# Urban CO2 Budget: Spatial and Seasonal Variability of CO2 Emissions in Krakow, Poland
## 2 Methods
### CO\({}_{2}\) Flux Measurements  
The CO\({}_{2}\) flux from soils and water surfaces within the city limits has been measured directly with chamber method [18; 22]. Net CO\({}_{2}\) flux from the urban ecosystem was quantified using the relaxed eddy accumulation method [22]. The chamber method has been thoroughly discussed in numerous studies (e.g., [23; 24]). Closed (non-steady state) chamber method employed in this study estimates CO\({}_{2}\) flux by measuring the rate of change of CO\({}_{2}\) concentration within the chamber volume over time. Assuming the air in the chamber headspace to be ideal gas, CO\({}_{2}\) flux density F [umol m\({}^{-2}\) s\({}^{-1}\)] from the area A [m\({}^{2}\)], which is covered by the chamber is proportional to the rate of CO\({}_{2}\) concentration change in the headspace, \(\partial\)c/\(\partial\)t [umol mol\({}^{-1}\) s\({}^{-1}\)]:  
\[\mathrm{F}=(\partial\)c/\(\partial\)t) (pV/RTA), \tag{1}\]  
where p stands for atmospheric pressure [Pa]; R is the universal gas constant equal to 8.31 J mol\({}^{-1}\) K\({}^{-1}\); T-air temperature [K]; V-chamber headspace volume [m\({}^{3}\)]. As a result of a diffusive character of CO\({}_{2}\) emission from the soil or water surface, the increase of CO\({}_{2}\) concentration in the headspace volume is best described by exponential function (e.g., [23]). Two different chamber designs have been employed in the study: (i) a stainless steel square-based chamber with the volume of 45 L; and (ii) a cylindrical, stainless steel and plexiglas chamber with  
Figure 3: The REA-AGH site marked by black dot in the center of the map and its immediate vicinity, with established CO\({}_{2}\) basic source types (map source: [21]). a volume of 27 L and a pressure compensation vent [25]. Both chambers have been equipped with stainless steel collars inserted into the ground to avoid leakages. Laboratory and in-situ tests have been performed with both chamber designs. Additionally, a triple-channel system has been designed to simultaneously measure CO\({}_{2}\) flux with three identical chambers located on an area within ten-meter radius from the concentration analyzer. The concentration of CO\({}_{2}\) in the headspace volume was measured with Vaisala CarboCAP GMP343 probe (Vaisala, Vantaa, Finland) and, starting from 2011, with Picarro G2101i analyzer (Picarro Inc., Santa Clara, California, USA). The initial measurement setup (2009-2011) has been thoroughly discussed in [18]. The chamber measurements of soil CO\({}_{2}\) emissions have been performed during a four-year period (2009-2013). Each month, on the same day for all of the sites, a single measurement of the flux was taken. First, chambers collars were pressed into the ground. Unlimited access to the sites meant that it was not possible to leave the collars in the ground, as it is recommended for this type of measurement [23; 25]. To compensate for the soil disturbance, chambers were deployed for flux measurement at least fifteen minutes after installing the collar. During this time, the measurement system was vented with ambient air, and the soil temperature and humidity were determined. Soil temperature was measured once around each collar, with a thermocouple probe thermometer at 5 cm depth. When the ground was frozen, the surface air temperature was recorded. Soil humidity was measured at a 5 cm depth three times around each collar with a Theta probe coupled with a Delta T hand-held reader. The collars were newly installed in the ground during each measurement campaign, so the chambers headspace volume varied accordingly. Chamber closure time for a single-chamber setup depended on CO\({}_{2}\) increase rate and varied between 10 and 30 min. In a triple-chamber setup the total closure time was 9 min, with a \"\(3\times 3\)\" sequence of concentration analysis combined with delaying of subsequent chamber closing.