Michael Bertolacci

Trajectory reconstruction in high-dimensional spatiotemporal chaos is often difficult due to the coupled challenges of structural model misspecification and prohibitive computational costs. We introduce in this work a Low-Rank Extended Rauch–Tung–Striebel Smoother (LR-ExRTSS) for use within the Statistical Finite Element (StatFEM) framework, combining a square-root retrospective smoother with a forward looking low-rank extended Kalman filter. We apply this grid-independent, retrospective scheme to the 2D anisotropic Kuramoto–Sivashinsky equation under a severe dynamical mismatch. We force a predictive model converging to a stable 1D steady state to track a truly chaotic 2D system using sparse, noisy observations. Results demonstrate that the LR-ExRTSS acts as a bridge between misspecified physics and chaotic reality by reintroducing transverse instabilities aggressively damped by the flawed model. Spectral analysis confirms that the efficacy of the scheme is based on its ability to span the unstable-neutral subspace of the true system, regardless of the subspace predicted by the model. This work establishes low-rank StatFEM as a computationally feasible framework for robust state estimation in high-dimensional systems under severe structural error.

Contributions from photosynthesis and other natural components of the carbon cycle present the largest uncertainties in our understanding of carbon dioxide (CO ₂ ) sources and sinks. While the spatiotemporal distribution of Earth's net surface flux (the sum of all contributions) can be inferred from atmospheric CO ₂ concentrations through flux inversion, attributing the net flux to its individual components remains challenging. The advent of solar‐induced fluorescence (SIF) satellite observations provides an opportunity to separate natural components by isolating gross primary productivity (GPP), the photosynthetic component of the net flux. Here, we introduce a novel statistical flux‐inversion framework that simultaneously assimilates observations of SIF and CO ₂ concentration, extending WOMBAT v2.0 (WOllongong Methodology for Bayesian Assimilation of Trace‐gases, version 2.0) with a hierarchical model of spatiotemporal dependence between GPP and SIF processes. We call the new framework WOMBAT v2.S, and we apply it to SIF and CO ₂ data from NASA's Orbiting Carbon Observatory‐2 (OCO‐2) satellite and other instruments to estimate natural fluxes over the globe during a recent six‐year period. In a simulation experiment that matches OCO‐2's retrieval characteristics, the inclusion of SIF improves the accuracy and uncertainty quantification of component flux estimates. Comparing estimates from WOMBAT v2.S, v2.0, and the independent FLUXCOM initiative, we observe that linking GPP to SIF has little effect on net flux, as expected, but leads to stronger seasonal cycles and altered zonal distributions in natural flux components.

Tropical lands play an important role in the global carbon cycle yet their contribution remains uncertain owing to sparse observations. Satellite observations of atmospheric carbon dioxide (CO₂) have greatly increased spatial coverage over tropical regions, providing the potential for improved estimates of terrestrial fluxes. Despite this advancement, the spread among satellite‐based and in‐situ atmospheric CO₂ flux inversions over northern tropical Africa (NTA), spanning 0–24°N, remains large. Satellite‐based estimates of an annual source of 0.8–1.45 PgC yr⁻¹ challenge our understanding of tropical and global carbon cycling. Here, we compare posterior mole fractions from the suite of inversions participating in the Orbiting Carbon Observatory 2 (OCO‐2) Version 10 Model Intercomparison Project (v10 MIP) with independent in‐situ airborne observations made over the tropical Atlantic Ocean by the National Aeronautics and Space Administration (NASA) Atmospheric Tomography (ATom) mission during four seasons. We develop emergent constraints on tropical African CO₂ fluxes using flux‐concentration relationships defined by the model suite. We find an annual flux of 0.14 ± 0.39 PgC yr⁻¹ (mean and standard deviation) for NTA, 2016–2018. The satellite‐based flux bias suggests a potential positive concentration bias in OCO‐2 B10 and earlier version retrievals over land in NTA during the dry season. Nevertheless, the OCO‐2 observations provide improved flux estimates relative to the in situ observing network at other times of year, indicating stronger uptake in NTA during the wet season than the in‐situ inversion estimates.

The magnitude and distribution of China's terrestrial carbon sink remain uncertain due to insufficient observational constraints; satellite column‐average dry‐air mole fraction carbon dioxide (XCO₂) retrievals may fill some of this gap. Here, we estimate China's carbon sink using atmospheric inversions of the Orbiting Carbon Observatory 2 (OCO‐2) XCO₂ retrievals within different platforms, including the Global Carbon Assimilation System (GCAS) v2, the Copernicus Atmosphere Monitoring Service, and the OCO‐2 Model Inter‐comparison Project (MIP). We find that they consistently place the largest net biome production (NBP) in the south on an annual basis compared to the northeast and other main agricultural areas during peak growing season, coinciding well with the distribution of forests and crops, respectively. Moreover, the mean seasonal cycle amplitude of NBP in OCO‐2 inversions is obviously larger than that of biosphere model simulations and slightly greater than surface CO₂ inversions. More importantly, the mean seasonal cycle of the OCO‐2 inversions is well constrained in the temperate, tropical, and subtropical monsoon climate zones, with better inter‐model consistency at a sub‐regional scale compared to in situ inversions and biosphere model simulations. In addition, the OCO‐2 inversions estimate the mean annual NBP in China for 2015–2019 to be between 0.34 (GCASv2) and 0.47 ± 0.16 PgC/yr (median ± std; OCO‐2 v10 MIP), and indicate the impacts of climate extremes (e.g., the 2019 drought) on the interannual variations of NBP. Our results suggest that assimilating OCO‐2 XCO₂ retrievals is crucial for improving our understanding of China's terrestrial carbon sink regime.

Tropical lands play an important role in the global carbon cycle yet their contribution remains uncertain owing to sparse observations. Satellite observations of atmospheric carbon dioxide (CO ₂ ) have greatly increased spatial coverage over tropical regions, providing the potential for improved estimates of terrestrial fluxes. Despite this advancement, the spread among satellite-based and in-situ atmospheric CO ₂ flux inversions over northern tropical Africa (NTA), spanning 0-24◦N, remains large. Satellite-based estimates of an annual source of 0.8-1.45 PgC yr ⁻¹ challenge our understanding of tropical and global carbon cycling. Here, we compare posterior mole fractions from the suite of inversions participating in the Orbiting Carbon Observatory 2 (OCO-2) Version 10 Model Intercomparison Project (v10 MIP) with independent in-situ airborne observations made over the tropical Atlantic Ocean by the NASA Atmospheric Tomography (ATom) mission during four seasons. We develop emergent constraints on tropical African CO ₂ fluxes using flux-concentration relationships defined by the model suite. We find an annual flux of 0.14 ± 0.39 PgC yr ⁻¹ (mean and standard deviation) for NTA, 2016-2018. The satellite-based flux bias suggests a potential positive concentration bias in OCO-2 B10 and earlier version retrievals over land in NTA during the dry season. Nevertheless, the OCO-2 observations provide improved flux estimates relative to the in situ observing network at other times of year, indicating stronger uptake in NTA during the wet season than the in-situ inversion estimates.

Our environment is undergoing rapid change as greenhouse gases warm the planet. Noel Cressie, Andrew Zammit-Mangion, Josh Jacobson, and Michael Bertolacci use WOMBAT, a Bayesian hierarchical statistical framework, to infer the spatio-temporal distribution of CO₂ surface fluxes

A Model Intercomparison Project (MIP) consists of teams who estimate the same underlying quantity (e.g., temperature projections to the year 2070). A simple average of the ensemble of the teams' outputs gives a consensus estimate, but it does not recognize that some outputs are more variable than others. Statistical analysis of variance (ANOVA) models offer a way to obtain a weighted frequentist consensus estimate of outputs with a variance that is the smallest possible. Modulo dependence between MIP outputs, the ANOVA approach weights a team's output inversely proportional to its variance, from which optimally weighted estimates follow. ANOVA weights can also provide a prior distribution for Bayesian Model Averaging of the MIP outputs when external evaluation data are available. We use a MIP of carbon‐dioxide‐flux inversions to illustrate the ANOVA‐based weighting and subsequent frequentist consensus inferences.

We present the AdaptSPEC-X method for the joint analysis of a panel of possibly nonstationary time series. The approach is Bayesian and uses a covariate-dependent infinite mixture model to incorporate multiple time series, with mixture components parameterized by a time-varying mean and log spectrum. The mixture components are based on AdaptSPEC, a nonparametric model which adaptively divides the time series into an unknown number of segments and estimates the local log spectra by smoothing splines. AdaptSPEC-X extends AdaptSPEC in three ways. First, through the infinite mixture, it applies to multiple time series linked by covariates. Second, it can handle missing values, a common feature of time series which can cause difficulties for nonparametric spectral methods. Third, it allows for a time-varying mean. Through these extensions, AdaptSPEC-X can estimate time-varying means and spectra at observed and unobserved covariate values, allowing for predictive inference. Estimation is performed by Markov chain Monte Carlo (MCMC) methods, combining data augmentation, reversible jump, and Riemann manifold Hamiltonian Monte Carlo techniques. We evaluate the methodology using simulated data, and describe applications to Australian rainfall data and measles incidence in the United States. Software implementing the method proposed in this article is available in the R package BayesSpec. Supplementary files for this article are available online.