Eddy Flux Measurements and Energy Balance Closure

Closure of the surface energy balance is an objective constraint on daytime eddy flux measurements. Over tall canopies many sites report (H + λ E)/(Rn - G) ≈ 0.7 whereas 100% closure is commonly achieved over short canopies. This observed failure of closure can be redressed to a large extent by proper consideration of averaging and coordinate rotation periods. At the majority of sites, coordinates are aligned by rotating post-facto into a frame that sets the mean vertical velocity /line{w} = 0 over the averaging period T. The covariance of a scalar c then reduces to the eddy covariance: /line{wc} = /line{w}~/line{c} + /line{w'c'} = /line{w'c'}. At other sites, coordinates are aligned with the long term wind field or other criteria and then /line{w} !=q 0 over the period T. At these sites the vertical mean advective component of the covariance, /line{w}~ /line{c} is often ignored because it is noisy and may exceed /line{w'c'}. Alternatively, the data series are detrended or filtered to reduce the unpredictable behaviour of /line{w}~/line{c}. All these processes have the potential to remove vital low frequency contributions to the covariance. It can be shown formally that rotating coordinates so /line{w} = 0 over the period T removes contributions to /line{wc} from motions with periods longer than T. At the same time contributions with period shorter than T are amplified. Setting /line{w}~/line{c} = 0 in long term coordinates or detrending or filtering the time series have equivalent effects. If the low frequency covariance lost is significant, then the energy balance will no longer close and other fluxes will be similarly affected. The amount of flux lost depends upon the averaging period T and the low frequency content of the cospectrum. Through analysis of data sets from forest sites in Scotland, Australia and Brazil, we have shown that daytime cospectra over tall forests in convective boundary layers have significant content at periods much longer than typical averaging times. Complex terrain further increases low frequency content. Extending averaging and rotation times from 15 minutes to 4 hours increased energy balance closure from 70% to 100% at the Australian and Brazilian sites and also increased carbon fluxes by ~ 20%. Over the short dense Scottish forest in mainly neutral conditions the low frequency content of /line{wc} was much smaller and the effect of increased averaging time was negligible.