Transcript No Slide Title

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
Erosive storms
Hudson deduced that only storms > 25 mm hr-1 are erosive.
Use records to determine what proportion of rain is erosive:
shaded area is
erosive rain
It has also been observed that it is mainly storms of over 25
mm that causes erosion
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Last updated: 26/05/98 18
Daily rainfall
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
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:
x
I
kT
n
( t c)
where I
=
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
I
k
n
( t c)
There is an equal probability of any point on each curve being
exceeded 1 year in T.
In Kenya, the equation is of the form:
I
80
( t  0.35 ) 0.9 6
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
250
Maximum instantaneous intensity
Intensity (mm/hour)
200
150
Intensities for very short durations for
East Africa
100
50
0
0
0.05
0.1
0.15
duration (hours)
0.2
0.25
Note maximum instantaneous
intensity 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 duration (hrs)
Mean storm intensity
(mm/hr)
Storm amount
(mm)
0.25
130.6
32.6
0.5
93.5
46.8
1
60.0
60.0
2
35.2
70.4
4
19.5
78.0
8
10.4
83.2
12
7.2
86.4
24
3.7
88.8
Table showing amounts and mean intensities corresponding to
storms of different duration occurring once in ten years in East
Africa
Storm Shape
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.
Little work done in analysing autographic rainfall charts in
tropics, let alone dry areas
time to peak
peak
= ??
mean
mean
duration
Area affects
Effect of area on rainfall amount
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:
P  Pme
 KA n
where:
P = average depth over area, A
Pm = maximum point rainfall at storm centre
K 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
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;
• length, slope, and roughness become of increasing
importance
Effect of annual and seasonal rainfall amounts on erosion
and land management
Less rain = less reliablity
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 & 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
Seasonality of rain and erosion
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]
P = mean annual rainfall
p = highest mean monthly rainfall
p2/P acts as an index of seasonal concentration of rainfall
In Malaysia, the equation is:
Y = 2.65 log (p2/P) + (log H)(tan S) - 1.56
where :Y, sediment yield is in g m-2 yr-1;
p2/P is in mm;
H the difference in height between top and bottom of
catchment (m);
S, the slope is in degrees.
In Malaysia, gully density is also a function of (p2/P)
p2/P > 50 mm
30 to 50 mm
< 30 mm
leads to
leads to
leads to
high risk
moderate risk
low risk
of gully erosion
Function ignores soils, topography & land use.
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.
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.
Infiltration curve
Storm
Philip's S
Philip's A
Duration
(min.)
Intensity
(mm/hr)
Amount (mm)
Excess (mm)
0.31
0.0062
720
7.2
86.4
75
0.56
0.013
480
10.4
83.2
68
0.86
0.025
240
19.5
78.0
60
1.35
0.044
240
19.5
78.0
54
2.08
0.076
120
35.2
70.4
47
3.3
0.132
60
60.0
60.0
36
5.08
0.234
60
60.0
60.0
25
8.0
0.41
30
93.5
46.8
11
Table: showing E. African storms which give maximum amounts of rainfall excess
for different infiltration curves.
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 based
on small runoff plots in Baringo, Kenya
They illustrate the use of small mass - balance plots for
developing ideas about priorities for 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 characteristic
based on:
 cover
 soil type and infilt ration characteristics
 slope (%).
Catchment characteristics for African conditions
(based on Hudson, 1971, Table 7.4)
Cover
Description
Factor
Dense grass
10
Scrub or medium grass
15
Cultlvated land
20
Bare or eroded soil
25
Soil type and inflltration eharaeteristies
Description
Infiltration
curve
Factor
Deep well drained soil
1
10
Deep soils with moderately
high permeability
2
15
Solls wlth
moderately
permeabillty
to
hlgh
3
20
Solls
wlth
moderate
permeabillty and depth
4
25
Soils wlth
moderately
permeability
to
low
5
30
Shallow soils or moderately
low permeabllity
6
35
Medium clays silty
loams, rocky surfaces
7
40
Heavy clays
8
45
Impervious surfaces
-
50
moderate
moderate
clay
Slope (%)
Description
Range
Factor
Very flat to gentle
0-5
5
Moderate
5-10
10
Rolling
10-30
15
Hilly or steep
30-80
20
Very steep / mountainous
80+
25
Catchment characteristics
Length of
catchment
30
(m)
35
40
45
50
55
60
65
70
75
80
90
100
140
1
1.4
1.8
2.2
2.6
3.0
3.4
3.8
4.2
5.0
5.8
6.6
7.4
200
1.1
1.6
2.0
2.4
3.0
3.5
4.2
4.9
5.6
6.5
7.5
8.1
8.9
245
1.3
1.7
2.3
2.9
3.4
4.0
4.8
5.7
6.7
7.6
8.6
9.6
10.6
285
1.4
2.0
2.5
3.0
3.8
4.6
5.5
6.5
7.5
8.5
9.5
10.5
11.5
350
1.5
2.0
2.7
3.4
4.2
5.2
6.2
7.3
8.5
9.8
11.0
12.2
13.4
400
1.5
2.1
2.8
3.5
4.6
5.6
6.7
7.8
9.2
10.5
12.3
13.8
15.3
Table of Peak run-off per unit catchment width for catchments of different lengths (l s-1 m-1). (Based on Table
7.5 in Hudson, 1973)
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
150 m
80 m
From table of catchment characteristics:
Bare or eroded soil
Rocky, i.e. impervious
Very steep
Total
=
=
=
=
25
50
25
100
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".
Catchment characteristics
Length of
catchment
30
(m)
35
40
45
50
55
60
65
70
75
80
90
140
1
1.4
1.8
2.2
2.6
3.0
3.4
3.8
4.2
5.0
5.8
6.6
200
1.1
1.6
2.0
2.4
3.0
3.5
4.2
4.9
5.6
6.5
7.5
8.1
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
100
7.4
8.9
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 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 the
table given the uncertainty in estimating the catchment
characteristic, C (the outer straight lines in the graph)
Hudson's method using power law relationship
24
22
Q predicted from equation (l/sec/m)
20
18
16
14
12
10
8
6
4
2
0
0
2
4
6
8
Q in table (l/ sec/m)
10
12
14
16