A Study on Inferring Diurnal Cycles of XCO$_2$ from Current and Future Space-Based Missions

Net ecosystem exchange (NEE) measures the net transfer of carbon between terrestrial ecosystems and the atmosphere, and is an important quantity for understanding land-atmosphere feedbacks and constraining the land-carbon sink. Atmospheric inverse models and biophysical models provide regional and global NEE estimates, but validation of these models is limited by the sparsity and distribution of flux towers that measure NEE. NEE can also be calculated from diurnal cycles of XCO$_2$ such as those observed by the Total Carbon Column Observation Network (TCCON). While TCCON sites themselves have the same physical limitations as flux towers, XCO$_2$ is a quantity that can be measured via remote sensing, and this leads to the possibility of obtaining NEE through global space-based observations. XCO$_2$ is observed by satellites such as the Orbiting Carbon Observatory 2 and 3 (OCO -2 and -3), which working together have the potential to observe locations between $\sim$ 52\textdegree{}S and 52\textdegree{} N twice a day but at a sparse temporal frequency. Here, we investigate the possibility of using machine learning (ML) to extrapolate full diurnal cycles from sparse space-based measurements, which could be in turn be used to derive NEE. Here, we assess ML's capabilities with current space-based missions, as well as how to optimize performance for potential future missions. We find that the current temporal sampling from OCO-2 and -3 is not ideal for this purpose, and our ML approach is not able to reliably infer either diurnal cycles or drawdown in simulations mimicking the times of day OCO-2 and -3 can observe the same location. A thrice-daily observation pattern, such as could be achieved with a GeoCarb-like (geosynchronous) instrument, provides much better performance. However, it is also essential that systematic biases between observations a different times of day be minimized or well characterized, as the ability to predict diurnal cycles or drawdown decreases when the standard error between the means of observations at different times of day exceeds $\sim$ 0.1 ppm.