# Urban CO2 Budget: Spatial and Seasonal Variability of CO2 Emissions in Krakow, Poland
## 2 Methods
### Urban CO\({}_{2}\) Budget Estimation  
Net CO\({}_{2}\) emissions from Krakow area, expressed in CO\({}_{2}\) flux density (\(\mu\)mol m\({}^{-2}\) year\({}^{-1}\)) or in CO\({}_{2}\) flux (M\(\rm{MCO_{2}}\) year\({}^{-1}\)), were estimated using the following balance equation:  
\[\rm F_{net}=C_{traff}+C_{res}+C_{ind}+R_{soil}+R_{riv}+R_{hum}-GPP_{U}, \tag{3}\]where \(\rm F_{net}\) is the total net flux from the ecosystem to the atmosphere; \(\rm C_{traft}\), \(\rm C_{res}\), \(\rm C_{ind}\) indicate flux components from fossil fuels combustion in traffic, individual households, and industry, respectively; \(\rm R_{soil}\), \(\rm R_{riv}\), \(\rm R_{hum}\) indicate biogenic flux components, including soil respiration and soil organic matter decomposition, emissions from rivers and other surface waters and respiration of city inhabitants, respectively. \(\rm GPP_{U}\) represents photosynthetic uptake flux of \(\rm CO_{2}\) by the local biosphere, with an index \(\rm U\) emphasizing urban ecosystem. To estimate photosynthetic uptake of \(\rm CO_{2}\), a local-scale budget was calculated for the source area of the REA-AGH site. On the scale of the REA-AGH source area (Figure 3), not all of the \(\rm CO_{2}\) sources indicated in Equation (3) were present. Within this area, the full \(\rm CO_{2}\) budget consists of traffic emissions, individual households, inhabitant respiration and biogenic source, which is composed of soil emissions and the photosynthetic uptake of local biosphere. Equation (3) has been used on this local scale to estimate the photosynthetic uptake of \(\rm CO_{2}\) from the atmosphere (gross primary production) in Krakow:  
\[\rm GPP_{U}=C_{tra}+C_{res}+R_{soil}+R_{hum}-F_{net} \tag{4}\]  
where \(\rm F_{net}\) is a net flux of \(\rm CO_{2}\) to the atmosphere measured by REA. Within the REA-AGH source area no industry or water courses are present. The \(\rm CO_{2}\) flux from fossil fuel combustion in traffic and individual households have been estimated utilizing the 2019 version of the Emission Database for Global Atmospheric Research (EDGAR) [34]. In this database, the city is represented by four grid cells, latitudinally arranged. In the western part of the city emissions from residential buildings dominate, whereas in the eastern part industry is located, including the heat and power plant and Nowa Huta ironworks. The REA-AGH site is located in the western part of the city. The same concerns soil \(\rm CO_{2}\) flux measurement sites (S1-S4) and two riverine measurement sites (R1 and R2). Anthropogenic emissions in the EDGAR inventory are categorized, according to the Intergovernmental Panel on Climate Change (IPCC)guidelines [35]. To obtain traffic and residential emissions, the corresponding categories were summed up for the grid cell where the REA-AGH site is located, and then divided by the grid cell area of to obtain averaged \(\rm CO_{2}\) flux density. To estimate emissions from human respiration, municipal records in a form of an interactive gridded map (grid size: \(100\times 100\) m) [21] have been used to determine the number of people who live in the REA-AGH source area permanently. Then, using an estimate of a single person respiration provided by Moriwaki and Kanda [6], a collective \(\rm CO_{2}\) flux (\(\rm R_{hum}\)) was calculated. The estimation was done under the assumption that an approximately constant number of people were present within the area at any time. The assumption was supported by a mixed purpose of the surrounding buildings (both residential and offices). Still, due to the fact that lots of students are moving through the university campus (and the REA-AGH source area) during the day, the resulting human respiration flux can be underestimated by this assumption. On a city scale, soil emissions of \(\rm CO_{2}\) in Krakow have been estimated, based on the chamber measurements and municipal land-use data [36]. Each of the undeveloped land cover types listed in the municipal land-use report were assigned to representative chamber measurement site.