Influences of observation errors in eddy flux data on inverse model parameter estimation

Abstract

Abstract. Eddy covariance data are increasingly used to estimate parameters of ecosystem models. For proper maximum likelihood parameter estimates the error structure in the observed data has to be fully characterized. In this study we propose a method to characterize the random error of the eddy covariance flux data, and analyse error distribution, standard deviation, cross-and autocorrelation of CO 2 and H 2 O flux errors at four different European eddy covariance flux sites. Moreover, we examine how the treatment of those errors and additional systematic errors influence statistical estimates of parameters and their associated uncertainties with three models of increasing complexity -a hyperbolic light response curve, a light response curve coupled to water fluxes and the SVAT scheme BETHY. In agreement with previous studies we find that the error standard deviation scales with the flux magnitude. The previously found strongly leptokurtic error distribution is revealed to be largely due to a superposition of almost Gaussian distributions with standard deviations varying by flux magnitude. The crosscorrelations of CO 2 and H 2 O fluxes were in all cases negligible (R 2 below 0.2), while the autocorrelation is usually below 0.6 at a lag of 0.5 h and decays rapidly at larger time lags. This implies that in these cases the weighted least squares criterion yields maximum likelihood estimates. To study the influence of the observation errors on model parameter estimates we used synthetic datasets, based on observations of two different sites. We first fitted the respective models to observations and then added the random error estimates described above and the systematic error, respectively, to the model output. This strategy enables us to compare the estimated parameters with true parameters. We illustrate that the correct implementation of the random error standard deviation scaling with flux magnitude significantly reduces the Correspondence to:G. Lasslop (gitta.lasslop@bgc-jena.mpg.de) parameter uncertainty and often yields parameter retrievals that are closer to the true value, than by using ordinary least squares. The systematic error leads to systematically biased parameter estimates, but its impact varies by parameter. The parameter uncertainty slightly increases, but the true parameter is not within the uncertainty range of the estimate. This means that the uncertainty is underestimated with current approaches that neglect selective systematic errors in flux data. Hence, we conclude that potential systematic errors in flux data need to be addressed more thoroughly in data assimilation approaches since otherwise uncertainties will be vastly underestimated.

Regional inversion of CO<sub>2</sub> ecosystem fluxes from atmospheric measurements: reliability of the uncertainty estimates

“…First, there can be annual biases in the eddy covariance measurements, due to imperfect data filtering and to gap-filling, which are large when compared to annual averages of the data, but, a priori, not when compared to monthly averages (Luyssaert et al, 2009;Lasslop et al, 2010). The weight of these biases for data averages is far larger than that of random measurement errors on individual data since the autocorrelation in time for these errors is negligible (Lasslop et al, 2008). Eddy covariance sites often also show large sinks which are due to the regrowing nature of local ecosystems for many of these sites (Jung et al, 2011), while the actual sink should be smaller in the larger scale model grid cells which merge such regrowing ecosystems with near-equilibrium of disturbed ecosystems.…”

“…Figure 2 shows the averages over all the time and space locations when and where CE-L4 data are available during each 30-day period within the CHIMERE domain, of the prior and inverted NEE at 0.5 • resolution and of the CE-L4 data. The spatial averaging over the different CE-L4 locations in Europe and over 30-day periods is assumed to strongly decrease the random measurement errors in the CE-L4 data (Lasslop et al, 2008) as well as the differences of representativity between these data and the estimates from the model which should be high when considering individual CE-L4 measurements (at a scale smaller than 1 km 2 ) and the corresponding 0.5 • ×0.5 • model grid cells, but which are assumed to be random, uncorrelated between the different measurement sites and not fully correlated over time at a given site. This assumption is supported by the good fit obtained by BR2011 between inverted estimates of NEE and spatially averaged CE-L4 data despite large misfits at individual sites.…”

“…They evaluated the results from the inversions by checking that the corrections applied by the inversions to the estimates from ORCHIDEE decreased the misfits to independent local flux measurements (at few hectares scale) from the CE eddy covariance flux towers during summer periods. Obviously, the inversion cannot solve the differences in space resolution between the model grid cells and the eddy covariance data nor the measurement error in these data (Hollinger and Richardson, 2005;Lasslop et al, 2008). However, the comparisons between the NEE estimates from the ecosystem or inversion model in the grid cells containing the locations of the flux towers and these measurements, both averaged over all flux tower locations in Europe and over 30-day periods, showed significant decrease of the misfits and a better fit with the temporal variability of the data due to inversion.…”

Quantifying the model structural error in carbon cycle data assimilation systems

“…Using measurements across different types of forest ecosystems, Richardson et al (2008) found that the random measurement errors range approximately from 0.2 to 0.8 gC m −2 d −1 , being somewhat proportional to the absolute flux magnitude, which means that the variance due to the measurement errors accounts for 1 to 25 % of the total observation variance. Additionally, Lasslop et al (2008) showed that no significant measurement error correlation remains at the daily time scale. From these elements, we conclude that the seasonal structure of the model error in ORCHIDEE is very similar to that of the observation error described above (the orange curve in Fig.…”

“…From this half-hourly data we compute daily means, in order to take advantage of the rapidly-declining autocorrelation of gap-filled halfhourly fluxes (see Fig. 5a in Lasslop et al, 2008).…”