## Abstract

A simple model of the conductivity gradient spectrum is developed and used to interpret oceanic conductivity microstructure observations. A principal goal is to estimate the correction factor *E* for inferring the temperature variance dissipation rate χ_{r′}, over a wide range of temperature and salinity gradients. The correction factor is defined as *E*≡χ_{c′}/χ_{r′}, where χ_{c′}, is the temperature variance dissipation rate inferred directly by integrating the measured conductivity spectrum. Three spectral forms of temperature and salinity fluctuations are used to model *E*: the Batchelor spectrum, a white dissipation spectrum, and a growing salt finger spectrum. Model results show that *E* depends on 1) the local temperature-salinity (*T*−*S*) relation *m*=*ds*/*dT*, 2) the spatial response function of the conductivity probe, 3) the degree of *T*−*S* correlation at high wavenumbers, 4) the forms of temperature and salinity spectra, and 5) the kinetic energy dissipation rate ε. Results also indicate that *E* can diverge significantly from unity, particularly when *m* is negative, ε is large, and temperature and salinity gradients are stable. For example. when *m*=−0.3 psu°C^{−1} and ε=10^{−6}m^{2} s^{−3},*E* is in the range 0.05–0.6, depending on the spectral form and *T*−*S* correlation. For growing salt finger spectra, *E* is in the range 1.2–2,4 over the range of density ratio 1.2≤*R*_{ρ}≤2.0, based on parameters from the area of the North Atlantic Tracer Release Experiment (NATRE). A general method is outlined for determining *E* from observations of conductivity microstructure and is applied to a dataset obtained during NATRE using the Cartesian diver profiler. Observed profiles exhibit high variability in *T*, *S*, *m*, and conductivity microstructure on vertical scales of a few meters. Because conductivity microstructure. at the NATRE site can result from either shear-driven turbulence or double-diffusive processes, a wide variety of spectral shapes is possible. These physical uncertainties lead to alternative possible estimates of *E*, hence χ_{r′}, which vary by factors of 10–20 for a few profile segments. However, χ_{r′}, is more typically constrained to within a factor of 2.