# Tracking Down the “Missing Energy” at Eddy Covariance Sites: Have Researchers Been Miscalculating Sensible Heat?

## Authors

Lianhong Gu^{1}* ([email protected]), Jeffrey D. Wood^{2}, **Paul J. Hanson ^{2,3}**,

**Melanie Mayes**,

^{2,3}**Daniel Ricciuto**

^{2,3}## Institutions

^{1}Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN; ^{2}University of Missouri, Columbia, MO

## URLs

## Abstract

The surface energy imbalance problem has plagued the eddy covariance community (EC) for decades. Essentially, when researchers add up all the measured heat fluxes and energy storages, balance is not achieved, and there is a significant non-zero residual that reflects a systematic underestimation of around 20%, which can be 100 W m^{-2} or more—hence the notional “missing energy”. The lack of closure calls into question the accuracy of the EC technique and/or knowledge of the micrometeorological system. Regardless of which is true, there are broad implications for downstream users of EC data. Eddy covariance data is widely used for validating Earth system and remote sensing models, and increasingly in applications that intersect with regulatory and legal spheres. Solving the EC energy imbalance problem is thus of prime importance to numerous scientific disciplines, and broader society. Despite many years of work, the EC community has not reached a consensus on the causes and remedies needed to solve the surface energy imbalance problem. Here, the team reexamines the surface energy imbalance problem through the lens of first principles of physical fluid mechanics and thermodynamics, hypothesizing that researchers have been using the wrong theory and equations for computing the sensible heat flux (*H*). Typically, *H *is determined from the eddy covariance between *w* and *T* (*w *and *T *are the vertical wind velocity and air temperature, respectively). The heat transport associated with the mean motion of air and several other terms are deemed small and unimportant, mainly due to the use of a “base temperature”, “from which each element of air is warmed (or cooled) during the vertical transfer of heat supplied (or removed) at the underlying surface” and from which actual air temperature is only several degrees different at most. Here the team shows that this theory is fundamentally flawed. Researchers will derive the net ecosystem sensible heat exchange from the fundamental equations of fluid mechanics and thermodynamics. Here, the team will present the new equation set and preliminary test results.