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Rating Curves

Rating Curves

  • Empirical relationship between state and discharge
  • Less time consuming than other methods
  • Applicable to streams where stage is easy to measure
  • Assumptions: stable channel bed, steady flow (constant velocities)

Q = a(h - h₀)^(b)

^(Where h = stage, H)_(⁰)^(= stage of no flow, a and b = empirical local parameters)

^(Weirs and flumes)

  • Pre-calibrated structures for small watersheds (< 800 ha)
  • Weirs and flumes: stable cross section; known empirical relationship between stage and discharge

Ideal conditions for installation:

  • Straight channel
  • Channel constriction (not expansion)
  • Stable bed and banks
  • Little or no overbank flow
  • Single channel
  • No backwater influence (tributary, estuary, ice, debris)
  • Little flow turbulence
  • Look for natural weirs

Dilution gauging

Method of gauging streams that have a high amount of turbulence and/or a very inconsistent cross-sectional area (e.g., most mountain streams)

  • Based on the proportional relationship between electric conductivity and concentration of tracers in water
    • Typical tracers: common salt, rhodamine dye
    • Very accurate if stream reach properly chosen
    • Reach (section between injection and measurement) should be approximately 25 times as long as stream width, with no channels entering or splitting away from it.
    • Sufficient turbulence is required to properly mix the solution
    • All dilution gauging requires the use of a tracer measurable at low concentrations
    • Tracer should not react with anything in the stream or be harmful to the environment

Common tracers

  • Salt (NaCl)
    • Inexpensive
    • Readily available
    • Simple to measure as electrical conductivity
  • Fluorescent dyes (e.g., rhodamine)
    • Detectable to parts per billion
    • Can assess mixing visually
    • Requires expensive fluorometers to measure

Empirical Equation

Manning's equation

Q = V X A

V = 1/n(R_(h)^(⅔)S^(½))

V = average velocity in stream cross-section [m/s]

R_(h) = hydraulic radius (m) = A / WP

A = Cross-sectional area m²

WP = wetted perimeter [m]

s = energy slope (approximated by water surface slope) [m m⁻¹]

n = roughness coefficient

Applicability of Manning

  • When there is no gauging station
  • When peak discharge is beyond highest measured stage
  • When peak discharge of previous flood is of interest