# Urban CO2 Budget: Spatial and Seasonal Variability of CO2 Emissions in Krakow, Poland
## 3 Results and Discussion
### Uncertainty Estimation for Components of the CO\({}_{2}\) Budget  
In order to assess how uncertain the estimated GPPU and Ftot values are, the uncertainty propagation law was applied to Equations (3) and (4). For the Rsoil term, a combination of a single flux measurement uncertainty of 7.0% (with 0.05 and 0.95 percentiles equal to 0.8% and 30.4%, respectively) and the standard deviations of seasonal mean flux at sites S1 and S3 were applied to obtain the respective uncertainty value of 0.28 umol m\({}^{-2}\) s\({}^{-1}\). Similarly, uncertainty of the CO\({}_{2}\) flux from the Vistula river was calculated as 0.31 umol m\({}^{-2}\) s\({}^{-1}\), with the flux results from all three measurement sites. The uncertainty of the single-point eddy covariance flux measurements have been recently assessed in Helsinki, with a recommendation for a general rule of thumb that a 12% CO\({}_{2}\) flux bias can be applied in densely built-up areas [37]. Additional systematic errors connected with possible undetected leakages of REA system were taken into consideration as well, and, thus, the overall relative uncertainty of the Fnet in the order of 20% was assessed. The differences between the reported emissions for the EDGAR database versions 4.2 and 5.0 were assumed as a measure of uncertainty of Ctra and Cind terms, 74% and 10% respectively. The same uncertainty was assumed for Cres term as for Cind. Human respiration term Rhum relative uncertainty was assumed to be 20%, to consider human movements and population changes in time. Applying the above estimations and uncertainty propagation law to Equation (4), the uncertainty of photosynthetic uptake flux (GPPU) estimate was assessed as 1.62 umol m\({}^{-2}\) s\({}^{-1}\) (50% relative), with the main source of uncertainty being the anthropogenic emissions inventory data. Similarly, applying the estimated uncertainty values to Equation (3), and additionally assuming that land cover data presented in Table 4 are certain, the annual CO\({}_{2}\) emission from municipal area of Krakow was assessed as 7.27 \(\pm\) 0.74 Mt CO\({}_{2}\) yr\({}^{-1}\). The estimation of Rsoil term based on the chamber measurements does not take into account aboveground respiration of high-rise green. In a temperate, humid climate, deciduous forest respiration (both autotrophic and heterotrophic; both belowground and aboveground) is a source of 1048 \(\pm\) 64 gC m\({}^{-2}\) annually, and the respective value for evergreen forests is 1336 \(\pm\) 57 gC m\({}^{-2}\) yr\({}^{-1}\)[51]. \begin{table}
\begin{tabular}{l c} \hline \hline
**Location** & **CO\({}_{2}\) Emission [kg CO\({}_{2}\) m\({}^{-2}\) yr\({}^{-1}\)]** \\ \hline London [8] & 35.5 \\ Florence [46] & 30.3 \\ Kraków (this study) & 22.3 \\ Basel [42] & 17.6–19.4 \\ Helsinki city center [45] & 17.4 \\ Copenhagen [47] & 12.8 \\ Lödz [41] & 10.8 \\ Helsinki university campus [48] & 6.5 \\ Essen [49] & 6.0 \\ Gliwice [50] & 2.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: CO\({}_{2}\) emissions from European cities reported in the literature. Forests cover 1731 hectares, or 5.3% of total Krakow area. According to the Regional Dictorate of the State Forests, 61.7% of that is coniferous and 38.3% is deciduous [52]. The remaining 633 ha of an area, which sums up to 23.64 km\({}^{2}\) in Table 4, under the category forests and parks, is covered by parks and orchards, so it was assessed that a majority of tree species in this land cover is deciduous (70%) and the rest is evergreen (30%). Using the fluxes estimated by [PERSON] et al. [51] and above fractions of deciduous and evergreen species, the CO\({}_{2}\) annual respiration of forests and parks in Krakow was assessed as 0.078 MtCO\({}_{2}\) and 0.026 MtCO\({}_{2}\) respectively, summing up to the total emission of 0.104 MtCO\({}_{2}\) from tree-covered areas in the city. Since the obtained value of 0.104 Mt CO\({}_{2}\) represents a maximum underestimation that might take place due to omitting aboveground respiration, it was assumed to be a reliable measure of this uncertainty.