Transcript Document

Applied Hydrology
Rainfall-Runoff Modeling
Professor Ke-Sheng Cheng
Dept. of Bioenvironmental Systems Engineering
National Taiwan University
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Runoff generating process
• Rainfall losses during a storm event
– Interception
– Depression storage
– Evaporation
– Infiltration
• Types of surface runoff
– Overland flow (sheet flow)
– Shallow concentrated flow
– Channel flow
– Interflow
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Watershed as a system of precipitation
input and streamflow output
• In natural condition each river receives water
only from its own drainage basin or catchment
area. Each catchment can, therefore, be
regarded as a system receiving inputs of
precipitation and transforming these into
outputs of eveporation and streamflow.
• In all but the driest areas output from the
catchment system is continuous but the inputs
of precipitation are discrete and often widely
separated in time.
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Annual hydrograph
Quickflow (Direct runoff)
Slowflow or baseflow
• The annual hydrograph typically comprises short periods of
suddenly increased discharge associated with rainfall events
and intervening, much longer, periods when straemflow
represents the outflow from water stored on and below the
surface of the catchment and when the hydrograph takes the
exponential form of the typical exhaustion curve.
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Flow paths of the sources of streamflow
(Shallow subsurface flow)
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Overland flow
• Overland flow comprises the water that, failing
to infiltrate the surface, travels over the ground
surface towards a stream channel either as
quasi-laminar sheet flow or, more usually, as
flow anastomosing in small trickles and minor
rivulets.
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• The main course of overland flow is the inability
of water to infiltrate the surface, and in view of
the high value of infiltration characteristic of
most vegetation-covered surfaces it is not
surprising that overland flow is a rarely
observed phenomenon.
• Conditions in which it assumes considerable
importance include the saturation of the
ground surface, the hydrophobic nature of
some very dry and sodic soils, the deleterious
effects of many agricultural practices on
infiltration capacity and freezing of the ground
surface.
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Interflow
Diagrammatic
representatio
n of the runoff
process.
Principle of
Hydrology, Ward
and Robinson.
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Overland flow
• Infiltration-excess overland flow
– Hortonian overland flow
• Saturation-excess overland flow
– Hewlettian overland flow
– Variable source areas (VSAs) overland flow
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• Horton overland flow describes the tendency
of water to flow horizontally across land
surfaces when rainfall has exceeded infiltration
capacity and depression storage capacity.
• Paved surfaces such as asphalt, which are
designed to be flat and impermeable, rapidly
achieve Horton overland flow. It is shallow,
sheetlike, and fast-moving, and hence capable
of extensively eroding soil and bedrock.
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• Horton overland flow is most commonly
encountered in urban construction sites and
rural dirt roads, where vegetation has been
stripped away, exposing bare dirt. The process
also poses a significant problem in areas with
steep terrain, where water can build up great
speed and where soil is less stable, and in
farmlands, where soil is flat and loose.
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• Hewlett overland flow is generated when a
rising water table intersects the soil surface.
Subsurface water then escapes from the soil
and flows downslope over the soil surface, This
exfiltrating water is termed return flow. That
portion of the hillslope over which return flow
emerges is saturated, so any rain failing on to it
is unable to penetrate the surface and also
flows downslope.
• Direct precipitation on to saturated areas and
return flow together constitute saturation
overland flow.
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• This type of overland flow is rare in desert
landscapes but is common in humid ones. It
typically occurs on valley floors and concave
foot slopes, in valley-head and valley-side
hollows, and in areas where the underlying
geology directs subsurface flow to the surface.
The extent of the saturated area varies both
between storms and within storms, and
controls the rate of overland flow.
There have been considerable numbers of studies on VSAs overland flow
in recent years. The topic is also important for non-point source pollution.
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Formation process of surface
runoff
Surface runoff
overland flow (sheet flow)
shallow concentrated flow
open channel flow
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Total streamflow during a precipitation
event includes the baseflow existing in the
basin prior to the storm and the runoff due
to the given storm precipitation. Total
streamflow hydrographs are usually
conceptualized as being composed of:
Direct Runoff, which is composed of
contributions from surface runoff and quick
interflow. Unit hydrograph analysis refers only
to direct runoff.
Baseflow, which is composed of contributions
from delayed interflow and groundwater runoff.
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Runoff hydrograph
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Surface runoff includes all overland flow as
well as all precipitation falling directly onto
stream channels. Surface runoff is the main
contributor to the peak discharge.
Interflow is the portion of the streamflow
contributed by infiltrated water that moves
laterally in the subsurface until it reaches a
channel. Interflow is a slower process than
surface runoff.
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Components of interflow are
quick interflow, which contributes to direct
runoff, and
delayed interflow, which contributes to baseflow.
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Groundwater runoff is the flow component
contributed to the channel by groundwater.
This process is extremely slow as compared
to surface runoff.
Basins with a lot of storage have a large
recessional limb.
Recession occurs exponentially for baseflow.
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Methods of baseflow separation
Fixed base method (A-B-D-E)
Variable slope method (A-B-C-E)
Straight line method (A-E)
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Inflection point method
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Curves AB and EF are considered as
ground water recession curves.
The ground water recession can be
described by the following equation
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
The recession limb of a hydrograph represents
withdraw of water from surface storage,
subsurface (inter) flow and groundwater flow.
Suppose that the recession curve can be
expressed by
Then the recession constant K is then taken as
the product of recession constants for three
individual components, i.e.,
where Ks, Ki and Kg are recession constants
associated with surface storage, interflow and
groundwater flow, respectively.
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Main factors affecting hydrograph
shape
Drainage characteristics: basin area, basin
shape, basin slope, soil type and land use, Watershed
drainage density, and drainage network geomorphology
topology. Most changes in land use tend to
increase the amount of runoff for a given storm.
Rainfall characteristics: rainfall intensity,
duration, and their spatial and temporal
distribution; and storm motion, as storms
moving in the general downstream direction
tend to produce larger peak flows than storms
moving upstream.
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Watershed geomorphology
Also need to consider the storm
duration and time of concentration.
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Time characteristics of hydrographs
Time to Peak, tp: Time from the beginning of
the rising limb to the occurrence of the peak
discharge.
The time to peak is largely determined by
drainage characteristics such as drainage
density, slope, channel roughness, and soil
infiltration characteristics. Rainfall distribution
in space also affects the time to peak.
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Time of Concentration, tc: Time required for
water to travel from the most hydraulically
remote point in the basin to the basin outlet.
For rainfall events of very long duration, the
time of concentration is associated with the
time required for the system to achieve the
maximum or equilibrium discharge.
The drainage characteristics of length and slope,
together with the hydraulic characteristics of
the flow paths, determine the time of
concentration.
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Lag Time, tl: Time between the center of
mass of the effective rainfall hyetograph and
the center of mass of the direct runoff
hydrograph.
The basin lag is an important concept in linear
modeling of basin response. The lag time is a
parameter that appears often in theoretical and
conceptual models of basin behavior. However, it
is sometimes difficult to measure in real world
situations.
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Many empirical equations have been proposed
in the literature. The simplest of these equations
computes the basin lag as a power function of
the basin area.
Time Base, tb: Duration of the direct runoff
hydrograph.
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Calculation of time of
concentration
Travel time, Tt : the time it takes for water to
travel from one location to another in a
watershed.
Time of concentration, Tc : the time at which
all of the watershed begins to contribute
direct runoff at the outlet.
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Calculation of Tc by NRCS TR-55
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集流時間之計算
水文設計應用手冊
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Event-based rainfall-runoff
modeling
 In modeling single floods, the effects of
evapotranspiration, as well as the interaction
between the aquifer and the streams, are ignored.
Evapotranspiration may be ignored because its
magnitude during the time period in which the flood
develops is negligible when compared to other fluxes
such as infiltration. Likewise, the effect of the streamaquifer interaction is generally ignored because the
response time of the subsurface soil system is much
longer than the response time of the surface or direct
runoff process. In addition, effects of other hydrologic
processes such as interception and depression storage
are also neglected.
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 Event-based modeling generally involves the
following aspects:
evaluation of the rainfall flux over the watershed I(x, t)
as a function of space and time;
evaluation of the rainfall excess or effective rainfall flux
as a function of space and time, Ie(x, t). Effective rainfall
is the rainfall available for runoff after infiltration and
other abstractions have been accounted for; and
routing of the rainfall excess to the watershed outlet in
order to determine the corresponding flood hydrograph,
Q(t).
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Assumption of hydrograph analysis
 Rainfall (excess rainfall) is uniformly distributed
over the whole watershed. As a result, direct runoff
begins at the beginning of effective rainfall.
Subwatershed
delineation is
often needed.
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Unit hydrograph analysis
 Sherman (1932) first proposed the unit hydrograph
concept.
 The Unit Hydrograph (UH) of a watershed is
defined as the direct runoff hydrograph resulting from
a unit volume of excess rainfall of constant intensity
and uniformly distributed over the drainage area. The
duration of the unit volume of excess or effective
rainfall, sometimes referred to as the effective
duration, defines and labels the particular unit
hydrograph. The unit volume is usually considered
to be associated with 1 cm (1 inch) of effective
rainfall distributed uniformly over the basin area.
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Unit hydrograph, UH(,t)
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Assumptions for a UH
 The effective rainfall has a constant intensity



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within the effective duration.
Effective rainfall is uniformly distributed over the
whole watershed.
The time base of the DRH resulting from an
excess rainfall of given duration is constant.
The ordinates of all DRH’s of a common time
base are directly proportional to the total amount
of direct runoff.
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Instantaneous Unit Hydrograph (IUH)
 Instantaneous unit hydrograph is the direct runoff
hydrograph resulted from an Impulse function
rainfall, i.e., one unit of effective rainfall at a time
instance.
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Definition of the Unit Impulse function
0, x  a
 ( x  a)  
1, x  a
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Remarks:
The time base of the IUH is the time of
concentration of the watershed.
The ordinate of the IUH at time t, IUH(t), is the
system’s response at time t.
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 Consider a watershed as a linear system and the
effective rainfall and direct runoff are respectively
the input and output of this system.
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Effective rainfall –
direct runoff conversion
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Matrix method for UH calculation
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Matrix form
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Example of UH calculation
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Conversion between unit hydrograph of
different durations
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Note that the S-curve is dependent on the
effective rainfall duration () associated
with the unit hydrograph.
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Relationship between IUH and the S
curve
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The ordinate of IUH(t) is proportional to the
slope of the S-curve at time t, i.e. dS/dt.
Note that the S-curve can be developed
using UH of various effective rainfall
durations (1/I); therefore, the slope of the Scurve may vary with I. However, the above
equation yields a unique IUH(t) due to the
(1/I) term.
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