In 2013, the community of mathematical scientists and educators focused its collective attention on the mathematics of planet Earth. In the course of the year, a grassroots organization grew into an international partnership of more than 150 scientific societies, universities, research institutes, and organizations. The project, known as “Mathematics of Planet Earth 2013” (MPE2013), received the patronage of UNESCO and was a truly unique event. It brought the challenges facing our planet to the attention of the mathematics research community in numerous lectures, seminars, workshops, and special sessions at conferences of the professional societies; it sponsored the development of curriculum materials for all educational levels; it organized many outreach activities, including an international juried exhibit of virtual and physical displays for use in museums and schools; and it presented a series of public lectures by renowned scientists showing the public how mathematics contributes to our understanding of planet Earth, the nature of the challenges our planet is facing, and how mathematicians contribute to their solution. At the end of the year, MPE2013 morphed into “Mathematics of Planet Earth” (MPE).

Atmospheric radiocarbon (¹⁴C) represents an important observational constraint on emissions of fossil-fuel derived carbon into the atmosphere due to the absence of ¹⁴C in fossil fuel reservoirs. The high sensitivity and precision that accelerator mass spectrometry (AMS) affords in atmospheric ¹⁴C analysis has greatly increased the potential for using such measurements to evaluate bottom-up emissions inventories of fossil fuel CO₂(CO₂ff), as well as those for other co-emitted species. Here we use observations of ¹⁴CO₂ and a series of primary hydrocarbons and combustion tracers from discrete air samples collected between June 2009 and September 2010 at the National Oceanic and Atmospheric Administration Boulder Atmospheric Observatory (BAO; Lat: 40.050° N, Lon: 105.004° W) to derive emission ratios of each species with respect to CO₂ff. The BAO tower is situated at the boundary of the Denver metropolitan area to the south and a large industrial and agricultural region to the north and east, making it an ideal location to study the contrasting mix of emissions from the activities in each region. The species considered in this analysis are carbon monoxide (CO), methane (CH₄), acetylene (C₂H₂), benzene (C₆H₆), and C₃–C₅ alkanes. We estimate emissions for a subset of these species by using the Vulcan high resolution CO2ff emission data product as a reference. We find that CO is overestimated in the 2008 National Emissions Inventory (NEI08) by a factor of ~2. A close evaluation of the inventory suggests that the ratio of CO emitted per unit fuel burned from on-road gasoline vehicles is likely over-estimated by a factor of 2.5. Using a wind-directional analysis of the data, we find enhanced concentrations of CH₄, relative to CO₂ff, in air influenced by emissions to the north and east of the BAO tower when compared to air influenced by emissions in the Denver metro region to the south. Along with enhanced CH₄, the strongest enhancements of the C₃–C₅ alkanes are also found in the north and east wind sector, suggesting that both the alkane and CH₄ enhancements are sourced from oil and gas fields located to the northeast, though it was not possible to rule out the contribution of non oil and gas CH₄ sources.

Climate change and its interactions with complex socioeconomic dynamics dictate the need for decision makers to move from incremental adaptation toward transformation as societies try to cope with unprecedented and uncertain change. Developing pathways toward transformation is especially difficult in regions with multiple contested resource uses and rights, with diverse decision makers and rules, and where high uncertainty is generated by differences in stakeholders’ values, understanding of climate change, and ways of adapting. Such a region is the Murray-Darling Basin, Australia, from which we provide insights for developing a process to address these constraints. We present criteria for sequencing actions along adaptation pathways: feasibility of the action within the current decision context, its facilitation of other actions, its role in averting exceedance of a critical threshold, its robustness and resilience under diverse and unexpected shocks, its effect on future options, its lead time, and its effects on equity and social cohesion. These criteria could potentially enable development of multiple stakeholder-specific adaptation pathways through a regional collective action process. The actual implementation of these multiple adaptation pathways will be highly uncertain and politically difficult because of fixity of resource-use rights, unequal distribution of power, value conflicts, and the likely redistribution of benefits and costs. We propose that the approach we outline for building resilient pathways to transformation is a flexible and credible way of negotiating these challenges.

Urban environments are the primary contributors to global anthropogenic carbon emissions. Because much of the growth in CO₂ emissions will originate from cities, there is a need to develop, assess, and improve measurement and modeling strategies for quantifying and monitoring greenhouse gas emissions from large urban centers. In this study the uncertainties in an aircraft-based mass balance approach for quantifying carbon dioxide and methane emissions from an urban environment, focusing on Indianapolis, IN, USA, are described. The relatively level terrain of Indianapolis facilitated the application of mean wind fields in the mass balance approach. We investigate the uncertainties in our aircraft-based mass balance approach by (1) assessing the sensitivity of the measured flux to important measurement and analysis parameters including wind speed, background CO₂ and CH₄, boundary layer depth, and interpolation technique, and (2) determining the flux at two or more downwind distances from a point or area source (with relatively large source strengths such as solid waste facilities and a power generating station) in rapid succession, assuming that the emission flux is constant. When we quantify the precision in the approach by comparing the estimated emissions derived from measurements at two or more downwind distances from an area or point source, we find that the minimum and maximum repeatability were 12 and 52%, with an average of 31%. We suggest that improvements in the experimental design can be achieved by careful determination of the background concentration, monitoring the evolution of the boundary layer through the measurement period, and increasing the number of downwind horizontal transect measurements at multiple altitudes within the boundary layer.

Globalization, the process by which local social-ecological systems (SESs) are becoming linked in a global network, presents policy scientists and practitioners with unique and difficult challenges. Although local SESs can be extremely complex, when they become more tightly linked in the global system, complexity increases very rapidly as multi-scale and multi-level processes become more important. Here, we argue that addressing these multi-scale and multi-level challenges requires a collection of theories and models. We suggest that the conceptual domains of sustainability, resilience, and robustness provide a sufficiently rich collection of theories and models, but overlapping definitions and confusion about how these conceptual domains articulate with one another reduces their utility. We attempt to eliminate this confusion and illustrate how sustainability, resilience, and robustness can be used in tandem to address the multi-scale and multi-level challenges associated with global change.

Large urban emissions of greenhouse gases result in large atmospheric enhancements relative to background that are easily measured. Using CO₂ mole fractions and Δ¹⁴C and δ¹³C values of CO₂ in the Los Angeles megacity observed in inland Pasadena (2006–2013) and coastal Palos Verdes peninsula (autumn 2009–2013), we have determined time series for CO₂ contributions from fossil fuel combustion (C_ff) for both sites and broken those down into contributions from petroleum and/or gasoline and natural gas burning for Pasadena. We find a 10 % reduction in Pasadena C_ff during the Great Recession of 2008–2010, which is consistent with the bottom-up inventory determined by the California Air Resources Board. The isotopic variations and total atmospheric CO₂ from our observations are used to infer seasonality of natural gas and petroleum combustion. The trend of CO₂ contributions to the atmosphere from natural gas combustion is out of phase with the seasonal cycle of total natural gas combustion seasonal patterns in bottom-up inventories but is consistent with the seasonality of natural gas usage by the area's electricity generating power plants. For petroleum, the inferred seasonality of CO₂ contributions from burning petroleum is delayed by several months relative to usage indicated by statewide gasoline taxes. Using the high-resolution Hestia-LA data product to compare C_ff from parts of the basin sampled by winds at different times of year, we find that variations in observed fossil fuel CO₂ reflect seasonal variations in wind direction. The seasonality of the local CO₂ excess from fossil fuel combustion along the coast, on Palos Verdes peninsula, is higher in autumn and winter than spring and summer, almost completely out of phase with that from Pasadena, also because of the annual variations of winds in the region. Variations in fossil fuel CO₂ signals are consistent with sampling the bottom-up Hestia-LA fossil CO₂ emissions product for sub-city source regions in the LA megacity domain when wind directions are considered.

Social roles are thought to play an important role in determining the capacity for collective action in a community regarding the use of shared resources. Here we report on the results of a study using a behavioral experimental approach regarding the relationship between social roles and the performance of social-ecological systems. The computer-based irrigation experiment that was the basis of this study mimics the decisions faced by farmers in small-scale irrigation systems. In each of 20 rounds, which are analogous to growing seasons, participants face a two-stage commons dilemma. First they must decide how much to invest in the public infrastructure, e.g., canals and water diversion structures. Second, they must decide how much to extract from the water made available by that public infrastructure. Each round begins with a 60-second communication period before the players make their investment and extraction decisions. By analyzing the chat messages exchanged among participants during the communication stage of the experiment, we coded up to three roles per participant using the scheme of seven roles known to be important in the literature: leader, knowledge generator, connector, follower, moralist, enforcer, and observer. Our study supports the importance of certain social roles (e.g., connector) previously highlighted by several case study analyses. However, using qualitative comparative analysis we found that none of the individual roles was sufficient for groups to succeed, i.e., to reach a certain level of group production. Instead, we found that a combination of at least five roles was necessary for success. In addition, in the context of upstream-downstream asymmetry, we observed a pattern in which social roles assumed by participants tended to differ by their positions. Although our work generated some interesting insights, further research is needed to determine how robust our findings are to different action situations, such as biophysical context, social network, and resource uncertainty.

Recent advances in fossil fuel CO₂ (FFCO₂) emission inventories enable sensitivity tests of simulated atmospheric CO₂ concentrations to sub-annual variations in FFCO₂ emissions and what this implies for the interpretation of observed CO₂. Six experiments are conducted to investigate the potential impact of three cycles of FFCO₂ emission variability (diurnal, weekly and monthly) using a global tracer transport model. Results show an annual FFCO₂ rectification varying from −1.35 to +0.13 ppm from the combination of all three cycles. This rectification is driven by a large negative diurnal FFCO₂ rectification due to the covariation of diurnal FFCO₂ emissions and diurnal vertical mixing, as well as a smaller positive seasonal FFCO₂ rectification driven by the covariation of monthly FFCO₂ emissions and monthly atmospheric transport. The diurnal FFCO₂ emissions are responsible for a diurnal FFCO₂ concentration amplitude of up to 9.12 ppm at the grid cell scale. Similarly, the monthly FFCO₂ emissions are responsible for a simulated seasonal CO₂ amplitude of up to 6.11 ppm at the grid cell scale. The impact of the diurnal FFCO₂ emissions, when only sampled in the local afternoon, is also important, causing an increase of +1.13 ppmv at the grid cell scale. The simulated CO₂ concentration impacts from the diurnally and seasonally varying FFCO₂ emissions are centered over large source regions in the Northern Hemisphere, extending to downwind regions. This study demonstrates the influence of sub-annual variations in FFCO₂ emissions on simulated CO₂ concentration and suggests that inversion studies must take account of these variations in the affected regions.

Large-N comparative studies have helped common pool resource scholars gain general insights into the factors that influence collective action and governance outcomes. However, these studies are often limited by missing data, and suffer from the methodological limitation that important information is lost when we reduce textual information to quantitative data. This study was motivated by nine case studies that appeared to be inconsistent with the expectation that the presence of Ostrom’s Design Principles increases the likelihood of successful common pool resource governance. These cases highlight the limitations of coding and analyzing Large-N case studies.

We examine two issues: 1) the challenge of missing data and 2) potential approaches that rely on context (which is often lost in the coding process) to address inconsistencies between empirical observations theoretical predictions. For the latter, we conduct a post-hoc qualitative analysis of a large-N comparative study to explore 2 types of inconsistencies: 1) cases where evidence for nearly all design principles was found, but available evidence led to the assessment that the CPR system was unsuccessful and 2) cases where the CPR system was deemed successful despite finding limited or no evidence for design principles. We describe inherent challenges to large-N comparative analysis to coding complex and dynamically changing common pool resource systems for the presence or absence of design principles and the determination of “success”. Finally, we illustrate how, in some cases, our qualitative analysis revealed that the identity of absent design principles explained inconsistencies hence de-facto reconciling such apparent inconsistencies with theoretical predictions. This analysis demonstrates the value of combining quantitative and qualitative analysis, and using mixed-methods approaches iteratively to build comprehensive methodological and theoretical approaches to understanding common pool resource governance in a dynamically changing context.

Institutions, the rules of the game that shape repeated human interactions, clearly play a critical role in helping groups avoid the inefficient use of shared resources such as fisheries, freshwater, and the assimilative capacity of the environment. Institutions, however, are intimately intertwined with the human, social, and biophysical context within which they operate. Scholars typically are careful to take this context into account when studying institutions and Ostrom’s Institutional Design Principles are a case in point. Scholars have tested whether Ostrom’s Design Principles, which specify broad relationships between institutional arrangements and context, actually support successful governance of shared resources. This article further contributes to this line of research by leveraging the notion of institutional design to outline a research trajectory focused on coupled infrastructure systems in which institutions are seen as one class of infrastructure among many that dynamically interact to produce outcomes over time.