rainfall-runoff modeling

ERS 482/682 (Fall 2002) Lecture 14 - 1

Rainfall-runoff modeling

ERS 482/682Small Watershed Hydrology

ERS 482/682 (Fall 2002) Lecture 14 - 2

What are models?

• A model is a conceptualization of a system– In hydrology, this usually involves the

responseresponse of a system to an external external stimulistimuli

runoffrunoff(discharge)(discharge)rainfallrainfall

ERS 482/682 (Fall 2002) Lecture 14 - 3

What are models?

• A model is a conceptualization of a system– In hydrology, this usually involves the

responseresponse of a system to an external external stimulistimuli

• Models are tools that are part of an overall management process

ERS 482/682 (Fall 2002) Lecture 14 - 4

Managementobjectives,

options,constraints

Modeldevelopment

andapplication

Makemanagement

decisions

Datacollection

ERS 482/682 (Fall 2002) Lecture 14 - 5

Why model?

• Systems are complex

http://water.usgs.gov/outreach/OutReach.html

ERS 482/682 (Fall 2002) Lecture 14 - 6

Why model?

• Systems are complex

• If used properly, can enhance knowledge of a system

• Models should be built on scientific knowledge

• Models should be used as ‘tools’

ERS 482/682 (Fall 2002) Lecture 14 - 7

Rules of modeling

• RULE 1: We cannot model reality– We have to make assumptions

• DOCUMENT!!!!

• RULE 2: Real world has less precision than modeling

ERS 482/682 (Fall 2002) Lecture 14 - 8

Precision vs. accuracy

• Precision– Number of decimal places– Spread of repeated computations

• Accuracy– Error between computed or measured value

and true value

error ofestimate

= field error + model error

ERS 482/682 (Fall 2002) Lecture 14 - 9

The problem with precise models…

we get more precision from model than is real

ERS 482/682 (Fall 2002) Lecture 14 - 10

Fundamental model concepts

DRIVERDRIVER

QQRESPONSERESPONSE

SYSTEMSYSTEMREPRESENTATIONREPRESENTATION

areatopography

soilsvegetationland use

etc.

ERS 482/682 (Fall 2002) Lecture 14 - 11

Basic model

Mathematical equations and

parametersDRIVERDRIVER RESPONSERESPONSE

SYSTEMSYSTEMREPRESENTATIONREPRESENTATION

ERS 482/682 (Fall 2002) Lecture 14 - 12

Figure 9-37 (Dingman 2002)

The wholeworld

The modelworld

ERS 482/682 (Fall 2002) Lecture 14 - 13

Runoff processes to model

ASSUMPTION!ASSUMPTION!

Small watershed

Table 9-8 (Dingman 2002)

ERS 482/682 (Fall 2002) Lecture 14 - 14

Effective water input, Weff

• Effective (excess) rainfall– Does not include evapotranspiration or

ground water storage that appears later

efeff QW ASSUMPTION!ASSUMPTION!

DSETWW ceff

where ET = event water evapotranspired during eventSc = canopy storage during eventD = depression storage during event = soil-water storage during event

usually small

antecedentsoil-watercontent, 0

ASSUMPTION!ASSUMPTION!

ERS 482/682 (Fall 2002) Lecture 14 - 15

Estimating Weffconstantfraction

constantrate

initialabstraction

infiltrationrate


ERS 482/682 (Fall 2002) Lecture 14 - 16

Estimating Weff

• SCS curve-number method

max

2

max

8.02.0

VWVW

Weff

where Vmax = watershed storage capacity [L]

W = total rainfall [L]

initialabstraction


ERS 482/682 (Fall 2002) Lecture 14 - 17

Estimating Weff

• SCS curve-number method

max

2

max

8.02.0

VWVW

Weff

where Vmax = watershed storage capacity [inches]

W = total rainfall [inches]

101000 CN

Based on land use in Table 9-12,soil group in Table 9-11, and

soil maps from NRCS

ERS 482/682 (Fall 2002) Lecture 14 - 18

Example 9-6Land cover

Soil group

Area (mi2)

Fraction of total area

Forest B 0.72 0.58

Forest C 0.15 0.12

Meadow A 0.26 0.21

Meadow B 0.11 0.09

58

72

30

58

Table 9-12

Given: W = 4.2 inTW = 3.4 hrA = 1.24 mi2

L = 0.84 miS = 0.08

From NRCSsoils maps

and GIS

ConditionII CN

54

5809.03021.07212.05858.0

CN

inches 52.81054

1000max V

inches 57.0

52.88.02.452.82.02.4 2

effW

ERS 482/682 (Fall 2002) Lecture 14 - 19

Example 9-6Land cover

Soil group

Area (mi2)

Fraction of total area

Forest B 0.72 0.58

Forest C 0.15 0.12

Meadow A 0.26 0.21

Meadow B 0.11 0.09

58

72

30

58

Table 9-13


L = 0.84 miS = 0.08

ConditionI CN

35 CN

inches 6.18max V

inches 012.0effW

X 38

X 53

X 15

X 38

ERS 482/682 (Fall 2002) Lecture 14 - 20

SCS method for peak discharge

r

Deff

pk T

AWq

484ft3 s-1

inches mi2

hr

ERS 482/682 (Fall 2002) Lecture 14 - 21


r

Deff

pk T

AWq

484

cWr TTT 6.05.0

From Table 9-9

ERS 482/682 (Fall 2002) Lecture 14 - 22


r

Deff

pk T

AWq

484

Example 9-7


L = 0.84 miS = 0.08

Weff = 0.57 in for Condition II

Tc = 0.44 hr from Table 9-9

hr 96.144.06.04.35.0 rT

1-3 s ft 17596.1

57.057.0484 pkq

ERS 482/682 (Fall 2002) Lecture 14 - 23

Rational method

• AssumesAssumes a proportionality between peak discharge and rainfall intensity

DeffRRpk AiCuq

where uR= unit-conversion factor (see footnote 7 on p. 443)CR = runoff coefficientieff = rainfall intensity [L T-1]AD = drainage area [L2]

proportionality coefficient

Q=CIA

ERS 482/682 (Fall 2002) Lecture 14 - 24

Rational method

• Additional assumptionsassumptions:– Rainstorm of uniform intensity

over entire watershed– Negligible surface storage

– Tc has passed

– Return period for storm is same for discharge

DeffRRpk AiCuq

Apply to small(<200 ac) suburbanand urban

watersheds

Q=CIA

ERS 482/682 (Fall 2002) Lecture 14 - 25

Rational method

• The proportionality coefficient, CR accounts for– Antecedent conditions– Soil type– Land use– Slope– Surface and channel roughness

DeffRRpk AiCuq

Q=CIA

ERS 482/682 (Fall 2002) Lecture 14 - 26

Rational method

• Approach– Estimate Tc

DeffRRpk AiCuq

Q=CIA

Figure 15.1 (Viessman and Lewis 1996)

– Estimate CR

Table 9-9

– Estimate ieff for return period T • Usually use intensity-duration-frequency (IDF)

curves

Table 9-10 or Table 10-9 (Dunne and Leopold 1978)

ERS 482/682 (Fall 2002) Lecture 14 - 27

Rational method

• Approach– Estimate Tc

DeffRRpk AiCuq

Q=CIA

– Estimate CR

Table 9-9

– Estimate ieff for return period T • Usually use intensity-duration-frequency (IDF)

curves

Table 9-10 or Table 10-9 (Dunne and Leopold 1978)

– Apply equation to get qp

Return period (yrs) Multiplier for CR

2-102550100

1.01.11.21.25

Viessman and Lewis (1996)

ERS 482/682 (Fall 2002) Lecture 14 - 28

Rational method vs. SCS CN method

• Rational method– Small (<200 acres) urbanized watershed– Small return period (2-10 yrs)– Have localized IDF curves

• SCS Curve Number method– Rural watersheds– Average soil moisture condition (Condition

II)

ERS 482/682 (Fall 2002) Lecture 14 - 29

Adaptations

• Rational method– Modifications for greater return periods– Runoff coefficients for rural areas (Table 10-

9: Dunne and Leopold 1978)

– Modified rational method for Tc TW

• SCS TR-55 method– Applies to urban areas– Has a popular computer program

ERS 482/682 (Fall 2002) Lecture 14 - 30

Adaptations

• SCS TR-55 method (cont.)– Approach

• Find the type of storm that applies from Figure 16.19 (Viessman and Lewis 1996)

• Use CN to determine Ia from Table 15.5 (Viessman and Lewis 1996)

• Calculate Ia/P• Find qu = unit peak discharge from figure for storm

type in cfs mi-2 in-1 (Viessman and Lewis 1996)• Find runoff Q in inches from Figure 10-8 (Dunne

and Leopold 1978) for P• Find peak discharge for watershed as Qp = quQA

ERS 482/682 (Fall 2002) Lecture 14 - 31

• Definition: hydrograph due to unit volume of storm runoff generated by a storm of uniform effective intensity occurring within a specified period of time

Unit hydrograph

AssumptionAssumption: Weff = Qef

Multiply unit hydrographby Weff to get storm

hydrograph

QQefef 1 unit

uniform

intensity

over TW

ERS 482/682 (Fall 2002) Lecture 14 - 32

Unit hydrograph development

• Choose several hydrographs from storms of same duration (~X hours) (usually most common/critical duration)

• For each storm, determine Weff and plot the event flow hydrograph for each storm

• For each storm, multiply the ordinates on the hydrograph by Weff

-1 to get a unit hydrograph• Plot all of the unit hydrographs on the same graph with the

same start time• Average the peak values for all of the unit hydrographs, and

the average time to peak for all of the hydrographs• Sketch composite unit graph to an avg shape of all the

graphs• Measure the area under the curve and adjust curve until

area is ~1 unit (in or cm) of runoff

Figure 9-45

End result: X-hr unit hydrograph

ERS 482/682 (Fall 2002) Lecture 14 - 33

Unit hydrograph application

• Multiply unit hydrograph by storm size• Add successive X-hour unit hydrographs

to get hydrographs of successive storms (Figures 9-46 and 9-47)

ERS 482/682 (Fall 2002) Lecture 14 - 34

Unit hydrograph

• Predicts flood peaks within ±25%• Need only a short period of record• Can apply to ungauged basins by

regionalizing the hydrograph– Synthetic unit hydrographs

ERS 482/682 (Fall 2002) Lecture 14 - 35

Synthetic unit hydrograph

• Unit hydrograph for ungauged watershed derived from gauged watershed– Example (Dingman 2002):

** exp

1Tt

Tth

– Example (Dunne and Leopold 1978):

3.0ctLP LLCT

LPW TT 18.0

LP

Dpp T

ACq

LPb TT 372

where Ct = coefficient (1.8-2.2)L = length of mainstream from outlet

to divide (miles)Lc = distance from outlet to point on

stream nearest centroid (miles)Cp = coefficient (370-440)Tb = duration of the hydrograph (hrs)

ERS 482/682 (Fall 2002) Lecture 14 - 36

-index

Figure 8-7 (Linsley et al. 1982)Figure 10-7 (Dunne & Leopold 1978)

rainfall-runoff modeling

Documents