESBest Practice 1 | Have a Plan

It is ‘best’ to have a plan. Rating curve development is a continuous learning process that requires continuous feedback. The curve can be no better than the �eld observations. The end uses of derived discharge data must be considered in evaluating whether the available �eld information is su�cient to derive data that are �t for the intended purpose. “The 5 Essential Elements of a Hydrological Monitoring Program” whitepaper discusses planning considerations including: Quality Management System, Network Design, Technology, Training, and Data Management.

Best Practice 2 | Understand the Science

It is ‘best’ to understand the science. There are many simplifying assumptions underlying the use of rating curves. To be e�ective, a comprehensive understanding of these assumptions is essential.

Best Practice 3 | Systematically Analyze the Data

It is ‘best’ to take a systematic approach to analyze the data, guided by procedure and informed by the science. Re�nement is best achieved within an orderly process.

Best Practice 4 | Manage the Variance

It is ‘best’ to ensure corrections accurately model dynamic in-channel processes that in�uence the hydraulic relation. If validity of the current method is ever in question, the fundamental model used to derive discharge and/or the system for gathering observations must be reviewed.

Best Practice 5 | Qualify the Derived Discharge Results

It is ‘best’ to qualify the results of any rating analysis. Firsthand �eld experience is the best source of information for the assessment of data quality.

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Best Practice 1 | Have a Plan

E�ective rating curves can only be produced in the context of an e�ective monitoring program. An e�ective monitoring plan includes a Quality Management System that

documents quality, service, and security objectives consistent with a client focus.

Site selection and/or stream engineering are critical predictors of success for the development and maintenance of rating

curves. Site access can a�ect the timing and frequency of �eld visits. Uniformity of �ow can a�ect the accuracy of

discharge measurements. The characteristics of the control features can a�ect the stability and sensitivity of the stage-discharge relation.

Highly e�ective hydrographers evaluate the suitability of technologies for reliability, accuracy, sensitivity, and precision requirements over the entire range of conditions. They constantly re-examine their network as better alternatives

emerge or location-speci�c experience increases.

Skills development by training is never complete. The quality of analysis of even the most experienced

hydrographers can bene�t from focused opportunities to hone their skill through training and knowledge sharing.

Access to a modern data management system that is optimized for advanced data analysis is also a key element of an e�ective

monitoring program. The whitepaper “The 5 Essential Elements of a Hydrological Monitoring Program” further describes modern strategies, industry

standards, and technologies used by expert hydrographers in building and maintaining e�ective monitoring plans.

Best Practice 2 | Understand the Science

The best hydrographers understand and employ a hydraulics based approach to curve �tting. They interpret the hydraulic factors in a larger context inclusive of the dynamic in�uences of hydrology, weather, �uvial geomorphology, aquatic, and riparian ecology. They ensure that all mathematical, statistical, and physical constraints have been addressed.

A key assumption of statistical approaches to curve �tting is that the data have the same probability distribution and are mutually independent. This assumption is almost invariably false for stage-discharge rating measurements. There is rarely an adequate sample size of well-spaced measurements per curve segment and per period of applicability for robust statistical analysis. Rating measurements can have uncorrected bias that is only qualitatively understood. The representativeness of rating measurements depreciates as a function of temporary conditions and/or transition between control regimes. Furthermore, the randomized residuals from a statistical curve �tting process make it impossible to understand, and hence model, dynamic processes.

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There are two key advantages of using a hydraulics based approach to stage discharge rating curves: (1) hydrographers can more e�ectively

evaluate curve shape and complexity, and (2) it becomes more intuitive to model systematic departures from the fundamental

controlling features.

Conservation of mass, energy, and momentum ensure that for any stream reach the sum of energy of �ow

(pressure, potential, and kinetic) and energy “lost” to forces resisting that �ow (friction, turbulence, and tension) remains constant. Skilled hydrographers understand the various forces and energy transitions: for example, they can readily observe e�ective head above point of zero �ow, sub- or super-critical �ow, onset of bank over�ow, and in�uence of cross-section features and stream bed composition. These

observations, correctly interpreted, can provide an a priori estimate of rating equation parameters.

A rating curve developed using a hydraulics based approach can be modi�ed using the same approach.

Systematic deviations from the curve can be readily explained by hydraulic factors that are known to be changing.

A conceptual cause and e�ect explanation for the variance forms working hypotheses that are tested by the examination of relevant

evidence. Demonstrably valid conclusions (e.g. in�uence of aquatic vegetation) are used to shape a response to the deviations from the rating curve

over time and with respect to stage.

Understanding the science is achieved by e�ective training as discussed in Best Practice 1 (BP 1) in the context of relevant �eld experience. Whereas a pure theorist will be frustrated by the uncertainties of a poorly constrained hypothesis, a pure experimentalist will be frustrated by the amount of variance in a poorly constrained trial and error solution. The most e�cient path to achieving rating curve pro�ciency is through experience and mentorship in the �eld grounded in e�ective theoretical training.

Best Practice 3 | Systematically Analyze the Data

Systematic analysis of the data is achieved by developing working hypotheses (see BP 2) and then rigorously testing these hypotheses against observations. This approach supports the use of all types of evidence in evaluating the truthfulness of a rating model. The evidence for this analysis must be curated and managed with care (see BP 1).

The o�set of the rating equation can be evaluated from �eld observations either explicitly (e.g. sill elevation) or implicitly (e.g. cross section analysis for channel control). The exponent of the rating curve can be estimated by considering the channel shape and velocity head through the controlling reach. The breakpoints in the rating curve and the range of e�ective transition across a breakpoint can be evaluated by cross section analysis and/or by considering the channel roughness and velocity head.

Given these key pieces of information, the task of �tting a rating curve to measurements is

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simply a matter of adjusting the plotting position and �ne tuning the initial estimates. ‘Goodness of �t’ for measurements to this initial plot of the

curve is a function of the validity of the assumptions made about the measurements and the control conditions.

In a perfect world, hydrographers would be working with ideal conditions. However, rating curves are needed for

the real world, making it necessary to systematically expose changing conditions or errors in assumptions and to develop context for appropriate mitigation.

The best hydrographers consider their �eld notes and measurement details when they evaluate deviations from the rating curve. When appropriate, they characterize the expected variance in hydraulic geometry with residual plots of the discharge-depth,

discharge-width, and discharge-velocity relations. They develop ratings for stage-area and stage-velocity,

if needed, to inform the shape of curve extensions.

Assumptions about control conditions are evaluated in the context of photographs, sketches, �eld notes, and in the

measurement details. The full history of rating measurements and curves is examined to identify trends, cycles, and transient

excursions from an assumption of stability. It is worthwhile to consider time series of the rating curve residuals in the context of the stage

hydrograph when developing a working hypothesis to explain any systematic departures.

Best Practice 4 | Manage the Variance

A well-conceived rating curve reveals changes in channel dynamics in a clear pattern of residuals. Change can be abrupt, in the case of debris on the control, or it can be gradual, when modeling the life cycle of aquatic plants. It can apply over the full range of stage (e.g. uniform deposition over the bed) or the in�uence can be limited to a speci�c range of stage (e.g. some types of vegetation e�ects).

Expert hydrographers mitigate systematic variance by modifying the rating model, either with shift corrections or by transitioning to a new curve. Residual variance about the curve can be highly informative of measurement uncertainty and/or control insensitivity.

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Recurring variance can be avoided by root cause analysis that results in preventive actions. Variance that is unavoidable needs to be investigated, with the investigation resulting in corrective actions. Knowledgeable hydrographers also look for unexpectedly low variance, for instance, when shifts in ratings are not detected because the frequency and/or timing of measurements are inadequate. In this case the rating curve analysis informs changes to the scheduling of �eld operations.

Managing variance is predicated on a comprehensive understanding of both the underlying in channel processes (see BP 2) and business processes (see BP 1). The development of highly e�ective corrective and preventive actions requires systematic analysis of the data in the context of governing physical and biological dynamics, and/or technological in�uences (see BP 3). The decisions for altering any data must conform to a trusted procedure (see BP 1).

Best Practice 5 | Qualify the Derived Discharge Results

The measurement and monitoring of discharge under natural conditions can be a wickedly di�cult undertaking. A common consequence of diverse

operational conditions is data of varying reliability.

The quality of data depends on �ve key considerations (see BP 1): compliance with a trusted procedure; site location;

site-speci�c suitability of the technology used; hydrographer training and experience; and the use of a

good data management system with advanced analysis and diagnostic capabilities. Evaluation of data quality must also consider the explanation (see BP 2) and supporting evidence (see BP 3) for the shape of the curve and approaches for modeling departures from the curve (see BP 4).

A hydrometric dataset is incomplete without a comprehensive explanation of data quality. This

includes dataset notes as well as ‘per value’ quality indicators. Data grading should be a true re�ection of

the con�dence with which the data can be used, and these grades should be understandable, consistent, and

reproducible. It is valuable to indicate the ‘approval level’ (aka ‘age’ and ‘version’) of the data to indicate the likelihood

for further review and possible revision of the data.

The best hydrographers proactively manage data quality. It is better to cause the data to be of high quality than to engineer quality after the

fact. In many cases the same factors that hurt data quality also hurt e�ciency, productivity, and service delivery.

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“It is easier to do a job right than to explain why you didn’t.”- Martin Van Buren

Stream hydrographers are held accountable for their work. The best stream hydrographers have found that using a rigorous, hydraulics-based approach makes it easier to perform, explain and defend their work.

This requires compliance with trusted procedures; evidence based evaluation of working hypotheses; modeling not only the form of the curve but also any deviations from the curve; root cause analysis of unexplained deviations; review and analysis for corrective and preventive actions; and quali�cation of the results.

Rating curve development begins before the gauge is even established. Consideration of the control sensitivity to discharge, �uvial geomorphology, aquatic biology, and any seasonal in�uences are a pre-condition for e�ective rating curves. The suitability of the gauging site is one of the best predictors for discharge measurement quality. The choices made in technologies used to monitor stage and to measure discharge take into consideration the in�uence of local conditions on technological performance.

The timing and frequency of �eld visits is a result of rating curve analysis rather than the other way around. The observations made during �eld visits are attentive to the hydrologic, hydraulic, biologic, and geomorphic details that are essential to understand the form, and limits for extension, of a rating curve as well as to explain potential departures from the curve.

The shape of the rating curve is constrained by the interpretation of parameters based on �eld observations. Segmentation of the rating curve, if required, is supported by physical evidence. Extrapolation beyond the calibrated range of the rating curve is physically realistic and supported by supplementary evidence. Modeling of departures from the curve is based on a deep understanding of the physical or biological processes in�uencing change in channel conveyance. All variables that are known to respond in harmony with the controlling forces for these physical processes are considered in evaluating transitions through time.

The process of developing e�ective rating curves is supported by e�ective data management. A wide range of curated evidence is readily available for meaningful interpretation and analysis. The intuitive shaping of curve form and extent is readily constrained by the explicit control of model parameters. The quali�cation of derived discharge is explicitly linked to the strength of the rating calibration.

Reliable stage discharge rating curves require investment in planning, technology, training, �eld operations, and software. Obtaining a discharge record is an expensive business. The alternatives to a best practices approach are never a wise use of limited hydrometric monitoring resources.

The ‘Best Practices’ approach to developing better rating curves is desirable for any scale of monitoring operation, from the operator of a single gauge through to the largest continental scale network. Hydrometric technologies are changing, data delivery is changing, and the demographic pro�le of stream hydrographers is changing. The best practices approach is not only resilient to change in any of these factors, but can exploit these changes for the continual betterment of data products and services. Ultimately, as a result of using the best practices approach water professionals can make better decisions for the equitable use, management, and protection of the world’s limited water resources.

CONCLUSION

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Aquatic Informatics™ Inc. provides leading software solutions that address critical water data management and analysis challenges for the rapidly growing environmental monitoring industry. It understands the challenges of environmental data management. Its �agship product AQUARIUS is carefully engineered to ensure a smooth transition to modern best practices for hydrometric data management.

AQUARIUS is the time series data management software used by the largest and most advanced hydrological and environmental monitoring agencies, including the USGS and Water Survey Canada, and it is scalable to �t the needs of any size of monitoring network. AQUARIUS has a simple design that combines an intuitive and e�cient user interface with the latest hydrological science and techniques. AQUARIUS allows hydrologists and technicians to manage the data they collect more quickly and to a higher level of quality, so they can deliver more e�ectively on the evolving demands of stakeholders.

AQUARIUS is fully con�gurable to adapt to and support any Quality Management System. AQUARIUS excels in retrospective data analysis as well as real-time continuous work �ow management. It has a unique portfolio of features for real-time sanity checking, error detection, data cleaning, data �agging, automatic bias corrections, and rating shift

Published by Aquatic Informatics

© 2014 Aquatic Informatics Inc. | 1.877.870.AQUA (2782) | info@aquaticinformatics.com | www.aquaticinformatics.com

Meet the AuthorStu Hamilton is dedicated to improving the science of water monitoring. He has 17 years of �eld experience in northern Canada, and nearly as many years in research and development and operational management with the Water Survey of Canada. Stu is an Associate Expert in Hydrology with the World Meteorological Organization (WMO); the Canadian Liaison with the Hydrometry Committee (TC 113) of the International Standards Organization (ISO); the current President of North American Stream Hydrographers (NASH); and a Member of the Open Geospatial Consortium (OGC) Hydrological Domain Working Group. Since 2009, Stu has been a Senior Hydrologist at Aquatic Informatics. For more insights from this author, you can read Stu’s Hydrology Corner blog here.

To watch a VIDEO demonstration of AQUARIUS or tolearn more, please visit www.aquaticinformatics.com

management to streamline quality controls. AQUARIUS automatically builds an auditable data processing, correction, and editing log, ensuring data defensibility. The AQUARIUS rating development tool is engineered to support the latest global standards set by the USGS, ISO, WMO, and OGC, to ensure the highest con�dence in calculations of �ow. Its �exible reporting and publishing tools include an extensive list of industry standard report templates and an integrated report template builder for customized reporting.

The AQUARIUS architecture is designed to manage and synchronize data from multiple networks for fast reliable solutions to di�cult water management issues. Advanced support for data migration ensures continuity with legacy systems and its state-of-the-art architecture ensures your system is secure, scalable, and integrated. The intuitive AQUARIUS toolboxes combined with comprehensivetraining and support resources ensure rapid deploymentand implementation in any operational environment.

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“This whitepaper originates from extensive and ongoing discussions with Marianne Watson, Hydrologist & Principal at Hydronet Ltd, comparing and contrasting methods used in North America versus New Zealand. Marianne continues to be an incredible source of knowledge and inspiration for understanding and communicating the science and practice of rating curve development. Thank you Marianne.” – Stu Hamilton