Arie Ben-Zvi

Assessment of transmission losses and groundwater recharge from runoff events in a wadi under shortage of data on lateral inflow, Negev, Israel

A hydrological–lithostratigraphical model was developed for assessment of transmission losses and groundwater recharge from runoff events in arid water courses where hydrological and meteorological records are incomplete. Water balance equations were established for reaches between hydrometric stations. Because rainfall and tributary flow data are scarce, lateral inflow, which is an essential component of the water balance equation, could not be estimated directly. The solution was obtained by developing a method which includes a hydrological–lithostratigraphical analogy. This is based on the following assumptions: (a) runoff resulting from a given rainfall event is related to the watershed surface lithology; (b) for a given event, the spatial distribution of runoff reflects the distribution of rainfall: and (c) transmission losses are uniquely related to the total inflow to the reach. The latter relationship, called the loss function, and the water balance equation comprise a model which simultaneously assesses lateral inflow and transmission losses for runoff events recorded at the terminal stations. The model was applied to three reaches of the arid Nahal Tsin in Israel. In this case study, the transmission losses were of the same order of magnitude as the flow at the major hydrometric stations. The losses were subdivided into channel moistening, which subsequently evaporates, and deep percolation, which recharges groundwater. For large runoff events, evaporation was substantially smaller than the losses. The mean annual recharge of groundwater from runoff events in the Tsin watershed was 4·1×106 m3, while the mean annual flow volume at the major stations ranged from 0·6 to 1·5×106 m3. Once in 100 years, the annual recharge may be seven times higher than the mean annual value, but the recharge during most years is very small. Copyright

Frequency and magnitude of runoff events in the and Negev of Israel

Abstract An event-based regional model for the frequency and magnitude of runoff events in the arid Negev of Israel has been developed. The model considers the number of events in a year, their arrival times, maximum observed discharges and volumes, the distribution of peak discharges and event volumes, and regional relationships between catchment area and magnitudes associated with 10- to 100-year recurrence intervals. The occurrence of events follows a negative binomial distribution with parameters estimated from the mean and the variance of the number of events in a year, which, in turn, are positively correlated with the mean annual depth of precipitation over the catchment. Arrival times of events follow the Pearson type-3 distribution. The enveloping curve of the maximum observed volumes is related to the catchment area by a power function. For catchments smaller than 250 to 300 km2 in area, the discharges and volumes associated with 10- to 100year recurrence intervals are found to be proportional to the catchment area. For large catchments, the discharge-area relationship may yield an inverse trend, and the volume may cease to increase as the area increases. Locations of the turning points for the relationships vary between watersheds.

Indices of hydrological drought in Israel

Abstract Indices of drought are formulated and examined on annual volumes of streamflow in Israel. Drought is defined as a severe shortage in the appearance of natural waters with respect to normal for place and time. The term severe shortage means here a deep, continuous and widely extended shortage. For reasons of generality, the normal and the shortage are described here by the mean and the standard deviation of the recorded data. In the examination, a deep shortage is considered to be the case when the annual volume of the streamflow is lower than the mean by at least one standard deviation. A continuous shortage is the case when the annual volumes are lower than the mean for at least four successive years. A widely extended shortage is the case when a deep or a continuous shortage extends over the entire region under consideration. The examination covers 14 rivers in Israel for which approximately homogeneous records are available for at least 30 years. The mean annual volume of flow in these rivers is from 0.85 to 399 × 10 6 m 3 , and the coefficient of variation is between 0.3 and 3.2. The examination reveals that within the time span of the available records there have occurred two events of an extended deep shortage and two events of an extended continuous shortage. The two kinds of extended shortage did not coincide, but they occurred shortly one after the other. According to our terminology, no drought occurred in Israel within the time of the available hydrological records.

Joint use of L-moment diagram and goodness-of-fit test: a case study of diverse series

Abstract Selection of a probability distribution for annual maximum discharges was carried through exploratory and confirmatory stages. The L-moment diagram was applied first in order to screen out inappropriate candidate distributions. The Anderson–Darling test was then applied in order to examine the descriptive performance of screened distributions. The effectiveness of this two-stage procedure was studied on an ensemble of diverse annual maximum discharge series recorded in Israel. The Generalized Pareto distribution was the only one of a number of candidate distributions whose theoretical relationship between L-moments followed closely enough the actual relationships in the case study. This distribution was well fitted to about one half of the discharge series, and satisfactorily fitted to the entire ensemble. It was concluded that such a two-stage procedure, which applies quantitative measures in both stages, would reduce the subjectivity involved with the selection of a probability distribution, thus improving the credibility of predicted high discharges.

Runoff peaks from two-dimensional laboratory watersheds

Based upon 578 laboratory hydrographs, a method has been developed to describe the magnitude and time of occurrence of the peak discharge. The experiments were conducted on a 40 × 40-ft. (12.2 × 12.2-m) large watershed and on portions of it. The independent experimentation variables were the rainfall intensity (up to 12 in.hr.−1 or 305 mm hr.−1), the rainfall duration (up to 8 min.), the main watershed slope (0.5–3%), the area exposed to rainfall (nine different configurations) and the surface roughness (two different materials). A time of concentration has been defined as the time from the initiation of the rainfall until the time when the discharge begins with a gradual approach towards its equilibrium state. This approach is described by a straight inclined line on a semilog plot of the hydrograph. The time of concentration is found to be proportional to the product of the rainfall intensity and the watershed slope raised to a power of −0.25. The proportionality coefficient is larger for the rougher surface, and also for watersheds (configurations) where the area exposed to rainfall is not adjacent to the outlet. The time of concentration, as is defined here, is not related to the length of flow along the watershed. The ratio of the peak discharge to the supply rate is found here as a linear function of the ratio of the rainfall duration to the time of concentration. A rainfall whose duration is equal to the time of concentration results in a runoff whose peak is equal to the supply rate. The functional relationship between the ratio of the peak discharge to the supply rate and the rainfall duration, that has been found in the laboratory, is identical to the original relationship for outdoor urban watersheds from which the rational formula was developed almost a century ago. The ratio of the time of peak to the time of concentration is found to be proportional to the ratio of the rainfall duration to the time of concentration raised to a power of ∼0.5. A similarity has been found between these results and the peak reduction factor found for small outdoor watersheds in Illinois.

Travel time of runoff crests in Israel

Abstract Travel times of crests of runoff events in rivers are determined from records of standard hydrometric stations which are located in series. For all the studied reaches, travel time decreases as discharge increases. Their relationship is formulated by use of a linear regression on logarithmic transformed data. The parameters of this relationship are regressed on the length and the slope of the reach and on the circularity of the watershed of the upstream station. The results for the individual reaches are found to be valid for application for either the upstream or the downstream station, but a regional formula can be derived only for the upstream stations.

Enhancement of runoff from a small watershed by cloud seeding

Abstract Daily volumes of runoff, from a small watershed, are compared, with respect to daily depths of precipitation, under randomly allocated cloud seeding. Enhancement is found with respect to rainfalls at the control and at the target area. The effect is evident by doubling the number of runoff days, by doubling the ratio to the volume of the precipitation, and by heightening the regression line for nonleading days in runoff sequences. With respect to the rainfall at the control, this heightening is about 40% of the mean volume per runoff day. The generation of the runoff is governed by the abstractions which consume 98% of the precipitated waters. The seasonal abstractions are distributed between an initial depth of 230 mm, a continuing rate of 3 mm−1 d on days between runoff events, and around 95% of the precipitation depth on days when runoff occurs. The runoff occurs in spells of consecutive days. For nonleading days, and when no snowmelt component is present, daily volume of the runoff is correlated with the daily depth of the rainfall on the watershed. Higher volumes are found in presence of a snowmelt runoff, and lower volumes are found for the leading days of the runoff spells. High rates of enhancement are found for the intense fraction of the rainfall, for the Eastern sector of the watershed and for the later portion of the rainy season. These nonuniformities in the rainfall enhancement seem to be the cause for the enhancement of the runoff with respect to the precipitation on the watershed.

Probability distribution of flow events in the Negev area of Israel

Abstract The occurrence of a flow in a wadi is a random event. The number of flow events in a season is assumed as resulting from a homogeneous Poisson process. The agreement between the observations and the expected distribution is tested by the χ 2 test. The combined record registered by three hydrometric stations is found consistent with the hypothesis.

Assessment of runoff enhancement by randomized cloud seeding in case of a carry-over flow

Abstract Daily volumes of runoff from two small watersheds, observed on randomly allocated seeded days are compared with volumes observed on unseeded days. The comparison is carried out against depths of precipitation at a control and over the watersheds. As the cessation of direct runoff lags a few days behind that of the rainfall, an assessment of the effect of seeding requires a separation of the runoff with respect to meteorological days. The separation is carried out by use of the exponential decay model. In the present case it is involves a higher degree of uncertainty than the conventional separation with respect to rainfall events. Therefore, the comparison is limited to the volumes of immediate runoff that reach the hydrometric stations on the same days as the precipitation. In order to set a yardstick for the effect of separation, daily volumes of measured streamflow are compared also. The assessment is carried out by use of the double ratio technique (i.e. the ratio of mean daily volume for seeded days to mean daily volume for unseeded days divided by the ratio of depths of precipitation on these days at the control). A linear regression of the flow against the precipitation is applied for a few cases where the correlation coefficient is higher than 0.6. The results of the two methods are positive and close to each other. The average rate of enhancement of the immediate runoff on all runoff days is about 65%, while the rate for days on which runoff series are not initiated is about 130% of the mean value for unseeded days. In addition, an enhancement is found in the number of days on which runoff is generated. The volume of runoff is found enhanced also with respect to the depth of precipitation upon the watersheds. A non-parametric test does not indicate a significant difference between the series of seeded and unseeded daily volumes. Yet, the results are consistent with those obtained earlier for a third watershed in the region, with results for annual volumes of springflow and streamflow and with changes observed in properties of the precipitation that are related to hydrologic processes. Therefore, we conclude that cloud seeding, under the conditions that prevailed in northern Israel in the years 1969/1970 to 1974/1975, enhances generation of direct surface runoff by 50–150% of its value on unseeded days.

Considering diversity in precipitation variability when updating seasonal flow forecasts

Abstract The Israel Hydrological Service forecasts the flow to Lake Kinneret by use of a hydrometeorological model which relates seasonal flow volumes to predicted annual depths of precipitation at representative stations. Issued forecasts include an array of 10 values assigned with the exceedance probabilities of 5–95%, as well as their average, which is an estimate of the expected value. A naive forecast is issued at the beginning of the precipitation season, and subsequent updating forecasts are issued during the season. Predicted annual depths of precipitation in an updating forecast are composed of the observed depth until the updating date and an array of predicted depths for the subsequent sub-season. No explicit relation was found between corresponding prior and subsequent depths concerning any updating date. But, the distribution of subsequent depths was found related to the category (i.e. low, medium, or high) of the corresponding prior depth. Empirical, parametric and non-parametric tests revealed a number of significant diversities in the distributions of later depths with respect to the corresponding categories of earlier depths. This diversity could result in considerable differences in the forecasted flow volumes, and is particularly important in cases of extreme situations, when management decisions are tied to revisions before the end of the precipitation season.