Transcript Hydrology Rainfall Analysis (1) - RSLAB-NTU

Hydrology
Rainfall - Runoff Modeling (I)
Prof. Ke-Sheng Cheng
Department of Bioenvironmental Systems Engineering
National Taiwan UNiversity
Formation process of surface
runoff
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Surface runoff
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overland flow (sheet flow)
shallow concentrated flow
open channel flow
Runoff hydrograph
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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:
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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.
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. Components of interflow are
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quick interflow, which contributes to direct runoff, and
delayed interflow, which contributes to baseflow.
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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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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The main factors affecting hydrograph shape are:
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Drainage characteristics: basin area, basin shape,
basin slope, soil type and land use, drainage density,
and drainage network 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.
Also need to consider the storm
duration and time of concentration.
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Hydrographs are also described in terms of the
following time characteristics:
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Time to Peak, tp: Time from the beginning of the rising
limb to the occurrence of the peak discharge.
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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.
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.
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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.
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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. 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.
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 SCS TR-55
集流時間之計算
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水文設計應用手冊
Event-based rainfall-runoff
modeling
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In modeling single floods, the effects of
evapotranspiration, as well as the interaction
between the aquifer and the streams, are
ignored.
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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:
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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).
Assumption of hydrograph analysis
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Rainfall (excess rainfall) is uniformly distributed
over the whole watershed. As a result, direct
runoff begins at the beginning of effective rainfall.
Unit hydrograph analysis
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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.
Unit hydrograph, UH(,t)
Assumptions for a UH
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The effective rainfall has a constant intensity
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.
Instantaneous Unit Hydrograph
(IUH)
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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.
Definition of the Unit Impulse
function
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Remarks:
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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.
Effective rainfall – direct
runoff conversion
Matrix method for UH calculation
Matrix form
Example of UH calculation
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.
Relationship between IUH and the S
curve
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 S-curve may vary with
I. However, the above equation yields a unique
IUH(t) due to the (1/I) term.
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