The Hydrology-Geomorphology
Interface: Rainfall. Floods, Sedimentation,
Jerusalem Conference, May 1999). IAHS Publ. no. 2 6 1 , 2000.
Land Use (Proceedings o f the
53
Runoff events in the Negev, Israel
ARTE BEN-ZVI & ISABELA SHENTSIS
Israel Hydrological Service, PO Box 6381, Jerusalem 91063, Israel
e-mail: arieb20(£Kvater.gov.il
Abstract Quantitative characteristics of runoff events in the arid Negev of
Israel are presented in a general form suitable for adaptation to other arid
areas. The principal results are condensed into two hydrological models. One
predicts the frequency and magnitude of runoff events, and the other assesses
transmission losses in a wadi reach. The first model is composed of statistical
formulae describing occurrence frequency of events within the year, number
of events in a year, distributions of peak discharges and volumes of events at
individual sites, and regional extensions of outcomes of these formulae. The
second model incorporates verbal lithostratigraphic information with records
on flow volumes at trunk stations into a quantitative assessment of tributary
contribution and transmission losses. It divides the assessed losses into
evaporation and aquifer replenishment. The models are regionalized with
regard to catchment area and geographical location, where the location reflects
spatial variations in physical properties that govern runoff generation and flow
processes.
Key words flood frequency; floods; Negev; regional model; runoff events; streamflow; surface
hydrology
INTRODUCTION
This paper summarizes recent reports by the Israel Hydrological Service, a number of
which were prepared within the Water Commission's Project to re-assess the utilizable
water potential in the Negev.
The Negev is an arid area in southern Israel. It has a triangular shape of about
10 000 km in size whose comers touch the Mediterranean, the Dead Sea, and the Gulf
of Eilat (Fig. 1). The eastern boundary of the Negev runs along the Arava Valley, a
segment of the Syrian-African Rift, having its lowest land elevation along the Dead
Sea shoreline at about -400 m a.m.s.l. A ridge of high mountains, reaching elevations
of up to about +1000 m a.m.s.l., runs through the central Negev in a northeastsouthwest direction. A wide valley, running from east to west, separates this ridge and
the Judean Mountains, upon whose flanks the northern boundary of the Negev is drawn.
Potential evaporation in the Negev exceeds 2000 mm year" . The mean annual
depth of precipitation ranges from 300 mm on the northern boundary to about 25 mm
at the southern tip. Precipitation falls infrequently; many events are of limited spatial
and temporal extent. Runoff events in minor catchments can be generated from rainfall
of only a few mm in depth (Yair et al, 1980; Schick, 1988). Yet, runoff in wadis
draining larger catchments requires rainfall events of at least 10-20 mm in depth.
Unfortunately, few meteorological stations are operated in the Negev so that
insufficient information regarding temporal and spatial distribution of precipitation is
available. The only dependable regional information on precipitation in this area is its
mean annual depth.
2
1
Arte Ben-Zvi
& Isabela
Shentsis
,'7v
Va
W
Î1
V^feAp^
Dead
Sea
2S 06
/
i
\
V /
^ ' , n
-
55&5
_ v.
—-
/
Wadis
Boundary of
the study area
Sea
Gulf of Elat
F i g . 1 H y d r o g r a p h i e m a p of the N e g e v .
•
Relevant
stations
Gulf of Elat
Runoff
events in the Negev,
Israel
55
Land in the Negev is generally devoid of vegetation. Exceptions are found near
small spring outlets, along some wadis where buried channels carry shallow perched
aquifers, and subsequent to rainfall events when short-lived grass flourishes. Rainfed
agriculture is practiced in the northern Negev, while irrigated crops are grown in the
wide valleys of the northern and the eastern Negev. Owing to the soil properties and
lack of vegetation cover, sheet flow is easily generated (e.g. Schick, 1988; Schick et
al, 1997). Yet, due to the high infiltration capacity in channel beds, most runoff events
vanish in their flow paths.
The hydrographie network of the Negev is displayed in Fig. 1. Most of the area
drains towards the Dead Sea. Another large area drains towards the Mediterranean Sea
and small areas drain towards the Gulf of Eilat and to depressions in the southern
Arava Valley. Four major wadis can be identified in the first drainage system and one
in the second system. These are Nahal (a Hebrew term for ephemeral watercourse)
Hiyon, Nahal Paran and Nahal Neqarot which drain towards the Dead Sea through the
northern Arava, Nahal Tsin which separately drains towards the Dead Sea, and Nahal
Besor which drains towards the Mediterranean Sea.
Owing to the long intervals between ranoff events, and the high rate of potential
évapotranspiration, low values of soil moisture antecede almost all runoff events
(Schwartz & Schick, 1990). Hence, the events can be considered, with little loss of
accuracy, as being independent of one another. This enables application of simple
probabilistic methods to the complete series of events and maximum use of the
information content of the data (e.g. Kisiel et al, 1971). Using this approach, the Israel
Hydrological Service has gradually developed an event-based regional model for the
frequency and magnitude of runoff events in the Negev (e.g. Ben-Zvi & Ben-Zvi,
1971; Ben-Zvi & Cohen, 1975; Ben-Zvi, 1982, 1991; Ben-Zvi & Meirovich, 1997;
Meirovich et al, 1998). An updated summary of the model is presented here.
Another important issue in the hydrology of arid areas concerns transmission
losses and aquifer replenishment from runoff events. The Israel Hydrological Service
has recently developed a hydrologic-lithostratigraphic model for assessing such
volumes (Shentsis et al, 1999). It incoiporates qualitative geological and lithostratigraphic information into a quantitative model. A summary of this model is also
presented here.
DATA
The models have been developed by analysis of data obtained from the extensive
network of hydrometric stations which has been operated for decades by the Israel
Hydrological Service. Each station is equipped with a battery-operated water level
recorder that can work unattended for eight months. Owing to destruction of stations
and approach roads by extreme floods and by vandalism, station records are not as
complete as desired. A number of stations have been moved to new locations, and
other stations have been abandoned. Due to the difficult operating conditions and long
travel distances, very few discharge measurements have been carried out in the Negev,
and the rating curves are derived by use of hydraulic formulae. High discharges were
determined by the area-slope method.
56
Arie Ben-Zvi
& Isabela
Shentsis
Data for 42 stations were collected for the construction of the regional model. The
operational periods of these stations range from four to 45 years, with an average of 18
years per station. The occurrence frequency of events was derived for stations
operating for at least five years. The statistical analysis of magnitudes of events was
limited to series containing at least 15 events recorded prior to September 1995.
Records of 24 stations, with an average length of 26 years, met this criterion. A list of
these hydrometric stations together with some descriptors of their catchments and flow
data is presented in Table 1. Their locations are displayed in Fig. 1; their density
decreases from north to south.
T a b l e 1 Station and c a t c h m e n t properties.
W a d i and site n u m b e r
A
(km )
N
n
Rain
(mm)
2 3 1 0 6 B e s o r at Nitsana R d
133
46
94
2 3 1 1 0 R e v i v i m at R e v i v i m
118
6
19
2
2 3 1 1 5 B e e r S h e v a at Z a r n u q
2 3 1 2 7 B e e r S h e v a at B e e r S h e v a
2 3 1 3 5 B e q a at B e e r S h e v a
2 3 1 3 7 B e e r S h e v a at H a t s e r i m
101
114
Q
(m
mci
g
s" ) ( m
m a x
3
6.30
3.77
1
3
V
(10 m )
mei
1
s" )
116
20.4
6
3
V„
(10 m )
6
0.115
1.11
0.045
0.211
405
24
104
176
15.7
875
0.286
10.8
1090
20
99
24.3
1000
45
239
0.756
0.014
24.1
96
233
157
1220
27
139
262
12.6
24.0
1.66
240
1.36
91
7
30
130
20
0.503
0.044
2 3 1 4 5 B e s o r at T s e e l i m
2378
10
45
164
19.7
1050
0.565
23.2
2 3 1 5 0 B e s o r at R e e m
33.7
2 3 1 4 0 S e c h e r at Y e r u h a m
2.50
1090
3
0.450
2630
32
120
201
28.2
1000
1.231
23155 G e r a r a t A z a R d
233
7
40
292
10.2
78
0.057
23160 G e r a r a t R e e m
658
34
189
289
5.35
400
0.191
2 5 1 9 0 L a v a n at N i t s a n a R d
192
47
122
92
9.2
439
0.149
3.35
55106 T s i n a t Medad Mt
5 5 1 1 0 T s i n at M a p a l A v e d a t
135
36
91
1.52
552
0.023
233
43
63
54
87
6.80
551
0.170
1.60*
6.02
5 5 1 4 0 T s i n at M a s o s
660
37
84
87
572
0.264
5.70*
66
47
109
90
106
5.01
2.73
0.031
64
15
42
0.030
0.275
0.698
1130
29
65
79
18.25
0.276
5.38
5 6 1 4 0 R a m o n at Elat R d
108
16
34
-
6.76
5 6 1 5 0 N e q a r o t at M a s a M t
697
38
73
59
5.77
640
0.101
0.042
3.70
2799
13
33
0.213
29.8*
16
32
-
1080
161
3350
46
84
32
17.35
1150
0.350
171
19
16
-
33.65
247
0.067
5 5 1 6 0 H a t h a at O r o n R d
5 5 1 6 5 M a m s h i t at O r o n R d
5 5 1 8 0 T s i n at A q r a b i m
5 7 1 5 0 Paran at H a l a m i s h M t
5 7 1 6 0 A r o d at C a n y o n
5 7 1 6 5 P a r a n at B o t t l e n e c k
5 7 1 8 0 T s i h o r at N a h a l P a r a n
19.6
12.0
8.17
32.9
99
300
72.6
89.4
0.058
3.18
15.3
1.67
0.62
30.0
1.05
A is c a t c h m e n t area, /V is n u m b e r of years of observation, n is n u m b e r of r e c o r d e d runoff events, R a i n is
m e a n annual depth of precipitation, Q is discharge, V is v o l u m e , subscript " m e d " refers to m e d i a n , and
" m a x " to m a x i m u m o b s e r v e d value, and * is reconstructed v a l u e .
N o t e : In s o m e cases, rain years are fewer than observation years.
Having chosen the event-based approach, it is necessary to define the events. In
our studies, an event is the occurrence of runoff at a site. It commences when the water
level rises above the stage corresponding to zero flow (or to a very low baseflow), and
ceases when the level first returns to that stage for at least 24 hours. The 24-hour
interval is introduced in order to distinguish a temporary cessation of flow, due to
transmission losses or asynchronous contributions from different tributaries, from
runoff resulting from different rainfall events. Application of a time criterion for such a
distinction might interfere with the statistical analysis (Ashkar & Rousselle, 1983) but
Runoff
events in the Negev,
57
Israel
it prevents the need for distinction between multi-peaked and overlapping events as
well as separating discharges of overlapping events, which might introduce new errors
into the computations. Peak discharge is the maximum momentary discharge that
occurred during the event. Event volume is the total volume of water that flowed
through the site during the event.
OCCURRENCE OF RUNOFF EVENTS
Almost all runoff events in the Negev result from rainfall events. Rainfall of a few mm
in depth may cause runoff from tiny catchments (e.g. Yair et al, 1980; Schick, 1988).
However, owing to interception and infiltration processes along the flow paths, runoff
from small catchments of 20 to 200 km in area occurs only due to rainfalls of about
5-20 mm, depending upon the intensity of the causative rainfall.
The mean number of runoff events per year varies from about 1 year" in the
southern Negev to 6 year" at the northwestern boundary. The mean and variance of the
number of events in a year are correlated with the mean annual depth of precipitation
over the catchment (Meirovich et al, 1998):
2
1
1
n = 0 . 6 8 + 0.019/'
2
S
(1)
= 0.29 + 0.033P
(2)
where n is mean number of events per year, P is mean annual depth of precipitation
over the catchment (mm year" ), and S is the variance of the number of events in a year.
The correlation coefficients for equations (1) and (2) are, respectively, 0.92 and 0.78.
Ben-Zvi (1991) has shown that the negative binomial function fits the distribution
of number of events in a year well. This function has two parameters that can be
determined from the values of n and S .
Runoff events occur in the Negev from late September to mid-May (Ben-Zvi et al,
1998). The occurrence frequency within the year attains its maximum value in the
central winter months of December to February, when the difference between
precipitation and potential évapotranspiration reaches its relative maximum value. This
annual cycle is well described by the normal and the Pearson III distributions (Ben-Zvi
& Meirovich, 1997). The parameters of these distributions can be determined from the
statistical moments of the arrival days of events at the hydrometric stations (Table 2).
The mean arrival day of runoff events in the Negev is mapped in Fig. 2(a) (BenZvi et al, 1998). Apparently, for the southern and eastern Negev, the mean day falls in
the first half of January, while for the northwestern Negev it falls in the second half.
The standard deviation of arrival days is longer than 70 days in the southern Negev and
shorter than 50 days in the north.
In accordance with accepted hydrological hypotheses, high runoff events are
expected to result from intense rainfall events. These occur more frequently in the
Negev during the autumn and spring months of September to November, and March to
May (Katsenelson, 1955, 1956; Sharon & Kutiel, 1986). Thus, although all runoff
events in the Negev appear more frequently in the mid-winter months, the higher ones
may tend to occur in the other months (N. Rosenan, unpublished file on floods, Israel
Meteorological Service, Bet Dagan, c. 1943; Greenbaum et al, 1998).
1
2
2
A rie Ben-Zvi
58
& Isabela
Shentsis
T a b l e 2 Arrival times of runoff events.
Station n o .
10-year h i g h events:
All runoff events:
Mean day
Std (days)
Skew
Mean day
23106
17/01
0.02
23110
22/01
50
52
Std (days)
13/12
77
23115
24/01
53
0.05
*
*
*
*
*
23127
22/01
51
0.28
23135
22/01
48
*
-0.09
19/01
42
23137
20/01
-
51
-0.09
24/12
80
23140
28/01
44
*
*
*
44
*
*
*
*
M W W (%)
23145
24/01
53
-0.15
0.34
23150
22/01
52
0.01
02/02
23155
19/01
41
0.10
*
*
23160
11/01
46
0.23
11/01
62
-
25190
18/01
50
0.20
12/01
75
-
55106
19/01
57
0.23
08/11
55110
14/01
57
0.26
16/11
25
34
2.50
26/10
26
0.54
55140
16/01
62
0.13
55160
15/01
55
0.36
55165
18/01
62
1.03
55180
07/01
59
0.26
56140
02/02
56
-0.28
56150
08/01
69
57150
06/01
73
57160
04/01
82
57165
12/01
57180
07/01
0.77
*
*
29/10
22
0.52
15/11
41
12.0
*
*
*
0.20
01/12
64
*
0.39
*
*
-
0.19
74
0.28
06/12
48
70
*
*
*
*
M W W is two-sided significance level (%) for the difference b e t w e e n arrival days of these a n d the lower
events: - not significant, * insufficient data.
Defining high runoff events as those for which the recurrence interval of their peak
exceeds 10 years, the mean arrival day of such events for catchments smaller than
1000 km size is mapped in Fig. 2(b) (Ben-Zvi et al, 1998). The map shows marked
differences within the Negev. The mean arrival day of high events in the Tsin and
Neqarot watersheds (eastern Negev) falls in October or November, whilst for the
northwestern Negev it falls in mid-January. The difference in arrival days between the
high and the other events in these watersheds is statistically significant. The statistical
parameters of arrival days (Table 2) indicate that the high events in the northern Negev
are concentrated in the central winter months, while in the southern Negev they are
distributed throughout the entire season.
2
MAGNITUDES OF EVENTS
Magnitudes of events depend upon the meteorological and physiographic properties of
the catchment. The principal meteorological properties in Israel are mean annual depth
of precipitation and the fraction of intense rainfall in the total depth (Yair et al, 1980;
Yair & Lavee, 1982; Schick, 1988; Shentsis et al, 1997). The physiographic ones are
catchment area, surface slope, and permeability of the upper strata (Shentsis et al,
1997; Meirovich et al, 1998).
Runoff
events in the Negev,
59
Israel
Similar to studies in many other regions, an enveloping curve was drawn for the
relationship between maximum observed discharge and appropriate catchment area.
This curve appears as a polygon in the log-log presentation of Fig. 3 (Meirovich et al.,
1998). The data for this curve were abstracted from all available information sources
for the Negev and Sinai. Evidently, the same envelope covers the data points
pertaining to all regions of the Negev and Sinai except for the Gerar watershed, which
lies at the northwestern comer of the Negev, and for which a lower curve envelopes
the data.
The relationship between maximum observed volume of events and catchment
area is shown in Fig. 4 (Meirovich et al., 1998). This new kind of relationship follows
the same logic as that for maximum observed discharges. The enveloping curve for the
entire Negev can be described by:
on
V =0.17A
(3)
m
6
3
where V,„ is the maximum observed volume of an event (10 m ) and A is catchment
area (km ).
2
60
Arte Ben-Zvi
& Isabela
Shentsis
10000-
1000
- J -
II
+
x
WD
at
100
ses
r
A- "
o
A
10
TTrrj
0.01
10
1
0.1
r
1000
100
10000
100000
Watershed Area, km
I
North Negev
0
Negev Highland
+
A
Arava
I Negev Highland, Arava, Dead Sea, Sinai
Dead Sea
X
Sinai
II North Negev (Gerar)
F i g . 3 M a x i m u m observed discharges.
1000
10
100
1000
10000
C a t c h m e n t area ( k m )
Fig. 4 M a x i m u m observed v o l u m e s .
100000
2
Equation (3) indicates that the maximum observed depth of runoff event declines
as catchment area increases. For catchments of 30 km in area, the maximum observed
depth is 63 mm, whereas for 3000 km catchments it is only 17 mm.
Assuming that the statistical distribution of extremely high events (which rarely
occur) continues the distribution of observed high events, a decision was taken to fit
2
2
Runoff
events in the Negev,
61
Israel
distributions to partial duration series of the recorded events. These series contain all
and only events whose magnitude (i.e. peak discharge or volume) exceeds a pre­
selected threshold value. Our procedure of selecting a distribution and determining its
proper parameter values involves the Anderson-Darling goodness-of-fit test and an
examination of the consistency and reality of results (Stephens, 1986; Ben-Zvi, 1994;
Meirovich et al, 1998).
The selection and fit of the distribution and its parameter values were separately
decided upon for the peak discharges and the volumes. For both variables, the
generalized Pareto (GP) distribution and the probability-weighted moments were
found superior to the other examined options. Their mathematical formulations are
(Hosking & Wallis, 1987):
Vk
F(X) = (1 - kXla)
for k £ 0
(4)
F(X) = exp(X/a)
for k = 0
(5)
a = 2MMi/(M-2Mi)
(6)
k^MI{M-2M )-2
(7)
x
where F(X) is exceedance probability of the variable X, k and a are parameters whose
values are estimated from the sample, Mis the mean value of the series members, and:
M =(l/n)(Z/*0'1))
(8)
in which the x s are values of X in increasing order of magnitudes, and n is the number
of events in the series.
The goodness-of-fit was tested for all partial duration series containing at least 15
members. An example of this fit is displayed in Fig. 5. Following Ben-Zvi (1994), the
series for which the Anderson-Darling test statistic attained its minimum value was
selected for the work.
For partial duration series, the recurrence interval of X, TLX) [years], is determined by:
t
T(X)=N/(n¥(X))
(9)
where N is the number of years of available records.
10000
_—
=
—
E
£ looo
•--+
H—
__ —
- .TT
4-r
:±
—
—
1
—
+
-1
- -
0.5 1 2
5
10
20 30 40 50 60 70 80
90
95
98 99
Exceedance probability (%)
F i g . 5 Goodness-of-fit of a distribution to a discharge series; P a r a n - B o t t l e n e c k .
62
Arie Ben-Zvi
& Isabela
Shentsis
Predicted magnitudes for 10 to 100 year recurrence intervals are presented in
Table 3, and parameter values for the best fitted GP distribution, in Table 4. The size
parameter, a, for the volume distribution generally increases as catchment area
increases, while the parameter for the discharge distribution increases minimally. Most
values of the shape parameter, k, attain a negative sign indicating that the series are
thick-tailed (i.e. unbounded).
The site-specific predictions were extended into a regional model that enables a
reasonable prediction of magnitudes of rare events at any site on a wadi in the Negev,
provided that its catchment area is at least 50 km . This was accomplished through
association of magnitudes of events of a given recurrence interval with catchment area of
the appropriate site. In general, five relatively homogeneous regions have been delineated
in the Negev. These are: (a) the Gerar, (b) the Besor (excluding Gerar), Lavan and Tsin
(excluding its trunk), (c) the Tsin trunk, (d) the Neqarot, and (e) the Paran watersheds. The
southern watersheds and the Arava valley are subsumed in the relationships for the Paran
region. The regional curves for 100-year magnitudes are displayed in Figs 6 and 7.
2
T a b l e 3 P r e d i c t e d values.
Station n o .
P e a k discharge ( m s"') for recurrence
interval of (years):
50
10
25
100
3
23106
70.8
97.8
23110
22.8
30.2
118
36.2
138
42.5
23115
319
487
637
809
23127
714
1009
1240
1470
23135
23137
23140
23145
23150
82.8
530
13.6
404
127
166
802
1040
17.7
659
609
23155
400
54.4
23160
163
250
25190
116
77.6
21.1
212
1310
24.7
930
1290
799
1020
98.2
6
3
V o l u m e ( 1 0 m ) for recurrence ; interval
of (years):
10
25
50
100
0.76
1.02
1.21
1.41
0.24
0.29
0.33
0.37
5.37
12.9
0.61
12.9
0.35
7.41
16.0
7.73
18.4
0.92
17.7
0.49
9.67
23.3
1.20
21.4
0.60
11.85
28.9
1.50
25.2
0.74
11.6
15.6
20.8
21.5
25.6
29.7
122
2.05
328
418
5.96
3.10
8.72
4.10
11.1
5.35
13.8
186
256
345
1.62
2.40
3.12
3.97
55106
73.4
149
230
342
0.40
0.70
0.99
1.35
55106*
71.5
142
216
317
0.59
1.03
1.39
1.81
132
244
354
493
1.72
3.07
4.30
5.74
55140
163
247
325
3.80
4.84
6.01
163
242
316
419
402
2.58
55140*
3.40
5.02
6.20
7.54
0.24
0.26
0.28
0.28
103
0.38
0.55
0.68
0.82
276
414
2.46
4.73
2.46
3.67
4.27
5.93
8.76
115
0.74
1.12
1.48
1.90
710
0.99
1.77
2.56
3.57
55110
55160
32.3
39.3
44.0
55165
41.7
63.0
55180
120
174
81.7
221
55180*
156
242
321
56140
46.4
56150
182
57150
57150*
69.2
90.3
48.2
373
345
632
506
904
1260
295
504
694
917
7.36
11.1
6.26
18.8
26.8
37.5
13.3
18.7
25.1
57160
83.7
105
118
129
0.59
0.80
0.96
1.12
57160*
79.4
101
113
123
0.48
0.68
0.82
0.95
57165
386
640
864
1120
7.82
57180
111
174
229
292
0.42
14.0
0.74
19.5
1.06
i n d i c a t e s values obtained via comparison with results for another station of longer observational period.
26.0
1.47
Runoff
events in the Negev,
Israel
63
T a b l e 4 P a r a m e t e r v a l u e s of the best-fitted distribution.
Station n o .
Discharg ;e series:
Qo ( m s'•')
3
23106
8.82
23110
0.05
a(mV)
29.9
5.76
23115
43.5
110
23127
100
17.4
305
23135
23137
130
198
23140
0.40
23145
10.5
23150
86.8
23155
3.03
61.6
133
0
3
6
3
fl(10 m )
k
0.01
0.136
0.277
-0.09
0.001
0.079
-0.20
-0.02
0.553
1.66
-0.15
1.32
0.147
3.11
0.217
-0.20
-0.21
-0.19
2.18
4.49
-0.05
-0.10
0.002
0.064
-0.20
-0.42
0.00
1.02
-0.37
-0.23
2.05
5.91
-0.01
-0.01
0.07
-0.19
0.379
-0.31
61.5
-0.19
-0.21
0.066
48.2
0.916
1.91
-0.17
25190
12.2
29.5
-0.34
0.149
0.424
-0.24
34.6
-0.45
0.045
0.182
-0.30
68.9
-0.33
0.281
0.990
-0.23
43.8
-0.26
0.478
0.900
-0.16
55140
3.95
25.0
19.2
12.6
6
K (10 m )
23160
55106
55110
0.20
30.2
V o l u m e series:
k
55160
3.61
12.3
0.14
0.049
0.158
0.64
55165
6.48
14.8
-0.18
0.048
0.146
-0.08
36.3
-0.20
0.275
0.807
-0.18
11.2
-0.25
0.093
0.206
-0.26
55180
56140
34.5
2.98
56150
16.3
94.9
-0.34
0.189
0.424
-0.36
57150
12.5
7.04
85.7
-0.41
0.226
2.60
-0.40
44.4
0.24
0.047
0.236
-0.19
1.54
4.65
-0.22
-0.18
0.00
0.155
-0.34
57160
57165
57180
148
0.20
204
44.4
0.01
2
In Fig. 6, the data points of rare discharges in catchments smaller than 250 km
vary about their regional curves due to the effect of surface lithology on infiltration
capacity. The curves for the Besor, Lavan and Tsin watersheds exhibit larger
discharges than those for the Paran and the Neqarot regions, which are exposed to a
more arid climate. Rare discharges in the Gerar region are considerably lower than
discharges in the other regions. This is probably due to the exposure of this watershed
to a semiarid climate, which can support a denser vegetation cover.
The differences between regional discharges are evident for the larger catchments,
which have longer flow paths, and their discharges are more affected by flood routing
and transmission losses. The rate of transmission loss depends upon the permeability
of the underlying strata, which is associated with its lithological composition. As the
lithostratigraphy of the upper strata shows great variations within short distances in the
Negev, the effect of transmission losses on volumes and discharges of events is of
local character.
Owing to these effects, and probably also to asynchronous contributions from
tributary wadis due to the small diameter of the causative raincells (e.g. Sharon, 1972;
Schick & Lekach, 1987), the regional peak discharges for large catchments may decline
as catchment area increases (see curves for the Besor and the Tsin trunk regions). The
transition from rising to declining trends depends upon the location of permeable strata
along the wadi and the topology of the channel network. An empirical determination of
the transition points also depends upon the availability of hydrometric data.
0
500
1000
1500
2000
2500
3000
3500
2
Catchment Area, km
F i g . 6 R e g i o n a l d i s c h a r g e - a r e a relationships.
35
0
500
1000
1500
2000
2500
2
Catchment Area, km
F i g . 7 R e g i o n a l v o l u m e - a r e a relationships.
3000
3500
Runoff
events in the Negev,
Israel
65
Rare event volumes (i.e. volumes of the 100 year events) for catchments smaller
than 250-300 km also exhibit the effects of surface lithology (see Fig. 7). The low rate
of increase of rare volumes with catchment area in the Tsin trunk and the Neqarot
regions indicates higher transmission losses along their channels (Shentsis et al,
1998a,b). Volumes of-rare events from large catchments in the Besor and the Paran
regions stop increasing as catchment area increases. This may result from a balance
between transmission losses and tributary contribution.
In Fig. 7, the curve for the Besor region exhibits the highest rare volumes in the
Negev. Its superiority to the Paran region may result from the greater rainfalls that it
enjoys. On the contrary, the relative inferiority of the Gerar region may result from its
exposure to a semiarid climate which can support a denser vegetation cover that
encourages infiltration.
The regional relationships between the magnitudes of rare events and catchment
area, drawn in the present model, are in contrast to traditional models where the
relationships increase monotonically. Such an increase is found in the Negev for small
catchments only. Owing to effects of flood routing, transmission losses, the limited
dimensions of causative raincells, and asynchronous contributions from tributary wadis
in large catchments, rare discharges may decline and rare volumes may cease to
increase as catchment area increases.
2
TRANSMISSION LOSSES
A large fraction of the volume of runoff that is generated in arid environments does not
reach the watershed outlet but is lost along the channels. Since the alluvial fill of the
channel beds is usually dry, it can absorb large volumes of water from running events.
In cases where the channels are hydraulically connected to deeper aquifers, a fraction
of the "lost" water percolates and replenishes the aquifers (Shentsis et al, 1999). The
other fraction, which remains as interception and soil moisture, evaporates back into
the atmosphere, leaving space to be refilled from subsequent runoff events.
Accurate assessment of the volume of transmission losses requires an elaborate
system of measurements which is only likely to be established in experimental water­
sheds (e.g. Renard et al, 1993; Schwartz & Schick, 1990; Sorman & Abdulrazzak,
1993, 1995; Abdulrazzak & Sorman, 1994; Schwartz, 1999). Assessments for other
watersheds ought to rely on incomplete records, analogy with experimental
watersheds, and creative assumptions. Two experimental assessments of transmission
losses have been carried out so far in the Negev (Schwartz & Schick, 1990; Schwartz,
1999). The first concerns a tiny watershed (0.5 km in area) and the second deals with
one reach of a major wadi that is incised into an impermeable marl stratum. A model
suitable for non-experimental wadi reaches has been introduced by Shentsis et al. (1999).
The model employs the water balance equation for runoff events that flow through
a reach stretching between two hydrometric stations. The equation for an individual
event is:
2
L=V +V -V
u
a
d
(10)
where V is volume, subscripts u, a, and d refer, respectively, to the upstream station,
tributary contribution, and downstream station, and L is transmission losses.
66
Arie Ben-Zvi
& Isabela
Shentsis
The lost volume can subsequently be subdivided into channel moistening which
ultimately evaporates, E, and deep percolation which replenishes aquifers, R. This is
formulated by:
E + R=L
(11)
In cases of shortage in records of causative rainfall and of tributary flow, as in the Negev,
no direct estimate can be prepared for the lateral inflow, thus leaving equation (10)
with two unknown variables. A solution was reached by introduction of a
hydrological-lithostratigraphic analogy based upon the following assumptions:
(a) depth of runoff resulting from a given rainfall event is determined by the watershed
surface lithology; (b) for a given runoff event, the relative flow volumes at different
sites reflect the spatial distribution of causative rainfall whilst the recurrence interval
of lateral inflow volume is equal to that of the volume at the downstream terminal
station; and (c) the volume of transmission losses during a flow event is uniquely
related to the total volume of inflow to the reach. Based upon these assumptions, a
transmission loss function could be constructed. This function and the water balance
equation comprise a model that simultaneously assesses volumes of lateral inflow and
transmission losses for flow events recorded at the terminal stations.
Employment of these assumptions involves lithostratigraphic mapping of the
watershed, selection of representative stations, and association of recurrence intervals
to runoff volumes at the stations. Any given catchment within the watershed may be
composed of a number of lithostratigraphically homogeneous sub-catchments. For
each sub-catchment, the runoff associated with a given recurrence interval is estimated
from records at its appropriate representative station. Upon quantification of these
assumptions and substitution into equation (10), the following expression is obtained:
L=V
u
+
VkiV,*-V
(12)
d
where i = 1, 2... enumerates sub-catchments within the catchment of the examined
reach, k is the ratio of area of the fth sub-catchment to that of the rth representative
station, and V,* is the runoff volume at the representative station whose recurrence
interval is equal to that of Va for the event considered.
Equation (12) can be directly solved for the recorded events. However, coarse
representation of the lifhostratgraphic composition, severe non-uniformity in the
spatial distribution of causative rainfall (e.g. Sharon, 1972; Schick & Lekach, 1987),
and possible over-simplification of the above assumptions might impair solution
accuracy. The random as well as the systematic components of error, in solutions for
individual events, can be reduced by accepting the hypothesis that a certain
relationship should exist between transmission losses and inflow:
t
(13)
L = F(V + V )
U
a
This hypothesis can be realized as an empirical loss function drawn with minimum
deviations from solutions of equation (12) for individual events. Equations (10) and
(13) compose a hydrological model which contains two unknowns, L and V , and can
be solved when F(V„ + V„) is determined (Shentsis et al, 1999).
In order to assess aquifer replenishment, that volume that moistens the channel
alluvial fill and evaporates after cessation of runoff events ought to be subtracted from
the assessed transmission losses. In cases of limited data availability, as is the case in
a
Runoff
events in the Negev,
Israel
67
the Negev, a simple technique should be selected for that purpose. The selection for
the Negev is based upon the following assumptions: (a) the rate of actual evaporation
is proportional to potential évapotranspiration and to the ratio of soil moisture to
porosity (Konstantinov, 1968; Deardorff, 1977); (b) initial soil moisture is equal to the
field capacity of the soil; and (c) since evaporation removes moisture from the soil, its
rate should exponentially decline over time:
e{i) = e(0) exp(-fe)
(14)
where t is time measured from the cessation of the event, e(t) is rate of evaporation at
time t, and k is a parameter assumed to be constant. The volume of evaporation during
the time elapsed between events, E, is the product of evaporation depth, which is
integrated from equation (14) through the interval between events, and the length and
width of the channel. In those cases where the computed volume of evaporation is
larger than the appropriate volume of transmission losses, the assessed volume is set as
E = L.
The model was first applied to three reaches of Nahal Tsin in Israel (Fig. 8)
(Shentsis et al, 1999). The mean annual volume of runoff at the Mapal, Masos and
Aqrabim stations, located on the main stem of Nahal Tsin, are respectively 0.6, 1.5,
and 1.4 10 m year" . The cumulative mean volume of lateral inflow to the three
reaches was assessed as 3.5 x 1 0 m year" , and the cumulative transmission losses as
3.2 x I 0 m year" . In comparison, Schwartz (1999) has revealed substantially smaller
losses for the reach located just downstream from those reaches and incised into an
impermeable marl stratum.
Shentsis et al. (1999) have found that the volume of transmission losses along their
studied reaches was of the same order of magnitude as that of the flow at the major
hydrometric stations and of the cumulative tributary contribution. The computed
volume of evaporation appeared to be equal to the entire losses from very small events,
whilst for large events the evaporation was substantially smaller than transmission
losses. The mean annual volume of aquifer replenishment from runoff events in the
main stem of Nahal Tsin and in its major tributaries was assessed as 4.1 x 10 m year" .
The 100 year volume of aquifer replenishment may be seven times higher than the
mean annual volume, whilst the volumes during most of the years are insignificant.
Annual values of the water balance components for one reach of Nahal Tsin are
presented in Fig. 9. Inspection of these data reveals that the largest assessed volume of
transmission losses was 8.5 x 1 0 m year" . No runoff was observed during nine of the
41 years considered. The annual volume of transmission losses over 20 years was
smaller than 1 x 10 m year" , resulting in insignificant aquifer replenishment.
The incorporation of verbal geological and lithological information into a
quantitative hydrological model helps surmount a shortage in hydrological and
meteorological records. This new approach was successfully applied for two additional
watersheds in the Negev (Shentsis et al, 1998a,b) and appears suitable for application
in other arid areas throughout the world.
As an example of the utility of the model, a loss function was constructed for the
Yael reach (Fig. 10) by use of data presented in Schwartz & Schick (1990). According
to the authors the lost water accumulates in the alluvial fill, and the capacity of this fill
is about 4500 m . Our analysis indicates that the transmission losses are controlled by
the volume of runoff and by the antecedent moisture of the alluvial fill. This moisture
x
6
3
1
5
6
3
3
1
1
6
6
6
3
3
1
3
1
3
1
ta
So
F i g . 8 Hydrological-lithostratigraphic m a p of N a h a l Tsin.
Runoff
events in the Negev,
Israel
69
2/1
54/5 56/7 58/9 60/1 6273 64/5 66/7 68/9 70/1 72/3 74/5 76/7 78/9 80/1 82/3 84/5 86/7 88/9 90/1 92/3 94/5
55/6 57/8 59/60 61/2 63/4 65/6 67/8 69/70 71/2 73/4 75/6 77/8 79/80 81/2 83/4 85/6 87/8 89/90 91/2 93/4
Year
F i g . 9 A n n u a l c o m p o n e n t s of the water b a l a n c e e q u a t i o n for the M a p a l — M a s o s r e a c h
of N a h a l Tsin.
5000
0
1000
2000
3000
4000
3
Total Inflow (m )
F i g . 10 Loss function for the N a h a l Y a e l reach.
5000
70
Arie Ben-Zvi
& Isabela
Shentsis
gradually declines with time elapsing from the last event, increasing the absorbing
capacity of the alluvial fill. This extends the conclusion of Schwartz & Schick (1990)
regarding the effect of inter-event volume of evaporation on transmission losses by
relating the losses also to the total volume of inflow. The example indicates that the
results of the long studies, carried out by Prof. Schick and his group on the tiny Nahal
Yael, can be associated to those pertaining to arid watersheds of larger sizes.
CONCLUDING REMARKS
Two comprehensive models have been presented for describing important features of
runoff events in an arid area. These features relate to engineering and scientific
interests in the state of water resources in such areas. The particular methods which
have been developed in our studies, may seem different from those developed in other
climatic areas but their suitability and reliability have been carefully examined. The
development of these methods could not have been accomplished without the richness
of records obtained from the patient, long, and extensive operation of the hydrometric
network by the Israel Hydrological Service under the harsh conditions prevailing in the
arid Negev.
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