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The ability to predict the trajectory of climate change requires a clear understanding of the emissions and uptake (a.k.a. surface fluxes) of long-lived greenhouse gases (GHGs). Furthermore, the development of climate policies is driving a need to constrain the budgets of anthropogenic GHG emissions. Inverse problems that couple atmospheric observations of GHG concentrations with an atmospheric chemistry and transport model have increasingly been used to gain insights into surface fluxes. Given the inherent technical challenges associated with their solution, it is imperative that objective approaches exist for the evaluation of such inverse problems. Because direct observation of fluxes at compatible spatiotemporal scales is rarely possible, diagnostics tools must rely on indirect measures. Here we review diagnostics that have been implemented in recent studies, and discuss their use in informing adjustments to model setup. We group the diagnostics along a continuum starting with those that are most closely related to the scientific question being targeted, and ending with those most closely tied to the statistical and computational setup of the inversion. We thus begin with diagnostics based on assessments against independent information (e.g., unused atmospheric observations, large-scale scientific constraints), followed by statistical diagnostics of inversion results, diagnostics based on sensitivity tests and analyses of robustness (e.g., tests focusing on the chemistry and transport model, the atmospheric observations, or the statistical and computational framework), and close with the use of synthetic data experiments (a.k.a. observing system simulation experiments (OSSEs)). We find that existing diagnostics provide a crucial toolbox for evaluating and improving flux estimates, but, not surprisingly, cannot overcome the fundamental challenges associated with limited atmospheric observations or the lack of direct flux measurements at compatible scales. As atmospheric inversions are increasingly expected to contribute to national reporting of GHG emissions, the need for developing and implementing robust and transparent evaluation approaches will only grow. [ABSTRACT FROM AUTHOR]

This review paper explores recent efforts to estimate state- and national-scale carbon dioxide (CO2) and methane (CH4) emissions from individual anthropogenic source sectors in the United States. Nearly all state and national climate change regulations in the US target specific source sectors, and detailed monitoring of individual sectors presents a greater challenge than monitoring total emissions. We particularly focus on opportunities to synthesize disparate types of information on emissions, including emissions inventory data and atmospheric greenhouse gas data. We find that inventory estimates of sector-specific CO2 emissions are sufficiently accurate for policy evaluation at national scale but that uncertainties increase at state and local levels. CH4 emissions inventories are highly uncertain for all source sectors at all spatial scales, in part because of the complex, spatially-variable relationships between economic activity and CH4 emissions. In contrast to inventory estimates, top-down estimates use measurements of atmospheric concentrations to infer emissions at the surface; these efforts have had little success identifying CO2 emissions from anthropogenic sources but have successfully identified sector-specific CH4 emissions in several opportunistic cases. We also describe a number of forward-looking opportunities that would aid efforts to estimate sector-specific emissions: fully combine existing top-down datasets, expand intensive aircraft measurement campaigns and measurements of secondary tracers, and improve the economic and demographic data (e.g., activity data) that drive emissions inventories. These steps would better synthesize inventory and top-down data to support sector-specific emissions reduction policies. [ABSTRACT FROM AUTHOR]

Matrix multiplication of two sparse matrices is a fundamental operation in linear Bayesian inverse problems for computing covariance matrices of observations and a posteriori uncertainties. Applications of sparse-sparse matrix multiplication algorithms for specific use-cases in such inverse problems remain unexplored. Here we present a hybrid-parallel sparse-sparse matrix multiplication approach that is more efficient by a third in terms of execution time and operation count relative to standard sparse matrix multiplication algorithms available in most libraries. Two modifications of this hybrid-parallel algorithm are also proposed for the types of operations typical of atmospheric inverse problems, which further reduce the cost of sparse matrix multiplication by yielding only upper triangular and/or dense matrices. [ABSTRACT FROM AUTHOR]

This article lays out the fundamentals of data assimilation as used in biogeochemistry. It demonstrates that all of the methods in widespread use within the field are special cases of the underlying Bayesian formalism. Methods differ in the assumptions they make and information they provide on the probability distributions used in Bayesian calculations. It thus provides a basis for comparison and choice among these methods. It also provides a standardised notation for the various quantities used in the field. [ABSTRACT FROM AUTHOR]

Numerous existing satellites observe physical or environmental properties of the Earth system. Many of these satellites provide global-scale observations, but these observations are often sparse and noisy. By contrast, contiguous, global maps are often most useful to the scientific community (i.e., level 3 products). We develop a spatiotemporal moving window block kriging method to create contiguous maps from sparse and/or noisy satellite observations. This approach exhibits several advantages over existing methods: 1) it allows for flexibility in setting the spatial resolution of the level 3 map, 2) it is applicable to observations with variable density, 3) it produces a rigorous uncertainty estimate, 4) it exploits both spatial and temporal correlations in the data, and 5) it facilitates estimation in real time. Moreover, this approach only requires a limited number of assumptions - that the observable quantity exhibits spatial and temporal correlations that are inferable from the data. We test this method by creating Level 3 products from satellite observations of CO2 (XCO2) from GOSAT, CH4 (XCH4) from IASI and solar-induced chlorophyll fluorescence (SIF) from GOME-2. We evaluate and analyze the difference in performance of spatio-temporal vs. recently developed spatial kriging methods. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present an overview of inverse modeling methods that have been developed over the years for estimating the global sources and sinks of CH4. It provides insight into how techniques and estimates have evolved over time, and what the remaining shortcomings are. As such, it serves a didactical purpose of introducing apprentices to the field, but it also takes stock of the developments so far and reflects on promising new directions. The main focus is on methodological aspects that are particularly relevant for CH4, such as its atmospheric oxidation, the use of methane isotopologues, and specific challenges in atmospheric transport modeling of CH4. The use of satellite retrievals receives special attention, as it is an active field of methodological development, with special requirements on the sampling of the model and the treatment of data uncertainty. Regional scale flux estimation and attribution is still a grand challenge, which calls for new methods capable of combining information from multiple data streams of different measured parameters. A process model representation of sources and sinks in atmospheric transport inversion schemes allows the integrated use of such data. These new developments are needed not only to improve our understanding of the main processes driving the observed global trend, but also to support international efforts to reduce greenhouse gas emissions. [ABSTRACT FROM AUTHOR]

Monitoring the terrestrial carbon cycle for responses to disturbances, caused for example by extreme climate events and insect outbreaks, has the potential to provide early warnings about ecosystem change. However, our capability to detect these carbon balance responses by atmospheric CO2 monitoring remains unknown despite sub-ppm comparability of many well-calibrated CO2 measurement sites. Here, this study explores how accurately atmospheric CO2 and transport models can detect imposed carbon flux anomalies against a background terrestrial flux. Air mass back trajectories from three CO2 monitoring stations in the central U.S. Rocky Mountains for one year (2008) were computationally simulated. To simulate reduced CO2 uptake, a constant +0.2 µmol C m-1 s-2 anomaly was added to all surface fluxes within perturbation domains of varying size. A spatially and temporally uniform 10°×10° +0.2 µmol C m-2 s-1 flux anomaly (+6 Tg C m-1) was detectable above a comprehensive model-data mismatch detection threshold in a large majority of months at each site, but only when the perturbation was located in the central Mountain West. The intensity of the perturbation and its area were important to detection, but the effect of area declined exponentially with increasing source-to-station distance. To further evaluate response, a more realistic spatiotemporally varying drought extracted from a dynamic global vegetation model with a monthly varying perturbation area (1°×1° to 5°×5°) and higher peak intensity (+0.8 µmol C m-2 s-1) was applied. Detectability of excess CO2 from this experiment by the nearest CO2 site (Utah) was similar to detectability of the largest (10°×10°) uniform perturbation. These experiments demonstrate disturbance and drought related carbon-cycle perturbations do create a discernible impact on the composite signal of atmospheric CO2 if sufficiently proximal to a measurement station. [ABSTRACT FROM AUTHOR]

The seasonal-cycle amplitude (SCA) of the atmosphere-ecosystem carbon dioxide (CO2) exchange rate is a useful metric of the responsiveness of the terrestrial biosphere to environmental variations. It is unclear, however, what underlying mechanisms are responsible for the observed increasing trend of SCA in atmospheric CO2 concentration. Using output data from the Multi-scale Terrestrial Model Intercomparison Project (MsTMIP), we investigated how well the SCA of atmosphere-ecosystem CO2 exchange was simulated with 15 contemporary terrestrial ecosystem models during the period 1901-2010. Also, we made attempt to evaluate the contributions of potential mechanisms such as atmospheric CO2, climate, land-use, and nitrogen deposition, through factorial experiments using different combinations of forcing data. Under contemporary conditions, the simulated global-scale SCA of the cumulative net ecosystem carbon flux of most models was comparable in magnitude with the SCA of atmospheric CO2 concentrations. Results from factorial simulation experiments showed that elevated atmospheric CO2 exerted a strong influence on the seasonality amplification. When the model considered not only climate change but also land-use and atmospheric CO2 changes, the majority of the models showed amplification trends of the SCAs of photosynthesis, respiration, and net ecosystem production (+0.19 % to +0.50 % yr-1). In the case of land-use change, it was difficult to separate the contribution of agricultural management to SCA because of inadequacies in both the data and models. The simulated amplification of SCA was approximately consistent with the observational evidence of the SCA in atmospheric CO2 concentrations. Large inter-model differences remained, however, in the simulated global tendencies and spatial patterns of CO2 exchanges. Further studies are required to identify a consistent explanation for the simulated and observed amplification trends, including their underlying mechanisms. Nevertheless, this study implied that monitoring of ecosystem seasonality would provide useful insights concerning ecosystem dynamics. [ABSTRACT FROM AUTHOR]

Water issues are rarely simple. At the global scale, water is at the focus of a powerful multifaceted challenge. Demands for both consumptive and nonconsumptive uses are growing, while climate change is at the same time decreasing availability in some places and increasing risks of heavy precipitation in many others. Through diverse mechanisms that interact with natural processes, human activities impact not only the quantity of water available but also its quality. Here we explore the multiway interactions among water, climate, energy, and food through a number of case studies illustrating the interconnected web of competing drivers, demands, and trade-offs that frame humanity's decisions about water use. The net result of this complex mix of drivers and processes is that water issues need to be addressed with a systems perspective. While a systems framing can be daunting, integrated approaches are fundamental to identifying and evaluating options for sustainable solutions. [ABSTRACT FROM AUTHOR]

Harmful algal blooms (HABs) are becoming increasingly common in freshwater ecosystems globally, raising complex questions about the factors that influence their initiation and growth. These questions have increasingly been answered through mechanistic and stochastic modeling efforts that rely on historical information about HABs in a given system for development, validation, and calibration. Therefore, understanding processes that control HABs is predicated on the ability to answer much more basic questions about what has actually occurred in a given system, namely questions of HAB occurrence, extent, intensity, and timing. Here we explore the state of the science in answering these basic questions; we use Lake Erie as a case study, where nearly two decades after the resurgence of HABs, a summer 2014 event caused a mandatory three day tap water ban for Toledo, Ohio. We find that, even for well-studied systems, unambiguous answers to basic questions about HAB occurrence are lacking, raising concerns about their use as a basis for addressing mechanistic questions about controlling factors. This ambiguity is found to be caused by differences in the methods used to track HABs, the specific harm being considered, the linkage to that harm (direct or indirect), the threshold defining harm, and spatiotemporal variability in sampling. Further work is therefore needed to integrate heterogeneous types of observations in order to better leverage existing and future monitoring programs, and to guide modeling efforts toward deeper understanding of HAB causes and consequences. [ABSTRACT FROM AUTHOR]

Understanding the response of the terrestrial biospheric carbon cycle to variability in enviroclimatic drivers is critical for predicting climate-carbon interactions. Here we apply an atmospheric-inversion-based framework to assess the relationships between the spatiotemporal patterns of net ecosystem CO2 exchange (NEE) and those of enviroclimatic drivers. We show that those relationships can be directly observed at 1° × 1° 3-hourly resolution from atmospheric CO2 measurements for four of seven large biomes in North America, namely, (i) boreal forests and taiga; (ii) temperate coniferous forests; (iii) temperate grasslands, savannas, and shrublands; and (iv) temperate broadleaf and mixed forests. We find that shortwave radiation plays a dominant role during the growing season over all four biomes. Specific humidity and precipitation also play key roles and are associated with decreased CO2 uptake (or increased release). The explanatory power of specific humidity is especially strong during transition seasons, while that of precipitation appears during both the growing and dormant seasons. We further find that the ability of four prototypical terrestrial biospheric models (TBMs) to represent the spatiotemporal variability of NEE improves as the influence of radiation becomes more dominant, implying that TBMs have a better skill in representing the impact of radiation relative to other drivers. Even so, we show that TBMs underestimate the strength of the relationship to radiation and do not fully capture its seasonality. Furthermore, the TBMs appear to misrepresent the relationship to precipitation and specific humidity at the examined scales, with relationships that are not consistent in terms of sign, seasonality, or significance relative to observations. More broadly, we demonstrate the feasibility of directly probing relationships between NEE and enviroclimatic drivers at scales with no direct measurements of NEE, opening the door to the study of emergent processes across scales and to the evaluation of their scaling within TBMs. [ABSTRACT FROM AUTHOR]

A mechanistic model was developed to predict midsummer bottom-water dissolved oxygen (BWDO) concentration and hypoxic area on the Louisiana shelf of the northern Gulf of Mexico, USA (1985-2011). Because of its parsimonious formulation, the model possesses many of the benefits of simpler, more empirical models, in that it is computationally efficient and can rigorously account for uncertainty through Bayesian inference. At the same time, the model incorporates important biophysical processes such that its parameterization can be informed by field-measured biological and physical rates. The model is used to explore how freshwater flow, nutrient load, benthic oxygen demand, and wind velocity affect hypoxia on the western and eastern sections of the shelf, delineated by the Atchafalaya River outfall. The model explains over 70% of the variability in BWDO on both shelf sections, and outperforms linear regression models developed from the same input variables. Model results suggest that physical factors (i.e., wind and flow) control a larger portion of the year-to-year variability in hypoxia than previously thought, especially on the western shelf, though seasonal nutrient loads remain an important driver of hypoxia, as well. Unlike several previous Gulf hypoxia modeling studies, results do not indicate a temporal shift in the system's propensity for hypoxia formation (i.e., no regime change). Results do indicate that benthic oxygen demand is a substantial BWDO sink, and a better understanding of the long-term dynamics of this sink is required to better predict how the size of the hypoxic zone will respond to proposed reductions in nutrient loading. [ABSTRACT FROM AUTHOR]

This study quantitatively estimates the spatial distribution of anthropogenic methane sources in the United States by combining comprehensive atmospheric methane observations, extensive spatial datasets, and a high-resolution atmospheric transport model. Results show that current inventories from the US Environmental Protection Agency (EPA) and the Emissions Database for Global Atmospheric Research underestimate methane emissions nationally by a factor of ∼1.5 and ∼1.7, respectively. Our study indicates that emissions due to ruminants and manure are up to twice the magnitude of existing inventories. In addition, the discrepancy in methane source estimates is particularly pronounced in the south-central United States, where we find total emissions are ∼2.7 times greater than in most inventories and account for 24 ± 3% of national emissions. The spatial patterns of our emission fluxes and observed methane-propane correlations indicate that fossil fuel extraction and refining are major contributors (45 ± 13%) in the south-central United States. This result suggests that regional methane emissions due to fossil fuel extraction and processing could be 4.9 ± 2.6 times larger than in EDGAR, the most comprehensive global methane inventory. These results cast doubt on the US EPA's recent decision to downscale its estimate of national natural gas emissions by 25-30%. Overall, we conclude that methane emissions associated with both the animal husbandry and fossil fuel industries have larger greenhouse gas impacts than indicated by existing inventories. [ABSTRACT FROM AUTHOR]

In 2011, Lake Erie experienced the largest harmful algal bloom in its recorded history, with a peak intensity over three times greater than any previously observed bloom. Here we show that long-term trends in agricultural practices are consistent with increasing phosphorus loading to the western basin of the lake, and that these trends, coupled with meteorological conditions in spring 2011, produced record-breaking nutrient loads. An extended period of weak lake circulation then led to abnormally long residence times that incubated the bloom, and warm and quiescent conditions after bloom onset allowed algae to remain near the top of the water column and prevented flushing of nutrients from the system. We further find that all of these factors are consistent with expected future conditions. If a scientifically guided management plan to mitigate these impacts is not implemented, we can therefore expect this bloom to be a harbinger of future blooms in Lake Erie. [ABSTRACT FROM AUTHOR]