1. AQUARIUS Time-Series Software™ Aquatic Informatics Inc.
Hydraulics for Hydrographers Natural Channel Controls and Rating Curves
AQUARIUS Time-Series Software™ Aquatic Informatics Inc.

2. Review of Basic Hydrodynamics What is a Control? Section Control
Preview
Review of Basic Hydrodynamics
What is a Control?
Section Control
Channel Control
Multiple Controls
Controlling Forces
Manning’s equation can be used to determine the stage-discharge relation for an ideal channel. However, natural channels are rarely ideal.
In this unit we will explore how our theoretical knowledge of hydraulic relations can be applied in the “real world”.
You will learn how to apply your knowledge of the stream conditions to estimate ‘realistic’ values for the parameters in the stage-discharge equation. You will learn how to estimate whether a composite curve should be expected and, if so, where break-points should be placed.

3. Our primary assumptions from Basic Hydrodynamics
Uniform flow
Approximately valid over short distances if changes in direction and spacing of flow lines are gradual enough.
Steady flow
Approximately valid over short enough intervals of time
(H- H0)~Pressure Head = dominant term in Energy Equation for most stream gauging reaches
Velocity Head varies proportional to Pressure Head
At critical flow, Velocity Head = ½ D therefore Total Head = 1.5 x (H-H0).

4. Implications
That the force in the downstream direction is equal to the resisting force (or else flow would be accelerating or decelerating through the reach)
We measure Head (H-H0) as in index of force in the downstream direction
The rating curve parameters are collections of similar terms from the energy balance equation – including the resisting forces

5. Forces resisting flow
where Hf=Head loss due to friction, K is a constant, ν = velocity, P= Wetted Perimeter, and L = Length of the channel.
‘K’ includes channel rugosity; sinuosity; shape; obstructions; as well as the density and kinematic viscosity of the water

6. Channel control is when L & P are dominant.
What is a control?
A control is the sum of all of the terms in the Head loss-to-friction equation, including the components of the constant K.
Channel control is when L & P are dominant.
Section control is the special case (i.e. Froude number = 1), where v2 is a known function of H-H0.

7. Specific Energy Curve
Froude < 1: Channel control downstream of gauge
Froude = 1: Section Control
Froude > 1: Velocity Head and channel control upstream of gauge

8. Approximation of Froude Number
Froude = 1 where there is a sharp break in channel slope (e.g. crest of weir, or riffle); or a channel constriction
Froude > 1 where there are standing waves
Froude < 1 if a wave from a pebble thrown in the stream can propagate in an upstream direction

9. Artificial Controls create the condition of Froude = 1
Froude Number = 1
Artificial Controls create the condition of Froude = 1
The rating equation can be explicitly evaluated based on geometry when Froude = 1.
Naturally occurring section controls are preferred as gauging locations
The exponent in the rating equation will be approximately 1.5 for a rectangular section; and 2.5 if the banks slope at a 45o angle

10. Section Control
Section control exists when the Gauge is immediately upstream of a section where the Froude number of the flow =1
Sub-critical
Sub-critical
critical
critical

11. Example of a section control, looking upstream

12. Tranquil flow – Pressure Energy is the dominant force driving flow
Froude < 1
Tranquil flow – Pressure Energy is the dominant force driving flow
The controlling reach extends downstream from the gauge some distance
Factors include: wetted perimeter, length, sinuosity, rugosity, channel shape and obstructions
The exponent will generally be approximately 1.67 for rectangular channels

13. The control section can be upstream of the gauge
Froude >1
Turbulent flow – Velocity Head is the dominant form of energy driving flow. No information from the channel downstream of the gauge can propagate upstream.
The control section can be upstream of the gauge

14. Multiple controls
Unconfined Alluvial streams are Self-Organizing systems that conform to the Least Action Principle (LAP) to trend toward Maximum Flow Efficiency (MFE).
However, there are many forces working against MFE – (e.g. geological features that resist erosion and/or transport; and biological encroachment of the floodplain) – and it is usually these forces that determine whether multiple controls exist.

15. A ‘Hypothetical’ Multi-Control Scenario
Section Control at low flow
Flow tumbling over streambed cobbles
Channel control at mid-flow
Cobbles are submerged.
Sub-critical flow where the parameters in the rating equation are a function of the channel downstream of the gauge.
Over-bank flow at high stage
Usually super-critical flow where the parameters of the rating equation are a function of Velocity Head and of the channel upstream from the gauge.

16. Overbank flow

17. Out of Channel (i.e. overbank flow) always requires special attention

18. Controlling Forces – Rugosity
Rugosity refers to the roughness of the stream-bed and stream banks.
A channel may be carved out of clays and silts, or paved with cobbles over the full range of stage in which case rugosity is captured in the rating curve coeficient.
Substantial changes in rugosity with respect to stage can result in a multiple-control rating – affecting both the coefficient and the exponent but not the offset

19. Controlling Forces - Sinuosity
Sinuosity refers to meanders in the stream channel
Sinuosity is primarily a consideration for tranquil flow where the control reaches for a long distance downstream of the gauge
The effect of sinuosity is captured in the coefficient of the rating curve.

20. Controlling Forces - Shape
Channel shape has a profound effect on the exponent of the rating curve, controlling the Head-Area relation, which in turn determines the specific weight of water available to generate velocity
Channel shape also affects the position of H0 and the Point of Zero Flow.
Channel shape can be quite dynamic, being affected by both geomorphologic and biologic forces

21. The shape of the channel can also control ratings
Murray River in September
Murray River in June

22. Controlling Forces - Obstructions
Natural obstructions, such as remnant boulders, may create channelized flow at low stage and critical flow at mid stage.
Man-made obstructions are generally continuous across the stream.
At a high enough stage, streambed obstructions become ‘drowned-out’ resulting in a multi-control rating curve

23. Controlling Forces – Properties of Water
The Density and Kinematic Viscosity of water both change as a function of temperature and of sediment load.
If a stream always has a high sediment load at high-flow and a low sediment load at low-flow, then the effects of these variables are captured in the exponent of the rating curve
If the pattern of sediment loading is not consistent with respect to stage then these factors will result in scatter around the rating curve
High Sediment Load increases Viscosity, which increases drag in the laminar layer thus altering the shape of the vertical velocity profile. If the vertical velocity profile is assumed, rather than measured, then these measurements will plot to the left of the rating curve

24. Velocity dominates the shape of the rating curve when Froude > 1.
Controlling Forces – v2
Velocity dominates the shape of the rating curve when Froude > 1.

25. Controlling Forces - P
The wetted perimeter is an important factor in the shape of the rating curve in complex channels
A change in control is likely when emergent obstructions become submergent.
A gradual change in control is likely as the effect of a relatively High-P stream bed gives way to relatively Low-P stream-banks at higher flows.
A change in control is likely when the stage encroaches on riparian vegetation which increases wetted perimeter

26. Controlling Forces - L
The length of the control section can be very short for a section control or very long for tranquil flow.
The length dimension changes as a function of velocity, which in turn changes as a function of Head. As such, the effect of length is generally captured in the exponent of the rating curve and does not typically result in a change in control.

29. The controlling features of stream channels are subject to change.
Preview
The controlling features of stream channels are subject to change.
In the lesson “Channel Dynamics and shift corrections” we will look at some of the causes of change and how AQUARIUS can accommodate those dynamic conditions

30. Recommended, on-line, self-guided, learning resources
USGS GRSAT training
World Hydrological Cycle Observing System (WHYCOS) training material
University of Idaho
Humboldt College
Comet Training – need to register – no cost

31. Thank you from the AI Team We hope that you enjoy AQUARIUS!