Global and Planetary Change 70 (2010) 64–75

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Global and Planetary Change

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Reconstructing an extreme flood from boulder transport and rainfall–runoff modelling: Wadi Isla, South Sinai,

Alan E. Kehew a,⁎, Adam Milewski a, Farouk Soliman b a Geosciences Dept., Western Michigan Univ., Kalamazoo, MI 49008, USA b Geology Department, Faculty of Science, Suez University, Ismailia, Egypt article info abstract

Article history: The Wadi Isla , a narrow steep bedrock and its , rises near the highest elevations Accepted 6 November 2009 of the Precambrian Sinai massif on the eastern margin of the tectonically active Gulf of Suez rift. The basin area Available online 17 November 2009 upstream from the mountain front is 191 km2 and downstream the wadi crosses a broad alluvial plain to the Red Sea. -transported boulders within the lower canyon (up to 5 m in diameter) and in a fan downstream Keywords: indicate extremely high competence. In one reach, a 60-m-long boulder berm, ranging in height from 3 to 4 m, lies palaeoflood along the southern wall of the canyon and contains boulders 2–3 m in diameter. Boulder deposits beyond the Sinai rainfall– mouth of the canyon generally appear to be less than several metres thick and are composed of imbricated, well- boulder transport sorted boulders. The last flood that deposited these boulders is believed to have been a debris torrent with a low flash floods content of fines. Mean intermediate diameter decreases from about 1.5 m just beyond the mouth of the canyon, where the width expands to 300 m, to about 0.5 m downstream to the point at which the is no longer confined on its south side. Using the empirical formula of Costa (1983), these clasts represent velocities decreasing from about 6.5 m s−1 to 3.7 m s−1. velocity and were also calculated within the canyon, using ,Costa's (1983) method and by the Manning equation. Parameters for the calculation include a channel width of 65 m, flow depth of 3.5 m (average height of the boulder berm), an average slope of 0.038 and a roughness coefficient of 0.06. The resulting values include a velocity range between 6.8 m s−1 and 7.3 m s1 and a corresponding discharge range of ∼1550 m3 s−1 to 1660 m3 s−1. A lower limiting discharge of 1320 m3 s−1 was obtained with an assumption of critical flow conditions. The boulder fan is much coarser than the older alluvial plain , suggesting an increase in flood magnitudes in more recent times — perhaps in response to renewed uplift of the mountain front and/or climate change. A calibrated rainfall–runoff model was developed using SWAT to estimate modern flood discharges in Wadi Isla. The magnitude of discharge from 1998–2006 did not exceed 500 m3 s−1.Artificial precipitation amounts (90 and 150 mm) were used to extrapolate from recent rainfall amounts to the amount of rainfall needed to produce a discharge range of 1320 m3 s−1 to 1660 m3 s−1. Results show that rainfall must range between ∼102 mm and 125 mm to produce this discharge. © 2009 Published by Elsevier B.V.

1. Introduction arid fluvial systems include those of Ely and Baker (1985), Webb et al. (1988), Wohl (1992), House and Pearthree (1995), and Greenbaum Fluvial activity in arid regions is typically dominated by large flash et al. (1998, 2000, 2006). The most common method of estimating floods that occur very infrequently, and whose geological record may peak discharges from palaeofloods is the step-backwater method, in persist for long periods of time (Tooth, 2000). Deposits of these events which palaeostage indicators of various types along with measured include slackwater sediment in high-level protected areas of bedrock channel slope and geometry are used to reconstruct the water-surface , coarse channel sediment deposited in response to changes profile during the flood and its associated discharge. in hydraulic conditions during the flood, and sediment transported In this study, a more rudimentary approach was used to estimate to depositional sites such as alluvial fans or plains. Because gauging the magnitude of a flood emanating from a wadi located in the rugged, stations or direct measurement of these events are extremely rare, high-relief terrain of the south of Egypt. Preservation palaeoflood hydrology is utilized to reconstruct the discharge, velocity, of a large accumulation of boulders assumed to have been transported and other variables of these rare flows. Palaeoflood studies focusing on and deposited by a single flood event immediately downstream from the mouth of the canyon enabled velocity calculations of the transport- ing flood to be made using empirical formulas. In addition, observa- ⁎ Corresponding author. tions of boulder size, palaeostage indicators, and channel dimensions E-mail address: [email protected] (A.E. Kehew). at several reaches in the lower canyon were used to calculate velocity

0921-8181/$ – see front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.gloplacha.2009.11.008 A.E. Kehew et al. / Global and Planetary Change 70 (2010) 64–75 65 and discharge from the Manning equation. The values obtained by region, including Gebel Umm Shomar (2586 m), which is just south of both methods were comparable, within the uncertainties of parameter Gebel Katherina (2637 m), the highest peak in the Sinai Peninsula. estimation. The rock walls of the canyon and its tributaries are extremely steep and rise 700 m or more above the floor of the wadi. 2. Tectonic and geological setting of the Wadi Isla drainage basin 3.1. Morphology of the lower canyon Wadi Isla, a steep canyon and its tributaries, occupies a 348–km2 drainage basin that drains a portion of the western side of the Sinai The magnitude of large floods that have moved through Wadi Isla massif, a faulted and uplifted block of Precambrian terrain located in can be estimated by the sizes of transported boulders both within the the south Sinai Peninsula (Fig. 1). Of this area, 191km2 comprises canyon and within a boulder fan deposit at the mouth of the canyon a steep bedrock canyon and its tributaries in the massif and the re- where the wadi is incised into the alluvial plain. Along the lower- mainder encompasses the alluvial reach of the wadi as it crosses the most reach of the canyon, older deposits of coarse, partially cemented broad El-Qaa alluvial plain on the west side of the massif. Uplift of this alluvium (Fig. 3) are truncated by during more recent floods. region is related to rifting of the Gulf of Suez, which lies just to the Similar cemented deposits in Nahal Zin in the were west, and is the northern extension of the Red Sea Rift. The Sinai sub- considered to be Pleistocene in age (Greenbaum et al., 2000). Boulder plate, bounded by the Suez rift to the west and the transform deposits form a variety of bedforms in the canyon including pendant on the east, formed by the separation of the Arabian and African plates bars associated with sharp bends in the canyon and boulder berms. beginning in the Tertiary. Flanking the Gulf of Suez on the eastern side Transport of boulders as large as 5 m in diameter is inferred by imbri- of the Suez rift is a series of normal faults and folds associated with cation with other boulders in these bedforms (Fig. 4). With the excep- rifting. Although Tertiary rocks in some of these blocks are exposed tion of one exposure, the boulder deposits lack finer, flood-deposited east of the Gulf of Suez in parts of the South Sinai, in the Wadi Isla area, sediment, such as the sandy and gravely alluvium that cover the wadi the El-Qaa Plain rises gradually from sea level to the steeply sloping bottom. The lack of interstitial fines indicates a change in flood regime mountain front composed of uplifted Precambrian igneous and meta- from the flood that transported the largest boulders to the smaller, morphic rocks. The Precambrian rocks of the Sinai Massif constitute more recent floods in the wadi which, based on regional investi- the uplifted eastern shoulder of the Suez Rift. The structural relief gations, should be hyperconcentrated (Lekach and Schick, 1982; of the Suez Rift shoulders reaches 4–5 km, which is a combination of Alexandrov et al., 2003). direct tectonic uplift of the rift flanks and isostatic uplift caused by erosion of tectonically uplifted crustal block (Garfunkel, 1988). The 3.2. Boulder berms topographic relief of the rift shoulder is significant, rising from sea level to peaks of 2500 m or more within a distance of about 50 km Boulder berms are linear ridges of coarse clasts deposited in a from the Gulf of Suez. streamwise orientation along channel margins by debris torrents— The El-Qaa Plain is approximately 20 km wide and slopes uni- high-velocity flash floods with sediment concentrations below the formly from elevations around 400 m at the mountain front to the transition to non-Newtonian debris flows. Debris flows deposit analo- Gulf of Suez. Structurally, the El-Qaa Plain is a secondary rift basin gous features known as debris flow (Carling, 1987). Boulder (Ghodeif, 2002) or half graben bounded by normal faults along the berms are formed in regions of flow separation associated with valley mountain front. Tertiary rocks are exposed on the western side of the widening or on the convex sides of channel bends (Carling, 1987, El-Qaa Plain north of the Wadi Isla area. 1989). In addition, boulder berms develop at the base of steps in The thickness of Quaternary alluvium underlying the El-Qaa Plain channel gradient where hydraulic jumps form in the centre of the is highly variable, reaching thicknesses of 500 m in places (Ghodeif, channel (Carling, 1995). occurs at peak flow conditions in 2002). Geomorphically, it resembles a bajada, although it lacks distinct the flow separation zone between downstream and recirculating flow. alluvial fans at the mouths of wadis emerging from the mountain front. Boulders are moved toward the channel margins by secondary flow Wadi Isla, along with other major wadis along the mountain front, are components (Carling, 1987). Carling (1987) also observed that the top currently incising their channels into the alluvial plain rather than of the boulder berm deposited during a flash flood of a small stream in building alluvial fans. Near the mouth of Wadi Isla, a scarp about 8 m England approximated the water-surface elevation at peak discharge high exposes older alluvium between the crest of the plain at the conditions. mountain front and the channel of the active wadi (Fig. 2). This incision A fresh, relatively well-sorted boulder berm extends for a length of may be a response to uplift of the mountain front, although a shift in approximately 60 m along the south wall of the canyon at one loca- fluvial regime due to Holocene climate change cannot be ruled out. tion (Fig. 5). Boulder size in the berm ranges between 2 and 3 m and Uplift of the Gulf of Suez rift shoulders has probably been occurring boulders are moderately well rounded. The lack of interstitial fines in since the initiation of rifting (Garfunkel, 1988; Gvirtzman, 1994). Based the deposit indicates that the transporting flood was a debris torrent on ages and elevations of wave-cut terraces marking former sea levels, rather than a debris flow. The channel has a width of 65 m in this Gvirtzman (1994) calculated an average uplift rate of 0.085 mm yr− 1 location and an erosional scarp occurs across the valley from the for the south Sinai since the high stand of the last interglacial sea level boulder berm. Remnants of an older, higher berm are also present in (∼120 ka B.P). The incision of the El-Qaa Plain by runoff through Wadi this reach of the wadi (Fig. 5a). The higher berm is more weathered Isla and other wadis dissecting the massif suggests either a more rapid and cemented and may be associated with an older period of flooding rate of uplift in Holocene time or more effective incision by runoff than is represented by the lower berm. A channel cross section can be events. The extreme coarseness in grain size of the boulder fan relative constructed at the location of the lower boulder berm, using the width to the older alluvium exposed in the erosional scarp may also indicate of 65 m and the height of the lower boulder berm of ∼3.5 m. that changes in climate have contributed to an increase in the mag- nitude of flood events occurring in the wadis. 3.3. Wadi Isla boulder fan

3. Geological and hydrological setting of Wadi Isla Channel width is approximately 30 m at the mouth of the bedrock canyon. Immediately downstream, the channel widens significantly The portion of the Wadi Isla drainage basin upstream of the El-Qaa (Figs. 6 and 7) and is confined by alluvial scarps on the north and alluvial plain in the rugged mountains of the Sinai Massif occupies south sides. The margin on the south side alternates between alluvial an area of about 190 km2. It rises near some of the highest peaks in and bedrock sections. This broad surface is mantled by boulders 66 A.E. Kehew et al. / Global and Planetary Change 70 (2010) 64–75

Fig. 1. Satellite image showing the Sinai Peninsula. Uplifted Precambrian rocks of the south Sinai massif are shown by the dark-coloured area. El-Qaa plain lies between the mountain front and the Gulf of Suez. The bedrock portion of Wadi Isla drainage basin is outlined in solid black. Also shown is the location of Wadi Girafi (dashed outline). A.E. Kehew et al. / Global and Planetary Change 70 (2010) 64–75 67

Fig. 2. The mouth of Wadi Isla canyon and the erosional scarp in El-Qaa Plain alluvium.

carried out of the canyon by flash floods. The boulder deposit consists that comes to rest on the bed (Brayshaw, 1984). Martini (1977) sug- of a network of longitudinal bars dissected by braided channels, essen- gests that imbrication clusters may also represent a line of clasts tially an expansion complex (Baker, 1984). Excellent examples of moving through the flow together that come to rest as a result of exceptionally large cluster bedforms (Martini, 1977; Brayshaw, 1984) velocity fluctuations or the development of imbrication. Once depo- on bar surfaces indicate declining competence and deposition on the sited, the cluster acts as a unit and much higher velocities are required bars (Fig. 8). Many striking examples of imbrication clusters are pres- to re-initiate motion. The exceptional size of boulders in some of the ent, in which a line of very coarse, imbricated clasts lies in a streamwise Wadi Isla fan imbrication clusters (Fig. 8a) must therefore represent orientation on the bar surfaces. Cluster formation can be initiated by the peak flow bed conditions of the largest flood to emerge from the deposition of moving clasts behind a particularly large “obstacle clast” bedrock canyon.

Fig. 3. The older, cemented alluvium within Wadi Isla canyon. 68 A.E. Kehew et al. / Global and Planetary Change 70 (2010) 64–75

diameter actually increases downstream from Traverse 8, although the boulders are noticeably more weathered and probably represent much earlier events. The boulders between the mouth of the canyon and Traverse 8 fine uniformly downstream and are considered to represent the deposit of a single flood event of high magnitude and low frequency that has been modified by subsequent floods of lower magnitude. Erosion of bar margins exposes the internal structure of the coarse bars (Fig. 8d). These exposures indicate that the bars are composed of imbricated, clast-supported, open-work cobbles and boulders, which is indicative of debris-torrent (low sediment concentration) rather debris-flow deposition. The single flood interpretation is based on: (1) the grada- tional fining of the deposit between Traverses 1 and 8; (2) the lesser degree of clast weathering relative to clasts located downstream of Traverse 8; (3) the large clast size in imbrication clusters, decreasing the possibility that a subsequent flood could have remobilized them; and (4) the lack of coarse boulder deposits thicker than a metre or two on the bar surfaces. Repeated flood inundation would be expected to produce thicker deposits.

4. Palaeohydrology

Palaeohydrological parameters of the most recent large flood can be estimated in several ways. The size of boulders transported within the canyon and on the boulder fan below the mouth of the canyon

Fig. 4. (a) A bar of large, imbricated boulders just upstream from narrowest section of the canyon. (b) An imbricated boulder within the canyon.

Boulder size data were measured at 28 stations on the fan (Fig. 9), located with a GPS receiver. The stations were positioned along 8 main traverses aligned roughly perpendicular to flow direction. The exact location of a station was chosen to be an area that contained boulders representative of the largest sizes in that particular part of the fan. Then, the intermediate axes of the 5 largest boulders within an area of approximately 50 m2 were measured. Channels dissecting the fan appear to be active during floods of lower magnitude than floods that could mobilize boulders on the intervening bars. The channel floors are mantled with sand and pebble to cobble size clasts much finer than those on the bar surfaces. These areas were avoided as measurement stations. Occasional outsize boulders are present in the deposit; these were not included in the analysis unless they happened to occur at one of the measurement stations. The general grain size of the clasts can be appreciated from Table 1, which lists both the mean intermediate diameter of boulders at each station as well as for all clasts measured in each traverse. Mean intermediate diameter decreases from 1.1–1.3 m in Traverses 1–4 to 0.6 m in Traverse 8, a distance of approximately 1.5 km. The slope of fan over this distance is 0.014, which is less than half the slope in the lower part of the canyon. The decrease in grain size over this part of the fan is best fit with an exponential function (Fig. 10). Downstream in the wadi from Traverse 8, the valley widens significantly, and boulders are present for several km. The erosional scarp in the alluvium on the north side of the channel gradually de- Fig. 5. Two views of the boulder berm in the lower canyon. The higher boulder berm is creases in height to less than 1 m and disappears. The wadi continues visible in the upper right corner of (a). Notice the clast-supported, open-work fabric to the Gulf of Suez coast as a broad shallow channel. Mean boulder indicative of debris-torrent origin. A.E. Kehew et al. / Global and Planetary Change 70 (2010) 64–75 69

Fig. 6. A portion of the Tur Sinai contour map (scale 1:250,000) showing the mountain front and El-Qaa Plain. Circles are locations of boulder measurements on the boulder fan and other points within the canyon. The contour interval is 50 m.

Fig. 7. The proximal part of a boulder fan just downstream from the mouth of the canyon. The white dashed lines show the top of the El-Qaa Plain surface, which has been incised by Wadi Isla floods. 70 A.E. Kehew et al. / Global and Planetary Change 70 (2010) 64–75

Fig. 8. Examples of imbrication and imbrication cluster bedforms. (a) An imbrication cluster composed of 2 m-diameter boulders on proximal portion of fan. (b) and (c) Imbrication clusters in the mid-fan area. (d) Exposure along a channel margin in the mid to distal area of the fan showing imbrication and openwork fabric. Flow direction shown by arrows. The scale bar in (b), (c), and (d) is 10 cm in length.

can be related to velocity though various theoretical and empirical not apply to the Wadi Isla floods. Kehew and Teller (1993) used a methods. In addition, the Manning equation can be applied to the variant of the Church (1978) method proposed by Komar (1987, 1989) reach with the boulder berm to estimate velocity and discharge. to account for selective entrainment of large clasts from a deposit of mixed sizes. Komar (1989) concluded that empirical calculations of 4.1. Shear stress shear stress associated with boulder transport based on uniform grains overestimate critical shear stress for clasts that are much larger than Several methods are available for reconstruction of palaeohydrol- the median. Depth estimates derived from the selective entrainment ogical parameters from the competence data derived from transported method (Kehew and Teller, 1993) resulted in lower, more realistic boulders. The two most common approaches rely on relationships values, probably because of the projection of large clasts above the bed between clast size and either critical shear stress or velocity. Critical and the lower critical shear stress necessary to entrain them. Critical shear stress can be related to particle size through the Shield's en- shear stress values in ephemeral desert are likely to be lower trainment function. Church (1978) used the critical shear stress asso- than humid perennial streams because of projecting clasts as well ciated with the maximum particle size to estimate depth: as a lack of bed (Gerson, 1977; Laronne et al., 1994; Bergman, 2007). τ γ ; ð Þ c = RS 1 4.2. Flow depth in which γ is density, τc is critical shear stress, R is hydraulic radius, for which depth is an approximation, and S is energy slope. Lord and Costa (1983) estimated flow depths of flash floods by four methods, Kehew (1987) used this method to estimate the depth of a glacial lake three of which are relevant to particles greater than 0.6 m in inter- outburst flood; the estimated depth was subsequently used in the mediate diameter: (1) the Manning equation, (2) unit stream power, Manning equation to estimate velocity and discharge. Lord and Kehew and (3) the Shield's function. Costa averaged values of the three (1987) speculated that this procedure overestimated depth because methods for various velocities and pairs of slope and Manning's n of the hyperconcentrated character of the flows, a condition that does values. For the average slope of lower Wadi Isla, 0.038, and a velocity A.E. Kehew et al. / Global and Planetary Change 70 (2010) 64–75 71

Fig. 9. Location of stations established for boulder measurement on the boulder fan. Grey lines are traverses numbered on the right. Mean velocity for each traverse (m s− 1) is given to the right of each traverse number; determined by using the mean diameter of all boulders measured on the traverse, based on Costa's (1983) formula. Mean boulder size for each station is listed in the upper left. of 9.1 m s− 1, the depth would range between 3.8 and 5.9 m. For a diameter against the arithmetic mean of the four velocity estimates velocity of 6 m s− 1, the depth would range between 1.9 and 2.88 m. and obtained the relationship given in Eq. (2): The height of the boulder berm in Wadi Isla (∼3.5 m) provides an : 0:487; ð Þ independent estimate of depth. In terms of Costa's estimates, this v =018dI 2 depth would correspond to a velocity between 6 and 9 m s− 1, depend- ing on Manning's n and slope. in which v is mean velocity and dI is intermediate particle diameter. Throughout the Wadi Isla canyon, boulders range in size up to 5 m in 4.3. Velocity and discharge estimates diameter. For a conservative estimate of velocity using Eq. (2), the mean velocity necessary to transport a 2-m boulder is 7.3 m s− 1, and 4.3.1. Costa's empirical method using the cross sectional area of 227.5 m2 at the boulder berm reach, Velocity is the other parameter that is typically obtained from discharge (Q=v×A) is estimated at 1660 m3 s− 1. This velocity would competence data in palaeofloods. Costa (1983) reviewed theoretical be expected to vary throughout the lower course of the wadi, as a and empirical methods for velocity estimation for boulders trans- function of channel width, slope and roughness. For example, within ported by flash floods on streams draining the Colorado Front Range the narrowest canyon reach (w=17 m), no boulders were deposited, of the Rocky Mountains. These flash flood events constitute a reason- indicating that velocities through this reach were probably high able analog to Wadi Isla in terms of drainage basin area, slope, channel enough to transport any available clast. Immediately upgradient from characteristics, and size of boulders transported. The basin response this reach is an imbricated bar of large boulders (∼3 m diameter) that to a rainfall event may differ because of the hyperarid climate of Wadi may have formed as velocity slowed upstream of a hydraulic at Isla and the lack of vegetation. Costa (1983) utilized two theoretical the narrow reach (Fig. 4a). Baker (1978) described similar phenomena methods and two empirical methods to calculate mean velocity as a associated with narrow canyons in the Channeled Scabland. function of clast diameter, for clasts that ranged from 50 to 3200 mm Using Eq. (2), velocities on the boulder fan at the mouth of the in diameter. The difference in velocity between the four methods canyon decline from about 6.54 to 3.7 m s− 1 over the 1500 m distance ranged between 17 and 30%. Costa (1983) then regressed boulder between Traverses 1 and 8 (Table 1, Fig. 9). 72 A.E. Kehew et al. / Global and Planetary Change 70 (2010) 64–75

Table 1 n value of approximately 0.06. In addition, Williams (1983) deter- Wadi Isla boulder data. mined a range of n values between 0.054 and 0.068 for a boulder-filled Traverse Station Boulder size (m) Mean for Distance Calculated channel in Sweden. Greenbaum et al. (2000) note that Manning's n is traverse from trav. velocity a parameter of low sensitivity when calculating discharges of large − 1 a (m) 1 (m) (m s ) floods. 1 6 1.0, 2.5, 1.7, 0.9 1.6 0 6.5 Assuming a rectangular channel cross section of width 65 m and 2 11 3.0, 1.5, 1.5, 1.34, 1.0 1.3 133 5.9 depth, 3.5 m, the hydraulic radius is 3.2 m. Inserting these values into 12 1.0, 1.0, 1.4, 0.7, 0.9 Eq. (3) yields a velocity of 6.8 m s− 1, which is similar to the velocity 13 0.7, 0.7, 0.9, 1.4, 1.1 − 1 3 17 1.0, 1.0,1.4, 1.5, 5.2 1.4 433 6.1 obtained from Eq. (1) for transport of a 2-m boulder (7.3 m s ). With 18 0.9, 0.9, 1.1, 1.2, 1.0 uncertainty in the Manning's n value as well as the local slope of the − 19 1.0, 1.2, 1.3, 1.1, 1.4 reach containing the boulder berm, 6.8 m s 1 is probably reasonable 4 22 1.1, 1.1, 1.1, 1.0, 1.2 1.2 555 5.6 as a mean flow velocity. Peak velocity would be expected to exceed 23 1.2, 1.2, 1.2, 0.9, 1.1 this value for short periods during the flood. Transported boulders of 24 0.5, 0.6, 0.8, 2.4, 2.0 5 27 0.6, 0.5, 0.5, 0.5, 0.8 0.8 666 4.6 3 m in size and greater are present within the canyon. 28 0.6, 0.8, 0.8, 1.0 Flood discharge can be estimated by multiplying the velocity value 29 0.8, 0.8, 0.7, 2.0, 0.7 obtained above, 6.8 m s− 1, by the cross sectional area of the channel at 6 32 0.35, 0.4, 0.5, 0.5, 0.6 0.6 1127 4.1 the site of the boulder berm, 227.5 m2, yielding a value of 1547 m3 s− 1. 33 0.5, 0.6, 0.45, 0.4, 0.48 3 − 1 3 − 1 34 0.7, 0.6, 0.85, 0.35, 0.7 Thus, a discharge range of 1550 m s to 1660 m s is obtained by 35 0.8, 0.8, 0.75, 0.75, 0.7 the application of Costa's (1983) empirical relationship for mean velo- 7 39 1.6, 1.0, 1.0, 0.9, 0.6 0.6 1216 4.1 city based on maximum transported clast size, and through the use 40 0.5, 0.5, 0.5, 0.5, 0.6 of the Manning equation, with reasonable estimates of energy slope, 41 0.35, 0.35, 0.3, 0.4, 0.27 cross sectional area, and roughness coefficient. The values used for 8 44 0.35, 0.35, 0.4, 0.51, 0.3 0.6 1416 4.1 45 0.9, 0.9, 0.75, 0.45, 0.6 cross sectional area and boulder size are conservative. 46 0.53, 0.6, 0.75, 0.8, 0.8 One implication of the velocity and depth values calculated above − 1 a 0.487 is that flow is supercritical. For example, at a velocity of 7.3 m s and v=0.18dI ; Costa (1983). a depth of 3.5 m, the Froude number (Fr=v/(gD)0.5) is 1.25. Froude numbers as high as 2.9 have been reported for a flash flood in the 4.3.2. Manning equation Sinai (Schick and Lekach, 1987) and as high as 1.57 for a flash flood in Velocity can also be estimated by the Manning equation (Eq. (3)), Arizona (House and Pearthree, 1995). However, Grant (1997) pro- if estimates of depth, slope and Manning's roughness coefficient (n) posed that mobile-bed streams self regulate themselves through flow can be made. In the equation: and bedform interactions to achieve a state of critical flow (Fr=1) and that supercritical flow is rarely achieved (Jarrett, 1984). Under = = − v = R2 3S1 2n 1; ð3Þ this hypothesis, which Grant (1997) also suggested may apply to bedrock channels, supercritical flow is limited spatially to very short R is the hydraulic radius (cross sectional area/), S is distances and temporally to short, transient intervals. If this the energy slope, and n is the Manning roughness coefficient. The hypothesis applies to the Wadi Isla flash flood, velocity could then boulder-berm reach is used for this calculation, in which the height be estimated as: of the boulder berm, 3.5 m, is used as a minimum estimate of depth : and the width of the channel is 65 m. The energy slope is approx- v = ðgdÞ0 5: ð4Þ imated by the average slope of the lower wadi, 0.038. A value of 0.06 was selected for Manning's n. Costa (1983) used a variable n value for For a flow depth of 3.5 m, Eq. (4) yields a velocity of 5.8 m s−1 and a 9 channels cut in resistant bedrock in the Colorado Front Range that discharge of 1320 m3 s−1 for the boulder-berm reach. These values are experiences flash floods. The n value ranged from 0.04 at a slope of considered to provide a lower boundary for a range of palaeohydrological 0.005 to 0.124 for a slope of 0.1. The Wadi Isla slope corresponds to an estimates, given the extreme size of transported boulders in the wadi.

Fig. 10. Plot of mean boulder size for each traverse versus distance from Traverse 1. The exponential trend line fit to data has the highest R2 value. A.E. Kehew et al. / Global and Planetary Change 70 (2010) 64–75 73

Numerous potential sources of error affect virtually all terms util- 5.2. Model calibration ized in the palaeohydrological methods described above. Costa (1983) compared empirical estimates of discharge to indirect slope-area Our attempts for calibrating the model are hindered by the ab- measurements made soon after flash floods in the Rocky Mountains sence of stream flow data in the study area. Given the similarity of and reported an average error of 28% for the empirical methods geological and hydrogeological settings in the Sinai Peninsula, we in small drainage basins. In contrast, the empirical methods over- used the Wadi Girafi watershed, which originates in Sinai and flows estimated the discharge by 76% for the Big Thompson flood, which into (Nahal Paran) for calibration purposes (Fig. 1). Calibration occurred in a large drainage basin. Because Wadi Isla is intermediate of modelled stream flow against observed stream flow data was in area between the small and large basins considered by Costa (1983), performed in accordance with instructions in the SWAT user manual the estimates presented here can probably be assumed to have a sim- (Neitsch et al., 2002) as well as in other published literature from ilar magnitude of error. SWAT users (e.g., Lenhart et al., 2002; Tolson and Shoemaker, 2007). The initial manual calibration involved the calibration of the modelled average annual watershed runoff against existing stream flow obser- 5. Modelling of flood magnitudes in Wadi Isla vation data. An automatic calibration was performed following the initial manual calibration. The shuffled complex evolution method Due to the lack of adequate hydrological monitoring stations in (SCE) (Duan, 1991; Sorooshian et al., 1993) implemented in SWAT many parts of the world, watershed modelling coupled with remote (Van Griensven, 2002) was used for automatic calibration. sensing plays an important role in estimating modern floods. Meth- odologies for rainfall–runoff computations that heavily rely on ob- 5.2.1. Calibration site servations extracted from a wide-range of global remote sensing data Wadi Girafi originates in Sinai and terminates in Israel and provides sets (TRMM, Landsat TM, AVHRR, AMSR-E, and ASTER) have previ- continuous streamflow measurements from 1998–2006 at the Bottle- ously been developed using the arid Sinai Peninsula and the Eastern neck Station received from the Israel Hydrological Service (Fig. 1; Desert (ED) of Egypt as test sites. Milewski et al. (2006) conducted a dashed outline). Wadi Girafi is similar to watersheds encountered two-fold exercise: First, precipitation events were identified from in the Sinai Peninsula in its geological and hydrogeological settings. TRMM data and verified using cloud detection and soil moisture There are four main rock unit outcrops: Quaternary alluvium, Creta- difference images acquired from temporal satellite data (AVHRR and ceous sandstone, Eocene limestone, and Precambrian volcanics. Wadi AMSR-E) before and after the selected precipitation events. Second, Girafi receives an average of 25 mm of precipitation or less per year a calibrated catchment-based, continuous (over 9 years), semi-dis- and events are infrequent and intense. Stream flow data were recorded tributed (Soil Water and Assessment Tool model; for the duration of TRMM events (1998–2006) located at the Bottle- SWAT) was adopted to provide a continuous simulation of the over- neck Station in the northern area of the watershed. land flow, channel flow, transmission losses, evaporation on bare soils and evapotranspiration (ET), , and groundwater 5.2.2. Calibration results recharge. The R2 value as well as Nash and Sutcliff's (1970) method was chosen to evaluate the coefficient of determination (R2) and model 5.1. Model development coefficient of efficiency (COE), respectively. An R2 value of 0.87 was determined to be sufficient for accepting model results. Similarly, the Using techniques described earlier we have developed a hydrol- coefficient of efficiency produced similar results to the R2 test with ogical model using SWAT in Wadi Isla to determine the magnitude of a value of 0.86, indicating a high degree of correlation between the modern flood events. Evaporation on bare soils and evapotranspi- observed and computed values of discharge. ration (ET) on vegetated canopy were calculated using the Penman– Monteith method (Monteith, 1981). A modified Soil Conservation 5.3. Model results Service (SCS) curve number method developed by Pilgrim and Cordery (1992) was adopted to estimate direct runoff using rainfall excess. Modern rainfall events (1988–2006) in Wadi Girafi indicate pre- Channel routing was conducted by using the Muskingum routing cipitation events ranging from 0–34 mm (Fig. 11; triangles). Using the method (McCarthy, 1938), whereby the average Manning's coeffi- cient for gravel bed was calculated according to aforementioned procedures. The following series of data sets were used as inputs into the model: (1) 3-hourly precipitation data (1998–2006 — TRMM), (2) digital elevation model — ASTER, (3) lithologic maps, (4) land use maps — AVHRR derived by the USGS, and (5) climatic maps of solar radiation, wind speed, air temperature, and relative humidity obtained from the Egyptian Meteorological Authority's Climatic Atlas. SWAT automati- cally integrates these data sets to provide temporal and spatial esti- mates for runoff and recharge in the investigated basins. Geometric parameters (drainage area, average channel slope, stream length, and stream connectivity) of the investigated sub-catchment were delineated from SRTM data applying GIS technologies in SWAT. The bulk of the physical properties of the sub-catchment were ex- tracted from the existing databases throughout previous studies for the Eastern Desert and Sinai Peninsula (Gheith and Sultan, 2002; Milewski et al., 2006). The saturated hydraulic conductivities of soils were estimated from field studies in and around southern Sinai. Trans- Fig. 11. Storm events for Wadi Isla from 1998–2005 correlated against modelled mission losses in the stream networks constitute 20–25% of the total discharges (triangles). Diamonds represent artificial rainfall amounts. The graph also precipitation which agrees with studies in similar settings (Ben-Zvi, shows the required rainfall amount (∼102 and ∼125 mm; stars) required to generate 1996; Shentsis et al., 1999). the minimum and maximum discharges estimated from palaeohydrological methods. 74 A.E. Kehew et al. / Global and Planetary Change 70 (2010) 64–75 calibrated model, average daily discharge amounts for modern rainfall Negev desert constitute the closest analog to flash floods in Wadi Isla. events can reach up to 500 m3 s− 1 in Wadi Isla. In order to estimate For a basin of approximately 200 km2, the discharges represented by rainfall amounts that would produce discharge amounts comparable these two curves range between approximately 900 and 2000 m3 s− 1. to our estimated palaeoflood, we used artificial precipitation. Artificial Therefore, by this measure also, the highest discharge estimate for precipitation amounts of 90 mm and 150 mm were applied to the Wadi Isla, 1660 m3 s− 1, appears to be reasonable, especially consid- model (Fig. 11; diamonds). An R2 value of 0.91 was found between ering that the elevations and relief are higher in the Sinai massif. the observed and artificial model results (Fig. 11). The high degree of Greenbaum et al. (2006), based on analysis of palaeofloods in the correlation indicates rainfall amounts must be approximately 125 mm Nahal Netafim basin, concluded that the climate in the Negev Desert in a 31-hour flood duration, the average recorded flood measurement was significantly wetter and floods were consequently larger during duration at the Bottleneck Station in Israel from 1998–2005 (Ben- the transition from Marine Isotope Stage (MIS) 3 to MIS 2 during a Zvi, 1996; Shentsis et al., 1999), to produce discharge amounts of period between 33 and 29 ka B.P. Although the Wadi Isla flood has not 1660 m3 s− 1. For the lower boundary of the discharge range, a rainfall as yet been dated, it is possible that this flood could have occurred event of ∼102 mm is needed to generate a flood of 1320 m3 s− 1. during that interval of time. Flood discharges can also be expressed in terms of unit discharge, 6. Comparison of flood reconstruction with documented floods Q/A, in which Q is peak discharge in m3 s− 1 and A is drainage basin area in km2. Unit discharge is more useful for comparing flood mag- A test of the palaeohydrological estimates derived in this project is nitudes for basins of different size, climatic regime, and topography. to compare the values with floods in similar drainage basins described For the bounding discharge values estimated for the Wadi Isla flood in the literature. occurring in bedrock canyons similar to Wadi (1660 and 1320 m3 s− 1) the corresponding unit discharge values Isla have been described from the west and southwest USA, Gulf Coast are 8.6 and 6.9. Although these values are much higher than unit region, and from previous studies in the Sinai and Negev discharges for large drainage basins (N500,000 km2), which peak at (Table 2). Flash floods in Colorado Rocky Mountains of the USA and approximately 0.12 (O'Connor et al., 2002), they are well within the the Gulf Coast area are similar in channel characteristics but are range of unit discharge values for floods in smaller basins, such as located in different climatic regimes. Costa (1983) compared the re- those shown on Table 2. In addition, they fall within the range of unit sults of his estimates using competence data to slope-area estimates discharge values for the Negev Desert (4.5–10) calculated from the for the same floods. The competence derived values underestimated discharge and basin area values mentioned above. flood parameters (velocity, depth, and discharge) for small basins, but overestimated discharge for the one large included (Big 7. Conclusions Thompson). The Wadi Isla basin is closer to the size of smaller basins studied by Costa (1983). A high magnitude flash flood in Wadi Isla, South Sinai, Egypt, was Drainage basin size does not appear to be a problem in generat- reconstructed using a variety of techniques. Competence methods and ing discharges of the magnitude described in this paper. A flood of the Manning Equation yield discharge values of values of 1550– 1130 m s− 1 occurred on Elm Creek, Texas, for example, a basin with 1660 m3 s−1 in the lower canyon of the wadi and velocities of 6.8– an area of only 12.2 km2 (Table 2). Similarly, a large flash flood on 7.3 m s− 1. These estimates are based on transport of large boulders Bronco Creek, Arizona occurred in a basin of 50 km2. The discharge of (2 m in diameter) using the height of a boulder berm as a palaeostage this flood was originally estimated as 2080 m3 s− 1 (Aldridge, 1972), indicator. Boulder size is conservative because considerably larger but reinterpreted by House and Pearthree (1995) as 750−850 m3 s− 1. transported boulders are present in the wadi. Minimum estimates This flood differs from Wadi Isla in that the channel is alluvial rather of velocity (5.8 m s− 1) and discharge (1320 m3 s−1) were made by than bedrock. assuming critical flow (Fr=1), and solving the Froude equation for With regard to the amount of rainfall in storm events that cause velocity. flash floods, the Sinai and Negev flash floods are obviously more At the mouth of the wadi, a broad, thin boulder bar was deposited as relevant to the flash flood described in this study. Rainfall amounts are the flood competence decreased. Velocities declined from ∼6.5 m s−1 much smaller than comparable floods in humid regions. In perhaps the to 3.4 m s−1 over a distance of 1500 m. Imbricate cluster bedforms com- closest analog to the flood reconstructed in this paper, the storm posed of 1–2 m size boulders are common on the fan. associated with the 1975 El-Arish flood dropped a maximum of 73 mm In order to estimate the amount of rainfall necessary to generate a of precipitation at St. Katherine's Monastery, which is very close to the flood of the calculated magnitude range in Wadi Isla, a calibrated headwaters of Wadi Isla. Because the age of the Wadi Isla flood is rainfall–runoff model (SWAT) was constructed using rainfall amounts unknown, it does not seem unreasonable that a localized precipitation extracted from TRMM data between 1998 and 2006 and extrapolated event of 115–125 mm would be possible. to the level necessary to produce a flood between 1320 m3 s− 1 and Envelope curves for measured floods (Meirovich et al., 1998) 1660 m3 s− 1. The corresponding precipitation range was ∼102– and mid-late Holocene palaeofloods (Greenbaum et al., 2006) in the 125 mm, which is about 50% higher than the rainfall recorded near

Table 2 Selected palaeohydrological reconstructions of floods in steep bedrock canyons in Egypt and the USA.

River/drainage Location Date Drainage Discharge Unit discharge Depth Velocity Transported Rainfall Reference area (m3 s− 1) (m3 s− 1 km− 2) (m) (m s− 1) boulder size amount (km2) (m) (mm)

Upper Texas, USA 1978 700 6792 9.7 15 3.72 2 N790 Baker (1984) Elm Creek Texas, USA 1972 12.2 1130 92.6 7 6.4 2 ″ Baker (1977) Big Thompson Colorado, USA 1976 88 884 10.0 3.23 7.92 2.8 NA Grozier et al. (1976) Big Thompson Colorado, USA 1976 790 1552 19.6 4.8 8.53 2.76 NA Costa (1983)a Wadi Wuheida Sinai, Egypt 1966 170 540 3.2 NA NA NA 50–70 Schick (1971) Wadi Watir Sinai, Egypt 1975 3100 1170 0.38 NA NA NA 21–73b Gilead (1975) Wadi Isla Sinai, Egypt ? 190 1320–1660 6.9–8.6 3.5 5.8–7.3 2–3 115–125 This report

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