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Hydrologic Statistics and Hydraulics


Chapter 12 Hydrologic Statistics and Hydraulics Storm Hydrograph Stream Hydrographs: A plot of discharge (= flow rate) or stage (= water level) versus time. – PowerPoint PPT presentation

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Title: Hydrologic Statistics and Hydraulics

Chapter 12
  • Hydrologic Statistics and Hydraulics

Storm Hydrograph
  • Stream Hydrographs
  • A plot of discharge ( flow rate) or stage (
    water level) versus time.
  • Stormflow Hydrograph
  • A plot of discharge or stage before, during, and
    after a specific storm.
  • Rising Limb
  • The steep advance portion of the hydrograph that
    reflects the onset of runoff
  • Falling Limb
  • Flow that tapers off gradually following the

  • Peak Stormflow
  • Generally produced by surface runoff, either by
    partial area contribution or Hortonian overland
    flow as well as direct precipitation on the
  • Interflow
  • Flow that takes longer to reach the channel
  • Dominates the falling limb of the hydrograph.
  • Baseflow
  • The flow before and after the storm
  • Generated principally by ground water discharge
    and unsaturated interflow.
  • Stormflow Volume
  • Total volume of streamflow associated with that
  • It can be determined from the area under the
    hydrograph when the hydrograph plots flow (not
    stage) vs time.

Hydrograph for 1997 Homecoming Weekend Storm
Stream Hydrograph
Flow behavior for different streams
Hydrograph Behavior
Hydrograph Behavior Also related to channel
Streamflow Variability
Measurement Units
  • cfs cubic feet per second
  • gpm gallons per minute
  • mgd million gallons per day
  • AF/day Acre-Feet per day
  • cumec cubic meters per second
  • Lps liters per second
  • Lpm liters per minute

Useful Conversions
  • 1 cfs ?
  • 2 AF/day
  • 450 gpm
  • 28.3 Lps
  • 1 m3/s 35.28 cfs
  • 1 mgd ? 1.5 cfs
  • 1 gpm 3.785 Lpm

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Weir Construction
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Weir Types
Weir Equations
  • Submerged Pipe
  • Q c ? r2 h1/2
  • Rectangular Weir
  • Q c W h3/2
  • V-notch Weir
  • Q c h5/2
  • where
  • Q is flow, cfs
  • c are weir coefficients
  • h is stage, ft
  • r is the pipe diameter, ft
  • W is the weir width, ft

Field Velocity Measurements
  • Flow Equation
  • Q v A
  • where
  • Q is the discharge, cfs
  • v is the water velocity, ft/s
  • A is the flow cross-sectional area, ft2

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Discharge Measurements
Manning's Equation
  • v (1.49/n) R2/3 S1/2
  • where
  • v is the water velocity, ft/s
  • n is the Manning's hydraulic roughness factor
  • R A / P is the hydraulic radius, ft
  • A is the channel cross-sectional area, ft2
  • P is the channel wetted perimeter, ft
  • S is the water energy slope, ft/ft

Mannings Equation
  • River Stage
  • The elevation of the water surface
  • Flood Stage
  • The elevation when the river overtops the natural
    channel banks.
  • Rating Curve
  • The relationship between river stage and discharge

Rating Curve
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  • Hydrologic Statistics
  • Trying to understand and predict streamflow
  • Peak Streamflow Prediction
  • Our effort to predict catastrophic floods
  • Recurrence Intervals
  • Used to assign probability to floods
  • 100-yr flood
  • A flood with a 1 chance in 100 years, or a flood
    with a probability of 1 in a year.

Return Period
  • Tr 1 / P
  • Tr is the average recurrence interval, years
  • P is exceedence probability, 1/years
  • Recurrence Interval Formulas
  • Tr (N1) / m
  • Gringarten Formula Tr (N1-2a) / (m-a)
  • where
  • N is number of years of record,
  • a 0.44 is a statistical coefficient
  • m is rank of flow (m1 is biggest)

Flood Prediction
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Peak Flows in Ungaged Streams
  • Qn a Ax Pn
  • where
  • A is the drainage area, and
  • Pn is the n-year precipitation depth
  • Qn is the n-year flood flow
  • Q2 182 A0.622
  • Q10 411 A0.613
  • Q25 552 A0.610
  • Q100 794 A0.605

Bankfull Discharge Qbkf 150 A0.63
Curve Number Method
  • Most common method used in the U.S. for
    predicting stormflow peaks, volumes, and
    hydrographs for precipitation events.
  • It is useful for designing ditches, culverts,
    detention ponds, and water quality treatment

Curve Number Method
  • P Precipitation, usually rainfall
  • Heavy precipitation causes more runoff than light
  • S Storage Capacity
  • Soils with high storage produce less runoff than
    soils with little storage.
  • F Current Storage
  • Dry soils produce less runoff than wet soils

  • r Runoff Ratio gt how much of the rain runs
  • r Q / P
  • r 0 means that little runs off
  • r 1 means that everything runs off
  • r F / S
  • r 0 means that the bucket is empty
  • r 1 means that the bucket is full
  • F P - Q
  • the soil fills up as it rains
  • Combining equations yields
  • Q P (P - Q) / S
  • Solving for Q yields
  • Q P2 / (P S)

  • S is maximum available soil moisture
  • S (1000 / CN) - 10
  • CN 100 means S 0 inches
  • CN 50 means S 10 inches
  • F is actual soil moisture content
  • F / S 1 means that F S, the soil is full
  • F / S 0 means that F 0, the soil is empty

Land Use CN S, inches Wooded areas 25
- 83 2 - 30 Cropland 62 - 71 4 -
14 Landscaped areas 72 - 92 0.8 - 4 Roads
92 - 98 0.2 - 0.8
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Curve Number Procedure
  • First we subtract the initial abstraction, Ia,
    from the observed precipitation, P
  • Adjusted Rainfall Pa P - Ia
  • No runoff is produced until rainfall exceeds the
    initial abstraction.
  • Ia accounts for interception and the water needed
    to wet the organic layer and the soil surface.
  • The initial abstraction is usually taken to be
    equal to 20 of the maximum soil moisture
    storage, S, gt Ia S / 5

  • The runoff depth, Q, is calculated from the
    adjusted rainfall, Pa , and the maximum soil
    moisture storage, S, using
  • Q Pa2 / (P_a S)
  • or by using the graph and the curve number
  • We get the maximum soil moisture storage, S, from
    the Curve Number, CN
  • S 1000 / CN - 10
  • CN 1000 / (S 10)
  • We get the Curve Number from a Table.

  • A typical curve number for forest lands is CN
    70, so the maximum soil storage is
  • S 1000 / 70 - 10 4.29"
  • A typical curve number for a landscaped lawn is
    86, and so
  • S 1000 / 86 - 10 1.63"

  • A curve number for a paved road is 98,
  • so S 0.20
  • Why isnt the storage equal to zero for a paved
  • The roughness, cracks, and puddles on a paved
    surface allow for a small amount of storage.
  • The Curve Number method predicts that Ia S / 5
    0.04 inches of rain must fall before a paved
    surface produces runoff.

Another CN Example
  • For a watershed with a curve number of 66, how
    much rain must fall before any runoff occurs?
  • Determine the maximum potential storage, S
  • S 1000 / 66 - 10 5.15"
  • Determine the initial abstraction, Ia
  • Ia S / 5 5.15 / 5 1.03"
  • It must rain 1.03 inches before runoff begins.
  • If it rains 3 inches, what is the total runoff
  • Determine the effective rainfall, Pa
  • Pa P - Ia 3" - 1.03" 1.97"
  • Determine the total runoff volume, Q
  • Q 1.972 / (1.97 5.15) 0.545"

Unit Hydrographs
Unit Hydrograph
Flood Routing
Unit Area Hydrographs
Unit Hydrograph Example
  • A unit hydrograph has been developed for a 100
    hectare watershed
  • The peak flow rate for a storm that produces 1 mm
    of runoff is 67 L/s
  • What is the peak flow rate for this same
    watershed if a storm produces 3 mm of runoff?
  • The unit hydrograph method assumes that the
    hydrograph can be scaled linearly by the amount
    of runoff and by the basin area.
  • In this case, the watershed area does not change,
    but the amount of runoff is three times greater
    than the unit runoff.
  • Therefore, the peak flow rate for this storm is
    three times greater than it is for the unit
    runoff hydrograph, or 3 x 67 L/s 201 L/s.

  • What would be the peak flow rate for a nearby
    50-ha watershed for a 5-mm storm?
  • Peak Flow Qp Qo (A / Ao ) (R / Ro )
  • where
  • Qp is the peak flow rate,
  • Qo is peak flow for reference watershed,
  • A is the area of watershed,
  • Ap is the area of reference watershed.
  • Q (67 L/s) (50 ha / 100 ha) (5 mm / 1 mm) 168
  • In this case, the peak runoff rate was scaled by
    both the watershed area and the runoff amount.

Forest Management
  • Forest streams have less stormflow and total flow
  • Forest litter (O-Horizon) increases infiltration
  • Forest canopies intercept more precipitation
  • higher Leaf-Area Indices (LAI)
  • Forest have higher evapotranspiration rates
  • Forest soils dry faster, have higher total storage

BMPs improve soil and water quality
  • Harvesting
  • High-lead yarding on steep slopes reduces soil
  • Soft tires reduces soil compaction
  • Water is filtered using vegetated stream buffers
  • Water temperatures also affected by buffers

  • Roads
  • Road runoff can be dispersed onto planar and
    convex slopes
  • Broad-based dips can prevent road erosion
  • Site Preparation
  • Burning a site increases soil erosion and reduces
  • Leaving mulch on soils increases infiltration
  • Piling mulch concentrates nutrients into local
    "hot spots"
  • Distributing mulch returns nutrients to soils
  • Some herbicides cause nitrate increase in streams

Agricultural Land Management
  • Overland flow is a main concern in agriculture
  • increases soil erosion, nutrients, and fecal
  • increases herbicides, pesticides, rodenticides,
  • Plowing
  • exposes the soil surface to rainfall (and wind)
  • mulching no-till reduces runoff and increases
  • terracing and contour plowing also helps
  • Pastures (livestock grazing)
  • increases soil compaction
  • reduces vegetative plant cover
  • increases bank erosion
  • rotate cattle between pastures and fence streams

Urban Land Management
  • Urban lands have more impervious surfaces
  • More runoff, less infiltration, recharge, and
  • Very high peak discharges, pollutant loads
  • Less soil storage, channels are straightened and
    piped, no floodplains
  • Baseflows are generally lower, except for
    irrigation water (lawns septic)

Benefits of Riparian Buffers
  • Bank Stability
  • The roots of streambank trees help hold the banks
  • When streambank trees are removed, streambanks
    often collapse, initiating a cycle of
    sedimentation and erosion in the channel.
  • A buffer needs to be at least 15 feet wide to
    maintain bank stability.
  • Pollutant Filtration
  • As dispersed overland sheet flow enters a
    forested streamside buffer, it encounters organic
    matter and hydraulic roughness created by the
    leaf litter, twigs, sticks, and plant roots.
  • The organic matter adsorbs some chemicals, and
    the hydraulic roughness slows down the flow.
  • The drop in flow velocity allows clay and silt
    particles to settle out, along with other
    chemicals adsorbed to the particles.
  • Depending on the gradient and length of adjacent
    slopes, a buffer needs to be 30-60 feet wide to
    provide adequate filtration.

  • Denitrification
  • Shallow groundwater moving through the root zones
    of floodplains is subject to significant
  • Removal of floodplain vegetation reduces
    floodplain denitrification
  • Shade
  • Along small and mid-size streams, riparian trees
    provide significant shade over the channel, thus
    reducing the amount of solar radiation reaching
    the channel so summer stream temperatures are
    lower and potential dissolved oxygen levels are
  • Buffers need to be at least 30 feet wide to
    provide good shade and microclimate control, but
    benefits increase up to 100 feet.
  • Organic Debris Recruitment
  • River ecosystems are founded upon the leaves,
    conifer needles, and twigs that fall into the
  • An important function of riparian trees is
    providing coarse organic matter to the stream
  • Buffers only need to encompass half the crown
    diameter of full-grown trees to provide this

  • Large Woody Debris Recruitment
  • Large woody debris plays many important
    ecological functions in stream channels.
  • It helps scour pools, a favored habitat for many
  • It creates substrate for macroinvertebrate and
    algae growth, and it forms cover for fish.
  • It also traps and sorts sediment, creating more
    habitat complexity.
  • Woody debris comes from broken limbs and fallen
  • The width of a riparian buffer should be equal to
    half a mature tree height to provide good woody
    debris recruitment.
  • Wildlife Habitat
  • Many organisms, most prominently certain species
    of amphibians and birds use both aquatic and
    terrestrial habitat in close proximity.
  • Maintaining a healthy forested riparian corridor
    creates important wildlife habitat.
  • The habitat benefits of riparian buffers increase
    out to 300 feet.

Chapter 12 Quiz
  • 1. A Curve Number of 95 is most likely typical
  • a. farmland b. forestland c. suburbs d.
    parking lot
  • 2. Manning's equation is used to measure (circle
  • a. flow depth b. flow velocity c. stream
    discharge d. flow area
  • 3.What is cross-sectional area, A, and discharge
    of a stream, Q, if the average depth is 9, the
    width is 20 feet, and the velocity is 27 ft/min
    (circle any)
  • a. A 15 ft2 Q 6.75 cfs
  • b. A 150 in3 Q 4,860 AF/yr
  • c. A 1.5 ft Q 400 in/day
  • d. A 180 in2 Q 3000 gpm
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