A Physically-Related Regional Model for Extreme Discharges in Israel

Hydrological Sciences- J'ournal-des Sciences Hydrologiques, 42(3) June 1997 391

A physically-related regional model for extreme discharges in Israel

ISABELA SHENTSIS, ARIE BEN-ZVI & SOLOMON GOLTS Israel Hydrological Service, PO Box 6381, Jerusalem, 91063 Israel

Abstract Israel is a small country which experiences wide variations in magnitudes of extreme discharges. A consistent model has been constructed for prediction of such discharges throughout the country. Extreme flow characteristics, geographical proximity, lithology, soils, and rainfall properties are the major factors in the delineation of relatively homogeneous regions within the country. For each region, discharge-area relationships are formulated in association with low exceedance probabilities. These relationships follow at-site predictions which have been prepared by fitting the log Pearson type III distribution to annual maxima series of peak discharges. For catchments larger than 100 km2 in area, the differences between the regional and the at-site predictions are small. Relatively high extreme discharges are found for the arid area where rainfall depth is low, for an area of steep slopes, for areas of low permeable lithology and soils, and for areas where the fraction of intense rainfall in the total depth of precipitation is high. For large arid catchments, the discharge- area relationships exhibit a negative trend. The model is simply applicable and appears suitable for other semiarid and arid areas. Modèle régional pour les débits de crues en Israël Résumé Israël est un petit pays qui, sur de courtes distances, connaît de grandes variations de topographie, de précipitations, de lithologie et par conséquent une grande variabilité des débits de crues. Un modèle destiné à estimer ces débits dans le pays a été établi. Les caractéristiques des écoulements extrêmes, la proximité géographique, la lithologie, les sols et les propriétés des précipitations sont les principaux facteurs permettant la délimitation de régions relativement homogènes à l'intérieur du pays. Pour chaque région, des relations débit-surface pour les faibles probabilités au dépassement ont été établies. Ces relations complètent des estimations fondées sur l'ajustement d'une loi Log Pearson 3 aux séries de débits annuels maximaux mesurés aux stations de jaugeage. Pour les bassins versants de plus de 100 km2, les différences entre les estimations du modèle régional et celles réalisées aux stations de jaugeage sont petites. Des débits extrêmes relativement importants peuvent être observés dans les régions arides où les précipitations sont faibles, les pentes sont abruptes, la perméabilité des sols est faible et où la fraction des pluies de forte intensité par rapport au total pluviométrique est élevée. Le modèle est d'application simple et convient aux régions arides et semi-arides.

INTRODUCTION

Israel is a small country which experiences wide variations over short distances in topography, precipitation, lithology, and soils, and consequently in magnitudes of extreme discharges. The southern half of the country is exposed to an arid climate, and the northern half to a semiarid Mediterranean climate. The summers are hot and dry and the winters are relatively cool and rainy. Runoff events occur in the

Open for discussion until 1 December 1997 392 Isabela Shentsis et al. winter season only. Duration of direct surface runoff ranges from 0 to 1000 h in a year. A few rivers carry a perennial or a seasonal baseflow. Statistical predictions of extreme discharges were prepared in the past for limited regions only (e.g. Ben-Zvi, 1982, 1996; Cohen & Ben-Zvi, 1983; Garti et al., 1996). No consistent regional model was published for the entire area of Israel. The difficulties in the development of such a model stem from the wide differences in magnitudes of extreme discharges within short geographical distances. Ben-Zvi (1988) attributed the diversity in maximal observed discharges to watershed lithology and to mean annual depth of precipitation. The present work regionalizes extreme discharges for the entire area which is the responsibility of the Israeli Government (including the West Bank, the Gaza strip and the Golan Heights), and relates them to exceedance probability, geographical region, lithology, soils, and rainfall. The model was constructed in two stages: one fits a probability distribution to records at gauged sites, and the other draws regional relationships for at-site discharges associated with low exceedance probabilities. This approach differs from that of some other recently published models (e.g. Hjalmarson & Thomas, 1992; Farquharson et al., 1992; Zrinji & Burn, 1994) by avoiding the use of dimensionless distributions and the mean annual flood, and by considering the relative occurrence of years of no runoff. The regions are delineated with respect to discharge-area relationships rather than to shapes of at-site distributions of discharge. The direct presentation of end results appears comprehensible to hydrologists, engineers, and non-professional decisionmakers.

DATA

The present study employs annual peak discharges recorded at 67 hydrometric stations of the Israel Hydrological Service. Information on the stations and their catchments is presented in Table 1. Record lengths vary from 16 to 56 years, with a median at 38 years. Catchment areas vary from 10 to 3350 km2. Twentyfive catchments are smaller than 100 km2 while five catchments are larger than 1000 km2. The hydrometric stations are operated, and the records are processed, through standard procedures. Annual maximum discharges were abstracted from records of sufficient com pleteness and accuracy. Catchment areas were based upon 1:50 000 topographical maps of the Survey of Israel. The other influential properties are assumed to be the geographical location, lithology, soils and precipitation. The lithology was deter mined from the 1:500 000 geomorphological map prepared by Nir (1985) with additional references to maps developed by Amiran & Nir (1970), and Picard (1970a,b). The soil associations were determined from the 1:500 000 map produced by Dan et al. (1975). Information about precipitation was obtained from the Israel Meteorological Service and adapted to watershed delineation by routine procedures of the Hydrological Service. A physically-related regional model for extreme discharges in Israel 393

Table 1 Stations and watershed properties. Region Sub-region Stream Station Area Preeip. Years no. (km2) (mm) I c* Keziv Gesher Haziv 131 873 48 I c* Ga'aton Ben-Ami 41 746 27 I c* Bet Ha'emeq Shavei Tsion 72 755 47 I c* Hilazon Yas'ur 158 703 47 I c Nahalal Railroad 41 757 27 I M-N Ha'shofet Hazorea 12 700 30 I c Bet Lehem Kfar Yehoshua 19 625 36 I c Qishon Quarry 694 546 42 I M-N Tsipori Tel Alil 211 599 40 I M-N Daliya Bat Shlomo 42 662 40 I M-N Daliya Haifa Rd. 70 645 46 I M-N Taninim Amiqam 51 656 28 I M-N 'Ada Giv'at Ada 18 641 46 I M-N Barqan Kefar Glickson 29 647 29 I C 'Ada Binyamina Rd. 66 638 36 I c 'Iron Sha'ar Menashe 61 649 31 I c Hadera Gan Shmu'el 519 609 42 I c Alexander Elyashiv 492 618 55 I M Amud Tiberias Rd. 124 550 44 I M Tsalmon Tiberias Rd. 103 550 33 II M Kana Yarhiv 240 619 39 II M Shilo Nahshonim 357 613 44 II C Yarqon Herzliya Rd. 953 611 54 II C Ayalon Lod 135 540 39 II c Natuf El-Al Jcn. 251 575 53 II M Bet 'Arif Migdal Afeq 46 575 37 II C Ayalon Bet Dagan Rd. 526 577 39 II M Soreq Motsa 78 603 19 II M Soreq Har Tuv 245 590 33 II M Harel Kefar Uriya 13 530 37 II M Soreq Yesodot 405 574 51 II C Eqron Bet El'azari 62 536 44 III C Guvrin Shafir 204 468 45 III M Haela Tel Tsafit 286 507 34 HI C Haela Gan Yavne 423 500 21 III C Lakhish Yavne Rd. 992 470 47 IV Shiqma Tel Milha 38 311 32 IV Adorayim Railroad 207 371 36 IV Shiqma Beror Hayil 378 366 44 IV Gerar Re'im 658 276 32 V Besor Nitsana Rd. 133 107 44 V Be'er She va Zarnuq 405 250 25 V Be'er She va Be'er Sheva 1090 240 21 V Beqa Be'er Sheva 96 165 44 V Be'er Sheva Hatserim 1220 258 23 V Besor Re'im 2630 200 30 V Lavan Nitsana Rd. 192 92 33 V Tsin Har Medad 135 70 38 V Tsin Avdat Fall 233 80 41 continued... 394 habela Shentsis et al.

Table 1 continued. Region Sub-region Stream Station Area Precip. Years no. (km2) (mm) VI* Tsin Masos 660 100 38 VI* Tsin Aqrabim 1130 100 30 VI Mamshit Oron Rd. 64 100 40 VI Neqarot Har Masa 697 60 36 VI Par an Bottleneck 3350 50 44 VII Snir Ma'ayan Baruh 526 1300 56 VII Hermon She'ar Yashuv 140 1100 54 VII Jordan Sede Nehemiya 800 900 49 VII 'lyon Metula 32 800 46 VII Dishon Metula Rd. 91 600 29 VII Hatsor Ayelet Hashahar 32 649 53 VII Jordan Obstacle Br. 1380 700 33 VIII Yardenon Lehavot Habashan 10 600 25 VIII Orevim Lehavot Habashan 40 600 34 VIII Meshushim Dardara 160 550 26 VIII Daga -200 Contour 104 550 17 IX Maliah Hamam 58 400 16 IX Qilt Yeriho 133 360 16 Legend: Area is catchment area; Precip. is mean annual depth of precipitation; Years is number of years on records; C is coastal sub-region; C* is northern sector of the coastal sub-region; M is mountainous sub-region; N is "Nari"; and V* is lower Tsin sub-region. Notes: Owing to data shortage some of the precipitation depths are grossly estimated. Region names appear in Table 2.

AT-SITE PREDICTIONS

In order to expedite preparation of the model, and to concentrate on the regional aspects, no preparatory study was carried out on the selection of the most appropriate distribution and fitting method. The work considers annual maxima series and fits them to the log Pearson type 3 (LP3) distribution by the method of moments. These selections provided, in the past, satisfactory results for a number of local and regional works (e.g. Cohen & Ben-Zvi, 1983). A typical phenomenon encountered within arid and semiarid climates is the non occurrence of runoff events during some hydroiogical years. This phenomenon makes impossible any direct computation of the parameters of a selected distribution for the entire period of observation. It interferes, also, with the computations of parameters of those distributions which can absorb zero values. A reasonable solution to this problem is achieved through a conditional probability approach. In this approach, the parameters are computed from discharges in years when runoff did occur, and the resulting probabilities are corrected by the ratio of the number of such years to the number of years on record: P(Q) = P*(Q)n/N (1) where P(Q) is the exceedance probability of a given discharge Q, N is the number of years on record, n is the number of years when runoff did occur, and P*(Q) is the A physically-related regional model for extreme discharges in Israel 395 exceedance probability obtained from a distribution fitted to annual maximum dis charges in the n years. The ratio of nIN in the study area varies from about 0.6 to 1. This ratio is lower where the mean annual depth of precipitation is lower. It is also lower for smaller catchments and for mountainous catchments of permeable bedrocks. Satisfactory fits of the LP3 distribution were found for series recorded at most of the hydrometric stations. However, wide deviations at the upper tail were found for a considerable number of stations. For these stations, the fit was revised by use of a graphical-analytical technique (Rojdestvenskiy & Chebotarjov, 1974). In this tech nique, the discharges are first plotted on a log-probability paper. Next, a curve is empirically drawn through the points such that the sum of its distances from the data points would be minimal. A revised value of the skewness coefficient is determined from the curve. This value, together with the sample mean and standard deviation, serve for extrapolation of the curve beyond the range of observations. The ex ceedance discharges are then determined from the curve.

REGIONALIZATION

Noting the high variability in the nIN ratio and in the parameters of the distribution for different stations, it was felt that preparation of dimensionless distributions for groups of stations, as is practised for many other areas (e.g. Cunnane, 1988), would not contribute to the applicability of a regional model for the present study area. A simpler approach of direct reference to discharges associated with selected ex ceedance probabilities was chosen here. This approach facilitates the acquaintance of hydrologists and other users with the end results of the work. Discharges associated with the exceedance probabilities of 1%, 2%, 4% and 10% were abstracted from the at-site distributions. For each watershed and selected probability, the discharges for the different sites were plotted against their proper catchment areas. Smooth curves were empirically drawn for each watershed with minimal deviations from the data points. Drawings for neighbouring watersheds, for which the curves exhibit similar trends, were combined into apparent homogeneous regions. In order to obtain reasonable transitions between curves for different exceedance probabilities, the four curves were simultaneously drawn such as to form a homogeneous family. A number of those regions were re-divided into two or three sub-regions. Fourteen regions and sub-regions, whose boundaries are delineated in Fig. 1, were formed by this procedure. The curves for the 1% exceedance probability are displayed in Fig. 2. Regional discharges, associated with the 1% exceedance probability for typical catchment areas, are presented in Table 2. The number of stations in a region varies from two to ten. Owing to the marked variability in discharge-area relationships, four regions and sub-regions are composed of two or three stations only. The curves for regions IX and (I+III)M were drawn with respect to curves for neighbouring regions. The curves for regions V and VI* were drawn with respect to results of a recent study on complete series of flow events in the Negev (Meirovich et al., 1996). Isabela Shentsis et al.

/ •^ / / y ~E / < .VI)" * =3 /!fV * ^ ïm\, $ •^îlWi-Villn

v jt'i ' -1 SLv// / ^ U: $ - : : s : < »p!^--/ V £ -~mk S V-?» Sv~--Z:( 'i * ^W VTYT7 / l i- —fo£3 -.. " -I* r""-'.J ' . I/'--*/'i pixv

3 s : ! ; •K Tft^S? f \ — s / i 1 f \ ^—_ / i"»ij _^ v y •'•'•/ „_c , ^^ ||«v/' y' /•""•-"•x^L fivS

L \\ V\Cv.'>\,-'\ >i l' ^î* ~'\- BJ \ V t,>~N--/^?p^Sî7 w^ » > y*/ -'s/ p\ ' v <^-\'-->*r '/ "-"?/ L E G E N D \ '. V_' M ~~~—~'J \ t f-". '/,'' =;»-.»v;y>-\ HYDROGRAPHIC \ \ < ,'-'• V / /'- NETWORK 1 \î /_'-"*—/ 1 /~'' \i, ,-i â HYDROMETRIC \/ '—Vl-V' / STATION

1 1 "*>—*. -V"/! / / \ / ' //ASI VIREGI0N NUMBER

1 .i, y^'; 1 SUB REGIONS ! 1 1 A- / j / •;:*-I.1 COASTAL PLAIN S ' ! •r ' # 1 t -^ I K - * / MOUNTAINS

)\ ^ Fig. I Delineation of extreme discharge regions. A physically-related regional model for extreme discharges in Israel 397

2000

1000 2000 3000 Watershed area (km"2) Fig. 2 Discharge-area relationships for 1% exceedance probability.

Table 2 Predicted 1 % peak discharges (m3 s'). Region no. Name Area (km2) 100 200 500 1000 IC* Northern 62 106 IC Mediterranean 123 196 279 298 IM 31 59 IM-N 217 II C Yarqon - Soreq 130 241 491 722 II M 84 143 237 IOC Lakhish 123 196 279 298 III M 31 59 IV N. Negev 103 198 435 712 V Negev Highlands 259 495 1091 1719 VI Arava 146 280 616 1009 VI* 552 453 VII Upper Jordan 79 141 259 336 VIII Golan 139 244 IX E. Shomron 389 650 Note: The curves for regions I and III are identical to each other.

Wide differences between the curves are observed in Fig. 2. This diversity appears to result from the variability in physiographic and meteorological properties of the watersheds. Quantification of effective properties is difficult, and, if successful, it would support delineation of a small number of regions with multi- 398 Isabela Shentsis et al. dimensional relationships between discharges and catchment properties. Such a regionalization requires more quantitative data and seems less certain than the regionalizing and sub-regionalizing concluded here. The sub-regionalizing mainly refers to the Mediterranean Sea watersheds where discharges recorded by stations located in the Coastal Plain and in wide valleys are much higher than those recorded by stations located in the mountainous areas. This is evident from Fig. 3, where the curves for regions I and III are presented at a larger

100 200 300 400 500 600 700 900 1000 Watershed area(km~2) • • Coastal Plain(C) • Mountains(M) X "Nari"(M-N) Fig . 3 Discharge area relationships for 1 % exceedance probability in regions I and III.

0.06-0.10 0.11-0.20 0.81-0.30 > 0.30 Model error (R) Fig. 4 Distribution of relative absolute difference for catchments larger than 100 km2. A physically-related regional model for extreme discharges in Israel 399 scale. The Figure serves also as an example for the empirical drawing of regional curves. The river names in Fig. 3 clarify the considerations in regional and sub- regional delineations. The discharges in the northern sector of the Coastal Plain are not as high as those in the other sectors. A particular sub-region was delineated, therefore, for this sector. An exceptional relationship is observed for the larger catchments in regions V and VI where extreme discharges decrease as catchment area increases. The turning point is unique for the watershed. The distinction between random fluctuations about regional relationships and consistent deviations among such relationships was aided by a statistical measure. The relative absolute differences, R, between the at-site predicted discharge, Q, and the discharge predicted from the regional curve for the station site, Q* is defined by: R = abs(<2* - Q)IQ (2) Inspection of the values of R reveals that most of the larger values are found for stations whose catchment area is smaller than 100 km2. Exclusion of these catchments substantially reduces the average value of R. The distribution of values for stations whose area is larger than 100 km2 is displayed in Fig. 4. For these stations, values of R < 0.05 are found in 35% of the cases associated with 1% to 4% exceedance probability, and R < 0.20 for 85% of them. This narrow distribution indicates that the delineated areas are sufficiently homogeneous. Application of the model is recommended, therefore, for catchments larger than 100 km2. The absolute value of the difference between Q* and Q is assumed to be a normally distributed random variable. Consequently, it can serve for determining confidence intervals for the drawing of regional curves. The intervals for the 1% exceedance probability are presented in Table 3. A comparison of values in Tables 2 and 3 supports the delineation of regions and sub-regions. For example, the difference in discharges between sub-regions C and M varies from 99 to 137 m3 s4, whereas the 95 % confidence intervals for these sub-regions are only 76 m3 s4 and 49 m3 s4.

Table 3 Accuracy estimates of the regional curves for 1% exceedance probability (m3 s"1). Regions RMS Confidence interval (%) 50 75 90 95 I-III C, IV 39 26 45 64 76 I-III M 25 17 29 41 49 V-VI 119 80 137 196 233 VII-IX 20 13 23 33 39 Legend: RMS is root mean square difference between Q* and Q.

The regional curves can mathematically be described by the equation: G = o(l - exp(-yft4)) (3) where Q is discharge, A is catchment area, and a and /? are parameters whose values are obtained from the graphs. Values of the parameters of equation (3) are listed in Table 4. 400 habela Shentsis et al.

Table 4 Parameter values for equation (3).

Region & sub- Prob. 1% Prob. 2% Prob. 4% Prob. 10% region a P* a P* a P* a P* IC* 215 34 170 34 130 34 85 34 IC 300 53 250 43 209 36 163 24 IM 325 10 260 10 210 10 118 10 IM-N 360 92 235 92 150 92 80 92 IIC 930 15 620 20 455 22 270 25 II M 290 34 230 34 175 34 200 15 III C 300 53 250 43 209 36 163 24 III M 325 10 260 10 210 10 118 10 IV 1200 9 870 9 640 9 380 9 V 3010 9 3010 6 3010 4 3200 2 VI 1700 9 1142 9 750 8 390 7 VII 370 24 380 19 400 15 465 9 VIII 570 28 510 28 435 28 320 28 IX 1180 40 730 40 460 40 320 28 Legend: Prob. is exceedance probability; a and /? are parameters of equation (2) where P = P*/W 000.

The declining segments of the curves for regions V and VI can be described by the equation: Q^Q.-yiA-Af (4) where Q, and A, are, respectively, discharge and catchment area at the turning point of the regional curve and 8 is an exponent. Values of the parameters of equation (4) are listed in Table 5.

Table 5 Parameter values for equation (4). Region V VI v* A, (km2) 950 2800 233 5 1.10 1.10 1.82 a 7 a r a r Prob. 1% 1730 0.150 1563 0.150 569 0.00065 Prob 2% 1308 0.120 1050 0.025 393 0.00045 Prob. 4% 952 0.090 268 0.00026 Prob. 10% 554 0.047 146 0.00013

APPARENT CAUSES OF THE DIVERSITY

The wide diversity among values of peak discharges for the different regions is attributed here to physical causes. A simple attribution of this kind was introduced by Ben-Zvi (1988) where mean annual depth of precipitation and lithologie groups were considered. The present attribution is more elaborate. The influential causes include A physically-related regional model for extreme discharges in Israel 401 lithology, morphology, soils, annual depth of precipitation and rainfall intensity. These causes directly affect the infiltration and hydraulic behaviour of a watershed. Viewing Table 2 and Fig. 2, the highest discharges occur in the arid Negev and in the steep Shomron mountain slopes (regions V, VI and IX) where mean annual depth of precipitation is lower than 400 mm. These regions carry a sparse vegetal cover which can do little to restrain raindrop energy and runoff velocity. For a 100 km2 catchment in these regions, the 1% peak discharge is about three times higher than that for a similar catchment located in almost any other region. An inverse discharge-area relationship, as appears for the larger catchments in regions V and VI, is hardly mentioned in the scientific literature. It can result from the hydraulic effects of flood routing along a long channel with out-of-phase tributary contributions and from intensive channel losses. Such losses are observed for two reaches of the Tsin Stream (Khavich & Ben-Zvi, 1996; Meirovich et al., 1996). Sharp differences over short distances are found in regions I to III where a Mediterranean climate prevails. Discharges from 100 km2 catchments lying in the mountainous sub-regions are one and a half to four times lower than those from a catchment lying in the coastal region. The difference between the sub-regions is evident even at stations for which only 10% of the catchment area lies in the coastal sub-region. It should be noted here that most of the mountainous watersheds drain towards the Coastal Plain area. Therefore, the catchments of many stations located in the coastal sub-regions extend onto the mountainous ones. This is particularly true for the larger catchments. As a result, the rate of increase of the discharge in such watersheds rapidly declines as the catchment area increases. This result is evident in Table 2 as well as in Figs 2 and 3. The difference between discharges in coastal and mountainous sub-regions is attributed to sharp transitions in lithology, soils and in rainfall intensity. The

Table 6 Relative distribution of lithological units (%). Region & sub-region 1 2 3 4 5 6 IC 27 IM 56 13 4 IIC 27 II M 63 10 HIC 48 III M 23 29 IV 4 11 9 47 29 V 11 31 35 23 VI 45 6 13 36 VII 38 45 17 VIII 4 6 90 IX 74 26 Unit definitions: 1 - Limestone chalk and dolomite 4. Loess 2 - Limestone in thin sedimentation 5~ Alluvial and sandy loam 3 - Calcareous crust ("Nari") 6- Basalt and volcanic tufa 402 Isabela Shentsis et al. lithology of the mountainous sub-regions is mainly of limestone chalk and dolomite, whereas that of the coastal and valley sub-regions is of alluvial sand, sandy loam and clay (Table 6). A relationship between lithology and soil associations for the different regions is presented in Table 7. Apparently, lithology and soils of the former sub- regions are more permeable than those for the latter ones.

Table 7 Lithology and soil associations coexistence. Lithology Region Soil associations 1 I - V A: Tera Rossas, Brown & Pale Rendzinas B: Brown Rendzinas & Pale Rendzinas VI X: Bare Rocks & Desert Lithosols IX A, B, X 2 IV -V M: Brown Lithosols & Loessial Arid Brown Soils S: Brown Lithosols & Loessial Serozems T: Sandy Regosols & Arid Brown Soils 3 I-VI B: Browns Rendzinas & Pale Rendzinas 4 IV, V S: Brown Lithosols & Loessial Serozems R: Loessial Serozems I - IV H: Grumosols Q: Solonchaks V: Sand Dunes V T: Sandy Regosols & Arid Brown Soils V: Sand Dunes VI Y: Reg Soils & Coarse Desert Alluvium VII H: Grumosol G: Hydromorphic & Gley Soils IX P: Alluvial & Brown Soils Q: Solonchaks W: Regosols VIII, IX F: Basaltic Brown Mediterranean Soils & Basaltic Lithosols D: Basaltic Protogrumosols, Basaltic Brown Grumosols & Pale Rendzinas

The mountainous and the coastal sub-regions enjoy similar depths of precipi tation, yet the fraction of intense rainfall within that depth over the coastal sub- regions is twice as large as that over the mountainous ones. Sharon & Kutiel (1986) showed that the depth of rain falling at intensities higher than 30 mm h"1 comprises 15 to 23% of the total depth of precipitation over the Dead Sea, the Arava and the Coastal Plain areas; 3% over the mountainous areas; and about 10% over the other areas of Israel. Ben-Zvi & Fanar (1996) found that about 20% of the total depth of precipitation over the Coastal Plain area, and less than 10% of the depth over the mountainous areas, falls at intensities higher than 20 mm h"1. It is worth mentioning here that no hydrometric station operates in Israel in sand dunes areas where hardly any runoff is generated. As a result, such areas are not included in the model but may be considered as forming a particular region. Other areas which are not included in the model due to a shortage of data lie on the A physically-related regional model for extreme discharges in Israel 403 mountain slopes draining towards the Dead Sea and the Lower Jordan River, These areas are depicted in Fig. 1. A particular relationship is found for small mountainous catchments whose surfaces are covered with calcareous crust (called "Nari" locally). Such catchments, of up to 100 km2 in size, generate discharges which are five times higher than those for other mountainous catchments of similar size. This peculiarity is evident in Fig. 3. "Nari" covered areas are found in regions I to III, but proper data are available for region I only. The discharge-area relationships for larger catchments, which are partially covered by "Nari", are complicated, and except for the example of Tsipori catchment depicted in Fig. 3, are not presented here. Another particular relationship is found for the Yarqon and Soreq watersheds (region II) where the discharges are higher than those occurring in the adjacent Mediterranean watersheds (regions I and III) while maintaining the sub-regional differences. These high discharges may be attributed to rainfall intensity. Sharon & Kutiel (1986) depicted for the coastal sub-region of region II the highest fraction in Israel of intense rainfall in the total depth of precipitation, yet they depicted no anomaly for the mountainous sub-region. Schein & Buras (1973) presented for region II the highest 12 h 5% depth of precipitation in Israel. On the contrary, Ben-Zvi & Fanar (1996) did not find any anomaly in the fraction of intense rainfall over region II. The lithologie composition of watershed surfaces is summarized in Table 6. Upon comparison with Tables 2 and 3, it can be concluded that limestone, chalk and dolomite surfaces are associated with relatively low discharges, whereas alluvial, sand loam, basalt, loess, and limestone in thin sedimentation surfaces are associated with high discharges. The lithologie composition can further be related with soil associations, as is presented in Table 7. Such a relationship can help in improving the model for catchments smaller than 100 km2, within which the lithology and soils are relatively uniform. This improvement is a subject for another study.

CONCLUSIONS

Diverse relationships between extreme discharges and catchment areas are observed in the area for which the Israeli Government has responsibility. Therefore, despite the small size of the country, it needs to be divided into a number of regions and sub- regions with homogeneous relationships. The diversity is attributed to lithology, soils, morphology, rainfall intensity, and depth of precipitation. Higher extreme discharges are associated with less permeable lithology and soil, steeper slopes, lower depth of mean annual precipitation and higher rainfall intensity. Particular effects are found for two physical features. One is the calcareous crust which covers the bedrocks of certain mountainous catchments and causes the genera tion of high discharges. The other is length and permeability of channels of large arid catchments where flood routing and losses lessen rare discharge magnitudes. For each region and sub-region, discharge-area relationships have been con structed with respect to four exceedance probabilities. The relationships for catchments larger than 100 km2 in size exhibit small deviations from the at-site 404 Isabela Shentsis el al. predictions. The model is applicable, therefore, for catchments whose areas range from 100 to 3500 km2. It seems that a further sub-division of the regions, with respect to additional physical variables would be required for the prediction of extreme discharges from smaller catchments. The present attribution of magnitudes of extreme discharges to physical variables appears valid for the delineation of homogeneous regions and discharge-area relationships in other semiarid and arid areas. It is also helpful for the planning of hydrometric networks. The graphical relationships between extreme discharges and catchment areas for clearly delineated regions and for given exceedance probabilities are comprehensible, and therefore easily applicable by hydrologists and engineers.

REFERENCES

Amiran, D. H. K. & Nir, D. (1970) Geomorphology; 1:500,000 Map II/l. Atlas of Israel, 2nd éd., Survey of Israel & Elsevier, Amsterdam, Netherlands. Ben-Zvi, A. (1982) Frequency and magnitude of runoff events in the Negev. Water Ml, 7, 127-133. Ben-Zvi, A. (1988) Maximal discharges observed in Israel. Environ. Geol. & Water Sci. 11, 15-20. Ben-Zvi, A. (1996) Quantitative prediction of runoff events in the Negev desert. In: Runoff, Infiltration and Subsurface Flow of Water in Arid and Semiarid Regions, ed. by A. S. Issar & S. D. Resnick, 121-130. Kluwer, Dordrecht, The Netherlands. Ben-Zvi, A. & Fanar, A. (1996) Effect of cloud seeding on rainfall intensity in Israel. Israeli. Earth Sci. 45, 39-54. Cohen, O. & Ben-Zvi, A. (1983) Sfikot unefahim bayarden ha'elyon veyuvalav (Discharges and volumes in the upper Jordan and its tributaries) (in Hebrew). Report Hyd/1/83, Israel Hydrological Service, Jerusalem, Israel. Cunnane, C. (1988) Methods and merits of regional flood frequency analysis. J. Hydrol. 100, 269-290. Dan, Y., Raz, Z., Yaalon, D. H. & Koyumdjisky, H. (1975) Soil Map of Israel, 1:500,000. Survey of Israel, Tel-Aviv, Israel. Farquharson, F. A. K., Meigh, I. R. & Sutcliffe, J. V. (1992) Regional flood frequency analysis in arid and semiarid areas. J. Hydrol. 138, 487-501. Garti, R., Getker, M. & Arbel, S. (1996) Model Tahles degem II, hashita leomdan sfikot techen venifhey neger shnatiyim leaganey Israel, shalav I: bhinat yitachnut hashita. (The SRS model type II, the method for estimation of design discharges and annual runoff volumes for the Israeli catchments, stage I: feasibility study of the method) (in Hebrew). Draft Report PL-22, Sediment Research Station, Emeq Refer, Israel. Hjalmarson, H. W. & Thomas, B. E. (1992) New look at regional flood frequency relations for arid lands. J. Hydraul. Engng. Div. ASCE 118, 868-886. Khavich, V. & Ben-Zvi, A. (1996) Ibudey mayim benahal Tsin (Channel losses in the Tsin stream) (in Hebrew). Report Hyd/7/96, Israel Hydrological Service, Jerusalem, Israel. Meirovich, L., Ben-Zvi, A. & Shentsis, I. (1996) Tediruth vegodel hageuyot banegev (Frequency and magnitude of flow events in the Negev) (in Hebrew). Report Hyd/9/96, Israel Hydrological Service, Jerusalem, Israel. Nir, D. (1985) Geomorphology; 1:500,000 Map 11. Atlas of Israel, 3rd éd., Survey of Israel & Carta, Jerusalem, Israel. Picard, L. (1970a) Geology; 1:500,000 Map III/l. Atlas of Israel, 2nd éd., Survey of Israel & Elsevier, Amsterdam, The Netherlands. Picard, L. (1970b) Lithology; 1:500,000 Map III/4B. Atlas of Israel, 2nd éd., Survey of Israel & Elsevier, Amsterdam, The Netherlands. Rojdestvenskiy, A. V. & Chebotarjov, A. I. (1974) Statisticheskiye metodi v gidrologiyi (Statistical Methods in Hydrology) (in Russian). GMI, Leningrad, USSR. Schein, Z. & Buras, N. (1973) Rainfall intensities in Israel. Isr. J. Earth Sci. 22, 15-30. Sharon, D. & Kutiel, H. (1986) The distribution of rainfall intensity in Israel, its regional and seasonal variations and its climatological evaluation. J. Climatol. 6, 277-291. Zrinji, Z. & Burn, D. H. (1994) Flood frequency analysis for ungaged sites using a region of influence approach. J. Hydrol. 153, 1-21.

Received 11 July 1996; accepted 19 November 1996