Surface runoff volume and duration Hydrographs – Time history of change of the flow rate (discharge)

The time may be given in different unit/base. For small catchment area, the hydrograph may given in time base of day or hour

The discharge is measured in the stream and includes contributions from both groundwater and surface runoff

Hydrograph

The hydrograph describes the whole time history, not only the peak value, of the changing of flow rate from a catchment due to a rainfall event rather than just the peak flow.

Rainfall (precipitation) loss and effective rainfall Rainfall loss: due to vegetation interception, soil infiltration etc. Effective rainfall: portion which contributes the surface runoff

Hydrograph The curve of flow rate starts before the rainfall event , where only a base flow exists.

tt eQQ α−= 0

The base flow is the groundwater contribution which go on discharging more and more slowly with time. Its trend without rainfall is close to an exponential curve

Qo: discharge at start of period; Qt: discharge at time t; α : coefficient of aquifer

The base flow exists during the rainfall event. Its trend is not exponential due to the recharge of the groundwater by the precipitation. may be estimated, though it may not be directly measured

Hydrograph Surface runoff represented by the area under the hydrograph minus the base flow

The Run-off start rising when the effective rainfall starts until reaching peak value (rising limb);

After the peak value appear, the effective rainfall continues to contribute the runoff, even after the rain stops, until the inflection point;

After the inflection point, it is generally considered that the runoff comes from the water temporarily stored in the soil (interflow)

Unit Hydrograph (TUH) Hydrograph of surface runoff resulting from effective rainfall falling in a unit of time such as 1hour or 1 day and produced uniformly in space and time over the total catchment area (Sherman, 1942)

In practice, a T hour unit hydrograph is defined as resulting from a unit depth (e.g. 1in, 1mm or 1cm) of effective rainfall falling in T hour over the catchment.

The magnitude chosen for T depends on the size of the catchment and the response time to major rainfall events. For larger catchment (over 1000km2) with longer response times, the TUH can be derived from weekly or even 10 day rainfalls.

Unit Hydrograph (TUH) Three simple properties under assumptions

Assume that the effective rainfall –surface runoff relationship does not change with time, i.e. the same TUH always occurs whenever the unit of effective rainfall in Th is applied. There is a direct proportional relationship between the effective rainfall and the surface runoff. n units of effective rainfall in time T produce a runoff with n times of discharge in TUH.

The principle of superposition applies to hydrographs resulting from contiguous and/or isolated periods of uniform-intensity net rain.

Unit Hydrograph (TUH) Weakness and inaccuracy of TUH Estimation of effective rainfall, which largely depends on the state of the catchment before the rainfall event, e.g. saturated ground and unsaturated ground results in different effective rainfall. Also it may be affected by other rainfall events.

It is assumed that the effective rainfall –surface runoff relationship does not change with time. In reality, the same rain event in different time (season) leads to different TUH. Seasonal TUH may be necessary.

The assumption that the effective rainfall is produced uniformly both in the time T and over the area of the catchment. This is rarely seen in reality

TUH from 8 storms

Unit Hydrograph (TUH) Derive TUH from single storm/rainfall event

(1)Determine the region where the runoff is larger than zero, i.e. points A (beginning of runoff) and B (end of runoff).

Analyze the recession curves both in front of the peak (consider the recession curve for the previous rainfall) and after the peak. Fit the recession curves using

Extend the recession curves. A and B can be defined at the locations where the fitted recession curves start leaving the hydrograph

Unit Hydrograph (TUH) Derive TUH from Hydrograph

(2)Determine the base flow for the purpose of calculating the runoff. In practices, we may directly link points A and B to roughly identify the base flow.

(3)For all records located between A and B, the corresponding runoff can be calculated as the ordinate between the hydrograph and the straight line.

(4)Calculate the total direct runoff volume by multiplying the sum of recorded runoff from step 3 by the time interval.

(5)The average depth of effective precipitation over the catchment area is the runoff volume divided by the area

Unit Hydrograph (TUH) TUH for different duration T

a T hour unit hydrograph is defined as resulting from a unit depth (e.g. 1in, 1mm or 1cm) of effective rainfall falling in T hour over the catchment.

For different duration T, TUH is different. It is necessary to derive TUH in terms of different duration T.

Unit Hydrograph (TUH) Changing a short duration TUH to a longer duration TUH

Apply the principle of superposition of the TUH. A long-duration TUH can be considered to be consist of multiple successive short-durations. Thus, the long-duration TUH can be obtained by superposing them.

Remember to divide the graph from the above step by the total amount of the effectively rainfall to get TUH

Unit Hydrograph (TUH) Changing a long duration TUH to a shorter duration TUH (S-curve method)

Hydrograph – Modify the duration of TUH S-curve: the total hydrograph resulting from a series of continuous uniform-intensity rainfall (duration of T) on the catchment.

E.g. 4 hour TUH

1) Plot the same TUH with T delay

2) Repeat Step 1 to plot the same TUH with nT delay

3) Add them together to get a S-curve

Hydrograph – Modify the duration of TUH To find a TUH with other duration, e.g. t2, using C-curve

4) Plot a similar S-curve with t2 delay

5) The difference between these two curve multiplied by the coefficient T/t2 is the TUH for a duration of t2

Not only suitable for changing a long duration unitgraph to a shorter duration unitgraph , but also suitable for changing a short duration unigraph to a longer duration unitgraph

Hydrograph – Averaged TUH In the same catchment, the TUHs for the same duration, derived from different records, are normally different,.

A typical or ‘average’ TUH is required to represent the characterise of the catchment.

The ordinates are NOT averaged

Only average the peak values and the values of the time from the beginning of runoff to the peak

The total area under the curve should be equal to unit runoff

Hydrograph – The instantaneous unit hydrograph The instantaneous unit hydrograph (IUH) is the hydrograph of runoff from the instantaneous application of unit effective rain on a catchment

Suppose a TUH with rainfall duration of t is generated, the TUH for other TUHs with different rainfall duration T is found using the S-curve method by

)(),( ,0, Ttt SSTttTU ∆−∆

=∆

Ordinates of the ∆T unitgraph derived from the t TUH

S-curve starting from t=0 and t= ∆T

Hydrograph – The instantaneous unit hydrograph

dtSdtUSS

TttTU t

Ttt)(),0()(),( ,0, =⇒−

∆=∆ ∆If ∆T is close to zero

IUH at any time IUH is a unique demonstration of a particular catchment’s response to rain, independent of duration;

TUH is the response to rain of a particular duration

The ordinate of a n-hour unitgraph at time t is the average ordinate of the IUH for n-hour before t.

Hydrograph – TUH as a percentage distributions Represents the unit graph in the form of percentages of total flow occurring in particular unit periods

TUH

Distribution graph

Since the discharge represented by a TUH is directly proportional to effective rainfall, the percentages in unit times will remain constant whatever the effective rainfall

Less precise than the TUH but is much better suited for iterative processes of derivation.

Hydrograph – TUH for composite rainfall events Due to the weakness/assumption of TUH, e.g. constant unit rainfall in terms of both duration time and catchment area, which is rarely seen in reality ;

In most cases, the rainfall intensity changes spatially and temporally, resulting a multi-peaked TUH

Very often, particularly on larger catchments, it is difficult to find enough single-peaked storm events in the available records to provide a fair sample for analysis. ;

Hydrograph – TUH for composite rainfall events How to duplicate TUH from hydrograph resulting from multi-rainfall events? Suppose the recorded hydrograph is due to n rainfalls with same duration t but different intensity. The runoff can be described using the same TUH Divide the time axis into many sub-domains with interval of t.

Hydrograph – TUH for composite rainfall events How to duplicate TUH from hydrograph resulting from multi-rainfall events? T =t, only the first rainfall contributes the runoff, therefore Q1=i1U(t)

T = 2t, only the first two rainfalls contribute the runoff, therefore Q2=i1U(2t)+i2U(t)

T = 3t, only the first three rainfalls contribute the runoff, therefore Q3=i1U(3t)+i2U(2t )+i3U(t)

T = nt, only the first three rainfalls contribute the runoff, therefore Qn=i1U(nt)+i2U((n-1)t )+i3U((n-2)t)…+inU(t)

Hydrograph – Synthetic unit hydrographs If there are no runoff/precipitation records available for generating a TUH, we need a synthetic unit hydrograph to analyze the runoff which is synthesised on the basis of past experience in other areas

Can be applied as first approximations to the unrecorded catchment

Snyder’s approach, considering hydrograph base width, peak discharge and basin lag (the time from the centre of gravity of the effective rainfall graph to the time when the peak runoff occurs)

Mass curves The total volumes of runoff from the beginning of the time serial to time (t) against the time.

Can be obtained by using the hydrograph. For each time interval, calculate the volumes by the product of discharge and time interval, then add each new volume to the previous total.

Very important for reservoir design

Required constant water demand

Start of driest period of record Reservoir assumed

Reservoir full again

Reservoir spilling water

Maximum required reservoir capacity to ensure water demand

Runoff accumulation-time curves

Record reservoir filling times from daily flow reading;

Since the river flow varies seasonally, the time taken to accumulate particular volumes of runoff (equivalent to reservoir filling times) will vary with the time of year that filling commences, as well as with the stored volume required;

Flow-duration curves

Shows the proportion of time during which the discharge there equals or exceeds certain values.

Upstream storage, such as lake, reservoirs, will modify the flow duration curves

Discharge in the figure may be expressed in terms of Q/Qm or BFI. Qm: mean flow discharge; BFI; base flow index, which is defined as the baseflow area/hydrograph area