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Horizontal "diffusion" of energy in CAM4-FV

Dear CESM-team
I am interested in the atmospheric heat budget and therefore I have diagnosed the terms of the thermodynamic energy equation on pressure levels (according to e.g., Holton 2014 - Formula 3.6) in CAM4-FV simulations.When calculating the heat budget (including advection, adiabatic compression/expansion and diabatic heating) I find a substantial residual, particularly in the lower troposphere and over topography. To my knowledge this is associated with subgrid processes (e.g., turbulence) and energy loss by friction and I can find CAM4 history files named "vertical diffusion (DTV)" and "horizontal diffusion (DUH,DVH)" which seem to account for these processes.The energy "diffusion" is also described in the CAM4-description by Neale et al. 2010: page25: "The only remaining issue regarding conservation of the total energy is the horizontal discretization and the use of the “diffusive” transport scheme with monotonicity constraint. To compensate for the loss of total energy due to horizontal discretization, we apply a global fixer to add the loss in kinetic energy due to “diffusion” back to the thermodynamic equation so that the total energy is conserved."However, I could not find a detailed description of the full equations which describe this "energy diffusion", particularly for the horizontal component.Therefore my questions:Can you help me to find the equations of this "diffusion"? How are the history fields DUH, DVH calculated? Is there a simple way to diagnose the complete thermodynamic energy equation for CAM4-FV based on specifically selected history fields? Many thanks and best regardsNick
 
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