Análisis de las verificaciones aplicado a un mega concurso: METAL 1 S.A p/ Conc Prev

In order to better understand previous findings we have a closer look at the covariance structure of the Urban-all simulation (Fig. 5.11). The prior covariance matrix (left panel) mainly shows diagonal values, which indicate the uncertainty in a parameter. Some parameter errors are also correlated (we will call this parameter correlation), indicated by off-diagonal values. A positive (negative) parameter correlation means that a positive deviation in one parameter has to be compensated by a positive (negative) deviation in the other parameter. This affects the cost of tuning a parameter and thus provides additional information to the inversion. Additionally, the presence of a parameter correlation between two variables means that they are difficult to differentiate from an atmospheric signal. In other words, if A and B are correlated a CO2 residual can be reduced

by tuning A or B, or both. The inversion system is unable to identify with which magnitude to correct either of the parameters. Unless the variables also affect another observed quantity in a different way, for example the mixing ratio of a co-emitted tracer.

The prior covariance matrix (Fig. 5.11, middle panel) shows that we assumed positive parameter correlations between tracer ratios from the same sector (road traffic: cars (7A) and HDV (7B), shipping: ocean (8A) and inland (8B)), but also between the RCO and RNOx of

road traffic. The reason is that the emission ratios are mainly determined by technological implementations that we think affect the subsectors equally. Moreover, we also assume the technology to impact the emissions of CO and NOx equally. In contrast, SO2 emissions

are usually reduced by desulphurization methods which is different from the techniques to reduce CO and NOx emissions. Therefore, we assume RSO2 not to be correlated with RCO

and RNOx. We indeed see that the prior errors show the same sign for the correlated

parameters and the optimized values of correlated parameters are both reduced or increased. The only exception is the RCO for road traffic, which is underestimated for cars

and overestimated for HDV. Our inversion is able to recognize the discrepancy between the RCO from cars and HDV as it decreases the one while increasing the other, unlike

suggested by the positive correlation. However, the corrections are in the wrong direction. Equally interesting is the posterior covariance matrix. The diagonal values in the prior covariance matrix are larger than in the posterior covariance matrix (Fig. 5.11, left panel), indicating that the uncertainty of the parameters is reduced. In contrast to the prior covariance matrix, the posterior covariance matrix (Fig. 5.11, right panel) displays a significant number of off-diagonal values. Note that this is an average matrix for all

OPTIMIZING A DYNAMIC EMISSION MODEL

129 fourteen days and that variations exist between the days. Therefore, the parameter correlations in this graph are not averaged out and are consistently present. Now the question is whether the presence of parameter correlations is beneficial (extra information) or harmful (difficult to discern variables) for the inversion.

Figure 5.11: Prior (middle panel) and 14-day average posterior (right panel) covariance matrix P from the run Urban-all. On the diagonal the variances (uncertainties in a variable) are shown, whereas off-diagonal values indicate covariances or correlations between different variables. The left panel shows the difference between the prior and posterior diagonal values. All differences are positive, indicating an uncertainty reduction.

If we compare the posterior uncertainties of a parameter for the individual days against the absolute sum of the correlations this parameter has with the other parameters for the same days, then we find a positive relationship for all parameters with correlation coefficients between 0.23 and 0.89 (on average 0.59). So days with a high posterior uncertainty of a parameter correspond to days where the error of that parameter also correlates strongly with errors of other parameters. A weak correlation means that a parameter is less sensitive to the presence of error correlations with other variables, therefore we will call this the sensitivity correlation. The weakest sensitivity correlations are related to the RNOx, RSO2 and emission factor of the industrial sector. These parameters

show little variability during the fourteen days and an average over the entire period gives a robust estimate of the true parameter values. The parameters with the strongest sensitivity correlations are RCO of households and road traffic (HDV). These parameters

show large fluctuations during the fourteen days and the 2-week average values tend to be dominated by a few outliers. If a few days can be selected on which the parameter correlations are weak (i.e. the atmospheric signal clearly contains information about this specific parameter), the top-3 estimate displayed in Fig. 5.7 can still give a good estimate of the parameter value, as is true for the household emission ratio. However, for road traffic (HDV) the parameter correlations always seem to have an effect and this parameter is less well-constrained.

A few parameters with a particularly large amount of strong parameter correlations are RCO from industry (3), RNOx from cars (7A) and RSO2 from ocean shipping (8A). Although

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these three emission ratios are improved during optimization, the remaining uncertainties are large. The optimized RCO of industry is 3.3 ppb/ppm with an uncertainty of about 25%,

the optimized RNOx of road traffic (cars) is 1.9 ppb/ppm with an uncertainty of about 28%

and the optimized RSO2 of shipping (ocean) is 3.3 ppb/ppm with an uncertainty of about

65%. These results suggest that the presence of parameter correlations in the posterior covariance matrix makes the optimization procedure more difficult for that specific parameter, due to the inability to isolate the effect of this parameter on the atmospheric observations. This results in poorly constrained parameters and/or large posterior uncertainties. However, this is only true when parameters are sensitive to parameter correlations (high sensitivity correlation). Why some parameters are more sensitive to the presence of parameter correlations than others needs to be investigated. One hypothesis is that the presence of parameter correlations is less problematic when the parameter can be discerned by another signal, for example from a co-emitted tracer.