Hydrostatic Densitometer for Monitoring Density in Freshwater to Hypersaline Water Bodies

water

Article Hydrostatic Densitometer for Monitoring Density in Freshwater to Hypersaline Water Bodies

Ziv Mor 1,2 , Hallel Lutzky 1 , Eyal Shalev 1 and Nadav G. Lensky 1,*

1 Geological Survey of Israel, Jerusalem 9692100, Israel; [email protected] (Z.M.); [email protected] (H.L.); [email protected] (E.S.) 2 The Fredy and Nadine Herrmann Institute of Earth Sciences, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel * Correspondence: [email protected]

Abstract: Density, temperature, salinity, and hydraulic head are physical scalars governing the dynamics of aquatic systems. In coastal aquifers, lakes, and oceans, salinity is measured with conductivity sensors, temperature is measured with thermistors, and density is calculated. However, in hypersaline brines, the salinity (and density) cannot be determined by conductivity measurements due to its high ionic strength. Here, we resolve density measurements using a hydrostatic densitometer as a function of an array of pressure sensors and hydrostatic relations. This system was tested in the laboratory and was applied in the Dead Sea and adjacent aquifer. In the field, we measured temporal variations of vertical profiles of density and temperature in two cases, where water density varied vertically from 1.0 × 103 kg·m−3 to 1.24 × 103 kg·m−3: (i) a borehole in the coastal aquifer, and (ii) an offshore buoy in a region with a diluted plume. The density profile in the borehole evolved with time, responding to the lowering of groundwater and lake levels; that in the lake demonstrated the dynamics of water-column stratification under the influence of freshwater discharge and atmospheric forcing. This method allowed, for the first time, continuous monitoring of density profiles in Citation: Mor, Z.; Lutzky, H.; Shalev, hypersaline bodies, and it captured the dynamics of density and temperature stratification. E.; Lensky, N.G. Hydrostatic Densitometer for Monitoring Density Keywords: hydrostatic densitometer; density measurement; hypersaline brine; coastal aquifer; in Freshwater to Hypersaline Water fresh–saline water interface; diluted plume Bodies. Water 2021, 13, 1842. https://doi.org/10.3390/w13131842

Academic Editor: Nicolò Colombani 1. Introduction Density, temperature, salinity, and equivalent freshwater hydraulic head are physical Received: 15 June 2021 scalars governing the dynamics of aquatic systems [1–5]. Characterization of spatiotem- Accepted: 29 June 2021 Published: 1 July 2021 poral variations in these scalars is crucial for understanding stratiﬁcation and circulation in aquatic systems [6–12]. Density is typically determined indirectly by measurements of

Publisher’s Note: MDPI stays neutral temperature and salinity, which are then used in an equation of state; the relationship of with regard to jurisdictional claims in conductivity to salinity and the equation of state have to be calibrated for each water–ion published maps and institutional affil- composition [10,13–16]. The temperature field is characterized using standard sensors iations. (thermistors, thermocouples, fiber optics) which are distributed spatially according to requirements and availability, and they can be measured temporally at a rate of up to a few times a second; these sensors are insensitive to water composition (e.g., [9,17]). Salinity is typically measured indirectly by electrical conductivity, a very practical and rapid measurement. However, the relationship between salinity and conductivity is sensitive to water Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. composition and does not apply to hypersaline brines where the salinity–conductivity This article is an open access article relationship is no longer monotonic [13]. Alternatively, salinity in hypersaline brine can distributed under the terms and be measured by collecting water samples at various depths and determining their ionic conditions of the Creative Commons composition in the laboratory, or by measuring the density of water samples from which Attribution (CC BY) license (https:// quasi-salinity is determined, i.e., the density exceeding the freshwater standard reference −3 creativecommons.org/licenses/by/ density of ~1000 kg·m at a reference temperature [10,13–16]. The accuracy of the den- 4.0/). sitometry approach is three orders of magnitude higher than that of ionic composition

Water 2021, 13, 1842. https://doi.org/10.3390/w13131842 https://www.mdpi.com/journal/water Water 2021, 13, 1842 2 of 15

(~0.001% and ~1%, respectively). However, the need to collect water samples has several disadvantages: a long and expensive procedure, a low vertical resolution that depends on the number of the sampling bottles, and a low temporal resolution limited by the rate of resampling. To improve the spatiotemporal resolution of density/salinity measurements, we developed the hydrostatic densitometer, a system for continuous measurement of in-situ vertical profiles of density (and temperature), from which salinity can be deduced by an equation of state. The principle of obtaining density measurements from vertical pressure differences is used in laboratory processes (e.g., dual-bubbler and d/p cells, see chapter 6.4 in [18]), with some inventions appearing more than 50 years ago (e.g., patent US3422682A). However, to the best of our knowledge, those apparatuses were designed to measure density in an open/closed tank in the laboratory; none were designed to measure density in the field (e.g., a water body, borehole), and they do not provide a solution for measuring several points at once for continuous vertical-profile monitoring. This paper is structured as follows: Section2 presents the theoretical considerations of the hydrostatic densitometer and its expected performance. Section3 describes the instruments used in this paper. Section4 presents the design of the laboratory tests and the design and settings of the field campaigns conducted in the Dead Sea. In Section5, we give the results of the laboratory tests and observations from a borehole in a coastal aquifer and a diluted plume in the hypersaline lake, and then discuss the challenges in marine applications. In Section6, we summarize our findings and present practical conclusions regarding the hydrostatic densitometer.

2. Theoretical Considerations of the Hydrostatic Densitometer We resolved in situ density utilizing pressure sensors and hydrostatic relations as described below (see Figure1 for notation and setup). The measured pressure at depth z (Figure1B) is the sum of the atmospheric pressure ( Patm), the hydrostatic pressure (Phyd ), and the dynamic stress (σ).

P(z) = Patm + Phyd(z) + σ(z). (1)

The hydrostatic pressure in the water column is determined as

Z Z Phyd(z) = ρ(z)gdz, (2) 0

where g is the acceleration due to gravity, and ρ(z) is the water density along the water column (at water surface, z = 0). The pressure difference between two vertically separated sensors located at depths d1 and d2 (Figure1A), eliminating the atmospheric pressure and the contribution of hydrostatic pressure above d1, is expressed as

Z d2 ∆P(z = d) = P (z = d2) − P (z = d1) = g ρ(z)dz + δσ, (3) d1 where δσ is the difference in the dynamic stresses between d1 and d2. The average density, ρ, at depth z = d, between d2 and d1 (Figure1A), is expressed as

1 Z d2 ρ(z = d) = ρ(z)dz. (4) d2 − d1 d1 If the dynamic stresses at d1 and d2 are similar and/or small compared to the hydro- R d2 static pressure, i.e., δσ g d1 ρ(z)dz, then Equations (3) and (4) yield

∆P (z = d) =∼ ρ(z = d)·g·H, (5) Water 2021, 13, x FOR PEER REVIEW 3 of 17

where H = d2 − d1, and z = d is between d1 and d2. Thus, the average density at depth z = d Water 2021, 13, 1842 is given below (Figure 1C). 3 of 15

∆푃 (푧 = 푑) 𝜌̅(푧 = 푑) = (6) 𝑔 ∙ 퐻 where H = d2 − d1, and z = d is between d1 and d2. Thus, the average density at depth z = d is givenThe precision below (Figure of the 1densityC). measurement, 훿𝜌̅(푧 = 푑), depends on the resolution of ∆P (z = d) the pressure measurement and on ρthe(z =verticald) = distance between the sensors, H (and on(6) the value of g at the site). For a given pressure-gsensor·H resolution (훿∆푃), the density precisionThe is precisionexpressed ofasthe density measurement, δρ(z = d), depends on the resolution of the pressure measurement and on the vertical distance between the sensors, H (and on the ∆푃 (푧 = 푑) + 훿∆푃 value of g at the site). For𝜌̅(푧 a= given푑) + pressure-sensor훿𝜌̅(푧 = 푑) = resolution (δ∆P.) , the density precision(7) is expressed as 𝑔 ∙ 퐻 ∆P (z = d) + δ∆P Thus, there is an inverseρ(z = relationd) + δρship(z = betweend) = the density precision. and the vertical (7) g·H distance resolution (Figure 2). Thus, there is an inverse relationship between the density precision and the vertical 훿∆푃 distance resolution (Figure2). 훿𝜌̅(푧 = 푑) ≅ . (8) 𝑔δ∙∆퐻P δρ(z = d) =∼ . (8) g·H

Figure 1. Schematic illustration of the setup of the hydrostatic densitometer. (A) Array of pressure Figuresensors 1. Schematic along a submerged illustration vertical of the chain.setup Theof the pressure hydrostatic sensors densitometer. represented ( byA) blackArray dots of pressure are located sensorsat z = alongd1 and a submergedz = d2 with verti a verticalcal chain. separation The pressure of H; z sensors= d is the represented midpoint betweenby black the dots sensors. are located(B) Pressure–depth at z = d1 and z = proﬁle; d2 with pressures a vertical at separationz = d1 and zof= Hd;2 zare = d representedis the midpoint with between black dots. the (sensorsC) Density. (B) Pressure–depth profile; pressures at z = d1 and z = d2 are represented with black dots. (C) Density proﬁle resolved from the pressure sensor and hydrostatic relations (Equations (4) and (6)). The profile resolved from the pressure sensor and hydrostatic relations (Equations (4) and (6)). The average density (Equation (6)) at depth z = d is represented with a black dot. average density (Equation (6)) at depth z = d is represented with a black dot.

Water 2021, 13, 1842 4 of 15 Water 2021, 13, x FOR PEER REVIEW 4 of 17

Figure 2.FigureResolution 2. Resolution of the hydrostatic of the hydrostatic proﬁler basedprofiler on based Equation on Eq (8).uation The density(8). The precisiondensity precision and the vertical-distanceand the resolutionvertical are anticorrelated,-distance resolution and the are performance anticorrelated, depends and on the the performance pressure sensor depends resolution. on the We pressure present sensor the solution of resolution. We present the solution of Equation (8) for three common pressure resolutions in typical Equation (8) for three common pressure resolutions in typical pressure transducers. Using this diagram, one can examine pressure transducers. Using this diagram, one can examine the feasibility of using the hydrostatic the feasibility of using the hydrostatic densitometer for a speciﬁc system with a given density gradient. densitometer for a specific system with a given density gradient. 3. Methods 3. Methods 3.1. Density Measurements Using the Hydrostatic Densitometer 3.1. Density MeasurementsTo explore Using thethe Hydrostatic vertical distribution Densitometer of the water density in a selected location, one To explore needsthe vertical to determine distribution the vertical of the positionwater density and the in numbera selected of sensorslocation, in one the hydrostatic needs to determinedensitometer the vertical (Figures position1A and and2 , the Equation number (8)). of Wesensors used an in arraythe hydrostatic of series 36XiW PAA densitometer (Figure0.8–2.3s 1A bar and pressure 2, Equation (and temperature) (8)). We used transducers an array of (Keller, series Winterthur,36XiW PAA Switzerland). 0.8– The −3 2.3 bar pressurepressure (and temperature) accuracy of the transducers transducers (Keller, is 1.15 × Winterthur,10 bar (corresponding Switzerland to). 0.05% The of full scale, ◦ −5 pressure accuracy2.3 of bar) the andtransducers the temperature is 1.15 × accuracy 10−3 bar is(corresponding 0.1 C. The pressure to 0.05% resolution of full scale, is 1.15 × 10 bar ◦ 2.3 bar) and the (0.0005%temperature of full accuracy scale) and is 0.1 the °C. temperature The pressure resolution resolution is 0.01 is C.1.15 × 10−5 bar (0.0005% of full scale)The and natural the temperature environment resolution is inherently is 0.01 noisy; °C. therefore, to differentiate between background noise and the signal, one can perform measurements at a high frequency and The natural environment is inherently noisy; therefore, to differentiate between carry out a statistical time-series analysis. We chose to measure at 10 Hz, which is the background noise and the signal, one can perform measurements at a high frequency and highest possible frequency for the measuring system used here, and we performed a 10 min carry out a statistical time-series analysis. We chose to measure at 10 Hz, which is the highest possible frequency for the measuring system used here, and we performed a 10 min average, which is the expected rate of environmental change. The data were recorded using a data logger (Model CR6, Campbell Scientific Inc., Logan, UT, USA).

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average, which is the expected rate of environmental change. The data were recorded using a data logger (Model CR6, Campbell Scientiﬁc Inc., Logan, UT, USA).

3.2. Other Methods for Density Determination To compare the density values from the hydrostatic densitometer, we measured density with the following commercial instruments: (i) an accurate laboratory density meter, oscillating U-tube, DMA 5000 (Anton Paar, Graz, Austria) with an accuracy of ±0.005 kg·m−3 (following [9,15,16]); (ii) a portable density meter, oscillating U-tube, DMA 35 (Anton Paar, Graz, Austria), with an accuracy of 1.0 kg·m−3; (iii) density measurements in the ﬁeld, performed with a portable submersible density meter DM-250 (Lemis, Montgomery, TX, USA), with accuracy up to ±0.3 kg·m−3 and resolution of 0.1 kg·m−3.

4. Experimental Design and Regional Setting 4.1. Verification of the Hydrostatic Densitometer from Freshwater to Hypersaline Brine As a preliminary step, before placing the hydrostatic densitometer system in the field, the system’s performance was examined in a set of controlled laboratory experiments. We tested the accuracy of the hydrostatic densitometer compared to commercial densitometers for water salinities ranging from Dead Sea brine (1242 kg·m−3) to distilled freshwater (996 kg·m−3). The pressure sensors were placed inside a specially designed aquarium to measure and examine all relevant pairs of sensors (i.e., the pairs that were placed in the field; see Section 4.3); five sensors were placed in the lower part of the aquarium, and five sensors were placed in the upper part, 1 m above (Figure3A). We started the experiment with the saltiest brine (halite-saturated Dead Sea brine) and diluted it in 10 steps of ~25 kg·m−3 until distilled freshwater was obtained. Each segment of the experiment lasted ~15 min, following complete stirring and homogenization of the water in the aquarium, where pressure was measured at a rate of 10 Hz, i.e., ~104 measurements per experimental step. For each water-dilution segment, (i) water was removed from the aquarium by a pump that sucked water from the bottom of the aquarium, (ii) distilled water was added to the aquarium bottom through a pipe, (iii) the water was mixed using the pump sucking water from the bottom and feeding it to the top to homogenize the brine, and (iv) the density of the brine was measured independently with the DMA 35 portable density meter, from both the bottom and top of the aquarium, to verify that homogeneity was achieved and for comparison with the hydrostatic densitometry approach. The experiment was performed on 24 May 2020.

4.2. Sensitivity of the Hydrostatic Densitometer to Variations in Temperature and Pressure We tested the sensitivity of the hydrostatic densitometer to variations in pressure and temperature. The tested range of temperature variations was that expected at the field sites (25–34 ◦C), and the tested pressure variations were up to a water depth of ~10 m (the maximum height of the experimental device). These tests enabled us to determine the vertical position of the sensors in the best overall performers, i.e., to choose the optimal sensor couples along the array of sensors from all possible couples. For the pressure-sensitivity test, the 10 pressure sensors (36XiW) were placed at the bottom of a 10 m column (Figure3B). Water was filled to the top and was removed to ~1 m intervals (0.1 bar), from 2.0 bar to 0.9 bar. The experiment was performed on 6 July 2020. For the temperature-sensitivity test, the 10 sensors were placed in a plastic pail filled with freshwater, inside a shaker incubator with controlled temperature (Qmax4000, Thermo Fisher, Waltham, MA, USA) (Figure3C). The temperature was varied from 25 ◦C to 34 ◦C at 1 ◦C intervals (Figure3C ), and each interval was held for a few hours to achieve thermal equilibrium. The experiment was performed from 11–13 May 2020. Water 2021, 13, 1842 6 of 15 Water 2021, 13, x FOR PEER REVIEW 6 of 17

Figure 3.3. LaboratoryLaboratory experimentexperiment design. (A) VerificationVerification ofof thethe hydrostatichydrostatic densitometerdensitometer inin waterwater density rangingranging fromfrom freshwaterfreshwater (FW) (FW) to to hypersaline hypersaline brine brine (DS (DS brine). brine) The. The sensors sensors were were placed placed on on a steela steel cage cage inside inside a a water water tank, tank, in in two two groups groups of of five five with with 1 1 m m vertical vertical separation. separation. ((BB)) SensitivitySensitivity ofof thethe hydrostatichydrostatic densitometerdensitometer to to variations variations in in pressure. pressure. The The 10 10 sensors sensors were were placed placed at at the the bottom bottom of of a a 10 m long column filled with freshwater. (C) Sensitivity of the hydrostatic densitometer to 10 m long column filled with freshwater. (C) Sensitivity of the hydrostatic densitometer to variations variations in temperature. The 10 sensors were placed in a pail of water inside a shaker incubator. in temperature. The 10 sensors were placed in a pail of water inside a shaker incubator.

4.3. Field Campaign Design and Regional Setting Our ﬁeldfield campaigns were were conducted conducted at at a a buoy buoy in in the the Dead Dead Sea Sea and and inin a borehole a borehole in inthe the Dead Dead Sea Sea coastal coastal aquifer. aquifer. The The Dead Dead Sea Sea is a is hypersaline a hypersaline terminal terminal lake lake located located on the on thelowest lowest land land surface surface on on Earth Earth (Figure (Figure A1 A1, Appendix, Appendix AA) )which which,, in in the the last last decade, decade, has has experiencedexperienced aa declinedecline inin lakelake levellevelat at a a rate rate of of ~1 ~1 m m·year·year−−11 [[19,20]19,20].. The DeadDead SeaSea salinitysalinity and density areare 340340 gg··LL −11 andand 1242 1242 kg kg·m·m−3−, 3respectively., respectively.

4.3.1. The Borehole Measuring Setup The fieldfield campaigncampaign inin thethe DeadDead SeaSea coastalcoastal aquiferaquifer waswas conductedconducted wherewhere significantsignificant changeschanges are expectedexpected to occuroccur withinwithin aa shortshort timetime becausebecause ofof thethe rapidrapid dropdrop ofof thethe DeadDead Sea’sSea’s lakelake level.level. The Dead SeaSea andand thethe adjoiningadjoining groundwatergroundwater systemsystem areare hydraulicallyhydraulically interconnected,interconnected, as as reflected reflected by bythe relativelythe relatively rapid rapid (a few (a days) few groundwater days) groundwater level response level toresponse level changes to level of thechanges Dead of Sea the [21 Dead]. The Seafresh–saline [21]. The water fresh interface–saline water also responds interface to also the

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droprespond in thes to lake’s the drop level in and the thelake’s eastward level and shift the of eastward the Dead shift Sea shoreline,of the Dead resulting Sea shore in rapidline, ﬂushingresulting of in the rapid Dead flushing Sea coastal of the aquiferDead Sea [22 coastal]. aquifer [22]. TheThe array of pressure sensors sensors was was installed installed in in the the EG26 EG26 borehole borehole (2” (2” diameter diameter pipe) pipe) (Figure(Figure4 A–C)4A–C) for for 84 84 days, days, from from 13 13 August August to to 5 November5 November 2020. 2020. EG26 EG26 is is currently currently (2021) (2021) lo- catedlocated ~70 ~70 m fromm from the Dead the Dead Sea shoreline. Sea shoreline. Following Following Equation Equation (8) and our(8) priorand knowledge our prior ofknowledge the vertical of structurethe vertical of the structure borehole of the water borehole column water [23], column the hydrostatic [23], the densitometer hydrostatic sensorsdensitometer were placedsensors at were 28 m, placed 28.5 m,at 3028 m, 3128.5 m, m, 34 30 m, m, and 31 35m, m34 belowm, and the 35 surface,m below along the asurface water, along column a water of ~8 column m (Figure of ~84 C).m (Figure The barometric 4C). The barometric pressure waspressure measured was measured at 12 m belowat 12 m the below surface, the surface, inside theinside borehole. the borehole. A water A water level level of 26.69 of 26.69 m below m below the surfacethe surface was measuredwas measured before before the system’s the system installation’s installation using using a manual a manual water water level level meter meter (model (model 101, Solinst,101, Solinst, Georgetown, Canada). ON, Canada).

FigureFigure 4. 4.( A(A)) EG26 EG26 borehole. borehole. ((BB)) SchematicSchematic illustrationillustration of EG26 borehole. ( (CC)) Schematic Schematic illustration illustration of of the the hydrostatic hydrostatic densitometer in the EG26 borehole. (D) Ein Feshkha (EF) research buoy. (E) Schematic illustration of EF buoy and the densitometer in the EG26 borehole. (D) Ein Feshkha (EF) research buoy. (E) Schematic illustration of EF buoy and the diluted plume due to freshwater inflow into the Dead Sea. The hydrostatic densitometer is represented by a dotted orange dilutedline. (F plume) Schematic dueto illustration freshwater of inflow the hydrostatic into the Dead densitometer Sea. The at hydrostatic the EF buoy. densitometer is represented by a dotted orange line. (F) Schematic illustration of the hydrostatic densitometer at the EF buoy. 4.3.2. The Dead Sea Diluted Plume Measuring Setup 4.3.2. The Dead Sea Diluted Plume Measuring Setup The second field campaign was conducted in the Dead Sea at the diluted plume fed by theThe Dead second Sea’s field largest campaign spring, was Ein conductedFeshkha (EF, in Figure the Dead A1 Sea, Appendix at the diluted A), discharging plume fed byaround the Dead 70 × 10 Sea’s6 m3 largest·year−1 through spring, Eina series Feshkha of ~10 (EF, tributaries Figure A1 along, Appendix ~1 km ofA shoreline), discharging [24]. × 6 3· −1 aroundThese point 70 sources10 m yearof freshwaterthrough inflows a series form of ~10 a diluted tributaries plume along that ~1spreads km of laterally shoreline over [24 ]. Thesethe Dead point Sea sources [8]. The of density freshwater difference inflows between form adiluted the inflowing plume freshwater that spreads and laterally the Dead over the Dead Sea [8]. The density difference between the inflowing freshwater and the Dead Sea brine is extreme, from 1.0 × 103 kg·m−3 to 1.24 × 103 kg·m−3. A schematic illustration of × 3 · −3 × 3 · −3 Seathe brineEF diluted is extreme, plume from setup 1.0 is shown10 kg inm Figureto 1.244E. 10 kg m . A schematic illustration of theTo EF measure diluted the plume plume setup dynamic is showns and in heat Figure fluxes4E. from it, we installed a research buoy ~250To m measureoffshore the the spring plume outflow dynamics at the and EF heat site fluxes (Figure from 4D, it,E). we The installed buoy is aanchored research with buoy ~250four mconcrete offshore blocks the spring(750 kg outflow each) at at15 the m EFwater site depth (Figure (Figure4D,E). 4E). The The buoy buoy is anchoredincludes withseveral four sensors concrete (above blocks and (750in the kg water each)); here at 15, we m present water depth data from (Figure the4 arrayE). The of pressure buoy in- cludessensors several (Figure sensors 4D–F), (above a two and-dimensional in the water); sonic here, we anemometer present data (WindSonic from the array, Gill of pressureInstruments sensors, UK (Figure), and 4aD–F), solar a radiation two-dimensional sensor (CNR4, sonic anemometer Kipp and Zonen(WindSonic, B.V., Gill the Instruments,Netherlands) Hampshire,(Figure 4D). UK), and a solar radiation sensor (CNR4, Kipp and Zonen B.V., Delft,The The hydrostatic Netherlands) densitometer (Figure4D). was installed on 3 February 2021. Following Equation (8) andThe our hydrostatic prior knowledge densitometer of the was vertical installed structure on 3 Februaryof the diluted 2021. plume Following [8], theEquation pressure (8) andsensors our were prior located knowledge at water of the depth verticals of 0.2 structure m, 0.6 m, of the1 m, diluted 2 m, 3 plumem, 4 m, [ 85], m, the 6 pressurem, 9 m, sensors were located at water depths of 0.2 m, 0.6 m, 1 m, 2 m, 3 m, 4 m, 5 m, 6 m, 9 m, and

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and 12.5 m; accordingly, the hydrostatic densitometer took measurements at water depths of 0.4 m, 0.8 m, 1.5 m, 2.5 m, 3.5 m, 4.5 m, 5.5 m, 7.5 m, and 10.7 m (Figure 4F).

5. Results and Discussion 5.1. Laboratory Experiment and Sensitivity Tests The performance of the hydrostatic densitometer (Equation (6)) was demonstrated in the laboratory using a set of nine pairs of pressure sensors (i.e., the pairs that were placed in the field; see Section 4.3) produced by two groups of five sensors with a vertical separation of 1 m (Figure 3A). The hydrostatic pressure difference (Equation (5)) between the nine pairs throughout the entire experiment is presented in Figure 5B, and the density values, calculated from the pressure difference (Equation (6)), are shown in Figure 5A. The dilution steps are seen as a reduction in pressure difference and density with each successive experimental step (Figure 5A,B, respectively). Instrument noise in the pressure- Water 2021, 13, 1842 difference measurements was twice the declared instrument’s resolution (up to ~3 × 108 of−5 15 bar) and was small compared to the signal due to dilution (~0.02 bar), which means that, in this range, the sensors are very precise. Similarly, the calculated density between the experimental steps was ~25 kg·m−3 and the noise was ~0.3 kg·m−3. The accuracy of the 12.5 m; accordingly, the hydrostatic densitometer took measurements at water depths of hydrostatic densitometer can be evaluated when comparing, for each of the experimental 0.4 m, 0.8 m, 1.5 m, 2.5 m, 3.5 m, 4.5 m, 5.5 m, 7.5 m, and 10.7 m (Figure4F). steps, the density based on hydrostatic pressure with the density measurement by the 5.standard Results density and Discussion meter (Figure 5C). To evaluate the sensitivity of the hydrostatic densitometer (or the pressure 5.1.difference) Laboratory to variations Experiment in and temperature Sensitivity and Tests pressure in the deployment environment, we conductedThe performance sensitivity tests, of the presented hydrostatic in densitometerFigures A2 and (Equation A3 (Appendix (6)) was A) demonstrated, respectively. in theFor laboratory a temperature using range a set of of 25 nine–34 pairs °C, the of pressureoffset of the sensors pressure (i.e., thedifferences pairs that between were placed seven in theof the ﬁeld; nine see sensor Section pairs 4.3) producedwas within by twothe declared groups of resolution ﬁve sensors (less with than a vertical ±2.3 × separation10−5 bar) of(Figure 1 m (Figure A2A–F3,A).H, Appendix The hydrostatic A); two pressure pairs of differencesensors (Figure (Equation A2G,I (5)), Appendix between A the) were nine pairswithin throughout the declared the accuracy entire experiment (less than ± is2.3 presented × 10−3 bar) in and Figure within5B, 2 and–3 times the density the declared values, calculatedresolution from(6 × 10 the−5 pressurebar and 4.2 difference × 10−5 bar (Equation for 8 °C (6)),variations, are shown Figure in Figure A2G,I,5A. Appendix The dilution A, stepsrespectively). are seen Therefore, as a reduction the two in pairs pressure with differencehigher sensitivity and density to temperature with each variations successive experimentalwere located at step water (Figure depth5A,B,s with respectively). relatively small Instrument temperature noise variation in the pressure-differences (i.e., 5.5 m and measurements10.7 m water depth was in twice EF buoy the declared, respecti instrument’svely; see Figure resolution 4F). (up to ~3 × 10−5 bar) and was smallThe sensitivity compared toof thethe signalpressure due difference to dilution to (~0.02 changing bar), the which pressure means from that, in~1.8 this bar range, to the~1.0 sensors bar is presented are very precise.in Figure Similarly, A3A,B (Appendix the calculated A). The density offset of between the pressure the experimental difference stepsranges was from ~25 ~2 kg × 10·m−5− bar3 and to ~26 the × noise 10−5 bar. was Once ~0.3 the kg· msensors−3. The are accuracy placed at ofa specific the hydrostatic site in densitometerthe field, one can overcome be evaluated these when sensitivities comparing, by calibrating for each ofthe the pressure experimental differences steps, and the densitythe hydrostatic based on density hydrostatic values pressure with a standard with the density density determination measurement (using, by the e.g., standard the densityDMA 5000 meter densitometer (Figure5C).) via sampling.

Figure 5. The hydrostatic densitometer laboratory experiment. The experiment lasted 6 h (24 May 2020), including 11 steps of water dilution from Dead Sea brine to distilled freshwater; the period of water mixing is excluded. The measured density and pressure difference for the nine pairs of pressure sensors presented in (A) and (B), respectively. (C) Measured density from the hydrostatic densitometer vs. the DMA 35 oscillating U-tube densitometer; the accuracy of the hydrostatic densitometer is conﬁrmed by the close ﬁt to the standard density measurement (1:1 line) with an R2 value of 0.99.

To evaluate the sensitivity of the hydrostatic densitometer (or the pressure difference) to variations in temperature and pressure in the deployment environment, we conducted sensitivity tests, presented in Figures A2 and A3 (AppendixA), respectively. For a temperature range of 25–34 ◦C, the offset of the pressure differences between seven of the nine sensor pairs was within the declared resolution (less than ±2.3 × 10−5 bar) (Figure A2A–F,H, AppendixA); two pairs of sensors (Figure A2G,I, AppendixA) were within the declared accuracy (less than ±2.3 × 10−3 bar) and within 2–3 times the declared resolution (6 × 10−5 bar and 4.2 × 10−5 bar for 8 ◦C variations, Figure A2G,I, AppendixA, respectively). Therefore, the two pairs with higher sensitivity to temperature variations were located at water depths with relatively small temperature variations (i.e., 5.5 m and 10.7 m water depth in EF buoy, respectively; see Figure4F). Water 2021, 13, 1842 9 of 15

The sensitivity of the pressure difference to changing the pressure from ~1.8 bar to ~1.0 bar is presented in Figure A3A,B (AppendixA). The offset of the pressure difference ranges from ~2 × 10−5 bar to ~26 × 10−5 bar. Once the sensors are placed at a speciﬁc site in the ﬁeld, one can overcome these sensitivities by calibrating the pressure differences and the hydrostatic density values with a standard density determination (using, e.g., the DMA 5000 densitometer) via sampling.

5.2. Coastal Aquifer—Borehole Stratification Observation The vertical stratification of the borehole in the coastal aquifer at the Dead Sea shore (see setup in Section 4.3 and Figure4) was documented continuously for 84 days by the hydrostatic densitometer deployed within a borehole. The atmospheric pressure (Figure6A ) was subtracted from the pressure measurement (Equation (1), Figure6B), to compute the hydrostatic pressure values (Equation (2), Figure6C). The time series of hydrostatic pressure (minus the initial pressure, Phyd − Phyd(t = 0)) of all sensors is shown in Figure6D. The monotonic decrease in pressure in all sensors is due to the decline in groundwater level, following the decline in lake level (the sensors are fixed to the borehole top). The rate of pressure change varies with depth (insert in Figure6D), with the deepest sensor showing the fastest rate of pressure decline. This means that the pressure difference between neighboring sensors increases with depth and with time. The density at different depths is presented in Figure6E, based on Equation (6), showing that density increases with depth. The density at all depths decreases with time because the sensors are fixed at a particular depth; the groundwater table decreases with time, and fresher water approaches each pair of sensors. Moreover, the rate of freshening of the water column (rate of density decrease) increases with depth, reflecting widening of the freshwater–saline interface. Figure7 presents the vertical profiles of pressure, temperature, and density at the beginning and end of the deployment. The temperature decreases with depth, at a gradient of ~0.2 ◦C·m−1 (Figure7B). The density increases with depth, from ~1070 kg ·m−3 (at a water depth of ~1 m, ~28 m below the surface) to ~1224 kg·m−3 (water depth of ~13 m, ~40 m below the surface) (Figure7C). The density profiles measured with two independent methods—the hydrostatic densitometer and the portable density meter (DM-250)—are similar. With time, the pressure measurements (Figure7A) show a decrease in pressure at all depths measured as a result of a decrease in water level and a decrease in density due to dilution of the water column.

5.3. Lake Stratification—Diluted Plume Observation Data from the stratified diluted plume on two consecutive days are shown in Figure8 . The temperature and density measured at different depths are presented in Figure8A,B, respectively, along with the atmospheric forcing, i.e., the wind speed and incoming solar radiation (Figure8C,D, respectively). The temperature and density measurements show clear stratification, where the shallowest sensors (0.2 m and 0.4 m, respectively) exhibit the highest temporal variations, peaking during the afternoon with a temperature higher by 3 ◦C and density lower by 6 kg·m−3, respectively. The deepest sensors (12.5 m and 11.7 m, respectively) show almost constant values of temperature and density. The two observation days present opposing wind and radiation forcing. On the first day, the wind speed was low (<4 m·s−1) and incoming radiation was high (~850 W·m−2), resulting in maximum thermal and density stratification at midday, with a difference between shallow and deep water of 3 ◦C and 6.5 kg·m−3. On the second day, the wind was strong (>5 m·s−1), higher than the threshold for mixing by wind-waves [8,9,11,25–27], and clouds reduced the incoming radiation (~400 W·m−2), resulting in reduced stratification, i.e., depth stratification of 0.3 ◦C and <3 kg·m−3. With the intensification of wind speed (7:00 a.m. on 10 April), the density of the shallow water (0.4 m, 0.8 m) increased and, concurrently, the density of the deeper water (5.5 m) decreased, both because of wind-induced mixing. Note that the process of dilution, mixing, and daily heating is limited to the upper layers (<7 m). Water 2021, 13, 1842 10 of 15 Water 2021, 13, x FOR PEER REVIEW 10 of 17 Water 2021, 13, x FOR PEER REVIEW 10 of 17

Figure 6. Temporal variations of the vertical properties at the coastal aquifer. (A) Atmospheric Figurepressure 6.. (BTemporal) Water pressure variations (Equation of the(1)) of vertical 28 m sensor properties. (C) Hydrostatic at the coastal pressure aquifer. (Equation ( A(3)) Atmospheric pressure.at the 28 m (B sensor) Water (assumingFigure pressure negligible 6. (EquationTemporal dynamic variations (1)) pressure). of 28 ofm sensor.the(D) verticalHydrostatic (C) Hydrostaticproperties pressure atat pressure theall depths, coastal ( Equation aquifer. ( (3)A)) Atmospheric atrelative the 28 to m initial sensor values (assumingpressure (Phyd − P. hyd(B negligible )( tW = ater0)). T pressurehe dynamic insert includes(Eq pressure).uation the ( 1depth)) of (D 28)of Hydrostatic them sensor sensors. .( C(E pressure)) HDensityydrostatic at all pressure depths, (Equation (3)) variation with time at different depths based on the hydrostatic densitometer (Equation (6)). (F) relative to initial valuesat the (P 28 m− sensorP (assuming(t = 0)). The negligible insert includesdynamic thepressure). depth ( ofD) the Hydrostatic sensors. pressure (E) Den- at all depths, Schematic illustration of the hydrostatichyd hyd densitometer in the EG26 borehole (see Section 4.3 for more relative to initial values (Phyd − Phyd (t = 0)). The insert includes the depth of the sensors. (E) Density sitydetails) variation. with time at different depths based on the hydrostatic densitometer (Equation (6)). variation with time at different depths based on the hydrostatic densitometer (Equation (6)). (F) (F) Schematic illustration of the hydrostatic densitometer in the EG26 borehole (see Section4 for Schematic illustration of the hydrostatic densitometer in the EG26 borehole (see Section 4.3 for more more details). details).

Figure 7. The borehole water profiles. Measured scalars along the borehole: (A) water pressure; (B) temperature; (C) density. The profiles were measured at the beginning and end of the deployment (dates in dd.mm.yy). The density profiles were measured with two independent methods: the hydrostatic densitometer and the portable density meter, showing good agreement (see text). Water 2021, 13, x FORWater PEER2021 REVIEW, 13, 1842 12 of 17 11 of 15

Figure 8. TimeFigure series 8. Time of the series stratiﬁcation of the ofstratification the diluted plume.of the Temperaturediluted plume. (A) Temperature and density (B )(A variations) and density with depth. (B) Atmosphericvariations forcing: with wind depth speed. (CA)tmospheric and solar radiation forcing: ( Dwind). Wind speed speed (C) above and solar 4 m·s −radiation1 is highlighted, (D). Wind as this speed is the −1 threshold forabove wind-wave 4 m·s mixing.is highlighted, as this is the threshold for wind-wave mixing.

5.4. Challenges and UntilPotential now, for we Dynamic have been Marine able toApplications explore the continuous variations of stratification only via temperature variation [8,28], which lacks the variations in salinity and density When the hydrostatic densitometer is placed in a dynamic marine environment, the stratification. This is the first documentation of continuous thermohaline stratification system design(density–depth should maintain and the temperature–depth array of pressure time sensors series) inupright the Dead; tilting Sea or (e.g., other due hypersaline to currents) will waterlead to bodies. changes in the vertical distance between the sensors and, thus, will result in lower calculated density. Possible ways of overcoming the tilting effect include using a large weight5.4. Challenges at the andbottom Potential of the for Dynamicdevice, or Marine adding Applications a tilt gauge to correct for the geometrical effect When of the the tilt hydrostatic, or both densitometer. Furthermore, is placed it is in possible a dynamic to marine incorporate environment, an the additional pressuresystem design sensor should in a maintain standard the arrayCTD of device, pressure enabling sensors upright; measurement tilting (e.g., of due to hydrostatic density,currents) in will addition lead to changes to other in the water vertical properties distance between, even the in sensors a hypersaline and, thus, will result in lower calculated density. Possible ways of overcoming the tilting effect include environment. This technique requires a way to isolate the hydrostatic pressure from the dynamic pressure following the lowering rate of the system, and to overcome the sensitivity to temperature and pressure variations by correcting the measured density. The importance of measuring density in buoyant flows is key to predict the dynamics of dense gravity currents, where the density of the fluid is controlled by the suspended sediment load, in addition to salinity and temperature. Gravity flows are known for their

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using a large weight at the bottom of the device, or adding a tilt gauge to correct for the geometrical effect of the tilt, or both. Furthermore, it is possible to incorporate an additional pressure sensor in a standard CTD device, enabling measurement of hydrostatic density, in addition to other water properties, even in a hypersaline environment. This technique requires a way to isolate the hydrostatic pressure from the dynamic pressure following the lowering rate of the system, and to overcome the sensitivity to temperature and pressure variations by correcting the measured density. The importance of measuring density in buoyant flows is key to predict the dynamics of dense gravity currents, where the density of the fluid is controlled by the suspended sediment load, in addition to salinity and temperature. Gravity flows are known for their importance as geofluids, as well as for their erosional capacity as coastal pipelines and infrastructures. Different buoyancies of the current lead to notable differences in the hydrodynamics (i.e., turbulent and mean velocities, bed shear stress, and turbulent stresses) and, consequently, to different processes of entrainment, transport, and deposition (e.g., [29,30]). The advantage of the hydrostatic densitometer is its ability to directly measure the fluid density and its variations with time and space and the fact that it does not require corrections of the concentration of suspended sediments.

6. Summary and Conclusions The hydrostatic densitometer method allows, for the first time, continuous monitoring of density profiles over a wide range of water densities (salinities)—from freshwater to hypersaline brine. The method requires pressure sensors that are vertically separated to apply the hydrostatic relations between pressure differences and average density between the sensors; a chain of sensors provides continuous measuring of density (and temperature) along the water column. We showed the applicability and accuracy of the hydrostatic densitometer in the laboratory, in a density range of 1–1.24 × 103 kg·m−3, with a deviation of the hydrostatic densitometer measurements from the density measured with the standard acoustic densitometer of up to 1 kg·m−3 (R2 = 0.99). In the coastal borehole, we installed six sensors along a water column of ~8 m. We presented the level lowering measured by all pressure sensors, at a rate of ~0.01 bar month-1, due to lowering of the Dead Sea level. The pressure differences between pairs of pressure sensors presented increasing density with depth, due to freshwater diluting the upper part of the aquifer over the hypersaline brine supplied by the lake. With time, density at all depths decreased at a rate of ~1.6 kg·m−3 per month, due to lowering of the upper diluted parts of the aquifer. The rate of density change increased with depth, reflecting widening of the freshwater–saline interface. The dynamics of the freshwater– saline interface associated with the rapid recession of the Dead Sea are documented here for the first time. Measurements of continuous changes in the width of the interface have never before been possible in such a saline environment. At the diluted plume in the lake, we deployed a chain of 10 pressure (and temperature) sensors along the upper 13 m of the water column; the chain was attached to a buoy, thus keeping the sensors at the same depth relative to the lake surface. The density profile showed increasing density with depth, due to dilution by freshwater discharges from coastal springs. The temperature also varied, typically decreasing, with depth. With time, density and temperature stratification changed dramatically due to the changes in wind intensity and the resultant mixing, as well as due to changes in solar radiative forcing. The design of a hydrostatic densitometer should account for the required depth and density resolution and the resolution of the pressure sensors. The highest resolution can be achieved by choosing the most accurate pressure sensor, from which the expected density resolution can be determined by choosing depth separation (Equation (8), Figure2). Thus, optimal setup of the sensor chain depends on the nature of the stratification in the specific aquatic system. Water 2021, 13, 1842 13 of 15

We conclude that the hydrostatic densitometer method can be used to examine the dynamics of hypersaline environments which, until now, was limited by a lack of appropriate sensors.

Author Contributions: Conceptualization, H.L., Z.M. and N.G.L.; methodology, H.L., Z.M. and N.G.L.; validation, H.L., Z.M. and N.G.L.; formal analysis, H.L., Z.M. and N.G.L.; investigation, H.L., Z.M. and N.G.L.; resources, N.G.L. and E.S.; data curation, H.L., Z.M. and N.G.L.; original draft preparation, Z.M. and N.G.L.; review and editing, H.L., E.S., Z.M. and N.G.L.; project administration, Water 2021, 13, x FOR PEER REVIEW 14 of 17 H.L., Z.M. and N.G.L.; funding acquisition, N.G.L. and E.S. All authors have read and agreed to the published version of the manuscript.

Funding:Funding:This This study study waswas fundedfunded by the Israel Science Science Foundation Foundation PI‐NGL PI-NGL (grant (grant #ISF‐1471/18) #ISF-1471/18) and and thethe US–Israel US–Israel Binational Binational Science Science FoundationFoundation PI‐NGL PI-NGL ( (grantgrant #BSF‐2018/035 #BSF-2018/035)) through through a joint a joint National National ScienceScience Foundation–US–Israel Foundation–US–Israel Binational Binational Science Science Foundation Foundation program program (grant (grant #BSF-2019/637 #BSF‐2019/637 PI-NGL PI‐ ). NGL). Institutional Review Board Statement: Not applicable. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data supporting the findings of this study are available from the correspondingData Availability author Statement: upon reasonable Data supporting request. the findings of this study are available from the corresponding author upon reasonable request. Acknowledgments: Raanan Bodzin, Uri Malik, Alon Moshe, and the R/V Taglit team (Silvy Go- nen,Acknowledgments: Meir Yifrach, and Raanan Shachar Bodzin, Gan-El) Uri Malik, are acknowledged Alon Moshe, and for the field R/V assistance, Taglit team and (Silvy Ali Gonen, Arnon is acknowledgedMeir Yifrach, for and assistance Shachar Ganin the-El data) are processing, acknowledged Yaniv for Munwes field assistance and Vladimir, and Ali Lyakhovsky Arnon is are acknowledged for assistance in the data processing, Yaniv Munwes and Vladimir Lyakhovsky are acknowledged for good discussions and consultations, and Moti Ginovker is acknowledged for acknowledged for good discussions and consultations, and Moti Ginovker is acknowledged for construction of the experimental water tank. We thank the editor Nicolò Colombani and three construction of the experimental water tank. We thank the editor Nicolò Colombani and three anonymousanonymous reviewers reviewers forfor theirtheir constructive comments. comments. ConflictsConflicts of of Interest: Interest:The The authorsauthors declare no conflict conflict of of interest. interest. The The funders funders had had no norole role in the in the designdesign of of the the study; study; inin thethe collection,collection, analyses, analyses, or or interpretation interpretation of ofthe the data; data; in inthe the writing writing of the of the manuscript,manuscript, or or in in the the decisiondecision to publish the the results. results.

AppendixAppendix A A

FigureFigure A1. A1.Study Study site: site: (A) regionalregional map map;; ( (BB) ) Dead Dead Sea Sea map. map. The The study study sites sites are are located located on onthe the westernwestern Dead Dead Sea Sea coast: coast: EinEin GediGedi borehole (EG) (EG) and and Ein Ein Feshkha Feshkha buoy buoy (EF). (EF).

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FigureFigure A2. A2.Sensitivity Sensitivity of of pressure pressure differences difference tos temperatureto temperature variations. variations. (A–I ()A Pressure–I) Pressure differences differences of Figure A2. Sensitivity of pressure differences to temperature−5 variations. (A–I) Pressure differences of the nine pairs of sensors. The Y-axis is ± 2.3 ×− 105 bar (the hydrostatic densitometer resolution). theof the nine nine pairs pairs of of sensors. sensors. TheThe Y--axisaxis is is ±± 2.32.3 × 10×−510 bar (thebar hydrostatic (the hydrostatic densitometer densitometer resolution resolution).).

Figure A3. Sensitivity of pressure differences to pressure variations: (A) pressure difference; (B) Figure A3. Sensitivity of pressure differences to pressure variations: (A) pressure difference; (B) pres- pressure measurement. sure measurement. Figure A3. Sensitivity of pressure differences to pressure variations: (A) pressure difference; (B) pressure measurement.

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