4.3 Data assimilation experiments
4.3.2 Experiments with seasonal canopy albedo parameters
Figure 4.9 shows the conditional mode and the ensemble spread in model space for experi-ments without inflation and for inflation with magnitudes 0.02 and 0.04 for the estimation
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before inflation 0.02 inflated 0.02
before inflation 0.04 inflated 0.04
Figure 4.9: Assimilation results for one seasonal canopy albedo parameter in the visible (left) and the near-infrared (right) domain. Dark-coloured lines show the results before inflation and the light-coloured lines show the results after inflation.
of a seasonal canopy albedo parameter. Without inflation, the ensemble collapses during the first few assimilation steps. As a result, the conditional mode estimate diverges and cannot follow the seasonality of the parameter. The estimates from experiments with in-flation follow the seasonal cycle of the parameter. The effects of the inin-flation are the same as described for the estimation of a fixed parameter in the previous section.
As before, the experiments in the subsequent comparison of the four methods used an inflation magnitude of 0.04. Figure 4.10 illustrates the effects of the different update methods on the estimates of the conditional mean and the conditional covariance in model space. First, all four methods yield estimates that follow the prescribed seasonal cycle up to random variations. But all four methods are shifted by a constant value from the true parameter value. The results are qualitatively the same in the visible and near-infrared domain, although the estimates for the near-infrared parameter are much closer to each other. In both domains, the KF without transformation yields the largest estimates of the conditional mode and the normal approximation to the transformed conditional pdf yields the smallest estimates. The estimates of the covariance scaling method and the modified method of Simon and Bertino (2012) are nearly identical and lie in between the other two methods. The estimated conditional covariance, shown by the ensemble spread, of the method based on Simon and Bertino (2012) is larger than for the other three methods.
4.3 Data assimilation experiments
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Figure 4.10: Assimilation results for one seasonal canopy albedo parameter of an evergreen PFT in the visible (left) and the near-infrared (right) domain. The ensemble spread is the spread after the update before the ensemble is inflated.
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Figure 4.11: Assimilation results for one seasonal canopy albedo parameter of a deciduous PFT in the visible (left) and the near-infrared (right) domain. The ensemble spread is the spread after the update before the ensemble is inflated.
Figure 4.11 is similar to Figure 4.10 and shows the same quantities but the estimated pa-rameter belongs to a deciduous vegetation type (Temperate Broadleaf Deciduous) whereas the parameter in Figure 4.10 was that of an evergreen vegetation type (Tropical Ever-green). In conjunction with Figures 4.4 and 4.5, we see that all four methods are able to constrain the parameter only when observations of the canopy are possible. When the canopy fraction decreases due to a decrease in LAI, the conditional mode diverges from the truth. During phases with a small or no observable canopy fraction, the ensemble spread also grows continuously. When the canopy fraction starts to increase again, the ensemble spread decreases and the conditional mode approaches the true value again. Further, for the deciduous PFT, the differences in the estimated conditional covariance between the modified method of Simon and Bertino (2012) and the other three update methods are larger than for the parameter of the evergreen PFT.
The results for other vegetation types are qualitatively similar to either Figure 4.10 or Figure 4.11 and are summarised in Figure 4.12 and discussed in section 4.4. The results for the visible and the near-infrared canopy albedo parameters are qualitatively the same, with the normal approximation to the transformed conditional pdf underestimating the parameters while the other three methods overestimate them.
As for the estimation of the constant parameters, the KF without transformation shows
4.3 Data assimilation experiments
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Estimation errors in visible canopy albedo parameters
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TropEv NH TempBrDec NH
ConifEv NH Grass NH
TropEv SH TempBrDec SH
ConifEv SH Grass SH
Figure 4.12: Bias and error variability of the conditional mode for the estimation of seasonal canopy albedo parameters. Horizontal lines indicate the mean error, vertical bars above and below indicate one standard deviation of the errors.
RMSE bias std of errors without transformation 0.052 0.017 0.020 normal approx. to cond. pdf 0.024 -0.007 0.010
covariance scaling 0.026 0.007 0.011
Simon and Bertino (2012) 0.030 0.010 0.011
Table 4.2: Overall root mean square error (RMSE), bias and standard deviation of errors for the estimation of seasonal canopy albedo parameters.
the largest absolute errors while the other three methods perform similarly. But contrary to the example with constant parameters, we see different error variations for the different vegetation types. The estimates for the deciduous vegetation type have a higher error variability than the for the evergreen types. And the estimates for the SH coniferous type also have a higher error variability than for the NH coniferous type.
Figure 4.13 shows the time-series correlations of the estimated parameters with the true values and the ratios of their standard deviations (for an explanation of the diagram see Taylor, 2001). The PFTs can be divided into two groups, with the deciduous types and the coniferous type on the southern hemisphere in one group and the other types in the second group. The first group exhibits low correlation values (∼ 0.6 and below) and a higher variability in the estimated time series than in the true time series. The second group has high correlation values (∼0.8 and above) and approximately the same temporal variability as the true time series.
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Figure 4.13: Taylor diagram of the estimated time series of seasonal canopy albedo pa-rameters.