# Urban CO2 Budget: Spatial and Seasonal Variability of CO2 Emissions in Krakow, Poland
## 2 Methods
### Statistical Analyses and Uncertainty Estimations  
Measurement uncertainty for a single \(\rm CO_{2}\) chamber flux analysis was calculated with the uncertainty propagation law applied on Equation (1). Out of the terms present in this equation, only the universal gas constant (R) is assumed to be exact. Uncertainty of concentration increase rate was derived from the regression fit parameters. Due to variable chamber height, the collar insertion height was being measured at 10 different points of the circumference and an average value and its standard deviation was determined to derive uncertainty of height measurement. Temperature and atmospheric pressure measurements were performed with an accuracy of 0.1 \({}^{\circ}\)C and 0.1 hPa, respectively. If the triple-chamber system was deployed, mean CO\({}_{2}\) flux result was calculated with uncertainty composed of the uncertainty of the average flux derived from propagation law and the standard deviation of an average flux calculated with a correction due to small number of samples (c\({}_{4}\) unbiased standard deviation estimation correction factor). The seasonally averaged CO\({}_{2}\) flux was calculated for each site, along with an unbiased standard deviation.  
Based on the horizontal wind direction, each REA flux result was assigned to one of the basic source zones (Figure 3). In addition to the mean and its standard deviation, the median flux values, along with the 0.05, 0.25, 0.75, and 0.95 percentiles, were calculated for each season within the respective spatial zones. Since by design REA provides a large set of data, the calculation of single flux measurement uncertainty is redundant, because its value remains negligible, compared to the dispersion of the obtained fluxes. Therefore, uncertainty of the median of REA flux was assessed based on the literature regarding eddy covariance measurements [37]. Additional systematic errors connected to possible undetected leakages of REA system were taken into consideration.  
At a spatial resolution of 0.1\({}^{\circ}\), different emission inventories in urban areas can differ by more than 100% [38]. Moreover, large differences for the same emission types for Krakow can be found between different versions of the same database. For instance, Krakow road transportation related CO\({}_{2}\) emission (IPCC category 1A3b [35]) reported in EDGAR version 4.2 published in 2011 was only 25% of the value that is reported in the recent (2019) version of this database for the same year; however some differences may occur due to changes in categories definition or database structure. Undoubtedly, inventory-related terms of Krakow CO\({}_{2}\) budget are burden with higher uncertainty compared to the measured fluxes, and it is difficult to assess a reliable uncertainty of those values. For a crude estimation, differences between the reported emissions for EDGAR database versions 4.2 and 5.0 were assumed as a measure of uncertainty of C\({}_{\text{tra}}\) and C\({}_{\text{ind}}\) terms in Equation (3), being equal 74% and 10% respectively. The change in the database structure meant that the residential emissions difference between different versions of EDGAR database was impossible to determine, so the same uncertainty was assumed for C\({}_{\text{res}}\) term as for C\({}_{\text{ind}}\).