While applying a former version of the ACASA model (ACASA_se3) for the Waldstein-Weidenbrunnen site, two major problems were encountered concerning the energy balance closure and the third-order turbulence closure of the model. Thus, the subsequent ACASA version (ACASA_4.0) includes improvements of these issues. These two model versions were compared to highlight the problems and the corresponding improvements.
For the Waldstein-Weidenbrunnen site during IOP-1 of the EGER project, the measured energy balance above the canopy was not closed, as was also found at many other sites (Aubinet et al., 2000). This unclosed energy balance in measurements is a well known issue that has not been solved yet (Foken, 2008b). SVAT-models are usually based on the conservation of energy, thus, these models close the energy balance using different internal mechanisms (Kracher and Foken, 2009). However, the ACASA_se3 model did not close the energy balance but attributed the missing energy to an error output. For IOP-1 this error above the canopy was substantial (intercept of 62 W m-2, Fig. 7a). Thus, an energy balance closure using the Bowen ratio to distribute the error to the sensible and latent heat fluxes was introduced for ACASA_4.0. As the ACASA_4.0 version included several other improvements, a modification of this model version was added to the analysis with the energy balance not being closed using the Bowen-ratio method. Fig. 7c shows an improvement of ACASA_4.0 without energy balance closure over ACASA_se3, but only using the ACASA_4.0 version with energy balance arrives at a completely closed energy balance (Fig. 7b). Even though time series of modeled errors and the measured residual above the forest canopy showed a daily cycle, large discrepancies were revealed between model results and measurements.
The energy balance closure was analyzed in more detail within the profile for the five-day
‘Golden Days’ period of IOP-1. The error had a distinct shape within the profile for ACASA_se3 and ACASA_4.0 without energy balance closure. A large negative maximum of the error in the upper part of the canopy for ACASA_se3 could be attributed to an error in the short-wave radiation calculations within the profile. A more realistic profile of net radiation within the canopy resulted in lower errors for ACASA_4.0 within the canopy. However, only the ACASA_4.0 model version with energy balance closure achieved a closed energy balance for all heights within the canopy. The chosen method to close the energy balance within ACASA intends to conserve the Bowen ratio by distributing the error according to the Bowen ratio to the sensible and latent heat flux. However, this method only worked well for positive Bowen ratios, but failed to maintain the value for the Bowen ratio within the lower part of the canopy where negative Bowen ratios occurred.
To study the nature of the error in the ACASA model versions more thoroughly, the GLUE methodology as performed in Staudt et al. (2010a, Appendix B) was applied to all three model
Figure 7: Energy balance closure (net radiation Rn versus the sum of sensible H, latent LE, ground G and storage S heat fluxes) above the canopy of the three model versions: (a) ACASA_se3, (b) ACASA_4.0 and (c) ACASA_4.0 without energy balance closure using the Bowen ratio method (no EBC) for the whole experiment duration (6 September – 7 October). Figure taken from Staudt et al. (2010b, Appendix C).
versions and the sensitivity of the mean error (mean of all half-hourly error values for the five-day period) of the 20000 model runs to all input parameters was analyzed. Surprisingly, there was no sensitivity to all model parameters but the leaf area index. Possible mean errors reached very large values of up to 10 times the measured mean residual for ACASA_se3 with increasing errors for larger leaf area index values (Fig. 8). A strong correlation of the mean error with the leaf area index values was also observed for ACASA_4.0 without energy balance closure, but other than for ACASA_se3 largest error values were obtained for small leaf area index values. As anticipated, the error in ACASA_4.0 with energy balance closure was zero for all tested parameter sets.
Figure 8: Sensitivity graph showing the mean error (W m-2) for the 20000 model runs across the range of the leaf area index (m2 m-2) for the GLUE analysis for all three ACASA model versions. The horizontal dashed line depicts the mean measured residual. Figure taken from Staudt et al. (2010b, Appendix C).
18 Results
The second problem found in the ACASA_se3 version concerned the third-order turbulence closure. Comparisons of measured and modeled profiles of third-order moments are plotted in Fig. 9, exemplarily for w'u'u' and w'w'w' normalized by u*3. Measurements were in the same order of magnitude as reported in the literature (e.g. Katul and Albertson, 1998). Trunk space values were small and the peak of the measured profiles was found in the upper half of the canopy.
Model results of ACASA_se3 for the two third-order moments were two to three orders of magnitude smaller than measurements, thus are not distinguishable from the y-axis in Fig. 9. An analysis of the source code revealed that these small values were due to a subroutine that set predefined limits, so-called ‘realizability constraints’, to all third-order moments. Loosening these ‘realizability constraints’ by multiplication with the factors 100, 1000 and 10000 allowed more realistic orders of magnitude. For w'w'w' this improved model results with a similar shape of the profile but an underestimation of measured values. However, larger ‘realizability constraints’ did not result in w'u'u' profiles that resemble the shape of the measured profiles.
Thus, in the ACASA_4.0 version the original Meyers and Paw U (1986) method of the calculation of the third-order moments was inserted again, as the ACASA_se3 version with its updated version of the Meyers and Paw U (1986) method resulted in problems explained above.
Third-order moments of ACASA_4.0 were more realistic than ACASA_se3 model results, with profile shapes that resemble measurements with small trunk space values and a maximum in the
Figure 9: Comparison of mean daytime modeled (lines) and measured (black dots, with its standard deviations) profiles of w'u'u' and w'w'w' normalized by u*3 above the canopy (models) and at the uppermost measurement height (measurements). For ACASA_se3 results are plotted for the original
‘realizability constraints’ (realize*1) as well as increased ‘realizability constraints’ by the factors 100, 1000 and 10000. Number of profiles used for averaging: N = 86. Figure taken from Staudt et al. (2010b, Appendix C).
upper part in the canopy. Even though model results were in the right order of magnitude, '
'
'ww
w measurements were underestimated by ACASA_4.0 and w'u'u' measurements were overestimated by ACASA_4.0. These different third-order moment calculation schemes and the modifications tested had influences on the first- and second-order velocity statistics.