Hydrologic Statistics & Hydraulic Behavior.
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Explore storm hydrographs, discharge measurements, river stages, flood predictions, and more in hydrologic studies. Learn about Manning's Equation, weir types, and curve number methods in this comprehensive guide.
Hydrologic Statistics & Hydraulic Behavior.
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Chapter 12 Hydrologic Statistics and Hydraulics
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.
Peak Stormflow: • Generally produced by surface runoff, either by partial area contribution or Hortonian overland flow as well as direct precipitation on the channels. • 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 storm • It can be determined from the area under the hydrograph when the hydrograph plots flow (not stage) vs time.
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
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
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
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
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 = (N+1) / m • Gringarten Formula: Tr = (N+1-2a) / (m-a) • where • N is number of years of record, • a = 0.44 is a statistical coefficient • m is rank of flow (m=1 is biggest)
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
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 facilities.
P = Precipitation, usually rainfall • Heavy precipitation causes more runoff than light precipitation • 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 => how much of the rain runs off? • 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
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, => 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.
Examples • 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 isn’t the storage equal to zero for a paved surface? • 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 volume? • 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 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.
