Runoff CalculationsPredicting Runoff Depth, Volume and Peak Flow

Environmental Hydrology

Lecture 11

Runoff ProductionA Refresher

• Horton overland flow

time

Infil

trat

ion

rate

, i (

mm

/hr)

Pre

cipi

tatio

n r

ate,

p (

mm

/hr)

p > i overland flow

Robert E. HortonImage source:American Geophysical Union

The HydrographA Refresher

Ward & Trimble, Fig. 5.11

Infiltration

Predicting Runoff and Storm Flow

• The Rational Equation (the SIMPLE model)

– Peak runoff discharge

• The Curve Number concept

– Storm runoff depth runoff volume

• The Graphical Peak Discharge method

– Peak runoff discharge

• Empirical Regression models

– e.g. USGS National Flood Frequency model

The Rational Method

AiCq ***008.1

Where…• q is peak flow in ft3/sec• C in an empirical coefficient• I is the rainfall intensity (in/h)• A is the catchment area (acres)

• The 1.008 factor is… 1 in/h * 1ft/12in *1h/3600sec * 43,560ft2/acre

Rational Coefficients

Concept: Soil Hydrogroups

• Group A: high infiltration (>0.3 in/h), low runoff

• Group B: moderate infiltration when wet (0.15 to 0.30 in/h), moderate runoff

• Group C: slow infiltration when wet (0.05 to 0.15 in/h), high runoff

• Group D: very low infiltration when wet (<0.05 in/h), very high runoff

Rational Method Assumptions and Limitations

• Rainfall is uniform

• Time of concentration (tc) is the time required for water to get from the most distant point in the watershed to the point of observation

• Peak runoff ≈ Peak rainfall intensity lagged by tc

• Frequency of runoff ≈ frequency of rainfall

• Best for small watersheds (<1 mile2)

Derivation of the CN equation

QFIP a

S

F

IP

Q

a

)(

SIa

Where…

P = precipitation (in)

Ia = initial abstraction (in)

F = cumulative infiltration (in)

Q = direct runoff (in)S = max. potential retention (in)

λ = coefficient, usually 0.2

)(

)( 2

SIP

IPQ

a

a

)8.0(

)2.0( 2

SP

SPQ

Mass Balance

Proportionality

SubstitutionS=f(P-Ia, Q)

Proportionality

Substitution

CN = curve number

inchesfor 101000

CN

S

mmfor 25425400

CN

STR-55 Manual, see also Mishra et al. 2006

Concept: Curve Numbers

TR-55 Manual

Curve Numbers for Cover Types

Ward and Trimble, after NRCS

Concept: Antecedent Moisture Content(based on previous 5-day P)

• AMC-1 (Dry)– Dormant season P <0.5 in– Growing Season P <1.4 in

• AMC-2 (Average)– Dormant season 0.5<P <1.1 in– Growing Season 1.4<P <2.1 in

• AMC-3 (Wet)– Dormant season P >1.1 in– Growing Season P >2.1 in

Curve Number Adjustments for AMC

Ward and Trimble, after NRCS

0.0

0.5

1.0

1.5

2.0

2.5

0 20 40 60 80 100

CN forAMC-II

Adj

ustm

ent F

act

or

AMC-III

AMC-II

AMC-I

Curve Number (TR-55)Assumptions and Limitations

• Describes average and not extreme events

• Does not explicitly account for storm duration or intensity

• The term Ia is ill-defined and has important influences on the derivation of CN’s

• Does not deal with snow or rain on frozen ground

• Should not be used for storms <0.5 in

• Does not explicitly deal with groundwater effects

• Don’t use if the weighted CN is <40, inaccurate

The Graphical Peak Discharge Method

Where…• q is the peak runoff (ft3/sec)

• qu is the unit peak discharge (ft3/sec per square mile per inch of rain or csm/in)

• A is area (square miles)• Q is the total runoff depth (from CN, in inches)• F is a ponding adjustment factor

FQAqq u ***

Can be used to relate Q from CN approach to q.Essentially relates storm volume to storm peak q.

The “graphs” of the Graphical Method

The Graphical MethodAssumptions and Limitations

• Homogenous land cover/use in catchment

• Only one main stream, or an balance network

• “ponding” is off-stream, not in-stream

• Need some idea of Ia

• Need tc = f(hydraulic length, maximum retention [S], land slope, return interval)

Empirical Regression Models

• Where• DA = drainage area• S = channel bed slope• P = reference precipitation (e.g. 2y/24h)• BDF = an index of development• IC = percent impervious cover• U = indices of other land uses• STR = percent lakes, ponds, wetlands• E = elevation effect• Qft = the reference discharge event (e.g. 2y/24h)• X, a, b, c,… are fitted coefficients

ift

ihgf

edcbRI

QESTRUIC

BDFXPSDAaq

)()()1()()(

)13()()()(

This equation is used by FEMA for national flood forecasting (See NFF model)

Later in Lab:Reconstructing Whole Hydrographs

• Unit Hydrographs

• Time-area method