Reflections on the surface energy imbalance problem

The ‘energy imbalance problem’ in micrometeorology arises because at most flux measurement sites the sum of eddy fluxes of sensible and latent heat (H + λE) is less than the available energy (A). Either eddy fluxes are underestimated or A is overestimated. Reasons for the imbalance are: (1) a failure to satisfy the fundamental assumption of one-dimensional transport that is necessary for measurements on a single tower to represent spatially-averaged fluxes to/from the underlying surface, and (2) measurement errors in eddy fluxes, net radiation and changes in energy storage in soils, air and biomass below the measurement height. Radiometer errors are unlikely to overestimate A significantly, but phase lags caused by incorrect estimates of the energy storage terms can explain why H + λE systematically underestimates A at half-hourly time scales. Energy closure is observed at only 8% of flux sites in the La Thuile dataset (http://www.fluxdata.org/DataInfo/default.aspx) with half-hourly averages but this increases to 45% of sites using 24 h averages because energy entering the soil, air and biomass in the morning is returned in the afternoon and evening. Unrealistically large and positive horizontal gradients in temperature and humidity are needed for advective flux divergences to explain the energy imbalance at half-hourly time scales. Imbalances between H + λE and A still occur in daily averages but the small residual energy imbalances are explicable by horizontal and vertical advective flux divergences. Systematic underestimates of the vertical heat flux also occur if horizontal u′T′u′T′ covariances contaminate the vertical w′T′w′T′ signal due to incorrect coordinate rotations. Closure of the energy balance is possible at half-hourly time scales by careful attention to all sources of measurement and data processing errors in the eddy covariance system and by accurate measurement of net radiation and every energy storage term needed to calculate available energy.

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