The Surface Energy Imbalance Problem

At most flux measurement sites, the sum of half-hourly averages of the eddy fluxes of sensible latent heat (H + λE) are 50 – 100 W m^-2 less than the available energy (A = R_n –G - S), where R_n is net radiation and G and S are changes in heat stored in soil and biomass This is the ‘energy imbalance problem' in micrometeorology, where either eddy fluxes of  H and  λE are underestimated and/or A is overestimated at half-hourly timescales. Lack of energy closure is caused by: 1) a failure to satisfy the fundamental assumption of one-dimensional transport for measurements on a single tower to represent spatially-averaged fluxes to/from the underlying surface; 2) measurement errors in: i) eddy fluxes, ii) net radiation and iii) changes in energy storage in soils, air, and biomass below the measurement height.

Review of the literature shows that radiometric errors are unlikely to cause significant overestimates of A at every flux measurement site globally, but phase lags between H + λE and A caused by incorrect estimates of G and S 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 a median slope of 0.75 for  H + λE versus A for half-hourly averages. Using 24h averages leads to energy closure at 45% of the La Thuile sites, and the median slope of H + λE versus A increases to 0.90. Increasing the averaging time reduces the bias in A because energy entering the soil, air and biomass in the morning is returned in the afternoon and evening.

Unrealistically large positive horizontal temperature gradients of 4 – 10 ºK km^-1 are needed for horizontal advective flux divergences to explain the 50 – 100 W m^-2 underestimate of H + λE compared to A. Similarly, unrealistically large mean vertical velocities and temperature gradients are needed for vertical advective flux divergences to account for the ‘missing' energy. Imbalances between H + λE and A still occur in daily averages but the small residual energy imbalances are explicable by positive and negative horizontal and vertical advective flux divergences. Systematic underestimates of the vertical heat flux also occur if horizontal u'T' covariances contaminate the vertical w'T'  signal due to incorrect coordinate rotations. An incorrect tilt angle of only 2º will cause a 5% underestimate of H + λE.

Closure of the energy balance is possible at half-hourly time scales by careful selection of horizontally homogeneous sites to satisfy the assumptions of one-dimensional transport underpinning eddy covariance measurements on single towers , 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.