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**Hydrology Rainfall - Runoff Modeling (I)**

Prof. Ke-Sheng Cheng Department of Bioenvironmental Systems Engineering National Taiwan UNiversity

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**Formation process of surface runoff**

overland flow (sheet flow) shallow concentrated flow open channel flow

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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: 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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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 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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**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:**

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.

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**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:**

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. 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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**Time Base, tb: Duration of the direct runoff hydrograph.**

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. 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 SCS 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 stream-aquifer 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.

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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 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**

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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 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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