STEM: Challenges and opportunities for mathematics education

Climbing Mountains, Building Bridges is a rich theme for exploring some of the “challenges, obstacles, links, and connections” facing mathematics education within the current STEM climate (Science, Technology, Engineering and Mathematics). This paper first considers some of the issues and debates surrounding the nature of STEM education, including perspectives on its interdisciplinary nature. It is next argued that mathematics is in danger of being overshadowed, in particular by science, in the global urgency to advance STEM competencies in schools and the workforce. Some suggestions are offered for lifting the profile of mathematics education within an integrated STEM context, with examples drawn from modelling with data in the sixth grade.

A Gradient-Based Comparison Measure for Visual analysis of Multifield Data

We introduce a multifield comparison measure for scalar fields that helps in studying relations between them. The comparison measure is insensitive to noise in the scalar fields and to noise in their gradients. Further, it can be computed robustly and efficiently. Results from the visual analysis of various data sets from climate science and combustion applications demonstrate the effective use of the measure.

Laboratory simulations show diabatic heating drives cumulus-cloud evolution and entrainment

Clouds are the largest source of uncertainty in climate science, and remain a weak link in modeling tropical circulation. A major challenge is to establish connections between particulate microphysics and macroscale turbulent dynamics in cumulus clouds. Here we address the issue from the latter standpoint. First we show how to create bench-scale flows that reproduce a variety of cumulus-cloud forms (including two genera and three species), and track complete cloud life cycles-e.g., from a ``cauliflower'' congestus to a dissipating fractus. The flow model used is a transient plume with volumetric diabatic heating scaled dynamically to simulate latent-heat release from phase changes in clouds. Laser-based diagnostics of steady plumes reveal Riehl-Malkus type protected cores. They also show that, unlike the constancy implied by early self-similar plume models, the diabatic heating raises the Taylor entrainment coefficient just above cloud base, depressing it at higher levels. This behavior is consistent with cloud-dilution rates found in recent numerical simulations of steady deep convection, and with aircraft-based observations of homogeneous mixing in clouds. In-cloud diabatic heating thus emerges as the key driver in cloud development, and could well provide a major link between microphysics and cloud- scale dynamics.

INST: An Integrated Steering Framework for Critical Weather Applications

Online remote visualization and steering of critical weather applications like cyclone tracking are essential for effective and timely analysis by geographically distributed climate science community. A steering framework for controlling the high-performance simulations of critical weather events needs to take into account both the steering inputs of the scientists and the criticality needs of the application including minimum progress rate of simulations and continuous visualization of significant events. In this work, we have developed an integrated user-driven and automated steering framework INST for simulations, online remote visualization, and analysis for critical weather applications. INST provides the user control over various application parameters including region of interest, resolution of simulation, and frequency of data for visualization. Unlike existing efforts, our framework considers both the steering inputs and the criticality of the application, namely, the minimum progress rate needed for the application, and various resource constraints including storage space and network bandwidth to decide the best possible parameter values for simulations and visualization.

InSt: an integrated steering framework for critical weather applications

Online remote visualization and steering of critical weather applications like cyclone tracking are essential for effective and timely analysis by geographically distributed climate science community. A steering framework for controlling the high-performance simulations of critical weather events needs to take into account both the steering inputs of the scientists and the criticality needs of the application including minimum progress rate of simulations and continuous visualization of significant events. In this work, we have developed an integrated user-driven and automated steering framework InSt for simulations, online remote visualization, and analysis for critical weather applications. InSt provides the user control over various application parameters including region of interest, resolution of simulation, and frequency of data for visualization. Unlike existing efforts, our framework considers both the steering inputs and the criticality of the application, namely, the minimum progress rate needed for the application, and various resource constraints including storage space and network bandwidth to decide the best possible parameter values for simulations and visualization.

Decadal Prediction. Can It Be Skillful?

A new field of study, “decadal prediction,” is emerging in climate science. Decadal prediction lies between seasonal/interannual forecasting and longer-term climate change projections, and focuses on time-evolving regional climate conditions over the next 10–30 yr. Numerous assessments of climate information user needs have identified this time scale as being important to infrastructure planners, water resource managers, and many others. It is central to the information portfolio required to adapt effectively to and through climatic changes. At least three factors influence time-evolving regional climate at the decadal time scale: 1) climate change commitment (further warming as the coupled climate system comes into adjustment with increases of greenhouse gases that have already occurred), 2) external forcing, particularly from future increases of greenhouse gases and recovery of the ozone hole, and 3) internally generated variability. Some decadal prediction skill has been demonstrated to arise from the first two of these factors, and there is evidence that initialized coupled climate models can capture mechanisms of internally generated decadal climate variations, thus increasing predictive skill globally and particularly regionally. Several methods have been proposed for initializing global coupled climate models for decadal predictions, all of which involve global time-evolving three-dimensional ocean data, including temperature and salinity. An experimental framework to address decadal predictability/prediction is described in this paper and has been incorporated into the coordinated Coupled Model Intercomparison Model, phase 5 (CMIP5) experiments, some of which will be assessed for the IPCC Fifth Assessment Report (AR5). These experiments will likely guide work in this emerging field over the next 5 yr.

Thermal physics of the atmosphere

Thermal Physics of the Atmosphere offers a concise and thorough introduction on how basic thermodynamics naturally leads on to advanced topics in atmospheric physics. The book starts by covering the basics of thermodynamics and its applications in atmospheric science. The later chapters describe major applications, specific to more specialized areas of atmospheric physics, including vertical structure and stability, cloud formation, and radiative processes. The book concludes with a discussion of non-equilibrium thermodynamics as applied to the atmosphere. This book provides a thorough introduction and invaluable grounding for specialised literature on the subject. Introduces a wide range of areas associated with atmospheric physics Starts from basic level thermal physics Ideally suited for readers with a general physics background Self-assessment questions included for each chapter Supplementary website to accompany the book

Overview of the West African monsoon 2011

Although the 2011 West African monsoon (WAM) season was, overall, near normal, rainfall was patchy. The irregularity of the rainfall during the crucial July-August-September (JAS) season proved difficult to predict - highlighting the significant challenges we continue to face for this region. The vagaries of the rainfall in sub-Saharan Africa have profound and often dire effects on African society and economy. To reduce the vulnerability of African communities to variations in the strength of the WAM, the scientific community needs to improve the reliability of forecasts so as to enable forward planning, and national governments need to adopt coordinated policies in order to increase their capacity to cope with extended periods of water shortages due to drought. With the launch of the Africa Climate Exchange (Afclix), the UK and African climate communies are working with both the humanitarian sector and policy-makers to channel the latest climate science into policy. Such policies have the potential to build resilience and in-country capacity for climate compatible development in sub-Saharan Africa. The emphasis is on ‘feet on the (African) ground’ mechanisms of knowledge-sharing activities at the science-policy interface.

A verification framework for interannual-to-decadal predictions experiments

Decadal predictions have a high profile in the climate science community and beyond, yet very little is known about their skill. Nor is there any agreed protocol for estimating their skill. This paper proposes a sound and coordinated framework for verification of decadal hindcast experiments. The framework is illustrated for decadal hindcasts tailored to meet the requirements and specifications of CMIP5 (Coupled Model Intercomparison Project phase 5). The chosen metrics address key questions about the information content in initialized decadal hindcasts. These questions are: (1) Do the initial conditions in the hindcasts lead to more accurate predictions of the climate, compared to un-initialized climate change projections? and (2) Is the prediction model’s ensemble spread an appropriate representation of forecast uncertainty on average? The first question is addressed through deterministic metrics that compare the initialized and uninitialized hindcasts. The second question is addressed through a probabilistic metric applied to the initialized hindcasts and comparing different ways to ascribe forecast uncertainty. Verification is advocated at smoothed regional scales that can illuminate broad areas of predictability, as well as at the grid scale, since many users of the decadal prediction experiments who feed the climate data into applications or decision models will use the data at grid scale, or downscale it to even higher resolution. An overall statement on skill of CMIP5 decadal hindcasts is not the aim of this paper. The results presented are only illustrative of the framework, which would enable such studies. However, broad conclusions that are beginning to emerge from the CMIP5 results include (1) Most predictability at the interannual-to-decadal scale, relative to climatological averages, comes from external forcing, particularly for temperature; (2) though moderate, additional skill is added by the initial conditions over what is imparted by external forcing alone; however, the impact of initialization may result in overall worse predictions in some regions than provided by uninitialized climate change projections; (3) limited hindcast records and the dearth of climate-quality observational data impede our ability to quantify expected skill as well as model biases; and (4) as is common to seasonal-to-interannual model predictions, the spread of the ensemble members is not necessarily a good representation of forecast uncertainty. The authors recommend that this framework be adopted to serve as a starting point to compare prediction quality across prediction systems. The framework can provide a baseline against which future improvements can be quantified. The framework also provides guidance on the use of these model predictions, which differ in fundamental ways from the climate change projections that much of the community has become familiar with, including adjustment of mean and conditional biases, and consideration of how to best approach forecast uncertainty.

On instabilities in data assimilation algorithms

Data assimilation algorithms are a crucial part of operational systems in numerical weather prediction, hydrology and climate science, but are also important for dynamical reconstruction in medical applications and quality control for manufacturing processes. Usually, a variety of diverse measurement data are employed to determine the state of the atmosphere or to a wider system including land and oceans. Modern data assimilation systems use more and more remote sensing data, in particular radiances measured by satellites, radar data and integrated water vapor measurements via GPS/GNSS signals. The inversion of some of these measurements are ill-posed in the classical sense, i.e. the inverse of the operator H which maps the state onto the data is unbounded. In this case, the use of such data can lead to significant instabilities of data assimilation algorithms. The goal of this work is to provide a rigorous mathematical analysis of the instability of well-known data assimilation methods. Here, we will restrict our attention to particular linear systems, in which the instability can be explicitly analyzed. We investigate the three-dimensional variational assimilation and four-dimensional variational assimilation. A theory for the instability is developed using the classical theory of ill-posed problems in a Banach space framework. Further, we demonstrate by numerical examples that instabilities can and will occur, including an example from dynamic magnetic tomography.

Thermal remote sensing of sea surface temperature

Sea surface temperature has been an important application of remote sensing from space for three decades. This chapter first describes well-established methods that have delivered valuable routine observations of sea surface temperature for meteorology and oceanography. Increasingly demanding requirements, often related to climate science, have highlighted some limitations of these ap-proaches. Practitioners have had to revisit techniques of estimation, of characterising uncertainty, and of validating observations—and even to reconsider the meaning(s) of “sea surface temperature”. The current understanding of these issues is reviewed, drawing attention to ongoing questions. Lastly, the prospect for thermal remote sens-ing of sea surface temperature over coming years is discussed.

Stakeholder perceptions of event attribution in the loss and damage debate

In 2013 the Warsaw International Mechanism (WIM) for loss and damage (L&D) associated with climate change impacts was established under the United Nations Framework Convention on Climate Change (UNFCCC). For scientists, L&D raises ques- tions around the extent that such impacts can be attributed to anthropogenic climate change, which may generate complex results and be controversial in the policy arena. This is particularly true in the case of probabilistic event attribution (PEA) science, a new and rapidly evolving field that assesses whether changes in the probabilities of extreme events are attributable to GHG emissions. If the potential applications of PEA are to be considered responsibly, dialogue between scientists and policy makers is fundamental. Two key questions are considered here through a literature review and key stakeholder interviews with representatives from the science and policy sectors underpinning L&D. These provided the opportunity for in-depth insights into stakeholders’ views on firstly, how much is known and understood about PEA by those associated with the L&D debate? Secondly, how might PEA inform L&D and wider climate policy? Results show debate within the climate science community, and limited understanding among other stakeholders, around the sense in which extreme events can be attributed to climate change. However, stake- holders do identify and discuss potential uses for PEA in the WIM and wider policy, but it remains difficult to explore precise applications given the ambiguity surrounding L&D. This implies a need for stakeholders to develop greater understandings of alternative conceptions of L&D and the role of science, and also identify how PEA can best be used to support policy, and address associated challenges.

Análise das adversidades climáticas no oeste paulista e norte do Paraná

Pós-graduação em Geografia - FCT