Urban Storm Drain Design: Rainfall-Runoff relations

Drainage Area• Drainage Area is the watershed area that

contributes runoff to a given point.• In urban design, it is usually measured in acres.• In developed areas, the boundaries of a

watershed are usually heavily influenced by man-made features (streets, curbs, etc) and so may be different than what natural topography would have dictated.

Time of concentration

• Time of concentration, Tc, is the travel time for a conceptual “drop” of water to travel from the most hydrologically remote point on the watershed to the “outlet”, or point of interest, under the assumed conditions.

• Tc is used as the rainfall averaging time for rainfall intensity.

• A constant intensity rainfall for at least Tc is assumed to produce the maximum watershed response for a given Annual Exceedance Probability (AEP).

• Tc is considered to be a physical property of each watershed.

Intensity–Duration–Frequency• Intensity of rainfall- the average rate of rainfall

(depth of rainfall per unit time) over a given time unit (5-minutes, 15-minutes, etc.).• Typically expressed in inches per hour

• Duration- the time span considered for a given calculation. • In urban drainage, the duration is usually the

longer of Tc, or a specified minimum time span.

• Frequency- denotes the probability of observing a given event, in this case a given intensity over a given duration.

Urbanization• Alteration of the landscape by development of man-

made features such as buildings, streets, and parking lots.

• Alters the character and pattern of both runoff generation and runoff mass transport compared to natural watershed.

• Urbanization usually results in:• Greater runoff rates.• Shorter time to peak.• Greater runoff volumes.• Greater runoff pollution.

Urbanization• Quantification of urbanization is a challenge. • Often pseudo-quantified by:

• Percent impervious area• Percent directly connected impervious area• Basin development factor

Impervious area• Area covered by “hardscape”, roofs, streets, parking

lots, or other surfaces that impede infiltration.• Simplistically is thought to increase runoff by

preventing infiltration.• Reduces magnitude of the infiltration component

of the loss function• Is a useful metric of urbanization and correlates to

the effects of urbanization that we expect.

Streets and flow in streets• Curb-and-gutter sections

Curb

Gutter

Inlet (Curb Opening + Grate)

Streets and flow in streets• Ditch sections

Streets and flow in streets• Flow in curb-and-gutter sections

Influences: time travel, losses

Improved flow paths• Streets and roads;• “improved” drainageways (straightened, widened,

cleared, lined, maintained);• Storm drains (sewers);• Reduced travel time;• Altered “critical duration”• Reduced losses• Reduced attenuation

Intensity–Duration relations• When a great deal of rainfall data is analyzed for

various moving time windows, the result is that as the duration of interest (size of the time window) increases, accumulated depth in that time window increases, but not at a proportional rate.

• The rate of increase diminishes with increasing duration.

• Therefore, the average intensity (depth/time) over the time window also diminishes

Discussion of time

Rational & Modified Rational equation• The “Rational Equation” is an equation that is used in

the vast majority of urban storm drain designs.• The basic equation (HDM) is:

• Z is a dimensional correction coefficient• C is a “runoff coefficient”• I is rainfall intensity for an appropriate duration

and frequency• A is contributing area, in acres.

Rational & Modified Rational equation• In U.S. Customary (English) units:• Q is in cfs• I is in in/hr• A is in Acres• K is dimensionless (Value =1 )• C is in

Rational & Modified Rational equation• In SI units:• Q is in cms• I is in mm/hr• A is in hectares (10,000 square meters)• K is dimensionless (Value = 360)• C is in

Rational Equation Assumptions• Assumes that all rainfall produces a proportional

runoff response• Assumes that we know what that proportion is (the

runoff coefficient)• Assumes that the design condition consists of

rainfall pulse of the chosen duration occurs isolated in time from other pulses, with no other rainfall influences.

Assumptions

Contributing area• The area contributing to a point of interest

contributes in a simple, linear way (essentially as a regular rectangle and as a kinematic wave)

• The area contributing to a point is small (the usual upper bound is 200 acres)

• The area contributing to a point is reasonably homogeneous

Time and intensity• The relationship between time and average

intensity is inversely proportional- as time of interest increases, average intensity decreases even though accumulated depth of precip increases.

• This relationship can be approximated by a smooth functional relationship to some degree.

• Such a functional relationship is not valid for very short time periods (the normal lower bound is 10 minutes).

Runoff coefficients• A “Runoff Coefficient” is essentially a constant of

proportionality; the fraction of rainfall that is seen as runoff.

• Runoff coefficients for the simple, basic Rational Equation (instantaneous discharge) act on the INTENSITY of rainfall for a chosen duration.

• Runoff coefficients for the Modified version of the Rational Equation act on the DEPTH of rainfall for a chosen duration.

• There is NO IMPLICATION that these two forms of runoff coefficient are equal (!!!!).

Runoff coefficients• Runoff coefficients are tabulated, and selected from

a land use description.

Summary

• Drainage Area, Time of Concentration, Urbanization • Intensity-Duration-Frequency• Sections

• Curb-and-Gutter• Ditch

• Rational Equation• Runoff Coefficients