# Analysis of Four Years of Global XCO\({}_{2}\) Anomalies as
## 3 Global XCO\({}_{2}\) Anomalies  
CO\({}_{2}\) has a long atmospheric lifetime and relatively large background concentrations (-410 ppm). Because of this, XCO\({}_{2}\) varies by only about 2% from pole-to-pole and over the seasonal cycle. Meanwhile, XCO\({}_{2}\) variations corresponding to anthropogenic sources are even smaller on the scale of the satellite sounding (2-4 km\({}^{2}\)). High precision is therefore essential to quantify XCO\({}_{2}\) anomalies associated with these sources. Methods like those used to map short-lived air pollutants, like NO\({}_{2}\), based on averaging out the outflow downwind from the emission sources, cannot be directly applied to space-based CO\({}_{2}\) measurements. The large CO\({}_{2}\) background and seasonal variability must be removed before being able to highlight the emission areas. In order to extract information about the anthropogenic and biogenic signatures from OCO-2 retrievals, we use the concept of XCO\({}_{2}\) anomaly [21], defined as the difference between the individual XCO\({}_{2}\) value measured by OCO-2 and the daily background:\[\text{XCO}_{2}(\text{anomaly}) =\text{XCO}_{2}(\text{individual})\] \[\qquad-\text{XCO}_{2}(\text{daily background}). \tag{1}\]  
This equation provides an anomaly value for each OCO-2 data point. Using the daily background allows us to remove the seasonal variability and the increasing trend of CO\({}_{2}\) concentrations. Once we obtain the anomalies for each OCO-2 measurement point, we define a spatial grid (e.g., \(1^{\circ}\times 1^{\circ}\), latitude-longitude) and calculate the mean at each grid point over a defined period of time. Figure 1 shows examples of mean XCO\({}_{2}\) anomalies for one day, one week, one month and one year. The resulting anomaly maps illustrate the areas where CO\({}_{2}\) is emitted (positive anomalies) into the atmosphere and those acting as sinks, where CO\({}_{2}\) is absorbed at the surface (negative anomalies). The strength of this approach is that it only uses satellite-based measurements and is not dependent on patterns in a priori fields, external data or other assumptions in atmospheric chemistry-transport models. Defining the area over which the daily background is calculated, is a critical step in the analysis. In [21], we focused on three selected anthropogenic emission areas: (1) North America, (2) Europe, northern Africa, and Middle East, and (3) East Asia. In this paper, our aim is to obtain comparable anomalies for different regions. In order to obtain the background, we calculate the daily medians for each 10-degree latitude band and linearly interpolate the resulting values to each OCO-2 data point. The median was chosen because it better represents the typical value in each latitude band, and it is not skewed towards extreme values. Figure 2 shows the daily XCO\({}_{2}\) background as a function of latitude interpolated at 1-degree resolution. The interpolation step removes the sharp latitudinal boundaries that would result if the daily medians at different latitude bands were used directly. In particular, we would obtain a sharp boundary between the northern high mid-latitudes (40\({}^{\circ}\)N-60\({}^{\circ}\)N) and lower latitudes during summer months due to the stronger (and shifted) CO\({}_{2}\) uptake. The median XCO\({}_{2}\) values for each 10-degree latitude band as well as their latitudinal distribution for selected days between September 2015 and September 2016 are included in Figure S1 (top and bottom panels, respectively). The background used in the calculation of the anomalies changes at different times of the year and over different regions. The peak of the seasonal cycle shifts during the year from the Northern to the Southern hemisphere. Also the amplitude of the seasonal cycle is much larger in the Northern Hemisphere due to the strong seasonal biospheric flux differences. Figure 2 also shows the XCO\({}_{2}\) values increasing by about 10 ppm from September 2014 to September 2018.