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