Runoff

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General Considerations

runoff is one of the two major compartments that precipitation can fill (the other is infiltration)

runoff can occur whenever water is applied to the ground at a higher rate than it can infiltrate
nearly all the water applied to a dry soil might infiltrate
with continued application, the soil begins to saturate, the water ponds on the surface and depressions are filled
once depression storage is filled, overland flow begins

overland flow is flow in thin sheets of water running over the surface of the ground

it usually does not go further than about 100’ before concentrating into rivulets

overland flow combines into stream channels where channel storage and stream flow occurs

Note: The term runoff can include both channel flow and overland flow.
sources of runoff

precipitation on bodies of water
precipitation on soil
snowmelt
groundwater flow from aquifers
interflow
return flows from irrigation
wastewater discharges

Runoff is produced by an interaction of precipitation and watershed

precipitation effects

type of precipitation has an effect

frozen water has a lower rate of runoff

duration

a longer storm leads to more runoff

amount

more rain gives more runoff

temporal variations in intensity

if the peak occurs early in the storm event (ie, an early storm); the peak flow will be lower
if the peak occurs later in the storm event; the peak flow will be higher

spatial distribution in precipitation

often assumed to be uniform (for lack of more info)

precipitation and flooding

the probable maximum flood (PMF) for a given return period can be used to size water carrying or containing structures

the PMF is predicted to occur if the PMP happens during the worst possible conditions (saturated soil) etc

watersheds vs drainage basins

a watershed is the land area contributing surface runoff to point
a drainage basin is the land area contributing both surface and subsurface water to a river and its tributaries

the area contributing runoff may increase with increasing precipitation since blocked areas may overflow

the imaginary lines that separate one watershed from another are called divides or topographic divides
likewise, drainage breaks separate drainage basins

basin characteristics affecting runoff

soil

texture, structure, compaction etc

land use and cover

vegetation
pavement
buildings

shape

the closer the center of area is to the outlet of the watershed, the higher the peak rate of runoff

stream patterns

dendritic
trellis: right angle tributaries running into long main stream
deranged: swampy areas

geology

lithologic effects

composition, texture and arrangement of rocks

structural effects

faults and folds

Factors Affecting Runoff

Effects of soil

soil characteristics greatly affect the degree of runoff versus infiltration

clay content reduces infiltration, especially after the ground is saturated with water (which swells the clay)

sandy soil or friable loams, both of which have low clay content, have higher rates of infiltration

more densely compacted soils have lower rates of infiltration

note: rainfall can actually compact soil
rainfalling directly on soil also tends to plug the opening in the ground with fines from near the surface (like espresso grind coffee in a melitta filter)

waterlogged soil has a lower rate of infiltration than dry soil

frozen soil has almost no infiltration (it may actually be coated with ice

thus the timing and dynamics of a storm event can have a great influence on the proportion of runoff

generally speaking, longer or repeated rains result in more runoff

human development of an area usually has a dramatic effect on increasing runoff

paving and roofs have essentially no infiltration
one of the engineering calculations that must be done when planning a development is the excess flood flow--this must be taken into account
diverted stormwater may have substantially poorer quality than native runoff (metals and oils etc from the streets and yards)

commercial and industrial establishments that discharge stormwater at a point are now subject to the restrictions of categorical wastewater discharge permit

Effects of vegetation

vegetation can greatly increase the rate of infiltration

hold water in place, buffer the release of water to the groundsurface
shield the soil surface from some of the effects of compaction by rainfall

clear cutting a forest can increase runoff and erosion disastrously, as can overgrazing and improper cropping

proper management reduces the effects
in fact, well conducted forestry (including some clear cutting) can increase the amount of snowmelt which is available for human use without dangerously increasing erosion
plowing along hillside contours (conservation tillage) tends to slowdown runoff and thus decrease erosion and increase infiltration

bare soil is bad

Erosion and rivers

water flow in streams is often turbulent (ie, not laminar or in smooth lines parallel to the stream bed)

different flow velocities will lift particles of different sizes

generally, smaller particles will be lifted by lower velocities
but, clay and silt (<0.06 mm) can be harder to erode

can be tightly packed (consolidated)
may not stick up into the flow enough

suspended matter abrades rocks etc
as the river cuts a stream channel, the
some material is dissolved by surface water passing over it

the process of erosion gives rise to stream beds

a drainage pattern develops like the veins on a leaf (assuming the surface is uniformly erodable-irregularities change the pattern (trellis or rectangular)
the entire area from which a river and its tributaries draw runoff is called a drainage basin or watershed

the divisions between drainage basins are ridges called topographic divides
these can be drawn on topo maps by always drawing at right angles to the contours

a fast young stream cuts rapidly and sharply into the rock (V-shaped cross section)

these narrow valleyed rivers have waterfalls and rapids caused by sudden drops in elevation along the stream bed

may be caused by erosion (Niagara) or glaciation (Yosemite)

slope wash and mass movement (collapse) of the valley walls tend to flatten the walls of the valley

a more mature river

cuts more laterally, increasing the number and size of side canyons
deposits some eroded material in the base of the valley
alternatively, the valley itself can be broadly eroded to form a plain

an old river has a broad floodplain at the base of the valley, the channel of the river can meander across it

the periodic flooding of the river enriches the floodplain with nutrients carried by the swollen river
the bed of the river can actually sit above the surrounding floodplain, with the stream channel separated by natural levees
the low-lying flood plains are also popular for housing, which can be a problem in the rainy season

building dikes can make the problem worse downstream

the base flow of a river is fed by springs

in a rain storm flow increases, the more widespread a storm is (over the drainage basin) the more flow increases
the plot of flow of a river is called the hydrograph

Flood protection

planning based on the 100 year (or other) flood

flood control or management measures:

reducing peak flows
dams
land use controls
early warning systems
insurance (often from Uncle Sam)

Precipitation/Runoff Relations

hydrographs

a plot of flow versus time is called a hydrograph
a stage hydrograph plots streamflow as stage or height
a discharge hydrograph plots streamflow as discharge or volumetric flow
there are four inputs that make up the streamflow shown on a hydrograph

channel precipitation
direct surface runoff
interflow
groundwater discharge, which contributes the baseflow

in the absence of precipitation, the hydrograph is real boring: a flat line at the level of base flow
some time after the beginning of precipitation, however, things change

at the start of direct runoff, the line becomes a concentration curve
this rising limb continues up to the crest segment
the curve then goes into recession; the falling limb continues until the end of the direct runoff
there may be minor decreases after the end of direct runoff representing decreasing interflow or groundwater exfiltration

if the peak flow comes quickly the watershed is said to be flashy (as in flash flood)

paved or bare flashy
forests reduce flashiness

streamflow quantities

what are the units of discharge?

in english units, cubic feet per second, million gallons per day, acre-feet per time
in metric, cubic meters per second

the amount of runoff from a basin from a given amount of precipitation is a property of the basin

in general we cant to calculate the volume or depth of runoff, the peak runoff rate and/or a storm hydrograph

SCS Runoff Curve Number Procedure

the SCS curve number method is useful for calculating depth of runoff from single storms in small watersheds (see Chap 3,7)

the Soil Conservation Service developed a procedure for estimating runoff from farms based on soil type, land use, etc

the techniques gives cumulative direct runoff (P_e) as a function of cumulative precipitation (P) described by a series of curves
the curves are assigned curve numbers (CN) between 0 (exclusive) and 100 (inclusive)
an impermeable surface has a CN of 100 (runoff = precipitation), others surfaces has a CN < 100
Table 3.18 summarizes the effects of soil cover complexes and soil types
if a watershed is mixed, you just take a weighted average CN
the antecedent moisture conditions are used to modify the CN:

dry conditions are AMC group I, normal conditions are AMC group II (this is what is tabulated), wet conditions are AMC group III
to get CN(I) or CN(III) from CN(II), use Table 3.19 or these formulae:

CN(I) = 4.2CN(II)/(10-0.058CN(II))

CN(III) = 23CN(II)/(10+0.13CN(II))

the method can also be used to estimate infiltration:

F_a = P - P_e - I_a

with I_a = 200/CN - 2; P_e = (P-0.2S)²/(P+0.8S); S=1000/CN-10

Peak Flow Formulas

The Rational Method (Section 7.6)

based on the formula:

q = 1.008CiA

to use this we need:

C = the runoff coefficient, which varies from 0.10 for wooded or undeveloped open areas to 0.95 for highly developed areas

you can use the table on p 378 to estimate

i = the average intensity of rainfall during the time of concentration

for maximums during some return period

use a set of IDF curves for our watershed
enter the IDF curve with a time = t_C and read off the expected intensity

A = the area of the watershed (up to several hundred acres)

1.008 = acre· in/cfs· hr

to get the t_C you can use the formulae in Section 3.6
or, the Kirpich equation is nice and simple:

t_c = 0.00778L^0.77S^-0.385

where:

t_c = the concentration time in minutes

L = the hydraulic length in feet

S = the mean slope along the hydraulic length expressed as a number (not a percentage)

note: the mean slope along the hydraulic length is easy:
S = (h_max-h_min)/L

SCS TR-20 and TR-55 Methods

there are actually three methods:
(1) the graphical method and (2) the chart method for estimating peak flows
and (3) the tabular method for synthesizing unit hydrographs
An easily readable version of these methods is given at http://peacecorps.mtu.edu/scs/index.html

all methods assume 24h of rainfall
we will look at the Graphical Peak Discharge Method first
applicable to watersheds up to 20 mi² or so
the formula is given by equation 7.45 (p 396)
to use method:

obtain CN

calculate the composite CN from percentages of land use
by the way, if you have a CN and some area is made impervious, you can quickly get the new CN by the formula:

with

CN_NEW = CN of area after paving

CN_OLD = CN before paving

%P = Percentage of area made impervious by paving

CN modification for <30% impervious area takes the amount of unconnected impervious area into account

instead of %P in the formula given above, use

%Pm = %P(1-0.53U) with U = unconn’d/total

calculate I_a = 0.2S
obtain P (ie, for 24 h storm)

also assumes 24 h, Type II storm

calculate I_a/P
calculate t_c

(This formula is the same as 3.49 on p 158)

with

t_L = the lag time in hours

L=length of watershed

G=average slope (as a number)

then:

t_C = t_L/0.6

note:

there are other suitable methods
t_C should be > 0.1 and < 10 h)(also necessary that there be only one stream or two streams with the same t_C)

use t_C and I_a/P to read q_u (cfs/mi²in) off Figure 7.9 (note: Fig 7.9d applies to Type III rainfall, which we have in CT; see Fig. 4.14 on p. 213 for other regions.)
calculate the net rain from the gross rain using

with S = 1000/CN - 10

get Fp for swamps and ponds in the watershed (if any) then multiply by A and Pe

Storm Water Hydrographs

definition

the hydrograph for a stream (or a point) is the plot of flow (Q) versus time for that point

they can be measured or computed (synthesized)
the area under the curve between time t₁ and t₂ has units of volume Þ it represents the total flow in that time interval
the hydrograph shows us the time and volume of peak flow during or following a storm

four things contribute to flow in a stream and hence to the hydrograph

base flow or groundwater discharge
channel precipitation
direct surface runoff
interflow

parts

concentration curve is the rising portion following the beginning of direct runoff sometime after the beginning of rainfall
crest segment is the portion near the peak of the curve
recession is the falling part of the curve following the crest

surface flow within a watershed

the formation of runoff from precipitation follows a progression:

there is a series of abstractions:

interception must be fulfilled before any action happens on the ground
infiltration begins once the rain starts hitting the ground
depression storage (deP-UDDLE-ression) begins once the surface of the ground is saturated and water starts to gather in small depressions
detention storage is the water held in larger pools

once these abstractions are filled then flow begins:

overland flow of sheets of water
channel flow to the outlet of the watershed

hydrograph components

groundwater (base flow)

any permanent stream has base flow fed by groundwater throughout the year
this is a more or less flat (descending) line on the hydrograph in the absence of recent storm activity
this may not increase during a storm but if groundwater is replenished by a storm, the base flow will increase over a period of days, weeks, months....

direct surface runoff

the rise of the hydrograph curve above base flow in the concentration curve is referred to as the direct runoff hydrograph
if it were to continue to rain, the curve continues to rise as contributions from farther and farther points in the watershed make it to the outlet

at the time that all points in the watershed have contributed something, there is an inflection point in the concentration curve
the abstractions continue to decrease and the curve continues to rise until an equilibrium is reached, the hydrograph continues flat from there

generally, it stops raining before equilibrium is reached, and the curve descends as water accumulated in storage flows out in the channel

interflow

contributes to the hydrograph similarly to surface runoff
shows increase shortly after rainfall begins (lags surface runoff only slightly) and continues for some time after rainfall ends

channel precipitation

always a component of the DRH since it is not subject to abstraction
starts and stops contributing with the beginning and end of rainfall

interflow and channel precip are usually clumped with surface runoff

Unit Hydrographs

the time constants define the shape of the hydrograph; you could argue as follows:

the shape is a function of the basin characeristics (as opposed to the storm)
of course, the length of the storm will determine whether the curve quickly drops back down, crests and falls, or remains some time at equilibrium
nonetheless, as long as some rains runs off, the hydrograph for a given duration of precipitation will look the same regardless of the amount of precipitation

the volume of runoff will only affect the vertical scale of the hydrograph

this idea is the basis of the unit hydrograph

definition

originally the unit hydrograph was the hydrograph produced by a one day storm that produced 1.0 inches of runoff (this was Sherman’s "unit graph")
now we define the X-hour unit hydrograph as the DRH for a storm with a duration of X hours and an intensity of excess rainfall of 1/X in/hr

notice that the area under the unit hydrograph is 1 inch
X can be any number, including numbers less than 1 hour

a unit hydrograph can be described by three factors:

time to peak
peak flow
shape

time to peak is a function of the basin lag time and the time of the rainfall excess (D--but we called this X before):

t_p = t_L + D/2

peak flow for the SCS unit hydrographs is given by equation 5.10:

q_p = 484A/t_p

there are a number of proposed shapes for unit hydrographs

SCS has a triangular and a curvilinear one
the triangular one is very simple

at t=0, Q=0
at t=t_p, Q=q_p
at t=2.67*t_p, Q=0

application

can you see the value of these things?

if we get a six hour storm, you just take a known six hour unit hydrograph (or make one up) and scale it (vertically) up or down depending on how much excess rain there was

to scale it, you multiply every flow value by the inches of excess rain (over the six hour storm)
the fine print:

the length of the storm must be the same as the length associated with the unit hydrograph

the unit hydrograph is based on the assumption of uniform rainfall distribution in the basin; to the extent that rainfall is not uniform, the scaled one will deviate from reality

also based on the assumption of a constant rainfall rate

there are ways around this, as we shall see

if we have varying rates of rainfall (and when don’t we? see fig 4.15, p 214) or extended periods of uniform rainfall we might be able to do the following (see example 5.6):

for a storm of duration N*D, with N an integer and D £ t_L:
split the hyetograph up into N segments of duration D
we assume that the rainfall is uniform over each of the segments
we form a hydrograph by plotting a unit hydrograph scaled to segment one, with the runoff commencing at the beginning of segment one
then we plot a unit hydrograph scaled to the rainfall in segment two, with runoff commencing at the beginning of segment two
etc, up to segment N
we add together the contributions from each of the hydrographs and the result is the hydrograph for the whole storm

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Anthony G Benoit abenoit@trcc.commnet.edu
(860) 885-2386

Revised