# Urban CO2 Budget: Spatial and Seasonal Variability of CO2 Emissions in Krakow, Poland
## 2 Methods
### CO\({}_{2}\) Flux Measurements
The CO\({}_{2}\) concentration increase recorded for a single chamber in this setup consisted of three parts, each three minutes long, with gaps in between, when the concentration in other chambers was measured. In order to perform measurements of CO\({}_{2}\) flux from water surfaces, a floating chamber has been designed. The chamber was constructed using a 74-L PVC container equipped with two floats, stabilizing its position on the water surface and an anchor. Both CarboCAP and Picarro analyzers were used to measure the CO\({}_{2}\) concentration in the headspace volume. The CO\({}_{2}\) emissions from Vistula river were measured at three sites (R1-R3, Figure 2) on monthly basis, for approximately one year. Measurements were performed from riverbanks in places free of dead zones and obstacles to water flow. An anchor was used to fix chamber position at a distance of several meters from riverbanks. Sites R1 and R2 were located within the backwater zones of navigation dams, characterized by low water velocities in the whole cross section of the river. River flow at site R3 was fast and turbulent. After flushing the system with ambient air, the chamber was put on the water surface. The closure time depended on the CO\({}_{2}\) increase rate, and usually varied between 10 and 40 min. In the meantime, water temperature, pH and electric conductivity were being measured in situ by portable sensors, and samples were collected for determination of alkalinity by the Gran titration method, and further calculation of partial pressure of dissolved CO\({}_{2}\) (pCO\({}_{2}\)) [17]. Relaxed eddy accumulation (REA) method is a modification of an established and widely used eddy covariance methodology. Eddy covariance method quantifies the flux of CO\({}_{2}\) that is being transported up (so-called updraft) and down (so-called downdraft) at the given location through the turbulent mixing of air; time-averaged covariance of vertical wind speed and concentration is a measure of net CO\({}_{2}\) flux (e.g., [26]). Due to the turbulent movement of air, a high frequency measurement (i.e., 10 Hz) of both vertical wind speed as well as concentration is required for eddy covariance. In contrast, relaxed eddy accumulation method allows for lower measurement frequency [27; 28]. Instead of direct measurement of fluctuations in concentration of the constituents of interest, it utilizes a system of fast-changing valves, which direct air according to vertical wind direction to one of two containers attached to the sampling system. The accumulation of air over a fixed time interval corresponds to time-averaging of eddy covariance method, but also allows for off-line gas concentration measurement with a slow analyzer. The CO\({}_{2}\) flux, F\({}_{c}\), is calculated as a product of updraft and downdraft CO\({}_{2}\) concentration difference (\(\Delta\)c), and standard deviation of vertical wind component, \(\sigma_{\rm w}\):  
\[\rm F_{c}=\beta\sigma_{\rm w}\ \Delta c, \tag{2}\]  
Where \(\beta=0.56\) is an empirical constant that accounts for a fixed sampling rate [29]. To maximize concentration difference between updraft and downdraft, a so-called dynamic dead band was introduced, meaning that for vertical wind speed less than a prescribed threshold value no sampling is performed. The threshold value is determined dynamically through running mean of vertical wind speed standard deviation [30]. The REA-AGH measurement system that was employed in Krakow was designed based on systems dedicated to aerosols and methane measurements [27; 28]. The system is composed of: (i) a 10 Hz three-dimensional anemometer Gill Windmaster Pro (Gill Instruments Ltd., Lymington, UK); (ii) a set of fast-changing electromagnetic valves that separate updraft and downdraft air samples along with a data logger CR-3000 (Campbell Sci, Logan, Utah, USA); (iii) two pairs of containers for sampled air; and (iv) Picarro G2101i analyzer.