What is Hydrograph Analysis?
Hydrograph
- A hydrograph is a chronological plot of the discharge in a stream plotted against time. OR
- Special graphs show changes in a river’s discharge over a period of time, usually in relation to a rainfall event. OR
- A hydrograph shows the flow rate (discharge) versus time past a specific point in a river, another channel, or conduit carrying flow. Flow rate is typically expressed in cubic meters or cubic feet per second (m3/s).
Basic Terms
The discharge is measured at a specific point in a river and is typically time variant.
- Rising limb: The rising limb of the hydrograph, also known as the concentration curve, reflects a prolonged increase in discharge from a catchment area, typically in response to a rainfall event
- Recession (or falling) limb: The recession limb extends from the peak flow rate onward. The end of storm flow (quick flow or direct runoff) and the return to groundwater-derived flow (base flow) are often taken as the point of inflection of the recession limb. The recession limb represents the water withdrawal from the storage built up in the basin during the earlier phases of the hydrograph.
- Peak discharge: The highest point on the hydrograph when the rate of discharge is greatest
- Lag time: The time interval from the centre of mass of rainfall excess to the peak of the resulting hydrograph
- Time to peak: Time interval from the start of the resulting hydrograph
- Discharge: The rate of flow (volume per unit time) passing a specific location in a river or other channel
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Factors affecting hydrograph shape
The shape of a hydrograph depends on the river's upstream and downstream flow characteristics. It also depends on various other parameters like time of concentration, base period, duration of the hydrograph, duration of rainfall etc. A proper hydrograph analysis can be done only with the help of these parameters. These factors of Hydrograph analysis can be categorized into the following parameters, which govern the shape of a hydrograph.
- 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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Why is Hydrograph Analysis Important?
Hydrograph analysis is important because it governs many river basin design parameters. It is important to get an idea about the flood condition of a river in its catchment basin. In the case of flood inundation regions of the catchment basin, it is important to get the velocity and discharge simultaneously. And it can be done with the help of hydrograph analysis. Here few more points are given that show the importance of hydrograph analysis.
- To find out the discharge patterns of a particular drainage basin
- Help predict flooding events, therefore influencing the implementation of flood prevention measures
- Hydrograph analysis is also carried out to the peak discharge of a river basin.
Relation Between Rainfall and Runoff
Rainfall is the amount of precipitation in any catchment basin, while runoff is the amount of precipitation in excess of the different losses. These losses include infiltration loss, vapourization loss etc. A rainfall in time and space that falls on a catchment produces a hydrograph. The given figure defines certain essential elements of the hydrograph resulting from a hyetograph( Rainfall intensity vs time).
Formation of Hydrograph
We apply the production and transfer functions to describe the processes that occur when the rain is transformed into a flow hydrograph (by Horton's postulate). The production function allows the determination of the net rain hyetograph starting from the total rain. The transfer function allows the determination of the hydrograph resulting from the net rain. The net rain represents the part of the total rain that contributes to the flow process. An asymmetric curve represents the hydrograph. The following formula represents peak flow:
Qp = C.i.A
| Where: | ||
| C | runoff coefficient (depends on the catchment characteristics) | |
| i | rainfall intensity in time tc | |
| A | area of catchment | |
It can be defined as:
- Response time of the catchment (tr) - It represents the time interval that separates the net rain gravity centre from the peak flow or sometimes the gravity centre of the flow hydrograph.
- Time of concentration (tc) - It is the time required by rain falling on the catchment to flow from the farthest point to the measuring point of the river. Thus, after time tc from the beginning of the rainfall, the whole catchment is considered to contribute to the flow. The value of the main intensity assumes that the rainfall rate is constant during tc and that all measured rainfall over the area contributes to the flow. The peak flow Qp occurs after the period tc.
- Rising limb(tm)- It is the time from the beginning of the rain to the peak of the hydrograph
- Base time (tb) - It represents the direct flow duration.
- Time to Peak(tp) - It is the time from the beginning of the rising limb to the occurrence of the peak discharge.
Total streamflow during a precipitation event includes the baseflow existing in the basin before the storm and the runoff due to the given storm precipitation. Total streamflow hydrographs are usually conceptualised as being composed of the following:
a) Direct Runoff It comprises contributions from surface runoff and quick interflow. Unit hydrograph analysis refers only to direct runoff.
b) Baseflow is composed of delayed interflow and groundwater runoff contributions.
c) Surface runoff includes all overland flow and all precipitation falling directly onto stream channels. Surface runoff is the main contributor to peak discharge.
d) 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.
e) Groundwater runoff is the flow component contributed to the channel by groundwater. This process is extremely slow compared to surface runoff.
Different Types of Hydrographs
As we know that the hydrograph is a curve which represents the discharge and time. It is based on the upcoming flow of rivers and many other factors. The curve of the hydrograph depends upon many parameters like the amount of rainfall, its duration, the hydrograph, etc. Based on these different hydrograph parameters, it can be classified in the following ways.
- Storm/Flood hydrographs - A storm hydrograph displays how a river's discharge can change over time in response to a rainfall event. The discharge of a river is just the amount of water passing a certain point every second. It is calculated by multiplying the cross-sectional area of the river by its velocity.
- Annual hydrographs
- Direct Runoff Hydrograph - Direct runoff hydrograph(DRH) resulting from one unit (e.g., 1 cm) of effective rainfall occurring uniformly over that watershed at a uniform rate over a unit period of time
What is Unit Hydrograph?
Sherman first suggested this method in 1932, and it has undergone many refinements since then.
- A unit hydrograph is the hydrograph of direct runoff resulting from one unit depth (1 cm) of rainfall excess occurring uniformly over the basin and at a uniform rate for a specified duration (D hours). OR
- A unit hydrograph (UH) is the hypothetical unit response of a watershed (in terms of runoff volume and timing) to a unit input of rainfall. It can be defined as the direct runoff hydrograph (DRH) resulting from one unit (e.g.,1 cm) of effective rainfall occurring uniformly over that watershed at a uniform rate over a unit period of time. As a UH applies only to the direct runoff component of a hydrograph (i.e., surface runoff), a separate determination of the baseflow component is required. OR
- It can be defined as the direct runoff hydrograph (DRH) resulting from one unit (e.g., 1 cm) of effective rainfall occurring uniformly over that watershed at a uniform rate over a unit period of time.
A UH is specific to a particular watershed and a particular length of time corresponding to the duration of the effective rainfall. The UH is specified as the 1-hour, 6-hour, or 24-hour UH, or any other length of time up to the time of concentration of direct runoff at the watershed outlet. Thus, there can be many unit hydrographs for a given watershed, each corresponding to a different duration of effective rainfall.
The following are essential steps in deriving a unit hydrograph from a single storm:
- Separate the baseflow and obtain the direct runoff hydrograph (DRH).
- Compute the total direct runoff volume and convert this volume into the equivalent depth of effective rainfall (in 1 cm) over the entire basin.
- Normalize the direct runoff hydrograph by dividing each ordinate by the equivalent volume (cm) of direct runoff (or effective rainfall)
- Determine the effective duration of excess rainfall. To do this, obtain the effective rainfall hyetograph (e.g., use the φ-index, the Horton) and its associated duration. This duration is the duration associated with the unit hydrograph.
Unit hydrographs are fundamentally linked to the duration of the effective rainfall event producing them. They can only be used to predict direct runoff from storms of the same duration as that associated with the UH, or from storms which can be described as a sequence of pulses, each of the same duration as that associated with the UH.
Formation of Unit Hydrographs for Different Effective Duration
A unit hydrograph for a particular watershed is developed for a specific duration of effective rainfall. When dealing with rainfall of different duration, a new unit hydrograph must be derived for the new duration. The linearity property implicit in the UH analysis can be used to generate unit hydrographs associated with larger or smaller effective rainfall pulse duration. This procedure is sometimes referred to as the S-curve Hydrograph method.
S-Curve Hydrograph Method
An S-hydrograph represents the basin's response to an effective rainfall event of infinite duration. Assume that a UH of duration D is known and that a UH for the same basin but of duration D’ is desired. The first step is to determine the S-curve hydrograph by adding a series of (known) unit hydrographs of duration D, each lagged by a time interval D. The resulting superposition represents the runoff resulting from a continuous rainfall excess of intensity 1/D.
Lagging the S-curve in time by an amount of D’ and subtracting its ordinates from the original unmodified S-curve yields a hydrograph corresponding to a rainfall event of intensity 1/D and duration D’. Consequently, to convert this hydrograph whose volume is D’/D into a unit hydrograph of duration D’, its ordinates must be normalized by multiplying them by D/D’. The resulting ordinates represent a unit hydrograph associated with an effective rainfall of duration D’
A hydrologic system (a basin) is said to be a linear system if the relationship between storage, inflow, and outflow is such that it leads to a linear differential equation.
Assumptions for Hydrograph Analysis
Various assumptions have been made for the formation of the hydrograph, and these assumptions are used in the hydrograph analysis. These assumptions are described as follows:
Time invariance:
The first basic assumption is that the direct-runoff response to a given effective rainfall in a catchment is time invariant. This implies that the direct runoff hydrograph for a given effective rainfall in a catchment is always the same irrespective of when it occurs.
Linear Response:
The direct-runoff response to the rainfall excess is assumed to be linear. This is the most important assumption of the unit-hydrograph theory. Linear response means that if an input X1(t) cause an output y1(t) an output x2(t) causes an output y2(t) then an input x1(t) + x2(t) gives an output y1(t) + y2(t). Consequently if x2(t) = rx1(t), then y2(t) = r1y1(t). Thus, if the rainfall excess in a duration D is r times the unit depth, the resulting DRH will have ordinates bearing ratio "r" to those of the corresponding D-hour unit hydrograph.
t'B = tB + (n-1)D
Where,
t'B = The base period of T hr U.H
tB = Base period of D hr U.H
Also, T>D
T = n.D where ‘n’ is an integer.
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What is Synthetic Hydrograph
A synthetic unit hydrograph retains all the features of the unit hydrograph but does not require rainfall-runoff data. A synthetic unit hydrograph is derived from theory and experience, and its purpose is to simulate basin diffusion by estimating the basin lag based on a certain formula or procedure.
Synder’s Method: Synder (1938), based on a study of many catchments in the Appalachian Highlands of the eastern United States, developed a set of empirical equations for synthetic unit hydrographs in those areas. These equations are used in the USA. And with some modifications in many other countries, and constitute what is known as Synder’s synthetic unit hydrograph.
(I) tp = Ct [L.LCa]0.3
Where,
tp = Time interval between mid-point of unit rainfall excess and peak of unit hydrograph in an hour
L = Length of the main stream
LCa = The distance along the main stream from the basin outlet to a point on the stream which is nearest to the centroid of basis (in Km)
Ct= Regional constant 0.3 < Ct < 0.6
(II) tp = Ct [(L.LCa)/(S)0.5]n
S = Basin slope.
N = Constant = 0.38.
(III) tr = tp/5.5
tr = Standard duration of unit hydrograph in the hour
(IV)QPS = 2.78 CPA/tp
Where, Cp = Regional constant = 0.3 to 0.92.
A = Area of the catchment in km2.
QPS = Peak discharge in m3/s.
(V) t'p = 0.955 tp+ 0.25 tr
where, tr = standard rainfall duration.
And t'p =Basin lag for non-standard U.H.
(VI) QP = 2.78 CPA/t'p
(VII) tB = (72 + 3tp) hour, for a large catchment.
tB = 5(tp + tR/2) hour, for the small catchment.
Where,
tB = Base time of synthetic U.H
(VIII) W50 = 5.87/q1.08
W50 = width of unit hydrograph in hour at 50% peak discharge.
(IX) W75 = (W50)/1.75
W75 = Width of U.H in hours at 75% peak discharge.
(X) q = QP/A
where QP = Peak discharge in m3/sec.
A = Area in km2.
| Important GATE Topics | |
| Fixed Beams | Solid Mechanics |
| Moment Of Inertia | Proof Resilience |
| Modulus Of Rigidity | Mohr's Circle |
| Castigliano's Theorem | Betti's Theorem |
| Statically Determinate | Statically Indeterminate |
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