## [1

where a is the thermal expansion coefficient for a water parcel of temperature T along the path from depth z to the surface. In lakes where the deep water is close to temperatures of maximum density Tmd, the thermal expansion coefficient is very small, a « 0, and, as a consequence, the difference between in situ temperature and potential temperatures is small 0 « T. In lakes with warmer deep waters, a can be considered constant. Figure 9 shows a monotonous potential temperature profile in Lake Malawi, Africa, which indicates stable stratification by temperature only.

Salinity, Electrical Conductivity and Electrical Conductance

Many substances in lake water are dissolved as ions. Hence electrical conductivity has been used to ad

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23.5 24 Temperature [

Figure 9 Profiles of (in situ) temperature Tand potential temperature near the deepest location of Lake Malawi on 13 September 1997. Reproduced from Boehrer B and Schultze M (2008) Stratification of lakes. Reviews in Geophysics, 46, RG2005, doi:10.1029/2006RG000210, with permission from American Geophysical Union.

23.5 24 Temperature [

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Figure 9 Profiles of (in situ) temperature Tand potential temperature near the deepest location of Lake Malawi on 13 September 1997. Reproduced from Boehrer B and Schultze M (2008) Stratification of lakes. Reviews in Geophysics, 46, RG2005, doi:10.1029/2006RG000210, with permission from American Geophysical Union.

quantify dissolved substances. For compensation purposes, the temperature dependence of electrical conductivity of a water sample is recorded, while scanning the relevant temperature interval. In most cases, a linear regression C(T) = aT + b is satisfactory to define the conductance, i.e., the electrical conductivity kref = C(Tref) = aTref + b at a certain reference temperature Tref. Most commonly, 25 °C is used for the reference:

In most surface waters, a value close to a25 = 0.02 K"1 is appropriate. Electrical conductance is used for a bulk measurement of concentrations of ionically dissolved substances, quantifying transports from changes in the conductance profile, and to base density regression curves on.

Oceanography uses electrical conductivity and temperature to calculate salinity in practical salinity units (psu), which gives a good indication for dissolved salt in grams per kilogram for ocean water and brackish water (water mixed from ocean water and fresh water). In limnetic systems, however, the composition of dissolved substances differs from that of the ocean. Even within some lakes, there are pronounced vertical gradients. As a consequence, salinity can only be used with reservation in limnic systems.

measure temperature and conductivity are implemented. As in most practical applications the difference between in situ and potential temperature is small; we use T for temperature. For lakes of low salinities (<0.6 psu), density can be approximated:

In lakes of a composition of dissolved substances similar to the ocean, the so-called UNESCO formula may be applied (e.g., Rassnitzer See in Figure 6), which is applicable for salinities above 2 psu. In cases where salinity cannot be used, calculation of density may directly be based on measurements of temperature and conductivity. For Lake Constance - Obersee, the following formula was proposed, where 20 °C was used as reference temperature for conductance k20:

adding the conductivity contribution in separate

Alternatively, if the dissolved substances are known, e.g., from chemical analysis, density can be calculated by adding the separate contributions:

where Cn is the concentration of the substance n (g kg-1). A short table of coefficients

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