River Nile water samples were to collect daily, by mid-day, at the middle of the Nile course, one kilometer south of Cairo University, starting late October 2016 and up to the present day. Sampling will be further going for one extra year span. Each water sample was to collect in two fractions, the first to fill a half-liter clean plastic bottle, while the second is a 13.80 ml fraction in a small glass vial, both filled to the top and carefully plugged. Water in the small vials was to reserve for the isotopic measurements, d18O and d2H (not shown in this work), whereas the half-liter bottles were to use in EC and pH measurements and the rest of their water volumes were to conserve in the refrigerator for later chemical analysis. The electrical conductivity, EC, and the pH readings were immediately obtained by HannaÔ Instruments double-electrode, whose reading was to automatically correct to 25°C. The chloride ion concentrations were also to measure using HannaÔ specific-ion electrode. Such immediate measurements and posterior chemical analyses were to run using the standard atomic absorption and titration methods at Cairo University and the Central Laboratory of the Ministry of Water Resources, Kanater Khayria Research Kernel, 20 km northwest of Cairo.
The determinations of the isotopic ratios, d180 and d2H, in the Nile water samples were to run abroad, after international shipment to Tunisia. Such determinations were to obtain using laser quenching (ABB LGR-ICOS Los Gatos Research Tunable-Diode Laser Analyzer) known as (Off-Axis Integrated Cavity Output Spectroscopy, OA-ICOS) at the Radio-Analyses et Environnement, LRAE, École Nationale d'Ingénieurs, ENIS), Sfax, Tunisia, in duplicates. In parallel with the daily in situ fresh Nile water sampling and measurements, lab experiments were to run (in the period April 18 to September 17, 2017), at Cairo University, to follow the changes in the EC and isotopic compositions (d18O and d2H) of Nile water stocks stored in multiple evaporation pans, first in the lab, and then in a class-A pan in the field, at the Water Resources Research Station, Zankaloune, Zagazeig, 100 Km northeast of Cairo, in Winter and Summertime of the year 2020. The chemical and isotopic changes in Nile water during non-steady-state evaporation experiments can give a further interpretation of the results of the daily Nile water samples collected, studied, and plotted in several years at Cairo, where the river water is only subject to steady-state evaporation. However, the detailed findings of the non-steady-state evaporation experiments are to publish elsewhere.
Fundamental Formula for PULSE Waveform Model
The PULSE waveform model (Eq 1.A and B, Eq. 2, and Fig 1) was to develop on ExcelÔ, where the built-in SOLVER macro was to run to obtain the values of model parameters by the minimization of the sum of squares of deviation. The divergence is between the daily measured EC and the calculated f (t), both in dS m-1 (or between the observed and predicted d18O/V-SMOW ‰, or the same again but for Cl ion concentrations). The computed f (t) was initially for the luminance, in the medical formula, WEB 1, that we have initially adopted to develop our PULSE carrier-signal model. Continuous posterior adjustments of the obtained values for model parameters were to manually carry out to get visual curve best fit as more EC values, Cl concentrations, and d18O data-point ratios were to add to the spreadsheet progressively. The PULSE model periodic-waveform is to use to generate the frequency response useful in the interpretation of the time-dependent hydrochemistry and isotope hydrology data sets. The model calculates the signal value, f(t) corresponding to each data-point, using either three parameters (L, m, and T) or five parameters (when the optional parameter b is to include, with its start factor g as internal modifier) in the periodic-time-versions (Eq 1.A and B) and the frequency-version (Eq 2). The start factor, g, is not shown in the equations since it is an internal modifier of the parameter b.
f(t) = L * [1 + (m - (mb /100)) * (sin(q/(T * 0.985547362)))]…………………… (1.A)
f(t) = L + (L * (m - (mb /100)) * (sin(q/(T * 0.985547362))))………………… (1.B)
f (t) = L + (L * (m - (mb /100)) * (sin(q * (f r * (1/0.985647362))))……………… (2)
L average of the pulse, mg l-1, or dS m-1, for ionic concentrations and EC, respectively, or in per mil for isotopes (e.g., d18O). The L value is constant for the record, and its unit is as for f(t),
m modulation ratio (called contrast) = (the maximum minus the minimum) divided by (the maximum plus the minimum), where the maximum and minimum values are for the signal value, f(t). on the y-axis, 0<m<1, in response to the angular frequency of the carrier input w, on the x-axis. However, m in the medical formula is the ratio of direct current, dc, to alternating current, ac, for the vision-test devices used in electrophysiological measurements, dimensionless. The product mL is the amplitude that shows the climax of the peak above the average value,
T periodic time = q/w = 2p/w, year,
t time, days, expressed in angle q , rad, in our formula (seconds in the medical formula),
q the angle used to express the date of the concerned day, = w t, and 2p = w T, rad,
w carrier input angular frequency, q/t = 2p/T = 2p f r, rad y-1 (rad sec-1 in the medical formula),
f r carrier frequency, y-1 (Hz in the medical formula),
b damping parameter used to modify the value of m partially. The b parameter is to further adjust the value of m via the start factor modifier, g, where b and g values are to control manually down the column used in computing f(t) in the spreadsheet, dimensionless,
g start factor used in modifying the value of the parameter b, dimensionless.
The roles of the primary parameters are
1- Amplitude modulation (modification) ratio. This parameter controls the peak amplitude, mL, and the peak-to-trough amplitude, 2mL, of the modulating signal (here the transmitted EC information) to perceive on the y-axis. The user may manually increase (modulate) or decrease (demodulate) the strength of the EC signal to force the waveform to fit the observed EC data-points tightly, after using its first value predicted by SOLVER.
2- Average of the modulating signal. This parameter shifts the vertical position of the whole modulating signal (here the EC information) relative to the y-axis. The value of the average parameter is first to insert freely and then to calculate as half of the two y-axis readings for the peak and trough of the waveform when the diagram gets populated with data-points
3- Periodic Time of the carrier signal. Changing the T value will result in changing the carrier frequency, f r = 1/T, that expresses the number of pulses of the waveform per year (to perceive on the x-axis). The T parameter controls the horizontal locus and pace, of the entire waveform pulses, on any diagram showing the relationship between the concerned variable and date. The value of the carrier frequency, f r, relates to the angular frequency of carrier input w, by double pi.