Many inverse problems in the atmospheric sciences involve parameters with known physical constraints. Examples include nonnegativity (e. g., emissions of some urban air pollutants) or upward limits implied by reaction or solubility constants. However, probabilistic inverse modeling approaches based on Gaussian assumptions cannot incorporate such bounds and thus often produce unrealistic results. The atmospheric literature lacks consensus on the best means to overcome this problem, and existing atmospheric studies rely on a limited number of the possible methods with little examination of the relative merits of each.

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 similar to 1.5 and similar to 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 similar to 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.

Robust estimates of hypoxic extent (both area and volume) are important for assessing the impacts of low dissolved oxygen on aquatic ecosystems at large spatial scales. Such estimates are also important for calibrating models linking hypoxia to causal factors, such as nutrient loading and stratification, and for informing management decisions. In this study, we develop a rigorous geostatistical modeling framework to estimate the hypoxic extent in the northern Gulf of Mexico from data collected during midsummer, quasi-synoptic monitoring cruises (1985-2011). Instead of a traditional interpolation-based approach, we use a simulation-based approach that yields more robust extent estimates and quantified uncertainty. The modeling framework also makes use of covariate information (i.e., trend variables such as depth and spatial position), to reduce estimation uncertainty. Furthermore, adjustments are made to account for observational bias resulting from the use of different sampling instruments in different years. Our results suggest an increasing trend in hypoxic layer thickness (p = 0.05) from 1985 to 2011, but less than significant increases in volume (p = 0.12) and area (p = 0.42). The uncertainties in the extent estimates vary with sampling network coverage and instrument type, and generally decrease over the study period.

Wetlands comprise the single largest global source of atmospheric methane, but current flux estimates disagree in both magnitude and distribution at the continental scale. This study uses atmospheric methane observations over North America from 2007 to 2008 and a geostatistical inverse model to improve understanding of Canadian methane fluxes and associated biogeochemical models. The results bridge an existing gap between traditional top-down, inversion studies, which typically emphasize total emission budgets, and biogeochemical models, which usually emphasize environmental processes. The conclusions of this study are threefold. First, the most complete process-based methane models do not always describe available atmospheric methane observations better than simple models. In this study, a relatively simple model of wetland distribution, soil moisture, and soil temperature outperformed more complex model formulations. Second, we find that wetland methane fluxes have a broader spatial distribution across western Canada and into the northern U.S. than represented in existing flux models. Finally, we calculate total methane budgets for Canada and for the Hudson Bay Lowlands, a large wetland region (50-60 degrees N, 75-96 degrees W). Over these lowlands, we find total methane fluxes of 1.80.24 Tg C yr(-1), a number in the midrange of previous estimates. Our total Canadian methane budget of 16.01.2 Tg C yr(-1) is larger than existing inventories, primarily due to high anthropogenic emissions in Alberta. However, methane observations are sparse in western Canada, and additional measurements over Alberta will constrain anthropogenic sources in that province with greater confidence.

In any data assimilation framework, the background error covariance statistics play the critical role of filtering the observed information and determining the quality of the analysis. For atmospheric CO2 data assimilation, however, the background errors cannot be prescribed via traditional forecast or ensemble-based techniques as these fail to account for the uncertainties in the carbon emissions and uptake, or for the errors associated with the CO2 transport model. We propose an approach where the differences between two modeled CO2 concentration fields, based on different but plausible CO2 flux distributions and atmospheric transport models, are used as a proxy for the statistics of the background errors. The resulting error statistics: (1) vary regionally and seasonally to better capture the uncertainty in the background CO2 field, and (2) have a positive impact on the analysis estimates by allowing observations to adjust predictions over large areas. A state-of-the-art four-dimensional variational (4D-VAR) system developed at the European Centre for Medium-Range Weather Forecasts (ECMWF) is used to illustrate the impact of the proposed approach for characterizing background error statistics on atmospheric CO2 concentration estimates. Observations from the Greenhouse gases Observing SATellite IBUKI (GOSAT) are assimilated into the ECMWF 4D-VAR system along with meteorological variables, using both the new error statistics and those based on a traditional forecast-based technique. Evaluation of the four-dimensional CO2 fields against independent CO2 observations confirms that the performance of the data assimilation system improves substantially in the summer, when significant variability and uncertainty in the fluxes are present.

Relieving phosphorus loading is a key management tool for controlling Lake Erie eutrophication. During the 1960s and 1970s, increased phosphorus inputs degraded water quality and reduced central basin hypolimnetic oxygen levels which, in turn, eliminated thermal habitat vital to cold-water organisms and contributed to the extirpation of important benthic macroinvertebrate prey species for fishes. In response to load reductions initiated in 1972, Lake Erie responded quickly with reduced water-column phosphorus concentrations, phytoplankton biomass, and bottom-water hypoxia (dissolved oxygen <2 mg/l). Since the mid-1990s, cyanobacteria blooms increased and extensive hypoxia and benthic algae returned. We synthesize recent research leading to guidance for addressing this re-eutrophication, with particular emphasis on central basin hypoxia. We document recent trends in key eutrophication-related properties, assess their likely ecological impacts, and develop load response curves to guide revised hypoxia-based loading targets called for in the 2012 Great Lakes Water Quality Agreement. Reducing central basin hypoxic area to levels observed in the early 1990s (ca. 2000 km(2)) requires cutting total phosphorus loads by 46% from the 2003-2011 average or reducing dissolved reactive phosphorus loads by 78% from the 2005-2011 average. Reductions to these levels are also protective of fish habitat We provide potential approaches for achieving those new loading targets, and suggest that recent load reduction recommendations focused on western basin cyanobacteria blooms may not be sufficient to reduce central basin hypoxia to 2000 km(2). (C) 2014 International Association for Great Lakes Research. Published by Elsevier B.V. All rights reserved.

Understanding the role of climate extremes and their impact on the carbon (C) cycle is increasingly a focus of Earth system science. Climate extremes such as droughts, heat waves, or heavy precipitation events can cause substantial changes in terrestrial C fluxes. On the other hand, extreme changes in C fluxes are often, but not always, driven by extreme climate conditions. Here we present an analysis of how extremes in temperature and precipitation, and extreme changes in terrestrial C fluxes are related to each other in 10 state-of-the-art terrestrial carbon models, all driven by the same climate forcing. We use model outputs from the North American Carbon Program Multi-scale Synthesis and Terrestrial Model Intercomparison Project (MsTMIP). A global-scale analysis shows that both droughts and heat waves translate into anomalous net releases of CO2 from the land surface via different mechanisms: Droughts largely decrease gross primary production (GPP) and to a lower extent total respiration (TR), while heat waves slightly decrease GPP but increase TR. Cold and wet periods have a smaller opposite effect. Analyzing extremes in C fluxes reveals that extreme changes in GPP and TR are often caused by strong shifts in water availability, but for extremes in TR shifts in temperature are also important. Extremes in net CO2 exchange are equally strongly driven by deviations in temperature and precipitation. Models mostly agree on the sign of the C flux response to climate extremes, but model spread is large. In tropical forests, C cycle extremes are driven by water availability, whereas in boreal forests temperature plays a more important role. Models are particularly uncertain about the C flux response to extreme heat in boreal forests.

We use geostatistical universal kriging and conditional realizations to provide the first quantitative estimates, with robust estimates of uncertainties, of the seasonal and interannual variability in hypoxic volume in Chesapeake Bay, covering early April to late October for 1985 to 2010, and explore factors controlling that variability. Results show that the time when the hypoxic volume reaches its maximum has moved from late to early July over the examined period, but that there is no trend in the seasonal-maximum hypoxic volume itself. No significant trend was found in the timing of onset of hypoxia, but the end of the hypoxic period has moved from October to September. Including nutrient loading from the Rappahannock River in addition to the Susquehanna and Potomac Rivers is found to be beneficial for explaining the interannual variability of hypoxia. Overall, January to May total nitrogen loads from these three rivers, April to August southwesterly and northeasterly winds, and April and May precipitation explain >85% of the seasonally averaged interannual variability in hypoxic volumes. Southwesterly winds affect hypoxia by increasing vertical stratification, while precipitation likely acts as a surrogate for nonpoint sources of nitrogen downstream from monitoring stations. The relative contribution of nutrient loading to the overall interannual variability suggests that 28-35% reductions in monitored nutrient loads may not be sufficient to achieve a corresponding reduction in hypoxic conditions as had been suggested in previous studies, at least in the short term.

The characterization of fossil-fuel CO2 (ffCO(2)) emissions is paramount to carbon cycle studies, but the use of atmospheric inverse modeling approaches for this purpose has been limited by the highly heterogeneous and non-Gaussian spatiotemporal variability of emissions. Here we explore the feasibility of capturing this variability using a low-dimensional parameterization that can be implemented within the context of atmospheric CO2 inverse problems aimed at constraining regional-scale emissions. We construct a multiresolution (i. e., wavelet-based) spatial parameterization for ffCO(2) emissions using the Vulcan inventory, and examine whether such a parameterization can capture a realistic representation of the expected spatial variability of actual emissions. We then explore whether sub-selecting wavelets using two easily available proxies of human activity (images of lights at night and maps of built-up areas) yields a low-dimensional alternative. We finally implement this low-dimensional parameterization within an idealized inversion, where a sparse reconstruction algorithm, an extension of stagewise orthogonal matching pursuit (StOMP), is used to identify the wavelet coefficients. We find that (i) the spatial variability of fossil-fuel emission can indeed be represented using a low-dimensional wavelet-based parameterization, (ii) that images of lights at night can be used as a proxy for sub-selecting wavelets for such analysis, and (iii) that implementing this parameterization within the described inversion framework makes it possible to quantify fossil-fuel emissions at regional scales if fossil-fuel-only CO2 observations are available.