Fit to Data

The overall quality of the fit to the data is embodied in the final value of the cost function. Strictly there is also a contribution from the mismatch between initial and predicted parameter values but this is much smaller than the data contribution. This is hardly surprising given the 10332 data points in the concentration dataset versus only 58 parameters. The final value of the cost function is 12316, with a value of 11766 resulting from the concentration mismatch. This suggests an adequate fit to the data, however only from years in which measurements were made at a site are attempt to fit in the extended dataset of GLOBALVIEW-CO₂ [2001]. The real number of observations is hence 6936 observations with any real input into the cost function.

6.4 Results and Discussion 95 1980 1985 1990 1995 2000 Year 340 360 380 400 CO 2 [ppm]

Figure 6.6: Time-series of atmospheric CO₂concentration at Mauna Loa, Hawaii. The black line denotes the measured val- ues, the red line the prognosed concentra- tion with the optimised parameter vector, the green line the simulated concentration as derived from the first guess parameter values including the erroneous spin-up pro- cedure and the blue line the first guess con- centrations with a corrected spin-up.

The average squared mismatch or reduced χ2statistic is the most common measure of the quality of a fit. In this case it is 1.69. In general a statistical consistent fit to the data would give a

χ2 of ≈ 1. The larger value here suggests that the model is incapable of fitting the data as well as the data uncertainties demand. Enlarged data uncertainties would propagate through the calibration algorithms to enlarged parameter uncertainties. Therefore, the uncertainty estimates on parameters should be regarded as slightly optimistic.

Figure 6.6 shows besides the observed and prognosed times-series of atmospheric CO₂ con- centration also two simulated time-series using the a priori parameter values from two different BETHY versions. The green line represents concentrations as simulated by BETHY 11 and shows a rather strange behaviour with a rapid increase of CO₂ during the first three simulation years. This is because the fast decomposing soil carbon pool was not in equilibrium at the beginning of the simulation period due to an error in the spin-up procedure. This error has been removed in BETHY 12 which can be seen by the blue line. The dramatic rise of simulated atmospheric CO₂ concentrations to almost 400 ppm is a consequence of the a priori assumption of a neutral biosphere over the simulation period (β = 1) and is apparent in both simulations as this is a fixed point determined by the background fluxes. However, all results presented here are derived from BETHY 11 and therefore, as mentioned above, are only preliminary. The optimal fit to the data seems to be rather good (as also discussed in the following) although it is derived from the erroneous BETHY 11 version.

Simulated time-series of CO₂ concentrations at a station can be decomposed into a climato- logical seasonal cycle and interannual variability, the latter often filtered to emphasize signals of key scientific interest. Here, the procedure of Thoning et al. [1989] is used for this decomposition and the fits are displayed exemplarily for four selected stations. Figure 6.7 shows seasonal cy- cles fitted to the simulated and observed concentration time-series at Point Barrow, Alaska and Niwot Ridge, Colorado. The uncertainties indicated by the dotted lines are the one standard deviation uncertainties averaged over the whole record. For both stations Niwot Ridge and Point Barrow the simulated seasonal cycle fits the observed data well. This is not entirely surprising as the full BETHY model itself constrained only by satellite data (here, the first assimilation

96 First results from a prototype Carbon Cycle Data Assimilation System (CCDAS)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month -15 -10 -5 0 5 10 [ppm]

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month -15 -10 -5 0 5 10 [ppm]

Figure 6.7: Simulated (red) and observed (black, with mean uncertainty) seasonal cycle of atm. CO₂for two sites: Niwot Ridge, Colorado (left) and Point Barrow, Alaska (right).

step) shows already a modelled seasonal cycle consistent with CO₂ measurements [Knorr, 1997]. There is a striking mismatch between simulated and observed concentrations in spring at Point Barrow station which is also already apparent in the original BETHY model [Knorr, 1997] and thus, seems to be a model inherent problem although the magnitude of the mismatch is largely reduced in this study here.

Figure 6.8 shows errors (simulated − observed) concentration time-series for Mauna Loa, Hawaii and South Pole filtered to retain periods greater than 80 days [Thoning et al., 1989]. The constant uncertainties are the averages over the yearly values used in the optimisation. The first thing to note is that, for both records, the mismatch in the first year (1979) is much bigger than the uncertainty which is clearly a result of the erroneous spin-up procedure. However, for the rest of the simulation period (1980 to 2000) differences are generally smaller than observational uncertainties, suggesting a good fit to the observations. There are periods (mainly the years 1984 and 1986) when trends in the observed and simulated time-series at Mauna Loa are clearly different. This mismatch seems most likely to indicate errors in sources which impact the measured concentrations as opposed to transport errors. The south Pole record shows a very good fit between the model and observations (neglecting the year 1979). This is encouraging for interpretations made at a global scale since South Pole, remote as it is from local sources, is probably the best available record of globally integrated concentrations at interannual timescales.