Nonlinear surface fit stability formula without any transition region for conventional breakwater design

Determining the optimum weight of the armor blocks is of vital importance in the design of conventional breakwaters. The widely used formulae in the literature include the transition region from plunging to surging waves. In this paper, it is aimed to investigate a new design formula without any transition region as an alternative to widely used Van der Meer formulae. The dimensionless parameters of Van der Meer formulae as well as newly generated variables are used as inputs. Nonlinear surface fit best subset regression model is used to find the optimum input combination that keeps the nonlinear relationships. All the input parameters, their second powers, and their two-way interactions are included in the regression analyses to obtain a nonlinear surface fit. Various goodness of fit statistics are applied to check the different perspectives of the model accuracy. It is demonstrated that the proposed model gives a realistic prediction of the stability number for critical data range. Especially for high values of stability number the proposed formula outperforms the benchmark formulae of Van der Meer and Etemad-Shahidi and Bonakdar. The other advantage is that it does not contain any transition region that depends on wave conditions. Besides, there is no need to include “number of waves” and “permeability” parameters into the equation.     

The Interface Configuration of the Fresh‐/Dead Sea Water – Theory and Measurements

The high‐density Dead Sea water (1.235 g/cm³) forms a special interface configuration with the fresh groundwater resources of its surrounding aquifers. The fresh groundwater column beneath its surroundings is around one tenth of its length compared to oceanic water. This fact alone indicates the vulnerability of the fresh groundwater resources to the impacts of changes in the Dead Sea level and to saltwater migration. Ghyben‐Herzberg and Glover equations were used to calculate the volumes of water in coastal aquifers which were replaced by freshwater due to the interface seaward migration as a result of the drop in the level of the Dead Sea. For that purpose, the dynamic equation of Glover approach has been integrated to accommodate that type of interface readjustment. The calculated amounts of freshwater which substituted salt Dead Sea water due to the migration of interface are 3.21 · 10¹¹ m³, from a Dead Sea level of –392 m to τ411 m below sea level. The average porosity of coastal aquifers was calculated to range from 2.8 to 2.94%. Geoelectric sounding measurements showed that areas underlying the coastal aquifers formerly occupied by the Dead Sea water are gradually becoming flushed and occupied by freshwater. The latter is becoming salinized due to the residuals of Dead Sea water in the aquifer matrix, the present salinity of which is lower than that of the Dead Sea water. At the same time salt dissolution from the Lisan Marl formation is causing collapses along the shorelines in the form of sinkholes, tens of meters in diameter and depth.     

Does the Actual Drop in Dead Sea Level Reflect the Development of Water Sources Within its Drainage Basin?

As a part of Jordan’s efforts to quantify the effect of the Dead Sea level decline on the precious groundwater resources of the surrounding aquifers, the authors analyzed the historic or predevelopment inflows and outflows of the Dead Sea basin and the resulting water balance which included precipitation, evaporation, surface‐ and groundwaters. The predevelopment situation was taken as the point of departure for the sake of this study. Furthermore, the present situation was analyzed in an attempt to quantify the groundwater inflows into the Dead Sea as a result of drop in the Dead Sea level. The groundwater component and the corresponding saltwater/freshwater interface were taken as the variables to balance the levels of the sea that would have been reached without the contribution of the uncontrolled groundwater inflows as a result of the salt/freshwater interface seaward migration. The present day water balance that includes all the water diversion projects from all riparians indicates serious declines in the Dead Sea level. The effects of the present day level declines on the fresh groundwater/saltwater interface indicate that considerable amounts of groundwater are driven into the Sea as a result of the seaward migration of the freshwater/saline water interface.     

Changes in the Dead Sea Level and their Impacts on the Surrounding Groundwater Bodies

In this paper the reaction of the salt‐/freshwater interface due to the changes in the Dead Sea level are elaborated at in details by using the inflows into the Dead Sea, the outflows due to evaporation losses and artificial discharges, and the hydrographic registrations of the Dead Sea level. The analyses show that the interface seaward migration resulted in a groundwater discharge of around 423 Mio m³ per meter drop in the level of the Dead Sea in the period 1994–1998 and of around 525 Mio m³/m in the period 1930–1937. The additional amount of groundwater joining the Dead Sea due to the interface seaward migration was 51 Mio m³ per one square kilometer of shrinkage in the area of the Dead Sea in the period 1930–1937 and 91 Mio m³/km² in the period 1994–1998. The riparian states of the Dead Sea are nowadays loosing 370 Mio m³/a of freshwater to the Dead Sea through the interface readjustment mechanisms as a result of their over exploitation of waters which formerly fed the Dead Sea.     

Differences between Humic Substances from Riverine,Estuarine, and Marine Environments Observed by Fluorescence Spectroscopy

Sixteen samples of fulvic acids and XAD‐4 fractions of riverine, estuarine, coastal, and open ocean origin have been studied by emission and synchronous molecular fluorescence spectroscopy. Certain features of the molecular fluorescence are related to the nature, the content, and the origin of those aquatic humic substances (HS). Riverine HS appear several times richer in fluorophores than marine HS, which can be well observed by emission fluorescence spectroscopy. Synchronous‐scan spectra of fulvic acids and of XAD‐4 fractions from the aquatic environments studied, emphasized the quality differences of their fluorophores. These features are useful as tracers of humic substances related with their natural environment source or even with their anthropogenic origin.