The Biason the Joule Heating Estimate: Small-Scale Variability Versus Resolved-Scale Model Uncertainty and the Correlation of Electric Field and Conductance

Abstract

Estimating the Joule heating rate using models of electric field and conductance requires removal of various biases, which arise because the models have uncertainty. This problem has been referred to as electric field variability, although variability of the conductance is also at issue. Variability of the conductance can contribute to the bias on Joule heating if it is correlated with the variability of the squared electric field. The term “variability,” however, includes two distinct sources of model uncertainty: physical fluctuations on a small scale below the resolution of the model (small-scale variability) and uncertainty in the model’s predictions even on the scale that it does resolve (resolved-scale model uncertainty). Previous work has tended to mix small-scale variability with resolved-scale model uncertainty in a way that may have led to confusion. In this work we separately analyze the small-scale variability and the resolved-scale model uncertainty using the Sondrestrom radar database, and we find that each gives a significant contribution to the bias on Joule heating. We also analyze the correlation of conductance and squared electric field, again in a way that distinguishes the effect of correlation over small scales from the effect of correlation of the resolved-scale model uncertainties. We explain that small-scale variability, being the result of actual physical fluctuations on small scales, is a more general quantity than resolved-scale model uncertainty; the latter is only defined with respect to a particular model.

Key Points

• Resolved-scale model uncertainty compared with small-scale variability using data
• A 20% underestimate of the Joule heating from small spatial scale variability
• A 50% underestimate of the Joule heating from resolved-scale model uncertainty