The isotopic composition and electrical conductivity frequently change with time in river water worldwide, on various time scales. Periodicity is also known for precipitation and other aqueous inputs. The time-series follow up of such variations is usually to proceed by many hydrologists. The major purpose is to gain a thorough understanding of the underlying phenomena and to plot the data accurately. However, there is no appropriate formula for the graphic illustration and mathematical expression of such fluctuations other than the complicated Fourier Series. Also, the use of the trigonometric sin function is not possible due to constraining the values between +1 and -1. In contrast, the isotopic compositions require negative and positive values on the y-axis corresponding to time on the -x-axis, while the hydrochemical concentrations only admit positive values. These constraints are entirely void in the flexible waveform PULSE model proposed in this work. In this model, we introduce a modified sinusoidal formula that has the exciting capability of freely controlling the graphic waveform, in a highly accommodating way, for plotting the time-series isotopic and hydrochemical pulses in conformity with field observations. Three main parameters, and two optional secondary parameters, are to use in our function, open to modification. The model is to use in ExcelÒ, whose SOLVER built-in macro may give the approximate values for the main parameters. Such values are then to improve to get the waveform best visual fit manually. We applied PULSE on EC, Cl, and d18O values for Nile water, Cairo, and progressively improved the parameters' values as new data was to obtain. The sexagesimal angles are to handle for plotting the sampling dates on the x-axis. The angle that corresponds to one day = 360°/356.24 days year-1 = 0.9856° day-1 = 0.0172 rad day-1. The regular ExcelÒ time and date-functions are also to use to assign the time-series sampling dates. The two optional parameters, b and g, are to use only to damp or expand a decayed or stretched future pulses; otherwise, the values of those secondary parameters should be zero. The parent of the fundamental PULSE formula is a flickering medical equation (Sinusoidal Amplitude-modulated Flicker Function) used in the optical-fitness experiments run for testing the human vision adaptation to light luminance, using the appropriate electrophysiological devices. PULSE stands alone in its hydrological category. This model offers a unique quantitative definition for the isotopic and hydrochemical pulses in successive waveforms, with adjustable values for its parameters, in response to the involved variable and the sampling dates. Measurements on Nile water, using daily river water sampling for several years, were to carry out. PULSE revealed its practical merits for an extensive Nile water data set. Such data are for d18O/V-SMOW ‰, EC dS/m, and Cl mg/l, PULSE works fine for such a riverine system. This application included a rare event of exceptional runoff suddenly imposed on Cairo Nile water composition by a scarce flash thunderstorm, where unusual waveforms were to assign to the isotopic and chemical trails of such abnormal runoff in the Sahara. Such a rare event was to use to get a backward look to the paleo-hydrology of the River Nile water composition in Egypt.
The isotopic compositions, electrical conductivity (EC), and ion concentrations frequently change with time in river water worldwide, on various time scales. Periodicity is also known for precipitation and other aqueous inputs. The time-series follow up of such temporal variations is usually to proceed by many hydrologists. The major purpose is to gain a thorough understanding of the underlying phenomena and to plot the data accurately. However, there is no appropriate formula for the graphic illustration and mathematical expression of such time-dependent fluctuations other than the complicated Fourier Series. Also, the use of the standard trigonometric sinusoidal function is not possible due to constraining the output of the values between +1 and -1. In contrast, the isotopic compositions require negative and positive values on the y-axis corresponding to time on the -x-axis, while the hydrochemical concentrations only admit positive values. These constraints are entirely void in the flexible waveform PULSE model proposed in this work. In this model, we introduce a modified sinusoidal formula that has the exciting capability of freely controlling the graphic waveform, in a highly accommodating way, for plotting the time-series isotopic and hydrochemical pulses in conformity with field observations. Three main parameters, and two optional secondary parameters, are to use in our model, open to modification. The model is to use in Excel®, whose SOLVER built-in macro may give the approximate values for the main parameters. Such values are then to improve to get the waveform best visual fit manually. We applied PULSE on EC, Cl, and δ18O values for Nile water, Cairo, and progressively improved the parameters' values as new data was to obtain. The sexagesimal angles are to handle for plotting the sampling dates on the x-axis. The angle that corresponds to one day = 360°/365.24 day-1 = 0.9856° day-1 = 0.0172 rad day-1. The standard Excel® time and date-models are also to use to assign the time-series sampling dates. The two optional parameters, β and γ, are to use only to damp or expand a decayed or stretched future pulses; otherwise, the values of those secondary parameters should be zero. The far parent of our fundamental PULSE formula is a three-parameter flickering medical equation (Sinusoidal Amplitude-modulated Flicker Model) used in the optical-fitness experiments run for testing the human vision adaptation to light luminance, using the appropriate electrophysiological devices. PULSE stands alone in its hydrological category. This model offers a unique quantitative definition for the isotopic and hydrochemical pulses in successive waveforms, with adjustable values for its parameters, in response to the involved variable and the sampling dates. Measurements on Nile water, using daily river water sampling for several years, were to carry out. PULSE revealed its practical merits for an extensive Nile water data set. Such data are for δ18O/V-SMOW ‰, EC dS m-1, and Cl mg l-1, PULSE works fine for such a riverine system. This application included a rare event of exceptional runoff suddenly imposed on Cairo Nile water composition by a scarce flash thunderstorm, where unusual waveforms were to assign to the isotopic and chemical trails of such abnormal runoff in the Sahara. Such a rare event was to use to get a backward look to the paleo-hydrology of the Nile water composition in Egypt.
The quantitative distribution of atmospheric vapor mixture, AVM, into three distinguished vapor endmembers is lacking in the literature. This work fills such a gap. The isotope ratio, d18OL, of rainwater in Winter, and artificial condensates in Summer, gave the 18OV contents of local AVMs at temperature-dependent equilibrium, downtown Cairo city, Nile Delta apex. We used our models, TIMAM, CLAW, and SIGNALS to process the d18OV and the commensurate specific humidity, S, values in several AVM data sets for determining the percent and mass contributions of three moisture origins and their temporal waveforms. The proportions and masses revealed Marine vapor dominance, followed by evapotranspiration. By far, the free Troposphere source showed a slight input. The quota of each constituent manifests a delayed waveform vs. AVM d18O influx, which shows a diurnal peak and a nocturnal tunnel. The moderate ET percent inputs in Winter, and by daytime, impose significant AVM 18O enrichment. In contrast, the high Maritime vapor inputs in Summer, and by night, stand behind the depleted AVM 18O content. The relationships between the mass input of each source and the AVM isotope ratio show significant dispersion for the negative trend of the diurnal-nocturnal Marine vapor in the two seasons. Such a high scattering is due to the mingling of northern wind-gust diurnal convection (marked by low Marine vapor input) and northern steady nocturnal advection (characterized by high Marine vapor input). Marine vapor waveform has a 12-hour time-lag by the intertwining of turbulent diurnal transmission, and steady nocturnal transport, through the long trajectory (180 km) from the Mediterranean coast to Cairo. In contrast, the relationships between ET mass input and AVM isotope ratio, on the one hand, and between the Troposphere vapor mass input and AVM isotope ratio, on the other hand, manifest low-dispersion positive and negative regressions, respectively. Such a low dispersion is due to the short transport pathway, the narrow range of the biological input (that increases only by daytime), and sharp Troposphere downdraft (moving northward in Winter but southward in Summer). Also, the ET waveform has a Zero-hour time-lag, like that of the Tropospheric vapor. Albeit the low S value of the Troposphere vapor pole, its impact on the AVM isotopic depletion is significant due to its extremely shallow 18O content. The increase of the Tropospheric input at low AVM S values is related to regional drought, as expected. The high S values, of Marine and biotic origins, usually go with temperature apogees, especially in Summertime, as anticipated. The used models help in improving the time-series simulation of evaporation runs, since using seasonal d18OV and S markers is better than using a snapshot. The ternary-vapor-source allocation procedure is a breakthrough in isotope hydrology. This thoroughly useful procedure will prove its ultimate benefits when the users get CRDS laser-controlled devices for the continuous measurements of the isotopic ratios in the local AVMs.
The isotopic compositions, electrical conductivity (EC), and ion concentrations frequently change with time in river water worldwide, on various time scales. Periodicity is also known for precipitation and other aqueous inputs. The time-series follow up of such temporal variations is usually to proceed by many hydrologists. The major purpose is to gain a thorough understanding of the underlying phenomena and to plot the data accurately. However, there is no appropriate formula for the graphic illustration and mathematical expression of such time-dependent fluctuations other than the complicated Fourier Series. Also, the use of the standard trigonometric sinusoidal function is not possible due to constraining the output of the values between +1 and -1. In contrast, the isotopic compositions require negative and positive values on the y-axis corresponding to time on the -x-axis, while the hydrochemical concentrations only admit positive values. These constraints are entirely void in the flexible waveform PULSE model proposed in this work. In this model, we introduce a modified sinusoidal formula that has the exciting capability of freely controlling the graphic waveform, in a highly accommodating way, for plotting the time-series isotopic and hydrochemical pulses in conformity with field observations. Three main parameters, and two optional secondary parameters, are to use in our model, open to modification. The model is to use in ExcelÒ, whose SOLVER built-in macro may give the approximate values for the main parameters. Such values are then to improve to get the waveform best visual fit manually. We applied PULSE on EC, Cl, and d18O values for Nile water, Cairo, and progressively improved the parameters' values as new data was to obtain. The sexagesimal angles are to handle for plotting the sampling dates on the x-axis. The angle that corresponds to one day = 360°/356.24 days year-1 = 0.9856° day-1 = 0.0172 rad day-1. The standard ExcelÒ time and date-models are also to use to assign the time-series sampling dates. The two optional parameters, b and g, are to use only to damp or expand a decayed or stretched future pulses; otherwise, the values of those secondary parameters should be zero. The far parent of our fundamental PULSE formula is a three-parameter flickering medical equation (Sinusoidal Amplitude-modulated Flicker Model) used in the optical-fitness experiments run for testing the human vision adaptation to light luminance, using the appropriate electrophysiological devices. PULSE stands alone in its hydrological category. This model offers a unique quantitative definition for the isotopic and hydrochemical pulses in successive waveforms, with adjustable values for its parameters, in response to the involved variable and the sampling dates. Measurements on Nile water, using daily river water sampling for several years, were to carry out. PULSE revealed its practical merits for an extensive Nile water data set. Such data are for d18O/V-SMOW ‰, EC dS m-1, and Cl mg l-1, PULSE works fine for such a riverine system. This application included a rare event of exceptional runoff suddenly imposed on Cairo Nile water composition by a scarce flash thunderstorm, where unusual waveforms were to assign to the isotopic and chemical trails of such abnormal runoff in the Sahara. Such a rare event was to use to get a backward look to the paleo-hydrology of the Nile water composition in Egypt.
The quantitative distribution of atmospheric vapor mixture, AVM, into three distinguished vapor end-members is lacking in the literature. This work fills such a gap. The isotope ratio, d18OL, of rainwater in Winter, and artificial condensates in Summer, gave the 18OV contents of local AVMs at temperature-dependent equilibrium, downtown Cairo city, Nile Delta apex. We used our models, SIMAM, CLAW, and SIGNALS to process the d18OV and the commensurate specific humidity, S, values in several AVM data sets for determining the percent and mass contributions of three moisture origins and their temporal waveforms. The proportions and masses revealed Marine vapor dominance, followed by evapotranspiration. By far, the free Troposphere source showed a slight input. The quota of each constituent manifests a delayed waveform vs. AVM d18O influx, which shows a diurnal peak and a nocturnal tunnel. The moderate ET percent inputs in Winter, and by daytime, impose significant AVM 18O enrichment. In contrast, the high Maritime vapor inputs in Summer, and by night, stand behind the depleted AVM 18O content. The relationships between the mass input of each source and the AVM isotope ratio show significant dispersion for the negative trend of the diurnal-nocturnal Marine vapor in the two seasons. Such a high scattering is due to the mingling of northern wind-gust diurnal convection (marked by low Marine vapor input) and northern steady nocturnal advection (characterized by high Marine vapor input). Marine vapor waveform has a 12-hour time-lag by the intertwining of turbulent diurnal transmission, and steady nocturnal transport, through the long trajectory (180 km) from the Mediterranean coast to Cairo. In contrast, the relationships between ET mass input and AVM isotope ratio, on the one hand, and between the Troposphere vapor mass input and AVM isotope ratio, on the other hand, manifest low-dispersion positive and negative regressions, respectively. Such a low dispersion is due to the short transport pathway, the narrow range of the biological input (that increases only by daytime), and sharp Troposphere downdraft (moving northward in Winter but southward in Summer). Also, the ET waveform has a Zero-hour time-lag, like that of the Tropospheric vapor. Albeit the low S value of the Troposphere vapor pole, its impact on the AVM isotopic depletion is significant due to its extremely shallow 18O content. The increase of the Tropospheric input at low AVM S values is related to regional drought, as expected. The high S values, of Marine and biotic origins, usually go with temperature apogees, especially in Summertime, as anticipated. The used models help in improving the time-series simulation of evaporation runs, since using seasonal d18OV and S markers is better than using a snapshot. The ternary-vapor-source allocation procedure is a breakthrough in isotope hydrology. This thoroughly useful procedure will prove its ultimate benefits when the users get CRDS laser-controlled devices for the continuous measurements of the isotopic ratios in the local AVMs.
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