Continued to Receive Rainfall at This Intensity for the Next

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3. Rainfall-runoff analysis

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3.1 Introduction
3.2 Rainfall characteristics
3.3 Variability of annual rainfall
3.4 Probability analysis
3.5 Rainfall-runoff relationship
3.6 Determination of runoff coefficients
3.7 Assessment of annual or seasonal runoff
3.8 Runoff plots

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3.1 Introduction

As defined in Chapter 1, water harvesting is the collection of runoff for productive use.

Runoff is generated by rainstorms and its occurrence and quantity are dependent on the characteristics of the rainfall event, i.e. intensity, duration and distribution. There are, in addition, other important factors which influence the runoff generating process. They will be discussed in section 3.5.

3.2 Rainfall characteristics

Precipitation in arid and semi-arid zones results largely from convective cloud mechanisms producing storms typically of short duration, relatively high intensity and limited areal extent. However, low intensity frontal-type rains are also experienced, usually in the winter season. When most precipitation occurs during winter, as in Jordan and in the Negev, relatively low-intensity rainfall may represent the greater part of annual rainfall.

Rainfall intensity is defined as the ratio of the total amount of rain (rainfall depth) falling during a given period to the duration of the period It is expressed in depth units per unit time, usually as mm per hour (mm/h).

The statistical characteristics of high-intensity, short-duration, convective rainfall are essentially independent of locations within a region and are similar in many parts of the world. Analysis of short-term rainfall data suggests that there is a reasonably stable relationship governing the intensity characteristics of this type of rainfall. Studies carried out in Saudi Arabia (Raikes and Partners 1971) suggest that, on average, around 50 percent of all rain occurs at intensities in excess of 20 mm/hour and 20-30 percent occurs at intensities in excess of 40 mm/hour. This relationship appears to be independent of the long-term average rainfall at a particular location.

3.3 Variability of annual rainfall

Water harvesting planning and management in arid and semi-arid zones present difficulties which are due less to the limited amount of rainfall than to the inherent degree of variability associated with it.

In temperate climates, the standard deviation of annual rainfall is about 10-20 percent and in 13 years out of 20, annual amounts are between 75 and 125 percent of the mean. In arid and semi-arid climates the ratio of maximum to minimum annual amounts is much greater and the annual rainfall distribution becomes increasingly skewed with increasing aridity. With mean annual rainfalls of 200-300 mm the rainfall in 19 years out of 20 typically ranges from 40 to 200 percent of the mean and for 100 mm/year, 30 to 350 percent of the mean. At more arid locations it is not uncommon to experience several consecutive years with no rainfall.

For a water harvesting planner, the most difficult task is therefore to select the appropriate "design" rainfall according to which the ratio of catchment to cultivated area will be determined (see Chapter 4).

Design rainfall is defined as the total amount of rain during the cropping season at which or above which the catchment area will provide sufficient runoff to satisfy the crop water requirements. If the actual rainfall in the cropping season is below the design rainfall, there will be moisture stress in the plants; if the actual rainfall exceeds the design rainfall, there will be surplus runoff which may result in a damage to the structures.

The design rainfall is usually assigned to a certain probability of occurrence or exceedance. If, for example, the design rainfall with a 67 percent probability of exceedance is selected, this means that on average this value will be reached or exceeded in two years out of three and therefore the crop water requirements would also be met in two years out of three.

The design rainfall is determined by means of a statistical probability analysis.

3.4 Probability analysis

A rather simple, graphical method to determine the probability or frequency of occurrence of yearly or seasonal rainfall will be described in this chapter. For the design of water harvesting schemes, this method is as valid as any analytical method described in statistical textbooks.

The first step is to obtain annual rainfall totals for the cropping season from the area of concern. In locations where rainfall records do not exist, figures from stations nearby may be used with caution. It is important to obtain long-term records. As explained in section 3.2, the variability of rainfall in arid and semi-arid areas is considerable. An analysis of only 5 or 6 years of observations is inadequate as these 5 or 6 values may belong to a particularly dry or wet period and hence may not be representative for the long term rainfall pattern.

In the following example, 32 annual rainfall totals from Mogadishu (Somalia) were used for an analysis (Table 13).

Table 13 - ANNUAL RAINFALL, MOGADISHU (SOMALIA)

Year	R mm	Year	R mm	Year	R mm	Year	R mm	Year	R mm
1957	484	1964	489	1971	271	1977	660	1983	273
1958	529	1965	498	1972	655	1978	216	1984	270
1959	302	1966	395	1973	371	1979	594	1985	423
1960	403	1967	890	1974	255	1980	544	1986	251
1961	960	1968	680	1975	411	1981	563	1987	533
1962	453	1969	317	1976	339	1982	526	1988	531
1963	633	1970	300

The next step is to rank the annual totals from Table 13 with m == 1 for the largest and m = 32 for the lowest value and to rearrange the data accordingly (Table 14).

The probability of occurrence P (%) for each of the ranked observations can be calculated (columns 4, 8, 12, 16, Table 14) from the equation:

where:

P = probability in % of the observation of the rank m
m = the rank of the observation
N = total number of observations used

Table 14 - RANKED ANNUAL RAINFALL DATA, MOGADISHU (SOMALIA)

Year	R	m	P	Year	R	m	P	Year	R	m	P	Year	R	m	P
	mm		%		mm		%		mm		%		mm		%
1961	960	1	1.9	1988	531	11	32.9	1966	395	21	64.0	1986	251	31	95.0
1967	890	2	5.0	1958	529	12	36.0	1973	371	22	67.1	1978	216	32	98.1
1968	680	3	8.1	1982	526	13	39.1	1976	339	23	70.2
1977	660	4	11.2	1965	498	14	42.2	1969	317	24	73.3
1972	655	5	14.3	1964	489	15	45.3	1959	302	25	76.4
1963	633	6	17.4	1957	484	16	48.4	1970	300	26	79.5
1979	594	7	20.5	1962	453	17	51.6	1983	273	27	82.6
1981	563	8	23.6	1985	423	18	54.7	1971	271	28	85.7
1980	544	9	26.7	1975	411	19	57.8	1984	270	29	88.8
1987	533	10	29.8	1960	403	20	60.9	1974	255	30	91.1

The above equation is recommended for N = 10 to 100 (Reining et al. 1989). There are several other, but similar, equations known to compute experimental probabilities.

The next step is to plot the ranked observations (columns 2, 6,10, 14, Table 14) against the corresponding probabilities (columns 4, 8,12,16, Table 14). For this purpose normal probability paper must be used (Figure 7).

Finally a curve is fitted to the plotted observations in such a way that the distance of observations above or below the curve should be as close as possible to the curve (Figure 7). The curve may be a straight line.

From this curve it is now possible to obtain the probability of occurrence or exceedance of a rainfall value of a specific magnitude. Inversely, it is also possible to obtain the magnitude of the rain corresponding to a given probability.

In the above example, the annual rainfall with a probability level of 67 percent of exceedance is 371 mm (Figure 7), i.e. on average in 67 percent of time (2 years out of 3) annual rain of 371 mm would be equalled or exceeded.

For a probability of exceedance of 33 percent, the corresponding value of the yearly rainfall is 531 mm (Figure 7).

Figure 7 Probability diagram with regression line for an observed series of annual rainfall totals -Mogadishu, Somalia

The return period T (in years) can easily be derived once the exceedance probability P (%) is known from the equations.

From the above examples the return period for the 67 percent and the 33 percent exceedance probability events would thus be:

i.e. on average an annual rainfall of 371 mm or higher can be expected in 2 years out of 3;

respectively i.e. on average an annual rainfall of 531 mm or more can only be expected in 1 year out of 3.

3.5 Rainfall-runoff relationship

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3.5.1 The surface runoff process
3.5.2 Factors affecting runoff
3.5.3 Runoff coefficients

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3.5.1 The surface runoff process

When rain falls, the first drops of water are intercepted by the leaves and stems of the vegetation. This is usually referred to as interception storage.

Figure 8 Schematic diagram illustrating relationship between rainfall, infiltration and runoff (Source: Linsley et al. 1958)

As the rain continues, water reaching the ground surface infiltrates into the soil until it reaches a stage where the rate of rainfall (intensity) exceeds the infiltration capacity of the soil. Thereafter, surface puddles, ditches, and other depressions are filled (depression storage), after which runoff is generated.

The infiltration capacity of the soil depends on its texture and structure, as well as on the antecedent soil moisture content (previous rainfall or dry season). The initial capacity (of a dry soil) is high but, as the storm continues, it decreases until it reaches a steady value termed as final infiltration rate (see Figure 8).

The process of runoff generation continues as long as the rainfall intensity exceeds the actual infiltration capacity of the soil but it stops as soon as the rate of rainfall drops below the actual rate of infiltration.

The rainfall runoff process is well described in the literature. Numerous papers on the subject have been published and many computer simulation models have been developed. All these models, however, require detailed knowledge of a number of factors and initial boundary conditions in a catchment area which in most cases are not readily available.

For a better understanding of the difficulties of accurately predicting the amount of runoff resulting from a rainfall event, the major factors which influence the rainfall-runoff process are described below.

3.5.2 Factors affecting runoff

Apart from rainfall characteristics such as intensity, duration and distribution, there are a number of site (or catchment) specific factors which have a direct bearing on the occurrence and volume of runoff.

i. Soil type

The infiltration capacity is among others dependent on the porosity of a soil which determines the water storage capacity and affects the resistance of water to flow into deeper layers.

Porosity differs from one soil type to the other. The highest infiltration capacities are observed in loose, sandy soils while heavy clay or loamy soils have considerable smaller infiltration capacities.

Figure 9 illustrates the difference in infiltration capacities measured in different soil types.

The infiltration capacity depends furthermore on the moisture content prevailing in a soil at the onset of a rainstorm.

The initial high capacity decreases with time (provided the rain does not stop) until it reaches a constant value as the soil profile becomes saturated (Figures 8 and 9).

Figure 9 Infiltration capacity curves for different soil types

This however, is only valid when the soil surface remains undisturbed.

It is well known that the average size of raindrops increases with the intensity of a rainstorm. In a high intensity storm the kinetic energy of raindrops is considerable when hitting the soil surface. This causes a breakdown of the soil aggregate as well as soil dispersion with the consequence of driving fine soil particles into the upper soil pores. This results in clogging of the pores, formation of a thin but dense and compacted layer at the surface which highly reduces the infiltration capacity.

This effect, often referred to as capping, crusting or sealing, explains why in arid and semi-arid areas where rainstorms with high intensities are frequent, considerable quantities of surface runoff are observed even when the rainfall duration is short and the rainfall depth is comparatively small.

Soils with a high clay or loam content (e.g. Loess soils with about 20% clay) are the most sensitive for forming a cap with subsequently lower infiltration capacities. On coarse, sandy soils the capping effect is comparatively small.

ii. Vegetation

The amount of rain lost to interception storage on the foliage depends on the kind of vegetation and its growth stage. Values of interception are between 1 and 4 mm. A cereal crop, for example, has a smaller storage capacity than a dense grass cover.

More significant is the effect the vegetation has on the infiltration capacity of the soil. A dense vegetation cover shields the soil from the raindrop impact and reduces the crusting effect as described earlier.

In addition, the root system as well as organic matter in the soil increase the soil porosity thus allowing more water to infiltrate. Vegetation also retards the surface flow particularly on gentle slopes, giving the water more time to infiltrate and to evaporate.

In conclusion, an area densely covered with vegetation, yields less runoff than bare ground.

iii. Slope and catchment size

Investigations on experimental runoff plots (Sharma et al. 1986) have shown that steep slope plots yield more runoff than those with gentle slopes.

In addition, it was observed that the quantity of runoff decreased with increasing slope length.

This is mainly due to lower flow velocities and subsequently a longer time of concentration (defined as the time needed for a drop of water to reach the outlet of a catchment from the most remote location in the catchment). This means that the water is exposed for a longer duration to infiltration and evaporation before it reaches the measuring point. The same applies when catchment areas of different sizes are compared.

The runoff efficiency (volume of runoff per unit of area) increases with the decreasing size of the catchment i.e. the larger the size of the catchment the larger the time of concentration and the smaller the runoff efficiency.

Figure 10 clearly illustrates this relationship.

Figure 10. Runoff efficiency as a function of catchment size (Ben Asher 1988)

It should however be noted that the diagram in Figure 10 has been derived from investigations in the Negev desert and not be considered as generally applicable to others regions. The purpose of this diagram is to demonstrate the general trend between runoff and catchment size.

3.5.3 Runoff coefficients

Apart from the above-mentioned site-specific factors which strongly influence the rainfall-runoff process, it should also be considered that the physical conditions of a catchment area are not homogenous. Even at the micro level there are a variety of different slopes, soil types, vegetation covers etc. Each catchment has therefore its own runoff response and will respond differently to different rainstorm events.

The design of water harvesting schemes requires the knowledge of the quantity of runoff to be produced by rainstorms in a given catchment area. It is commonly assumed that the quantity (volume) of runoff is a proportion (percentage) of the rainfall depth.

Runoff [mm] = K x Rainfall depth [mm]

In rural catchments where no or only small parts of the area are impervious, the coefficient K, which describes the percentage of runoff resulting from a rainstorm, is however not a constant factor. Instead its value is highly variable and depends on the above described catchment-specific factors and on the rainstorm characteristics.

For example, in a specific catchment area with the same initial boundary condition (e.g. antecedent soil moisture), a rainstorm of 40 minutes duration with an average intensity of 30 mm/h would produce a smaller percentage of runoff than a rainstorm of only 20 minutes duration but with an average intensity of 60 mm/h although the total rainfall depth of both events were equal.

3.6 Determination of runoff coefficients

For reasons explained before, the use of runoff coefficients which have been derived for watersheds in other geographical locations should be avoided for the design of a water harvesting scheme. Also runoff coefficients for large watersheds should not be applied to small catchment areas.

An analysis of the rainfall-runoff relationship and subsequently an assessment of relevant runoff coefficients should best be based on actual, simultaneous measurements of both rainfall and runoff in the project area.

As explained above, the runoff coefficient from an individual rainstorm is defined as runoff divided by the corresponding rainfall both expressed as depth over catchment area (mm):

Actual measurements should be carried out until a representative range is obtained. Shanan and Tadmor recommend that at least 2 years should be spent to measure rainfall and runoff data before any larger construction programme starts. Such a time span would in any case be justified bearing in mind the negative demonstration effect a water harvesting project would have if the structures were seriously damaged or destroyed already during the first rainstorm because the design was based on erroneous runoff coefficients.

When plotting the runoff coefficients against the relevant rainfall depths a satisfactory correlation is usually observed (see Figure 11).

Figure 11. Rainfall-runoff relationships, Baringo, Kenya (Source: Finkel 1987)

A much better relationship would be obtained if in addition to rainfall depth the corresponding rainstorm intensity, the rainstorm duration and the antecedent soil moisture were also measured. This would allow rainstorm events to be grouped according to their average intensity and their antecedent soil moisture and to plot the runoff coefficients against the relevant rainfall durations separately for different intensities (see Figure 12).

Rainfall intensities can be accurately measured by means of a continuously recording autographic rain gauge.

It is also possible to time the length of individual rainstorms and to calculate the average intensities by dividing the measured rainfall depths by the corresponding duration of the storms.

Figure 12. Runoff coefficients in relation to rainfall intensity, rainfall duration and antecedent soil moisture. Measured on loess soil with sparse vegetation. Ground slope 1.5%. (Source: Siegert 1978)

When analysing the measured data it will be noted that a certain amount of rainfall is always required before any runoff occurs. This amount, usually referred to as threshold rainfall, represents the initial losses due to interception and depression storage as well as to meet the initially high infiltration losses.

The threshold rainfall depends on the physical characteristics of the area and varies from catchment to catchment. In areas with only sparse vegetation and where the land is very regularly shaped, the threshold rainfall may be only in the range of 3 mm while in other catchments this value can easily exceed 12 mm, particularly where the prevailing soils have a high infiltration capacity. The fact that the threshold rainfall has first to be surpassed explains why not every rainstorm produces runoff. This is important to know when assessing the annual runoff-coefficient of a catchment area.

3.7 Assessment of annual or seasonal runoff

The knowledge of runoff from individual storms as described before is essential to assess the runoff behaviour of a catchment area and to obtain an indication both of runoff-peaks which the structure of a water harvesting scheme must withstand and of the needed capacity for temporary surface storage of runoff, for example the size of an infiltration pit in a microcatchment system.

However, to determine the ratio of catchment to cultivated area, as described in chapter 4, it is necessary to assess either the annual (for perennial crops) or the seasonal runoff coefficient. This is defined as the total runoff observed in a year (or season) divided by the total rainfall in the same year (or season).

The annual (seasonal) runoff coefficient differs from the runoff coefficients derived from individual storms as it takes into account also those rainfall events which did not produce any runoff. The annual (seasonal) runoff-coefficient is therefore always smaller than the arithmetic mean of runoff coefficients derived from individual runoff-producing storms.

3.8 Runoff plots

Runoff plots are used to measure surface runoff under controlled conditions. The plots should be established directly in the project area. Their physical characteristics, such as soil type, slope and vegetation must be representative of the sites where water harvesting schemes are planned.

The size of a plot should ideally be as large as the estimated size of the catchment planned for the water harvesting project. This is not always possible mainly due to the problem of storing the accumulated runoff. A minimum size of 3-4 m in width and 10-12 m in length is recommended. Smaller dimensions should be avoided, since the results obtained from very small plots are rather misleading.

Care must be taken to avoid sites with special problems such as rills, cracks or gullies crossing the plot. These would drastically affect the results which would not be representative for the whole area. The gradient along the plot should be regular and free of local depressions. During construction of the plot, care must be taken not to disturb or change the natural conditions of the plot such as destroying the vegetation or compacting the soil. It is advisable to construct several plots in series in the project area which would permit comparison of the measured runoff volumes and to judge on the representative character of the selected plot sites.

Around the plots metal sheets or wooden planks must be driven into the soil with at least 15 cm of height above ground to stop water flowing from outside into the plot and vice versa (see Figure 13). A rain gauge must be installed near to the plot. At the lower end of the plot a gutter is required to collect the runoff. The gutter should have a gradient of 1% towards the collection tank. The soil around the gutter should be backfilled and compacted. The joint between the gutter and the lower side of the plot may be cemented to form an apron in order to allow a smooth flow of water from the plot into the gutter. The collection tank may be constructed from stone masonry, brick or concrete blocks, but a buried barrel will also meet the requirements. The tank should be covered and thus be protected against evaporation and rainfall. The storage capacity of the tank depends on the size of the plot but should be large enough to collect water also from extreme rain storms. Following every storm (or every day at a specific time), the volume of water collected in the rain gauge and in the runoff tank must be measured. Thereafter the gauge and tank must be completely emptied. Any silt which may have deposited in the tank and in the gutter must be cleared.

Figure 13. Standard layout of a runoff plot (Source: Siegert 1978)

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