USE OF THE EFFECTIVE TEMPERATURE CONCEPT TO ACCOUNT FOR TEMPERATURE VARIATION IN CLUMPED ISOTOPE MEASUREMENTS OF GAR SCALES

We have recently developed a new calibration for measuring terrestrial surface temperatures using the clumped isotopes Δ₄₇ of the carbonate ion in the bioapatite scales of garfish (Gray and Brandon, in review). Our contribution here is to describe how the effective temperature concept can be used to account for the variable temperature history of our modern samples. Our calibration is based on a sampling of modern gars from a latitudinal transect extending from Mexico and across the US Midwest. Gars scales provide an ideal isotope thermometer for terrestrial settings. Gars live in shallow depths (< 3 m) in rivers and lakes, are non-migratory, and their scales grow continuously over their lifespan (~8-14 years). As ectotherms, their body temperature is equivalent to ambient water temperature.

The effective temperature is defined as the steady temperature that would produce the same Δ₄₇ value as produced by the variable temperature experienced by the sample. The method has a long history: Pallmann et al., 1940; Lee, 1969; McCoy, 1987; Rogers, 2007; 2008. It is designed for any system where growth or production, P, is well-defined by an Arrhenius function, P ∝ exp(-E_a/RT), where E_a is the activation energy, T is temperature (K), and R is Boltzman’s constant. The surface temperature variation is usually represented by a harmonic series with a mean (annual) temperature T_m and sin functions with parameters ΔT_d and ΔT_s equal to the average range for daily and seasonal temperature variations (Rogers, 2007, 2008). We used the Daymet V4 climate dataset to estimate these parameters for sample locations. The temperature function is then combined with the Arrhenius function to determine an average value for P. The Metabolic Theory of Ecology (Brown et al., 2004) demonstrates that growth rates across a large range of organisms, including fish, have a fixed E_a = 60 kJ/mol. This value allows us to find T_e for each of our sample locations. We find that T_e is the same as T_m in the tropics, but can be 12 °C greater than T_m in mid-latitude settings. We anticipate that this approach will be useful for calibration and prediction of temperature using other geochemical methods.