RAINFALL AND RUNOFF IN RELATION TO EROSION

Introduction

Rainfall & runoff relationships relevant for design of:

• terraces

• water harvesting

• interception drains

• waterways

• protection works

Frequency of storms of different intensities

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

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Last updated: 26/05/98 18:55

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

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 generatorAnalyse rainy days using Gamma function

Daily rainfall

Excel module which demonstrates Gamma distribution

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:

where I = intensity (mm/hr)t = storm duration hrsT = return period in yearsk, c, n and x are empirical constants. x may be 0 in

which case

n)ct(kI

There is an equal probability of any point on each curve beingexceeded 1 year in T.

n

x

)ct(kTI

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:

96.0)35.0t(80I

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2 0.25

duration (hours)

Inte

nsi

ty (

mm

/ho

ur)

Intensities for very short durations forEast Africa

Maximum instantaneous intensity

Note maximum instantaneousintensity for 10 years is about 234 mm hr-1

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.

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

Storm Shape

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.

duration

time to peak

mean

peak mean

= ??

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.

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.

One type of equation that has been used to describe variation is:

nKAmePP

where:P = average depth over area, APm = maximum point rainfall at storm centreK and n are constants

The effect of area on runoff percentage

from Ben Asher, 1988

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

• 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;

Less rain = less reliablity

Effect of annual and seasonal rainfall amounts on erosion and land management

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

Erosion rates worst in low rainfall areas (e.g. 300 - 600 mm/year).

Reasons are that in such areas, vegetation cover is low & rainis not insignificant as it is in arid regions (rain cannot erode ifit does not rain)

In Kenya, maximum sediment yield occurs when: 30 mm < (R-E) < 60 mm

Seasonality of rain and erosion

P = mean annual rainfallp = highest mean monthly rainfall

Sediment yield as a function of seasonality

In many areas of the tropics, catchment sediment yield = f(p2/P)[mainly based on research in Malaysia]

In Malaysia, the equation is:

Y = 2.65 log (p2/P) + (log H)(tan S) - 1.56where :-Y, sediment yield is in g m-2 yr-1; p2/P is in mm; H the difference in height between top and bottom ofcatchment (m); S, the slope is in degrees.

p2/P acts as an index of seasonal concentration of rainfall

In Malaysia, gully density is also a function of (p2/P)

p2/P > 50 mm leads to high risk30 to 50 mm leads to moderate risk

< 30 mm leads to low risk

of gully erosion

Function ignores soils, topography & land use.

Runoff volume and intensity

Mass balance

Runoff = rainfall - infiltrationRunoff rate = rainfall rate - infiltration rate

Only true at a point isolated from contributions fromupslope.

Can use for up to 5 ha but best to restrict to catchmentlengths of the order of tens of metres.

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

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

Some examples of rainfall - runoff relationships basedon small runoff plots in Baringo, Kenya

They illustrate the use of small mass - balance plots f ordeveloping ideas about priorities f or SWC.

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 characteristicbased on:

cover

soil type and infiltration characteristics

slope (%).

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

Example:

Width of farm across slope = 80 m.Distance from farm to top of catchment = 150 mCatchment is very steep, rocky area with little vegetation.

Find the peak flow

80 m

150 m

From table of catchment characteristics:

Bare or eroded soil = 25Rocky, i.e. impervious = 50Very steep = 25Total = 100

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-offin the Catchment Characteristic column headed "100".

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 ratesso an estimate of I60 - the infiltration occurring in thefirst hour was used

By analysing all possible combinations of n, K, S, L in Hudson’s table, the following equation was found linkingthe parameters

Q = 0.13n- 0.285 K- 0.238 S0.154 L0.642

n is an estimate of Manning’s n

K is an estimate of I60 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 thetable given the uncertainty in estimating the catchmentcharacteristic, C (the outer straight lines in the graph)

Hudson's method using power law relationship

0

2

4

6

8

10

12

14

16

18

20

22

24

0 2 4 6 8 10 12 14 16

Q in table (l/ sec/m)

Q p

red

icte

d f

rom

eq

uat

ion

(l/s

ec/m

)