## 3 Earth Surface Modelling Advances and Links with EO Datasets
### Land-Atmosphere Fluxes
#### 3.2.4. \(\text{CO}_{2}\) Anthropogenic Fluxes and Co-Emitters  
In the atmospheric source inversion community, the use of satellite data to constrain trace gas fluxes was made possible through the adoption and adaptation of data assimilation techniques already in use at operational NWP centers. As a result, two methods have emerged: Four-Dimensional Variational (4D-Var) and Ensemble Kalman Filter (EnKF) [200] The computational efficiency of 4D-Var to solve high-dimensional inverse problems and its ability to accommodate a large amount of remote-sensing measurements over long periods of time, made 4D-Var a method of choice in the source inversion community. However, the development and maintenance of adjoint models in variational approaches can be cumbersome. On the other hand, EnKF-based methods use a small ensemble of perturbed model simulations to represent and propagate the error statistics explicitly, while similar methodological difficulties characterize DA in NWP and source inversion problems, it is worth noting some specific aspects of the latter. First, while the prior (or background) information in NWP DA systems is associated to prognostic variables of the model that are often directly observed, the source  
Figure 16. Seasonal cycles over different climates (**top**: energy limited—northeastern US, **middle**: Mediterranean climate in Spain, **bottom**: rainforest in the Amazon) as assessed using different sources of data: Vegetation Optical Depth (VOD) at high (X-band), medium (C-band) or low frequency (L-band), Enhanced Vegetation Index (EVI) and Solar-Induced Fluorescence (SIF) using the GOME-2 satellite data.  
inversion problem involves model parameters that are usually measured only indirectly, making the quality of the optimised sources strongly dependent upon the accuracy of the transport model itself. Additionally, the prior error statistics prescribed for the bottom-up emission sources are often very uncertain owing to the sparsity of the available observational network [201]. These uncertainties in the transport model and the prior error emissions can translate into large errors in the inferred posterior estimates. Although current methodologies used for top-down atmospheric source inversions have reached a high level of sophistication enabling efficient and scalable computation of the posterior estimates along with their information content (i.e., posterior errors, observational constraints), the lack of observations to provide source estimates at accuracies and spatio-temporal resolutions compatible with environmental policy requirements is a key remaining limitation. The advent of satellite missions dedicated to air quality and carbon cycle observations (Sentinel-5P, GeoCarb) will be a milestone toward building such policy-relevant monitoring systems and will provide an unprecedented opportunity to improve the synergy between Earth surface models and numerical simulations of atmospheric dynamics across time scales, from NWP to climate modeling. In turn, such inverse modeling tools can be exploited to conduct instrumental design experiments that can inform mission strategies and requirements [202], and optimize scientific outcomes.