Stage-Discharge Rating Curves – Geophysics or Religion?


Almost everything we know about our global freshwater resources is due to the humble stage-discharge rating curve.

The vast majority of all flow data ever produced is the derived result of a transform from a variable that is easy to monitor continuously (stage) to a variable that is impossible to directly measure continuously (discharge).

This means we are dependent on rating curves for advancements in hydrological science; for flood forecasting; for drought management; for engineering designs that provide us with physical safety, transportation, water supply and waste disposal; for water management policies and decisions that ensure energy and food security.  There are social, recreational and environmental health benefits to knowing water flow.

Given that this knowledge is so fundamental to our safety, health and prosperity one would expect global consensus on the science and practice of rating curve development and management.

The basic principles of fluid flow and the physical properties of water have been known for centuries. One could argue that the rating curve represents a fairly straightforward geophysical process relating the properties of water to the conveyance capacity of the channel at a unique location. For practical use, solving the Saint-Venant equation is an onerous proposition. However, the solution can be greatly simplified by acceptance of a few simplifying assumptions.

Introducing assumptions to the problem take us out of the realm of geophysics and into the realm of belief systems.

There are two primary dogma that yield many distinct belief systems:

The Reductionist Dogma:

It is believed that, for each channel control feature (there can be more than one), the standard equation Q=B(H-e)a is a very useful approximation. In this equation discharge (Q) is a power (a) function of stage (H) corrected with an offset value (e) multiplied by a coefficient (B). It is widely accepted that the coefficient represents information about channel width, slope and roughness, the offset represents an effective cease-to-flow elevation and the exponent represents information about channel shape.

  1. A high level of trust is put in human observations of the control conditions to: i) verify that fundamental assumptions are valid and ii) to provide interpretation of the correct form of the rating as guided by gaugings.
  2. A high level of trust is put in the assumptions implicit for statistical regression to calibrate a simple rating curve shape in a way that minimizes a performance metric for the fit of the curve to selected gauging’s (e.g. root mean square error).

The Holistic Dogma:

It is believed that the relationship between stage and discharge is inherently too complex to reliably be reduced to simple mathematics. The relationship is best represented as a table of rating points, a set of equations or a polynomial function.

  1. A high level of trust is put in experienced hydrographers hand-drawn rating curves. The curves may be generated on paper or by using a computerized graphical editor that reproduces the experience of visually identifying the form of the rating.
  2. A high level of trust is put in the assumptions implicit for statistical regression to calibrate a complex rating curve shape in a way that minimizes a performance metric for the fit of the curve to selected gauging’s (e.g. root mean square error).
  3. A high level of trust is put in actual gaugings. An investment in high frequency of gaugings is preferred over an investment in rating interpretation.
  4. A high level of trust is put in the analysis of the cross sectional survey data. An investment in analysis is preferred over an investment in gauging frequency.

Science arguments can be systematically resolved. Belief system arguments cannot.

As with the major religions these belief systems tend to be centered in geographic strongholds. Evangelical hydrographers who go on a mission to preach the gospel of their system to non-believers get boiled alive by the natives. There is little opportunity for discourse between practitioners of different belief systems.

Notwithstanding many historical, geographic, cultural and political influences on the development and persistence of different belief systems, there could be great value if everyone produced their data the ‘best’ possible way. The most likely outcome of religious adherence to deeply entrenched tradition is that nobody is producing their data the best possible way. The ‘best’ approach has yet to be discovered and that will require consideration and synthesis of the best of the best ideas arising from every tradition. That cannot happen until practitioners from different belief systems are actively working together and sharing ideas.

The ratings workshop in Christchurch NZ last spring is one small step toward enlightenment. We can do better. There is much still to be learned.

I would like to specifically call for feedback on this post. What is your experience with rating curve development? Does the metaphor of religion resonate with you? If so, what do you believe? If not, where is the evidence that science prevails over belief? Could there be a geophysical explanation for the global distribution of belief systems (e.g. a belief system may be optimally adapted to local geography, hydrology and hydraulic conditions)?


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11 responses to “Stage-Discharge Rating Curves – Geophysics or Religion?”

  1. I don’t think religion is a fair comparison to curve development. You draw a line that includes as many measurements as possible within your tolerance and work with it. Many technologists spend far too much time agonizing over minute variations at breakpoints to a curve without realizing that how you interpret subsequent variations from the curve is more important than the actual line.
    I have gauged rivers with 40 years or more of record that have not required open water shift corrections to be applied. I have gauged streams that shift every visit or have no real rating – beaver dam affected creeks. Describing and documenting how and why the stage-discharge relationship changes over time is the challenge.
    A curve is a model and how you interpret and document the variations and change to that model over time is the important and most difficult thing to teach about stream gauging.

    Trying to gauge streams with a stage discharge curve when none really exists or is drowned out by backwater is hard. This is where new research is required most.

    • Hi Kim, You express a very pragmatic perspective where, to paraphrase George Box, the curve doesn’t have to be correct it just has to be useful. Perhaps that is all there is to the matter.
      However, I hope that it is premature to give up on the idea that a curve can be both truthful and useful. For one thing if we were better at developing curves that are truthful we would stop trying to use ratings at sites where there can be no unique rating.

  2. Ferdinand Quiñones July 5, 2016 at 2:45 pm

    This is more hogwash, trying to turn a simple adequate empirical relationship into sophisticated science with big words. A good streamgager will perform frequent calibration flow measurements to validate the application of the rating curve. These measurements provide a satisfactory measure of variance between flow and stage (as “regulated” by the “control” of the cross section used for the stage measurements) at the segment of the channel where the rating is developed. And flow calculations in natural channels can be adjusted with a simple or complex series of “shift curves”. The only thing that can be gained by trying to oversophiticate this simple but effective procedure is more $’s in somebody’s pocket resulting from these big words.

    • Hi Ferdinand,
      I agree that ratings are the most useful way of monitoring discharge. I don’t want to disparage the practice for either theoretical or financial reasons.

      We differ in opinion on the current state of the art. We each have our own experiences that we base our opinions on. The difference in our opinions is important but those differences can only be resolved, or reconciled, if they can be reduced to disprovable statements.

      If I were to restate my opinion in a single statement it would be “The practice of rating curve development and management is currently immature.” I think that statement could be disproven in a simple experiment where a difficult rating problem is given to hydrographers from different regions of the world representing their different training, methods, techniques and technologies. If all hydrographers can derive the same, or substantially the same, hydrograph from the same data then my belief is demonstrably false.

      However, if my opinion is valid then what can we do about it? My premise is that enough people have been solving the problem from different perspectives for a very long time. All practitioners have something to contribute to the conversation. A fully mature practice for rating curves will result from global consensus on what works best. That conversation hasn’t happened yet.

      If your particular approach to resolving rating problems is, in fact, the best way then why hasn’t the rest of the world adopted your standards, protocols, training, methods, techniques and technology?

  3. A great post Stu.
    However, I have news for you. When you ventured down south to Christchurch there were indeed rumours of oil heating up in a vat, and maybe there was also mention of “skinning alive”, and “sharp stakes”. There was also discussion about building a wall, but we couldn’t find someone to pay for it.

    The Christchurch workshop allowed me to transition some of my long held beliefs on rating curves, some of which fitted into the dogma category. We had points of view from 5 regions using different approaches. One big learning I took away from the workshop, was that in many cases we are indeed using similar underlying approaches. When I broke down the USGS shift method, which my dogma told me was old fashioned and indeed rather an odd approach, the underlying principles were often much the same as those that I practice myself here in New Zealand. What was apparent is that our ‘rating language’ is quite different, and herein lies many of the difficulties we find when we begin conversing about rating techniques.

    It brought to mind a conversation with a friend who headed off to the Solomon Island to do volunteer work as an Engineer for 3 years. Before he went, his training included a lengthy exercise where they spilt all volunteers into 4 groups, took them off and taught them a language. He learnt for instance, that fish was called a certain word. What they were not told, was that the other three groups were all told that that same word in their language meant cow, or rhubarb (say). The groups were brought back together and asked to do some trading and work on co-operative projects. Bedlam reigned, and frustration turned to anger at times. My point of course, is that any international conversation about ratings is fraught without a common language, and long held beliefs take days or months, not several conversations, to change.

    Coming back to the reductionist and holistic approaches Stu describes, following the Christchurch workshop I reached a firm conclusion that any rating editor should be hard wired with hydraulic guidance (which usually should be followed), but ultimately the rating calibration should be less constrained and free to follow expert intuition and prior experience at the site. I particularly like the work Jerome Le Coz is doing to derive rating shape, but as a calibration centric hydrologist, my preference would be to use that as strong guidance only. In time, as the hydraulic estimates in BaRatin become more sophisticated, perhaps incorporating slope, I might place all of my trust in that method to derive rating shape.

    I might therefore, be seen as an ‘inter-dogma’ fence sitter. Instead, I simply believe there are strengths in each approach which can be used. As an example, I like the USGS approach which requires the control(s) to be described by equation parameters. The reason I like this however, is not the because of the equations and parameters used, but because of the explicit need to consider what the control has done. Here in NZ we advocate describing changes in rating shape by what has happened in the control, but we’re not forced to, and that’s not strong enough.

    I liked the comment posted by Kim Epp. Any conversation about ratings invariably concentrates on rating shape, perhaps because of the interesting mathematical and hydraulic components. The timing of rating changes is invariable glossed over, and rating editors often lack some basic tools to help in this regard. There is no doubt that in unstable rivers, the time that ratings apply over is a dominant factor affecting accuracy of a flow series. It’s only when you have spent considerable time working on unstable rivers, with a dataset of frequent gaugings to assist you, that you appreciate the extent of this issue.

    An excellent discussion point Stu, and thank you for continuing to bring this up.

    • Hi Martin,
      Your story about the problem of language gets to the heart of the matter. I would add to that by saying that if your only tool is a hammer then every problem starts to look like a nail. In other words, the technology that you have frames how you think about the problem. I see differences in fundamental comprehension of many of the basic concepts that seem to be dependent on the technology the audience is familiar with. At least that is the way I explain to myself the blank stares that I get (like a dog watching television) as soon as I start talking to an audience who use a technology that I am not personally familiar with;-)
      I fully agree with you about the advantages of the USGS-style ratings (of course!). But part of the point of this post – and I think Terry Kenney would agree with me – is that there is a lot that North Americans can also learn from the way that New Zealanders do their ratings. There is a lot of accumulated wisdom in the new NEMS standard for ratings that will complement the USGS-style ratings very effectively. Maori Tapu and Mana can find their place in a global best practice for ratings.

  4. Julio Morales July 5, 2016 at 5:02 pm

    I guess we all have our local experiencia and trust our dedicación to good streamgauging and stage monitoring by water level sensors or other methods. We all adapt out consideraciones to each site, to each river and basins. I monitor rivers with volcanic asand sabe in 6500mm/year basins that are real headaches. Also highly polluted streams that seem like waste water channels. All behave different. I believe is more of a relationship of the hydrographer and his stations.

    • Hi Julio,
      I am glad you made this comment. It affirms something that I ‘believe’ should be a ‘best’ practice – that the hydrographer who manages the ratings should have personal experience with the gauge. It is my ‘belief’ that observations of the stream in all different seasons at all different stages are essential to understanding the true nature of the rating relationship as it varies with stage and with time. In time, field procedures may evolve to a point where there is sufficient documentation of all relevant factors to make it possible for a 3rd party to develop a good relationship without first-hand experience but I don’t ‘believe’ we are there yet, at least not for difficult rating problems such as you are faced with.
      I am aware that many people don’t share my beliefs. However, it remains to be proven that it is possible for someone lacking personal experience to outperform someone who has extensive personal experience with a gauge, regardless of their choice of method. There is much more to ratings than just the gaugings.

  5. Hi Stu,

    Thanks for your reply.

    I should clarify that while I was complementing the aspect of the USGS approach that requires people to explicitly consider the hydraulic components and how they have affected the parameters of the standard equation, it wasn’t an overall endorsement of the USGS method – which you seem to imply! But it’s a perfectly adequate method, and enough on that.

    Picking up on the posts above, I remain very committed to the philosophy of getting plenty of gaugings to guide the shape of a rating curve. Mic Clayton (Australian Hydrographer) once expressed the need to ‘gauge the shit out of it’, and that’s good advice! Of course if you also hold expert hydraulic knowledge, and you’re aware of the rating history at the site, you’ll be much, much better off. The reality is however, we can’t use the Clayton approach for many reasons – economic, geographic etc, so Stu’s comment that ‘there is much more to ratings than just gaugings’ is more than valid, it’s a necessary understanding.

    Ferdinand’s earlier sentiments in this thread have validity when you consider a simple rating relationship at a stable site, but the complexity of dealing with rating curves off volcanic areas (Julio’s experience), or gravel streams off young geology with high rainfall (New Zealand, and many other regions), requires the Clayton Method above, which may not be possible. The only alternative then, is to employ some very smart thinking backed by plenty of alternative observations.

    There is no doubt we all have our preconceptions. There is also no doubt that all of us will be learning about rating curves until we retire. There is no doubt we can all learn from each other. The more international conversations we have among the people that have been gauging and drawing ratings for many years, the better.

  6. Hydrology is the science where we are accepting results with some acceptable degree of error.Standardising stage discharge curve for particular gauge site is difficult.It is always with some error.It is the knowledge and experience of that particular site of the hydrologist selecting points to draw the curve,makes the curve more accurate.Manual fitting of gauge discharge curve gives more accuracy.

  7. Good discussion here on rating curves, something I’m very interested in. I come at it from a slightly different position, I’m a hydrologist and a flood modeller, not a hydrographer. In Victoria, Australia we have seen many rating curves where they are rated really well up to a point (lets say around bankfull and slightly above), then really poorly for flood flows. Just so happens I’m interested in floods, so that poses a problem for me.

    In the past there has been a standoff between hydrographers and flood modellers who both have staunchly defended their approaches to estimating flows, this has been entirely unhelpful. Fortunately this is changing in Victoria. Now we are starting to see hydrographers and flood modellers working together to develop the best possible rating curve possible. Hydrographers using amazing equipment and providing highly accurate flow gaugings for developing the rating curve in channel, combined with the flood modellers complex 2D models which can resolve floodplain flows and dynamic interactions with bridges and causeways which can significantly impact the shape of the rating curve for out of bank flows.

    Combining the strengths of these two disciplines will result in significantly improved streamflow estimation.

    Ben Tate
    Water Technology

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