Hydraulic Geometry

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Hydraulic Geometry
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Hydraulic Geometry

• Relationships between the mean stream channel
  form and discharge both at-a-station and
  downstream along a stream network in a
  hydrologically homogeneous basin.
• Independent variable discharge (Q) (climate or
  anthropogenic controls)
• Dependent variables width (w), depth (d),
  velocity (v)

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Leopold and Maddock (1953)

• Expressed the hydraulic geometry relationships
  for a channel in the form of power functions of
  discharge as
• w aQb d cQf v kQm
• Where w width, d depth, v velocity
• a,c,k,b,f,m are constants
• exponents indicate rate of increase in a
  hydraulic variable (w,d,v) with increasing Q

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• Because Q is a product of wdv
• Q (aQb) (cQf) (kQm) or
• Q ack Q bfm
• Therefore ack and bfm must 1
• Exponents change with location, climate, and
  discharge conditions

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Quasi-equilibrium Condition

• Tendency for river to establish equilibrium
• between dominant discharge and sediment load
• Adjustments in width, depth, velocity, roughness,
  water slope
• Processes are differential, mutually changing
  no true equilibrium, quasi-equilibrium

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FISRWG
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General Relationships

• w,d,v increase downstream, therefore Q gt
  downstream
• Depth influences velocity much more significantly
  than slope
• Once considered that the relationships were
  climatically controlled anthropogenic signal
  increasing. Balance?

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Two Types of Analyses

• At-a-site hydraulic geometry (Leopold and
  Maddock, 1953) uses mean values over a certain
  period, such as a week, a month, a season, or a
  year.
• Downstream hydraulic geometry (Dunne and Leopold,
  1978) involves spatial variation in channel form
  and process at a dominant discharge.

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Regional Hydraulic Geometry Curves

• log-log plots comparing channel dimensions (top
  width, mean depth, and cross-sectional area)
• at 'bankfull' or effective discharge (usually
  between the 1.1 and 1.9 year return interval)
  versus drainage area.

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WARSSS, from Dunne and Leopold, 1978
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Regional Curve Equations Eastern United
States(Estimated from Dunne and Leopold, 1978)

• Wbkf 14 DA 0.399
• Dbkf 1.5 DA 0.294
• Abkf 21 DA 0.679

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Fenneman
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Regional Curve Equations(Ohio, from Sherwood and
Huitger, 2005)

• Wbkf 18 DA 0.356
• Dbkf 1.52 DA 0.265
• Abkf 27.1 DA 0.621
• Qbkf 93.3 DA 0.637

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Gray, H.H., 2001, Map of Indiana Showing
Physiographic Divisions, IGS Misc. Map 69
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Rosgen (1994)

• bankfull maximum depth (dmbkf)
• floodprone area width (Wfpa)
• bankfull surface width (Wbkf)
• bankfull mean depth (dbkf)

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Rosgen Stream Type Level II Morphological
Description

• Determined by
• Entrenchment ratio
• Width/depth ratio
• Sinuosity
• Water surface slope
• Channel materials D-50

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Entrenchment RatioWfpa / Wbkf
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Channel Geometry

• Sinuosity
• Slope
• Entrenchment Ratio

Flood width
Flood width
Bankfull
C5
ER2.5
G4
ER1.3
Flood Width Bankfull Width
Entrenchment Ratio
Robinson, 2006
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Width/Depth RatioWbkf / dbkf
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FGM
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Influence of Slope (S)

• S important in maintaining equilibrium
• Model - graded, concave up long profile
• Slope adjusts with sediment load, climate,
• S is an adjustable property
• Observation as Q ? slope is maintained
• River must then change other variables to
  accommodate Q
• So gtQ gtv as a result of gtd, ltroughness, or
  both
• Downstream ltS, gtv results in gtd

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Ritter
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Effect of Slope
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USGS