## 6 Sensitivity Analyses for the Retrieval of GOME-2A SiF Using PCs
### Number of PCs  
In addition to the baseline retrieval, which uses 35 PCs, we performed retrievals for the four test months using 15, 25 or 45 PCs while keeping all other settings the same. The results are summarised in Table 3 and presented in terms of differences with respect to the baseline of 35 PCs. The comparison includes only grid boxes over land. In a qualitative sense, we find that global maps when using only 15 PCs show patches with negative values as well as large patches with highly positive values. The patches with negative SiF values more or less disappear when using 25 PCs or more and SiF patterns correspond much better to actual vegetation patterns. SiF values tend to be lowest for the baseline retrieval with 35 PCs (also when compared to the retrieval with 45 PCs). A sufficient number of PCs is needed to capture the spectral variability of atmospheric transmission. When this number has been reached, one would in principle not expect the retrieval outcome to change much when more PCs are added. The correlation between SiF values for 25 and 35 PCs is about as high as between SiF values for 45 and 35 PCs: this correlation is well above 0.9. However, we see that differences between SiF values for 25 and 35 PCs, in terms of RMS, absolute value of the mean difference and the standard deviation, are higher. The mean difference between SiF values for 45 and 35 PCs has reduced to 0.07 mW/sr/m\({}^{2}\)/nm and it seems justified to not further increase the number of PCs from 35 to 45 as the two conditions already resemble each other and we do not want to use more PCs than needed. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Number of PCs** & **Month** & **RMS** & **Mean** & **STD** & **R** & **Slope** & **Intercept** & **N** \\ \hline \multirow{4}{*}{15} & January & 0.85 & \(-0.11\) & 0.85 & 0.67 & 0.39 & 0.44 & 28,844 \\  & April & 0.80 & 0.54 & 0.59 & 0.83 & 0.39 & 0.00 & 37,706 \\  & July & 1.52 & 1.00 & 1.14 & 0.85 & 0.29 & 0.16 & 44,326 \\  & October & 0.74 & 0.32 & 0.67 & 0.79 & 0.40 & 0.13 & 40,786 \\  & **All** & **1.06** & **0.49** & **0.94** & **0.74** & **0.32** & **0.19** & **151,662** \\ \hline \multirow{4}{*}{25} & January & 0.20 & 0.09 & 0.18 & 0.99 & 0.82 & 0.04 & 28,844 \\  & April & 0.25 & 0.19 & 0.16 & 0.97 & 0.76 & \(-0.06\) & 37,706 \\  & July & 0.90 & 0.69 & 0.58 & 0.94 & 0.48 & 0.00 & 44,328 \\  & October & 0.51 & 0.34 & 0.39 & 0.95 & 0.58 & \(-0.01\) & 40,786 \\  & **All** & **0.57** & **0.36** & **0.45** & **0.92** & **0.56** & **0.03** & **151,664** \\ \hline \multirow{4}{*}{45} & January & 0.15 & \(-0.06\) & 0.13 & 0.99 & 1.13 & \(-0.01\) & 28,844 \\  & April & 0.18 & 0.09 & 0.15 & 0.97 & 0.78 & 0.01 & 37,706 \\ \cline{1-1}  & July & 0.17 & 0.11 & 0.13 & 0.99 & 0.84 & 0.01 & 44,328 \\ \cline{1-1}  & October & 0.22 & 0.12 & 0.18 & 0.98 & 0.77 & 0.01 & 40,786 \\ \cline{1-1}  & **All** & **0.18** & **0.07** & **0.17** & **0.97** & **0.86** & **0.01** & **151,664** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Various statistical parameters describing the difference between retrieved SiF values for the months of January, April, July and October 2013 when using 15, 25 or 45 PCs as compared to 35 PCs (baseline). Only grid boxes over land are taken into account. Parameters are the root-mean-square difference (RMS), the mean difference and the standard deviation (STD) of the difference, the correlation coefficient (_R_), the slope and intercept of the regression line, and finally the total number of valid monthly grid box pairs (_N_) from which differences are calculated. The difference is defined as SiF(test) \(-\) SiF(baseline) and the regression line as SiF(baseline) = intercept + slope \(\times\) SiF(test). All correlations are highly significant. The unit of SiF values is mW/sr/m\({}^{2}\)/nm, as before. When more PCs are used there is the potential danger of overfitting or noise fitting. This would show up in the retrieval results as retrieved SiF values becoming noisier. The comparison with flux tower GPP is important here.