1. RAINFALL AND RUNOFF IN RELATION TO EROSION Introduction Rainfall & runoff relationships relevant for design of: terraces water harvesting interception drains waterways protection works

2. Frequency of storms of different intensities

3. Hudson deduced that only storms > 25 mm hr -1 are erosive. Erosive storms Use records to determine what proportion of rain is erosive: shaded area is erosive rain

4. It has also been observed that it is mainly storms of over 25 mm that causes erosion

5. Gamma functions required to model daily rainfall throughout the year - can now be done in Excel. Find proportion of dry days in each month - can model using random number generator Analyse rainy days using Gamma function Daily rainfall Excel module which demonstrates Gamma distribution

6. Intensity - duration - amount relationships For agricultural purposes, 1 in 10 year rainfall event is used. Intensity - duration relationship is family of storms related by equations of the form: whereI=intensity (mm/hr) t=storm duration hrs T=return period in years k, c, n and x are empirical constants. x may be 0 in which case There is an equal probability of any point on each curve being exceeded 1 year in T.

7. where I is measured in mm/hour and t is in hours. This predicts an “instantaneous” intensity of about 220 mm hr -1 Other values for instantanous intensities quoted in the literature range from about 150 mm hr -1 to about 250 mm hr -1 In Kenya, the equation is of the form:

8. Intensities for very short durations for East Africa Maximum instantaneous intensity

9. Note maximum instantaneous intensity for 10 years is about 234 mm hr -1

10. Raudkivi (1978) points out that such equations refer to complete storms and that within-storm intensities for a given duration are rather lower than for complete storms with the same duration. For example the maximum 1 hour rainfall depth in a 24 hour storm is only 85% of that in an single 1 hour storm of the same frequency.

11. Following table illustrates how maximum storm amount and intensity change for different durations

12. Storm Shape

13. Little work done in analysing autographic rainfall charts in tropics, let alone dry areas Storms of same amount will give different amounts of runoff - see diagram from Schwab Ratio of peak to mean intensity is also an important parameter for modelling (very little analysis but 3.5 to 1 may be typical) Ratio of time of peak to storm duration is another parameter Tropical storms tend to have peak in first half Recording rain gauges are essential.

14. duration time to peak mean peak mean = ??

15. Effect of area on rainfall amount Area affects Short rainfall events in arid areas are very localised - as you go out from the centre the average of the sampled area rainfall will decrease quickly For longer storms, rain may be more widespread - as you go out from measured point, average will be more similar to that measured at the centre.

17. Example: for a storm falling over a 50 sq mile sample area, of 30 minute length, average rainfall will be 69% of the maximum point rainfall. Approaches 100% for very long storms or small areas.

18. One type of equation that has been used to describe variation is: where: P = average depth over area, A P m = maximum point rainfall at storm centre K and n are constants

19. The effect of area on runoff percentage from Ben Asher, 1988

20. Larger catchments  lower proportion of rainfall running off catchment e.g. In Israel : - 30% runoff from 0.02 ha; 10% from 5000 ha in Israel. It is an over-simplification to extrapolate run-off plot data to large catchments. Basis of design of Water Harvesting systems - small catchments more efficient at producing runoff

21. length, slope, and roughness become of increasing importance Runoff percentage is less from larger catchment because: greater time for infiltration because at end of the most intense part of storm, excess continues to flow from the top of catchment, infiltrating into soil as it does so; larger catchments will usually have larger amounts of interception and depression storage;

22. Less rain = less reliablity Effect of annual and seasonal rainfall amounts on erosion and land management

23. Semi- arid areas are more prone to erosion in (b), the fact that runoff increases with rainfall is superimposed on a curve similar to (a) – erosion rate per unit of runoff is decreasing but there is more runoff

24. Erosion rates worst in low rainfall areas (e.g. 300 - 600 mm/year). Reasons are that in such areas, vegetation cover is low & rain is not insignificant as it is in arid regions (rain cannot erode if it does not rain) In Kenya, maximum sediment yield occurs when: 30 mm < (R-E) < 60 mm

25. Seasonality of rain and erosion

26. P = mean annual rainfall p = highest mean monthly rainfall Sediment yield as a function of seasonality In many areas of the tropics, catchment sediment yield = f(p 2 /P) [mainly based on research in Malaysia] In Malaysia, the equation is: Y = 2.65 log (p 2 /P) + (log H)(tan S) - 1.56 where :- Y, sediment yield is in g m -2 yr -1 ; p 2 /P is in mm; H the difference in height between top and bottom of catchment (m); S, the slope is in degrees. p 2 /P acts as an index of seasonal concentration of rainfall

27. In Malaysia, gully density is also a function of (p 2 /P) p 2 /P > 50 mmleads tohigh risk 30 to 50 mmleads tomoderate risk < 30 mm leads tolow risk of gully erosion Function ignores soils, topography & land use.

28. Runoff volume and intensity Mass balance Runoff = rainfall - infiltration Runoff rate = rainfall rate - infiltration rate Only true at a point isolated from contributions from upslope. Can use for up to 5 ha but best to restrict to catchment lengths of the order of tens of metres.

29. The following table was calculated from a simple computer program which calculated rainfall excess (runoff) for soils with different infiltration characteristics and assuming runoff does not start until the infiltration rate equals the rainfall rate.

30. Implications for design of protective structures:- for sandy soils, greatest excess is for short intense storm for clay soils, greatest excess is for long low intensity storm

32. Hudson’s Method for determining peak runoff rate Deterministic approaches (e.g. based on kinematic wave equation) have been developed but cumbersome to use. Empirical methods of which a common one for African conditions is due to Hudsons research in Zimbabwe (then Rhodesia) are simplest for field workers. Hudson’s method involves calculating a catchment characteristic based on:  cover  soil type andinfiltration characteristics  slope (%).

33. Catchment characteristics for African conditions (based on Hudson, 1971, Table 7.4)

37. Example: Width of farm across slope=80 m. Distance from farm to top of catchment=150 m Catchment is very steep, rocky area with little vegetation. Find the peak flow 80 m 150 m

38. From table of catchment characteristics: Bare or eroded soil=25 Rocky, i.e. impervious=50 Very steep=25 Total=100

39. The value lies between 7.4 and 8.9 - say, 7.65 l s -1 m -1 Therefore: Peak Flow = 7.65 x 80 = 612 l s -1 In the Table, interpolate under "Length of Catchment" between 140 and 200 to estimate the values for Peak Run-off in the Catchment Characteristic column headed "100".

40. Adding parameters in methods like Hudson’s is not something that happens much in nature. Natural processes usually involve a power law relationship. Hudson’s column 1 is really a measure of Manning’s n Column 2 could be thought of indicating infiltration rates so an estimate of I60 - the infiltration occurring in the first hour was used By analysing all possible combinations of n, K, S, L in Hudson’s table, the following equation was found linking the parameters Q = 0.13n - 0.285 K - 0.238 S 0.154 L 0.642

41. n is an estimate of Manning’s n K is an estimate of I 60 in mm hour -1 S is in m/m L is in m Q is in l s -1 m -1 As you would expect, peak runoff, Q is lower for rougher catchments lower for catchments with higher infiltration rates, greater for longer catchments The estimate is within a reasonable range of the values in the table given the uncertainty in estimating the catchment characteristic, C (the outer straight lines in the graph)