As one of the first steps of the application of the ACASA model, values for a large range of input parameters have to be specified by the user. To support these parameter choices, the sensitivity and uncertainty of the ACASA_4.0 model version was studied with the help of the GLUE methodology (Beven et al., 2000). This study was performed for two 5-day periods of IOP-1 and IOP-2 (‘Golden Days’). Even though model response to parameter sets is the focus of the GLUE methodology, the sensitivity of single parameters can be assessed by plotting likelihood measures versus parameter values. Such sensitivity plots are displayed in Fig. 5a-f for the sensitivity of the sensible heat flux (H), the latent heat flux (LE) and the NEE above the canopy to the value of the leaf area index (lai). First of all, the different ranges of the likelihood measures for the three fluxes for the two IOPs revealed a different performance for the three fluxes, with generally better results for the 10% best model runs for the sensible heat flux than for the other fluxes, and with the largest range of likelihood measures for the NEE. For the latent heat flux, the performance for the 10% best model runs was generally better for the colder fall period than for the warmer summer period. All three fluxes are sensitive to the value of the lai, as most of the lai values of the ‘behavioural’ parameter sets (10% best parameter sets) were within the lower half of the lai range. The cumulative frequency curves for the three fluxes in Fig. 5g and Fig. 5h deviate from the diagonal line that represents the initial uniform parameter distribution. Such a deviation indicates parameter sensitivity, with the steepest parts of the curves showing most frequent and thus optimal parameter values. Such a strong sensitivity for all three fluxes as to the lai value was only seen for a few parameters. For the parameters analyzed, a large range of responses was observed: e.g. to a few parameters only one flux was sensitive to whereas for some parameters the cumulative frequency curves for the different fluxes indicated optimal parameter values from deviating parameter ranges. Also, the sensitivity for the three fluxes to some of the parameters was not the same for both IOPs
Influential parameters for the three fluxes were identified by a comparison of the parameter distribution for the 10% best model runs to the original uniform parameter distribution with the Kolmogorov-Smirnov test. Thus, a list of influential parameters for the three fluxes for the two study periods was obtained by Staudt et al. (2010a, Appendix B). The influential parameters and also its number differed for the three fluxes. Plant physiological parameters, that were included in this sensitivity analysis additionally to the input parameters being user definable in the original ACASA version, were also among the influential parameters. There were also differences in the ranking and occurrence of influential parameters for the two time periods from different seasons.
However, about one third of the input parameters were not influential for the fluxes, indicating the problem of parameter equifinality, a problem also reported in several GLUE studies for
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Figure 5: Sensitivity graphs showing the range of the single-objective coefficients of efficiency for the best 10 percent parameter sets (left: IOP-1, right: IOP-2) for the sensible (H, a and b) and latent (LE, c and d) heat flux and the NEE (e and f) across the range of the leaf area index, lai [m2 m-2]. The vertical dashed line denotes the reference parameter value. Cumulative frequencies are plotted in (g) and (h) for the three fluxes as well as for the combined likelihood measure with the diagonal solid line showing a uniform parameter distribution for comparison. Figure taken from Staudt et al. (2010a, Appendix B).
complex process-based models (e.g. Franks et al., 1997; Schulz et al., 2001; Prihodko et al., 2008).
For the NEE, the lai and the basal microbial respiration rate were among the most influential parameters. As the effective basal microbial respiration rate depends also on the lai, an interaction between these two parameters was observed. These results were used to analyze the calculations of soil respiration in ACASA and to suggest improvements of the used algorithms.
1Diploma thesis of Andreas Schäfer (2010) was co-supervised by Katharina Staudt.
Figure 6: Predictive uncertainty bounds (5th and 95th quantile) and observed values (black dots) for the sensible heat flux (H, a), the latent heat flux (LE, b) and the net ecosystem exchange (NEE, c) for the coefficient of efficiency (IOP-1, dotted lines: individual best 10%, solid lines: combined). Figure taken from Staudt et al. (2010a, Appendix B).
The last step in this analysis was the calculation of uncertainty bounds for the best 10% model runs for the two IOPs (Fig. 6 for IOP-1). Measured values for all three fluxes were captured by these uncertainty bounds well, proving the ability of the ACASA model to reproduce these fluxes for our site. Figure 6 also includes uncertainty bounds for the three individual fluxes that were derived from conditioning on all three fluxes concurrently, thus from a combined coefficient of efficiency. These uncertainty bounds were smaller and encompassed less measured values. For IOP-2, this was especially evident for the NEE, where maximum daytime values were not captured by the combined uncertainty bounds.
A study applying the ACASA model at the Waldstein-Weidenbrunnen site for a longer time period than shown here was performed for the exceptionally warm year 2003 in a diploma thesis by Schäfer (2010)1. Testing ACASA for a one-year period allowed drawing conclusions about the ACASA model for different seasons of the year and especially for a dry summer period. As found for the GLUE analysis, best overall performance in terms of the coefficient of efficiency was observed for the sensible heat flux. For the very warm and dry month of August, agreement with measured above-canopy fluxes was less for the latent heat flux and the NEE than during the other months, with an overestimation of latent heat fluxes and an underestimation of the NEE.
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