THE INFLUENCE OF STORM CHARACTERISTICS ON RUNOFF GENERATION AND CONNECTIVITY IN SEMI-ARID AREASS
Reaney
(1), L J Bracken (née B
ull) (2)and M
J Kirkb
y(1)
(1), School of G
eograp
hy, University of Leed
s, Leeds, LS
2 9JT, UK
, (2)Dep
artment of G
eograp
hy, University of D
urham, D
urham, D
H1 3LE
Em
ail: s.reaney@g
eog.leed
s.ac.uk Fax: 44 113 233 3308 Web
: ww
w.g
eog.leed
s.ac.uk/peop
le/s.reaney/
The Connectivity of
Runoff M
odel (C
RU
M)
The model developed to investigate the controls on
runoff
generatio
n and
flo
w
dynam
ics in
semi-arid
en---vironments
is the
Connectivity
of R
unoff M
odel(C
RU
M). The m
odel is divided into vertical and horizon-tal com
ponents and distributed on a grid structure. Thevertical
comp
onent rep
resents intercep
tion, surface
detention
storage,
surface d
epression
storage,
soilm
oisture storage and recharge, (Figure 1).
The horizontal interactions occur only as overland flowbecause lateral flow
through the soil is negligible insem
i-arid environments. The flow
routing between the
grid cells uses the FD8 algorithm
(Quinn et al.1991)
which uses m
ultiple flow directions and hence allow
sboth the dispersion and concentration of flow
. The flowvelocity is determ
ined by the Darcy-W
eisbach equation.
Pre-d
efined S
torms
A set of pre-defined storm
hydrographs havebeen developed to investigate the influence ofthe tem
poral structure of the rainfall on thegeneration
and transm
ission of
runoff. The
storms all deliver 80 m
m of rainfall over a tw
ohour period (Figure 3). The storm
characteris-tics and the runoff coefficients are show
n inTable 1.
pulse length0
510
1520
25
0.0
0.1
0.2
0.3
0.4
0.5
0.6
maxim
um rainfall intensity (m
m hr
-1)
0100
200300
400500
0.0
0.1
0.2
0.3
0.4
0.5
0.6
total rainfall (mm
)0
510
1520
2530
35
0.0
0.1
0.2
0.3
0.4
0.5
0.6
CO
V0.0
0.51.0
1.52.0
2.53.0
runoff coefficientrunoff coefficient
runoff coefficient
runoff coefficient
0.0
0.1
0.2
0.3
0.4
0.5
0.6
total rainfall (mm
)0
510
1520
2530
35Qpeak
Qpeak
0 2 4 6 8
maxim
um rainfall intensity (m
m hr
-1)
0100
200300
400500
0 2 4 6 8
Figure 5 D
ischarge characteristics with varable rainfall
The total rainfall depth shows a positive relationship w
ith both the peak discharge and the runoffcoefficient. This is related to the decrease in the infiltration rate w
ith increasing total rainfall.H
owever, there is a large am
ount of scatter in the plots with the sam
e rainfall depths producingvastly different am
ounts of flow from
the slope. This range of results relates to both the distrib-ution of rainfall intensities and the tem
poral structure of the storm.
The maxim
um rainfall intensity results show
threshold behaviour related to the intensity requiredto exceed in the soil infiltration capacity. H
owever, the infiltration capacity w
as 55 mm
hr -1w
here-as the threshold is located at 84 m
m hr -1. This difference relates to the am
ount of excess water
required to fill the surface depression store and allow the connection betw
een the runoff gener-ation point and the slope outflow
.
As the storm
length increases, the range of runoff coefficients increases. The rate of increase inthe m
aximum
runoff coefficient rises above a pulse length of five minutes and levels off after 13
minutes. The increase at five m
inutes relates to the time required to fill the surface depression
store and for the runoff to reach of the outflow. The levelling off of the range of runoff coefficients
at 13 minutes relates to the total travel tim
es across the surface.
The CO
V does not show
a consistent relationship with the runoff coefficient. There are large
variations in the runoff coefficient for a certain CO
V value. This therefore suggests that the tem
-poral structure, as w
ell as the variability, plays a significant role in the generation of runoff.
Introduction
The generation of high magnitude flood events at the catchm
ent scale in semi-
arid areas are caused by a combination of precipitation characteristics including
amount, intensity, duration and spatial distribution (W
olman and G
erson 1978;C
osta 1987). At the sm
all scale many investigations have focused on the influ-
ence of plot scale properties such as vegetation (Cerda, 1995; B
ergkamp et al,
1996; Imeson et al, 1992), soils and slopes (P
arsons et al 1997; Martinez-M
ena etal 1998). H
owever, there have been a lim
ited number of investigations into how
the characteristics of the rainfall input into semi-arid system
s influences the gen-eration and transm
ission of runoff.
The study uses the Connectivity of R
unoff Model (C
RU
M) to investigate how
thecharacteristics of rainfall input to sem
i-arid areas influence the runoff produced atthe base of a hillslope. A
simple theoretical hillslope, characteristic of a sem
i-aridregions, has been subjected to a range of storm
events. The storm events have
been generated in two w
ays. The first set uses pre-defined storm hydrographs
and the second set uses stochastically generated storms. The stochastic rainfall
generator has been used to generate two sets of storm
s. The first set consists ofa fixed duration and depth w
ith variable per minute intensities and the second set
of storm has variable storm
s depths and durations.
Rg
Recharg
e
Canop
y
Soil S
tore
Runon
Infiltration
Runoff
Detention S
tore
Dep
ressionS
torage
Rd
Rt
Rn
Figure 1 Vertical m
odel structure
TAB
LE1 S
torm C
harts and runoff coefficiences
STO
RM
MA
X IN
TEN
SITY
(mm
hr-1)
ME
AN
INTE
NS
ITY(m
m hr
-1)C
OV
RU
NO
FF C
OE
FFICIE
NT
a40.0
40.00.00
25.3%
b109.1
40.01.23
57.9%
c109.1
40.01.23
56.9%
d109.1
40.01.23
55.8%
e80.0
40.00.58
37.1%
f80.0
40.00.58
35.2%
g83.2
40.00.60
26.2%
h170.3
40.00.95
26.9%
similar runoff coefficients. These values are
only slightly greater than from storm
a with
constant rainfall. This suggests that the runoffw
hich was generated during the high intensity
rainfall is rapidly infiltrated during subsequentlow
rainfall intensity periods. This shows the
importance of the tem
poral fragmentation of
the high
intensity rainfall
during the
stormevent.
Stochastically G
enerated S
torms
The stochastic rainfall was generated using a M
onte Carlo m
odel to select randomrainfall intensities. The M
onte Carlo m
odels uses a distribution function fitted to theintense rainfall sections of a m
easured time series, equation 1.
Where rfi
is the rainfall intensity (mm
hr-1), –is the m
ean per minute rainfall
intensity, ais a coefficient and prob
is the probability of that rainfall intensity. For am
easured rainfall record from S
E S
pain, a=
1.74 (R2 =
0.98).
rfi =–ln(1–prob).601a
Results 2
To investigate which properties of the rainfall
time series control the am
ount of discharge thatleaves the slope, the test hillslope w
as subject-ed to 1000 storm
realisations of varying intensityand duration. These storm
pulses varied from 1
to 20 minutes and from
40 mm
hr -1to 90 m
m
hr -1, Figure 5.
Results 1
The impact of variable rainfall on the discharge is show
n in the box plots, Figure 4. These plots compare
the difference between the runoff leaving the slope from
a rainfall pulse of 75 mm
hr -1for five m
inutes deliv-ered at constant and variable intensity. The variable rainfall increases the m
edian discharge. The maxim
umdischarge volum
e simulated w
as 3.65 m3; this is 480 %
greater than with constant rainfall. H
owever, 25.9
% of the sim
ulations produced a discharge volume less than the constant rainfall, w
ith the minim
um dis-
charge of 0.13 m3. The m
edian peak dischargeis very sim
ilar between the constant and variable
rainfall. There is a greater spread of values with
the variable rainfall, to a maxim
um of 1.38 m
3
min
-1.
Constant
Variab
le
peak discharge (m min )
0 1 2 3 4 5
Constant
Variab
le 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
3 -1
total discharge (m )3
Figure 4 B
ox plots of d
ischarge w
ith constant and varab
le rainfall
Acknow
ledg
ments
This work w
as funded by a School of G
eography, University of Leeds studentship and financial support
from the E
U P
ES
ER
A project.
References
Bergkam
p, G., C
amm
eraat, L.H., and M
ertinez-Fernandez, J. 1996. 'Water m
ovement and vegetation patterns on shrubland and an abandoned field in tw
o desertification threatened areas in S
pain', E
arth Surface P
rocesses and Landforms, 21, 1073-1090.
Cerda, A
. 1995. 'Spatial distribution of infiltration on the m
atorral slopes in a Mediterranean environm
ent, Genoves, S
pain', in Fantechi, R., P
eter, D., B
labanis, P. and Rubio,
J.L. (Eds), D
esertification in a E
uropean Context: P
hysical and Socio-econom
ic Impacts, E
uropean Com
mission, B
russels, 427-436.C
osta, J.E. 1987. A
comparison of the largest rainfall - runoff foods in the U
nites States and the P
eople's Republic of C
hina and the world. Journal of H
ydrology, 96, 101-115.Im
eson, A.C
. Verstraten, J.M., van M
ulligen, E.J., and S
evink, J. 1992. 'The effects of fire and water repellency on infiltration and runoff under M
editerranean type forest', Catena, 19, 345-361.
Lasanta, T., Garcia-R
uiz, J.M., P
erez-Rontom
e, C. and S
ancho-Marcen, C
. 2000. 'Runoff and sedim
ent yield in a semi-arid environm
ent: the effect of land managem
ent after farmland
abandonment.' C
atena 38, 265-278.M
artinez-Mena, M
., Albaladejo, J. and C
astillo, V.M. 1998. 'Factors influencing surface runoff generation in a M
editerranean semi-arid environm
ent: Chicam
o watershed, S
E S
pain.' Hydrological
Processes 12, 741-754.
Parsons, A
.J., Wainw
right, J., Abraham
s, A.D
. and Sim
anton, J.R. 1997. D
istributed dynamic m
odelling of interrill overland flow. H
ydrological Processes, 11, 1833-1859.
Quinn, P., B
even, K., C
hevallier, P., and Planchon, O
. 1991: The prediction of hillslope flow paths for distributed hydrolgical m
odelling using digital terrain models; H
ydrological Processes,
5, 59 - 79W
olman, M
.G. and G
erson, R. 1978. R
elative scales of time and effectiveness of clim
ate in watershed geom
orphology, Earth S
urface Processes and Landform
s, 3, 189-208W
ainwright, J. and P
asons, A.J., 2002: The effect of tem
poral variations in rainfall on scale dependency in runoff coefficients; Water R
esources Research, 38, art 1271
Conclusions
The defined storms show
ed that the temporal structure of the storm
event has a significanteffect on the generation and transm
ission of runoff. The highest runoff coefficient was
obtained when the high intensity rainfall pulse w
as located at the start of the storm.
The importance of the tem
poral structure of the rainfall time series is clearly dem
onstratedby the M
onte Carlo based sim
ulation results. From the M
onte Carlo generation of 200
storms w
ith the same rainfall depth and duration, it w
as found that the amount of runoff
leaving the slope was highly variable. The m
ajority of the realisations gave a greater runoffcoefficient than w
ith constant rainfall intensity. How
ever, 25.9 % of the realisations gave a
lower total discharge and 51.2 %
gave a lower peak discharge. These results contrasts w
iththe findings of W
ainwright and P
arsons (2002) who found that the use of variable intensity
rainfall always resulted in an increase in the am
ount of runoff leaving a slope.
The modelling results from
the variable length of depth storms show
ed that no one statisti-cal property is able to explain the variations in the runoff coefficients the m
odelling results.The statistical properties do not directly consider the tem
poral structure of the rainfall time
series. This work suggests that the tem
poral structure, as well as the variability, plays a
significant role in the determination of the runoff response to a storm
event.
Test Hillslop
e
The test hillslope has a slope length of 50 m at a gradient of
6°and relates to hillslopes found in the field. The infiltration
model param
eters relate to results from a rainfall sim
ulationexperim
ent from a non-vegetated area w
ith stones at a scrubsite.
Figure 2 shows the discharge hydrograph and the depression
storage from a 5 m
inute storm event at an intensity of 75 m
mhr -1. This rainfall pulse is related to a low
frequency, highm
agnitude storm event. The peak discharge is 0.008 m
3s
-1
and the total discharge is 0.76 m3
giving a runoff coefficient of4.87 %
.
1a
time (second
s)
050
100150
200250
300350
4000.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
depression storage depth (m)
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
Rainfall (mm hr)
050100
150
200
250
300
dischargedepression storage
rainfall
Figure 2
Discharg
e hydrog
raph from
the test hillslope
discharge (m s )3 -1
ab
cd
ef
020
4060
80100
1200 20 40 60 80
100120140160180
020
4060
80100
1200 20 40 60 80
100120140160180
040
80120
0 20 40 60 80100120140160180
040
80120
0 20 40 60 80100120140160180
gh
time (m
inutes)0
4080
1200 20 40 60 80
100120140160180
040
80120
0 20 40 60 80100120140160180
040
80120
0 20 40 60 80100120140160180
040
80120
time (m
inutes)tim
e (minutes)
time (m
inutes)tim
e (minutes)
time (m
inutes)tim
e (minutes)
time (m
inutes)
-1rainfall intensity (mm hr )-1rainfall intensity (mm hr )
-1rainfall intensity (mm hr )-1rainfall intensity (mm hr )
-1rainfall intensity (mm hr )-1rainfall intensity (mm hr )
-1rainfall intensity (mm hr )-1rainfall intensity (mm hr )
0 20 40 60 80100120140160180Fig
ure 3 Pre-d
efined storm
s
Results
The results show that the tem
poral structure of the rain storm can have a significant influ-
ence on the amount of w
ater leaving the slope. Storm
a has a constant rainfall intensity andproduces the low
est amount of discharge. The second set of storm
s have a greater maxi-
mum
rainfall intensity at 109.1 mm
hr -1and produce m
ore runoff that storm a. M
ore runoffis obtained from
storm b w
hich has the high intensity storm at the beginning of the storm
.The rainfall during the rest of the tim
e series helps the transmission of the runoff.
Storm
e has a linear increase in intensity and storm f has a linear decrease. S
torm e gives
more runoff and can be related to the w
etting up of the soil before the higher intensity,runoff generating, rainfall. These storm
s show a different behaviour to storm
s b and c andshow
the importance of conditioning the soil surface for runoff generation.
Storm
s g and h have variable rainfall with storm
h having the greater amount of variability.
Storm
g has a maxim
um rainfall intensity of 83.2 m
m h
-1and storm
h has a maxim
um inten-
sity of 170.3 mm
hr -1. Despite the large difference in the m
aximum
intensities, they give
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urham
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