## 2 Materials and Methods
### Data Preparation  
We first group the daily, spatially irregular SIF and XCO\({}_{2}\) measurements and their corresponding measurement error variances by month and average both the measurements and the measurement error variances onto a regular grid with a 0.05-degree spatial resolution (around 5.6 km \(\times\) 5.6 km at the Equator), which aligns with the MODIS Climate Modeling Grid. This resolution is the same order of magnitude as that of the OCO-2 footprint and, by averaging multiple measurements, we effectively reduce the measurement error at this resolution [1]. For illustration purposes, we restrict the gridded data used in our analysis to a large region over North America within latitude and longitude boundaries of 22 to 58 degrees North and \(-\)125 to \(-\)65 degrees East, respectively. This region, which includes the conterminous United States, is similar to that considered by [24], and features heterogeneous land-cover types over which to evaluate the coSIF data product.  
As an indicator of photosynthetic activity, SIF is expected to exhibit an inverse relationship with XCO\({}_{2}\). Indeed, the monthly time series in Figure 1 show that SIF and XCO\({}_{2}\) follow strong seasonal patterns that are shifted relative to one another, with the annual maxima in SIF occurring about one month before the annual minima in XCO\({}_{2}\). To leverage this dependence, we use both SIF data and XCO\({}_{2}\) data one month ahead in a multivariate spatial statistical model. We present our results for four months in 2021 to represent the four seasons in North America. For SIF, we use February, April, July, and October 2021, and hence we group these with the XCO\({}_{2}\) data from March, May, August, and November 2021, respectively. For each pair of months, the columns of Figure 2 offer histograms of the OCO-2 data at a 0.05-degree resolution, along with the number of data points available in each month. As in Figure 1, Figure 2 shows that larger XCO\({}_{2}\) values follow months in which SIF values are small, and that XCO\({}_{2}\) decreases after months in which SIF values are larger. Additionally, Figure 2 shows that there is more variability in the summer months: July (SIF) and August (XCO\({}_{2}\)). This variability is due to increased SIF activity in certain productive regions, which in turn leads to additional spatial variability in XCO\({}_{2}\). Figure 3 shows the spatial distribution of the OCO-2 data at a 0.05-degree resolution for the summer months. Notice the spatial variability in both SIF and XCO\({}_{2}\), as well as the large gaps where there are no data.  
Figure 1: Time series of OCO-2 SIF and XCO\({}_{2}\) averaged by month for data available between September 2014 and February 2022 over North America. The gap in both datasets near the middle of 2017 is due to a time period when the OCO-2 satellite was offline.  
Figure 3: OCO-2 data over North America averaged over a month and gridded to 0.05-degree resolution. **Top**: SIF in July 2021. **Bottom**: XCO\({}_{2}\) in August 2021. The 0.05-degree cells containing the data are enlarged for visibility. The red squares outline two validation blocks considered in Section 3.3.  
Figure 2: Histograms of OCO-2 data over North America averaged over a month and gridded to 0.05-degree resolution. **Top panels**: SIF in February, April, July, and October 2021. **Bottom panels**: XCO\({}_{2}\) in March, May, August, and November 2021. Panel legends indicate the number of data points available in each month.