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A Practical Approach to Lake Water Density from Electrical Conductivity and Temperature Santiago Moreira, Martin Schultze, Karsten Rahn, Bertram Boehrer

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A Practical Approach to Lake Water Density from Electrical Conductivity and Temperature Santiago Moreira, Martin Schultze, Karsten Rahn, Bertram Boehrer A practical approach to lake water density from electrical conductivity and temperature Santiago Moreira, Martin Schultze, Karsten Rahn, Bertram Boehrer To cite this version: Santiago Moreira, Martin Schultze, Karsten Rahn, Bertram Boehrer. A practical approach to lake wa- ter density from electrical conductivity and temperature. Hydrology and Earth System Sciences, Eu- ropean Geosciences Union, 2016, 20 (7), pp.2975 - 2986. 10.5194/hess-20-2975-2016. hal-01587454 HAL Id: hal-01587454 https://hal.archives-ouvertes.fr/hal-01587454 Submitted on 3 May 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License Hydrol. Earth Syst. Sci., 20, 2975–2986, 2016 www.hydrol-earth-syst-sci.net/20/2975/2016/ doi:10.5194/hess-20-2975-2016 © Author(s) 2016. CC Attribution 3.0 License. A practical approach to lake water density from electrical conductivity and temperature Santiago Moreira1,2,3, Martin Schultze1, Karsten Rahn1, and Bertram Boehrer1 1UFZ-Helmholtz-Centre for Environmental Research, Department Lake Research, Brueckstrasse 3a, 39114 Magdeburg, Germany 2Laboratoire des Sciences du Climat et de l’Environnement, LSCE/IPSL, CEA-CNRS-UVSQ, Université Paris-Saclay, 91191 Gif-sur-Yvette, France 3Institute of Hydrobiology, TU-Dresden, Zellescher Weg 40, 01217 Dresden, Germany Correspondence to: Santiago Moreira ([email protected]) Received: 22 January 2016 – Published in Hydrol. Earth Syst. Sci. Discuss.: 17 February 2016 Revised: 3 June 2016 – Accepted: 20 June 2016 – Published: 22 July 2016 Abstract. Density calculations are essential to study strat- 1 Introduction ification, circulation patterns, internal wave formation and other aspects of hydrodynamics in lakes and reservoirs. Cur- rently, the most common procedure is the use of CTD (con- Density is one of main physical quantities governing the hy- ductivity, temperature and depth) profilers and the conversion drodynamics, stratification, and mixing in lakes and reser- of measurements of temperature and electrical conductivity voirs. Water quality in lakes is controlled by biological and into density. In limnic waters, such approaches are of limited biogeochemical processes which depend on the availability accuracy if they do not consider lake-specific composition of of oxygen in deep waters and nutrients in surface waters. solutes, as we show. A new approach is presented to corre- Both phenomena are controlled by the duration and exten- late density and electrical conductivity, using only two spe- sion of the turnover period, which is dependent on density cific coefficients based on the composition of solutes. First, gradients. Therefore, density is a very important variable in it is necessary to evaluate the lake-specific coefficients con- numerical models for the simulation of the behaviour of lakes necting electrical conductivity with density. Once these coef- under changing conditions, e.g. due to management mea- ficients have been obtained, density can easily be calculated sures or phenomena related to global climate change. based on CTD data. The new method has been tested against The density of lake water (at atmospheric pressure) de- measured values and the most common equations used in the pends on temperature and dissolved water constituents. Since calculation of density in limnic and ocean conditions. The re- temperature, chemical composition and concentrations may sults show that our new approach can reproduce the density vary over time, from lake to lake or even within a particular contribution of solutes with a relative error of less than 10 % lake due to seasonal stratification or meromixis, numerical in lake waters from very low to very high concentrations as models of lakes calculate the density internally. There are well as in lakes of very particular water chemistry, which is several approaches to calculate water density in lakes. Most better than all commonly implemented density calculations of them are general equations that do not always reflect spe- in lakes. Finally, a web link is provided for downloading the cific properties of lakes. If enough measurements of density corresponding density calculator. for the relevant temperature range are available and compo- sition and concentrations of the main constituents are con- stant, regressions can be used to generate a mathematical for- mula for density in a specific lake (e.g. Jellison et al., 1999; Vollmer et al., 2002; Karakas et al., 2003). If the composi- tion is constant and the main constituents are ions, electrical conductivity or salinity may be used as an easy-to-measure Published by Copernicus Publications on behalf of the European Geosciences Union. 2976 S. Moreira et al.: Lake water density from electrical conductivity and temperature proxy for concentrations (Bührer and Ambühl, 1975; Chen based on density measurements of the monimolimnion and and Millero, 1986; Pawlowicz and Feistel, 2012). mixolimnion of the Waldsee. Imboden and Wüest (1995) discussed the influence of dis- Boehrer et al. (2010) evaluated the contribution of the dif- solved substances on (potential) density because both the ferent cations and anions separately in terms of partial mo- concentration and chemical composition of the total dis- lal volumes and implemented an algorithm, RHOMV (http: solved solids change considerably from lake to lake (see e.g. //www.ufz.de/webax), to calculate density with a second- Boehrer and Schultze, 2008). The effects of dissolved solids order approximation for temperature dependence and ionic on density stratification have been studied in lake-specific in- strength dependence. Pawlowicz et al. (2011) implemented vestigations in Lake Malawi (Wüest et al., 1996) and in Lake the LIMBETA method that calculates density from composi- Matano (Katsev et al., 2010). In some cases, the specific con- tion. Another approach comes from Pawlowicz et al. (2012) tribution of ions such as calcium, carbonate or dissolved iron where the authors propose to use TEOS-10 but replace can control the permanent stratification in lakes such as in seawater salinity with specific salinities obtained and cor- La Cruz (Spain) (Rodrigo et al., 2001), Cueva de la Mora rected for freshwaters. This limnic salinity can be calcu- (Spain) (Sanchez-España et al., 2009) or Waldsee (Germany) lated using the chemical composition by summing up all (Dietz et al., 2012). the dissolved solutes (Sasoln/ or by summing up only the Density of pure water can be calculated using mathemat- dissolved ions (Saionic/ and correcting this value with the dens ionic ical expressions such as those in Kell (1975) or Tanaka et dissolved Si(OH)4, Sa D Sa C 50.6 × [Si(OH)4] al. (2001). Density calculations of natural waters require ad- (mol kg−1/. Based on partial molal volumes (RHOMV), Di- ditional terms to include the contributions of dissolved sub- etz et al. (2012) separated the contributions of solutes for stances. Specific formulas have been developed for ocean freshwater lakes. Moreira et al. (2011) based density on conditions. The UNESCO equations developed by Fofonoff the composition of solutes in their model to reproduce the and Millard (1983) have been the standard for a long period. permanent stratification of the Waldsee numerically using They used temperature and practical salinity based on electri- RHOMV to include the reactivity of substances in the density cal conductivity measurements. Because seawater conditions (see also Nixdorf and Boehrer, 2015). are a known reference and the approaches provide stable re- These prior studies therefore highlight the necessity of in- sults over a wide range of temperatures and electrical con- cluding the chemical composition to obtain an accurate cal- ductivity, these have been applied in limnic systems and im- culation of density. However, we accept the need for a practi- plemented in numerical models such as DYRESM (Imberger cal density approach, which can easily be implemented, such and Patterson, 1981; Gal et al., 2009), ELCOM (Hodges and as a mathematical formula that relates density to temperature Dallimore, 2007), GOTM (Burchard et al., 1999; Umlauf et and electrical conductivity. In this manuscript, we develop al., 2005) or CE-QUAL-W2 (Cole and Buchak, 1995). Re- coefficients for such a formula from the chemical composi- cently the ocean standard was replaced by the new Ther- tion. We provide an algorithm – RHO_LAMBDA (from ρλ/ modynamic Equation of Seawater 2010 (TEOS-10; IOC et – to obtain such coefficients and demonstrate the applicabil- al., 2010). However, as the composition of solutes differs ity of the approach with water from Rappbode Reservoir. greatly from the ocean, density calculation based on ocean We also provide an appropriate assessment for the Rapp- conditions can only be of limited accuracy. Pawlowicz and bode Reservoir case and compare the accuracy with other Feistel (2012) have considered the application of TEOS-10 approaches currently in use for limnic waters. For a quantita- (IOC et al., 2010) in several cases different
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