ASCE HEC-RAS SeminarJanuary 25, 2006
Session 1AFlow Estimates
Quotes As far as the laws of mathematics refer to
reality, they are not certain; as far as they are certain they do not refer to reality. Albert Einstein
An independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observation. Niels Bohr
Topics of Session
Review of Synthetic Hydrographs Hydrograph Timing Parameters Hydrograph Shapes
Selection of Parameters in Hydrographs News NRCS Guidance : Ia and CN
Effects of Parameter Uncertainty Importance of Thresholds of Behavior
Flow Estimates Estimating the flow from existing and
predicted conditions in a basin is often considered a ‘black art’ due to it’s uncertainty. But, the design analysis must be competed, with or without understanding. Better design decisions are possible by considering uncertainty, and recognition that changes often reflect “steps” or thresholds.
Synthetic Hydrographs
Are used where rainfall-runoff data is not available.
Are based on observed behavior incorporation ‘parameters’ to be applied in new locations.
Incorporate a great deal of uncertainty due to the nature of runoff processes.
Acceptable Methods in Area
SBUH Linear Reservoir Model Developed in urban basins and reflects simplified
hydrograph behavior. SCS (NRCS) Dimensionless Unit Hydrograph.
Based on thousands of observations across the nation, predominantly agricultural lands which implies many other characteristics. Requires convolution of inputs (But computers work cheap)
BOTH REQUIRE TIMING PARAMETERS BOTH REQUIRE A RUNOFF DEPTH CALCULATION BOTH REQUIRE A STORM HYDROGRAPH
SBUH Input
Routing Parameter Timing Parameter Storm Hydrograph Effective Runoff Depth
Usually from NRCS CN method due to data availability
WHY SBUH?
Not a compelling reason to use in design, but very useful to see effects of input.
Not significantly different from NRCS and much simpler.
No matter how nice a suit you put on a pig, he’s still a pig.
SBUH Calculations w/Uncertainty
Runoff at 15 min dt
0.0
5.0
10.0
15.0
0.00 6.00 12.00 18.00 24.00Time (hr)
Flo
w (
cfs)
15 min calc tc 40
15 min calc tc 5
Location of Basins for CN
State Town State Town
Arizona Safford New Mexico Albuquerque
Arkansas Bentonville New Mexico Mexican Springs
California Santa Paula New York Bath
California Watsonville Ohio Coshocton
Colorado Colorado Springs Ohio Hamilton
Georgia Americus Oklahoma Muskogee
Idaho Emmett Oregon Newberg
Illinois Edwardville Texas Garland
Maryland Hagerstown Texas Vega
Montana Culbertson Texas Waco
Nebraska Hastings Virginia Dansville
New Jersey Freehold Wisconsin Fenimore
NRCS Unit Hydrograph Input
CN Curve Number Complex Reflects ALL Soil AND Surface conditions
Ia Initial Abstraction Ratio Reflects the soil losses prior to runoff
ARC Antecedent Runoff Condition (AMC) Time of Concentration
Reflects the speed runoff exits the basin K Shape Factor
Reflects the base time (system memory) for input
NRCS Hydrograph Properties ALL inputs, except, K vary in time and
space and all are also unknowable The combination of statistical variation
and our state of ignorance of the true conditions produces uncertainty.
The recent NRCS update to the important NEH-4 (Hydrology) is Part 630. In it the variation of CN, and ARC (used to be called AMC), is discussed. IMPORTANT CONCEPT
NEH Hydrology Part 630
See Chapter 9 for tables of CN of Urban Lands
See Chapter 10 for: Development of CN and Ia/S Determination of ROD (Q) Alternate CN
Run Off Depth ROD (Q)
From: Curve Number and Initial Abstraction
Least sq’s for WS26030 Coshocton, OH, BA 303 acres. For the natural data (squares): S = 4.0974 inches, CN = 70.8, = 0.0179, R2 = 50.50%, and SE = 0.32 inch.
For the ordered data (triangles): S = 2.0943 inches, CN = 82.6, = 0.1364, R2 = 99.17%, and SE = 0.0372 inches.
ARS WS26030 Coshocton, Ohio
0
1
2
3
4
5
6
0 1 2 3 4 5 6
Rainfall P (inch)
Dire
ct R
unof
f Q
(in
ch)
Q = POrdered
Natural
Many Events at One Basin
ARS WS26030 Coshocton, Ohio cumulative frequency
0
0.08
0.16
0.24
0.32
0.4
0 20 40 60 80 100
Percent Less than
Ia/S
An example of the array of found by event analysis for watershed 26030
Many Events at 134 Basins
ARS Data Event Analysis Lambda Distribution
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0 20 40 60 80 100
Percentage Less Than
Media
n L
am
bda =
Ia/S
Cumulative frequency distribution of values from Event Analysis method 134 Basins
Summary Results of values from model fitting Natural Data Ordered Data
N TotalEvent
Max Mean Median Min Max Mean Median Min
ARS 134 12499 0.5766 0.0555 0.0001 0 0.9682 0.1491 0.0736 0
USLE 137 11140 0.996 0.0997 0 0 0.9266 0.1581 0.061 0
Others 36 4392 0.4727 0.04 0 0 0.9793 0.0992 0.0044 0
Total 307 28031 0.996 0.0734 0 0 0.9793 0.1472 0.0618 0
From: “ Curve Number: Beyond the Handbook”
0
1
2
3
4
5
0 1 2 3 4 5
P(in)
Q(i
n)
Hastings, Nebraska WS44028 (1941-1954)
CN(II) = 85
CN(III) = 94
CN(I) = 70
ROD (Q) vs P for ARC I and III
Modified Runoff Eq’n
Using Ia/S=0.05 the runoff equation becomes Q = (P-0.05S)2/(P+0.95S) P0.05S
Q = 0 P0.05S
However, the S values in the above equation are not the same as previously used assuming Ia/S=0.20. They are defined on a system of Ia/S==0.05. The result of conversion is:
S0.05=1.33S0.201.15
Modified Curve Numbers
100 CN0.05 = -------------------------
1.879[100/CN0.20 –1]1.15 + 1
Comparative hydrographs for conjugate
CNs
0
400
800
1200
1600
2000
0 1 2 3 4 5
Time - hr
Dis
char
ge -
ft3 /s
ec
CN0.20 = 90
CN0.20 = 70
CN0.20 = 50
P = 3.60 in - 3 hrNEH4 Type B Distributiontc = 0.50 hrDA = 640 Ac
NRCS Guidance NRCS now recommends that CN be
determined from local measurements rather than from tabled values.
Even IF measurements were available and IF they were utilized the variation of results is very large.
Design should not ignore the uncertainty of input.
Hydrograph Timing Estimates
The ASCE Manual of Practice for Hydrology lists many timing estimates developed for various regions and various land uses. These are given in your handouts.
The NRCS publications provide the ‘handbook’ equation in PART 630 Chapter 15.
Hydrograph Shape Factor K Just as having a single CN for a
specific soil cover complex is not possible having a single hydrograph shape for all runoff events is also not possible.
Variations in shape occur from: Slope Soil Swamps, Ponds etc
Shape and Memory Time
The “standard” NRCS hydrograph shape has a memory time that is 8/3 the time to peak. Since a unit hydrograph must contain a 1-inch volume of runoff, this defines the shape, and the magnitude of the peak flow.
Shape Calculations
Hydrograph Shape k=((2*(5280)^2)/(12*3600))*((A*ROD)/(Tb/Tp)*Tp)for A=1 mi^2 Qp=((A*(ROD/12)*2*(5280)^2)*(Tp/Tb)*(1/3600))For ROD =1 inch Qp=K*A*ROD/TpTp= 1 hour Vol=A*(ROD/12)*5280^2=1/2*Tb*Qp*3600
Tb/Tp k1.666667 774
2 645 `2.333333 5532.666667 484
3 4303.333333 387
4 323
Triangular Unit HydrographsK= 774.4 K= 645.3333 K= 553.1429 K= 484 K= 430.2222 K= 387.2 K= 322.6667Q t Q t Q t Q t Q t Q t Q t
0 0 0 0 0 0 0 0 0 0 0 0 0 0774.4 1 645.3333 1 553.1429 1 484 1 430.2222 1 387.2 1 322.6667 1
0 1.666667 0 2 0 2.333333 0 2.666667 0 3 0 3.333333 0 4
Effect of Base Time on Shape Factor K
0
100
200
300
400
500
600
700
800
0 0.5 1 1.5 2 2.5 3 3.5 4
T/Tp (hr)
Qp
/RO
D (
cfs/
mi^
2) 774
645
553
484
430
387
323
Relevance of Shape?
The original SCS hydrograph data was collected on agricultural lands in the mid-west and southeast.
Is it reasonable to assume a rain event in Spokane on Browne’s Mtn. will result in the same shape as one in Georgia on a peanut farm?
My Example 5 years ago a CED project looked at runoff
from an undeveloped basin near Glenrose and 57th. We installed a water level recorder and a v-notch wier and monitored rain events for 3 1/2 years to compare to the predicted runoff to confirm CN in Spokane. Result?
NO RUNOFF IN CHANNEL AT ALL DESPITE A STOCK POND IN DRAW!
Your conclusions?
Design Example 20 acre site 12 acres CN 71, 8 acres CN
97. Tc is 45 min Tlag is 30 min. Variation of each parameter is defined Both the SBUH with uncertainty and the
HEC-HMS SCS method are used to estimate flow from a P of 2.2 inches in a SCS Type II storm Ia=0.07 S
SMADA observed for K changes? Haestad Culvertmaster software used
Culvert Schematic
HW 105.0
Invert 101.0
TW Varies
Invert 100.0
L=125 ft.
Q Varies