Rainfall Runoff Relationships - 1 | Engineering Hydrology - Civil Engineering (CE) PDF Download

Introduction 

it was explained what a hydrograph is and that it indicates the response of water flow of a given catchment to a rainfall input. It consists of flow from different phases of runoff, like the overland flow, interflow and base flow. Methods to separate base flow from the total stream flow hydrograph to obtain the direct runoff hydrograph as well as infiltration loss from the total rainfall hyetograph to determine the effective rainfall have been discussed. In this lesson, a relationship between the direct runoff hydrograph of a catchment observed at a location (the catchment outlet) and the effective rainfall over the catchment causing the runoff are proposed to be dealt with.

We start with discussing how the various aspects of a catchment’s characteristics affects the shape of the hydrograph.

Hydrograph and the catchment’s characteristics 

The shape of the hydrograph depends on the characteristics of the catchment. The major factors are listed below.

Shape of the catchment

A catchment that is shaped in the form of a pear, with the narrow end towards the upstream and the broader end nearer the catchment outlet (Figure 1a) shall have a hydrograph that is fast rising and has a rather concentrated high peak (Figure 1b).

Figure 1. (a) Pear shaped catchment with narrow end towards upstream and blunt end towards outlet (b) Corresponding hydro graph for a hypothetical rainfall

A catchment with the same area as in Figure 1 but shaped with its narrow end towards the outlet has a hydrograph that is slow rising and with a somewhat lower peak (Figure 2) for the same amount of rainfall.  

FIGURE 2 (a) Catchment with narrow end towards outlet (b) Corresponding hydrograph for a hypothetical rainfall

Though the volume of water that passes through the outlets of both the catchments is same (as areas and effective rainfall have been assumed same for both), the peak in case of the latter is attenuated.

Size of the catchment

Naturally, the volume of runoff expected for a given rainfall input would be proportional to the size of the catchment.  But this apart, the response characteristics of large catchment ( say, a large river basin) is found to be significantly different from a small catchment (like agricultural plot) due to the relative importance of the different phases of runoff (overland flow, inter flow, base flow, etc.) for these two catchments.  Further, it can be shown from the mathematical calculations of surface runoff on two impervious catchments (like urban areas, where infiltration becomes negligible), that the non-linearity between rainfall and runoff becomes perceptible for smaller catchments.

Slope

Slope of the main stream cutting across the catchment and that of the valley sides or general land slope affects the shape of the hydrograph.  Larger slopes generate more velocity than smaller slopes and hence can dispose off runoff faster.  Hence, for smaller slopes, the balance between rainfall input and the runoff rate gets stored temporally over the area and is able to drain out gradually over time.  Hence, for the same rainfall input to two catchments of the same area but with with different slopes, the one with a steeper slope would generate a hydrograph with steeper rising and falling limits.

Here, two catchments are presented, both with the same are, but with different slopes. A similar amount of rainfall over the flatter catchment (Figure 3) produces a slow-rising moderated hydrograph than that produced by the steeper catchment (Figure 4). 

Effect of rainfall intensity and duration on hydrograph 

If the rainfall intensity is constant, then the rainfall duration determines in part the peak flow and time period of the surface runoff.  

The concept of Isochrones might be helpful for explaining the effective of the duration of a uniform rainfall on the shape of hydrograph.  Isochrones are imaginary lines across the catchment (see Figure 5) from where water particles traveling downward take the same time to reach the catchment outlet.  

FIGURE 5. Typical isochrones over a catchment

If the rainfall event starts at time zero, then the hydrograph at the catchment outlet will go on rising and after a time‘Δt’, the flow from the isochrone I would have reached the catchment outlet. Thus, after a gap of time Δt, all the area A1 contributes to the outflow hydrograph.

Continuing in this fashion, it can be concluded that after a lapse of time ‘4Δt’, all the catchment area would be contributing to the catchment outflow, provided the rain continues to fall for atleast up to a time 4Δt.  If rainfall continues further, then the hydrograph would not increase further and thus would reach a plateau.  

Effect of spatial distribution of rainfall on hydrograph 

The effect of spatial distribution of rainfall, that is, the distribution in space, may be explained with the catchment image showing the isochrones as in Figure 6. Assume that the regions between the isochrones receive different amounts of rainfall (shown by the different shades of blue in the figure).  

FIGURE 6. Areas of catchment subjected to different amounts of rainfall

If it is assumed now that only area A1 receives rainfall but the other areas do not, then since this region is nearest to the catchment outlet, the resulting hydrograph immediately rises. If the rainfall continues for a time more than ‘Δt’, then the hydrograph would reach a saturation equal to re.A1, where re is the intensity of the effective rainfall.  

Assume now that a rainfall of constant intensity is falling only within area A4, which is farthest from the catchment outlet. Since the lower boundary of A4 is the Isochrone III, there would be no resulting hydrograph till time ‘3Δt’.

If the rain continues beyond a time ‘4Δt’, then the hydrograph would reach a saturation level equal to r_e A₄ where r_e is the effective rainfall intensity. 

Direction of storm movement

The direction of the storm movement with respect to the orientation of the catchments drainage network affects both the magnitude of peak flow and the duration of the hydrograph. The storm direction has the greatest effect on elongated catchments, where storms moving upstream tend to produce lower peaks and broader time base of surface runoff than storms that move downstream towards the catchment outlet. This is due to the fact that for an upstream moving storm, by the time the contribution from the upper catchment reaches the outlet, there is almost no contribution from the lower watershed.  

Rainfall intensity

Increase in rainfall intensity increases the peak discharge and volume of runoff for a given infiltration rate. In the initial phases of the storm, when the soil is dry, a rainfall intensity less than infiltration rate produces no surface runoff. Gradually, as the rain progresses, the soil saturates and the infiltration rate reduces to a steady rate.

The relation between rainfall intensity and the discharge, strictly speaking, is not linear, which means that doubling the rainfall intensity does not produce a doubling of the hydrograph peak value. However, this phenomenon is more pronounced for small watersheds, such as an urban area. However in the catchment scale, due to the uncertainty of all the hydrological parameters, it might be assumed that the rainfall runoff relation follows a linear relationship. This assumption is made use of in the unit hydrograph concept, which is explained in the next section. 

The Unit Hydrograph 

The Unit Hydrograph (abbreviated as UH) of a drainage basin is defined as a hydrograph of direct runoff resulting from one unit of effective rainfall which is uniformly distributed over the basin at a uniform rate during the specified period of time known as unit time or unit duration. The unit quantity of effective rainfall is generally taken as 1mm or 1cm and the outflow hydrograph is expressed by the discharge ordinates. The unit duration may be 1 hour, 2 hour, 3 hours or so depending upon the size of the catchment and storm characteristics. However, the unit duration cannot be more than the time of concentration, which is the time that is taken by the water from the furthest point of the catchment to reach the outlet. 

Figure 7 shows a typical unit hydrograph.  

FIGURE 7. A typical unit hydrograph

Unit hydrograph assumptions 

The following assumptions are made while using the unit hydrograph principle: 

1. Effective rainfall should be uniformly distributed over the basin, that is, if there are ‘N’ rain gauges spread uniformly over the basin, then all the gauges should record almost same amount of rainfall during the specified time.
2. Effective rainfall is constant over the catchment during the unit time.
3. The direct runoff hydrograph for a given effective rainfall for a catchment is always the same irrespective of when it occurs. Hence, any previous rainfall event is not considered. This antecedent precipitation is otherwise important because of its effect on soil-infiltration rate, depressional and detention storage, and hence, on the resultant hydrograph.
4. The ordinates of the unit hydrograph are directly proportional to the effective rainfall hyetograph ordinate. Hence, if a 6-h unit hydrograph due to 1 cm rainfall is given, then a 6-h hydrograph due to 2 cm rainfall would just mean doubling the unit hydrograph ordinates. Hence, the base of the resulting hydrograph (from the start or rise up to the time when discharge becomes zero) also remains the same.  

Unit hydrograph limitations

Under the natural conditions of rainfall over drainage basins, the assumptions of the unit hydrograph cannot be satisfied perfectly. However, when the hydrologic data used in the unit hydrograph analysis are carefully selected so that they meet the assumptions closely, the results obtained by the unit hydrograph theory have been found acceptable for all practical purposes.

In theory, the principle of unit hydrograph is applicable to a basin of any size. However, in practice, to meet the basic assumption in the derivation of the unit hydrograph as closely as possible, it is essential to use storms which are uniformly distributed over the basin and producing rainfall excess at uniform rate. Such storms rarely occur over large areas. The size of the catchment is, therefore, limited although detention, valley storage, and infiltration all tend to minimize the effect of rainfall variability. The limit is generally considered to be about 5000 sq. km. beyond which the reliability of the unit hydrograph method diminishes. When the basin area exceeds this limit, it has to be divided into sub-basins and the unit hydrograph is developed for each sub-basin. The flood discharge at the basin outlet is then estimated by combining the subbasin floods, using flood routing procedures.   

Note:

Flood Routing: This term is used to denote the computation principles for estimating the values of flood discharge with time and in space, that is, along the length of a river. Details about flood routing procedures may be had from the following book: M H Chaudhry (1993) Open channel hydraulics, Prentice Hall of India

Application of the unit hydrograph

Calculations of direct runoff hydrograph in catchment due to a given rainfall event (with recorded rainfall values), is easy if a unit hydrograph is readily available. Remember that a unit hydrograph is constructed for a unit rainfall falling for a certain T-hours, where T may be any conveniently chosen time duration.  The effective rainfall hyetograph, for which the runoff is to be calculated using the unit hydrograph, is obtained by deducting initial and infiltration losses from the recorded rainfall.  This effective rainfall hyetograph is divided into blocks of T-hour duration.  The runoff generated by the effective rainfall for each T-hour duration is then obtained and summed up to produce the runoff due to the total duration.