Infographics are a form of data visualization combining data, information, and statistics. Over the last ten years, infographics have become a popular method for displaying concise information, where infographics are a useful tool for classroom instruction. A high-quality infographic presents complex data in an aesthetically pleasing and simplistic format that allows student to understand more rapidly. Research within mathematics and climate science uses many elements of infographics. This work presents a series of electronic posters in an infographics style which explain hot topics in the mathematics of climate. These posters are designed to be used within standard undergraduate mathematical courses to provide students with concrete examples of how mathematics is incorporated within the climate sciences.

We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we introduce a feedback between species abundances and resources via abiotic factors. This model is apparently the first of its kind to include a feedback mechanism coupling climate and population dynamics. Moreover, we take into account self-limitation effects. The model explains the coexistence of many species, yet also displays the possibility of catastrophic bifurcations, where all species become extinct under the influence of abiotic factors. We show that as these factors change there are different regimes of ecosystem behavior, including a possibly chaotic regime when abiotic influences are sufficiently strong.

Perhaps the most iconic feature of melting Arctic sea ice is the distinctive ponds that form on its surface. The geometrical patterns describing how melt water is distributed over the surface largely determine the solar reflectance and transmittance of the sea ice cover, which are key parameters in climate modeling and upper ocean ecology. In order to help develop a predictive theoretical approach to studying melting sea ice, and the resulting patterns of light and dark regions on its surface in particular, we look to the statistical mechanics of phase transitions and introduce a two-dimensional random field Ising model which accounts for only the most basic physics in the system. The ponds are identified as metastable states in the model, where the binary spin variable corresponds to the presence of melt water or ice on the sea ice surface. With the lattice spacing determined by snow topography data as the only measured parameter input into the model, energy minimization drives the system toward realistic pond configurations from an initially random state. The model captures the essential mechanism of pattern formation of Arctic melt ponds, with predictions that agree very closely with observed scaling of pond sizes and transition in pond fractal dimension.

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We propose a generalization of the classical Goody model by taking into account greenhouse gas emission effects. We develop an asymptotic approach that allows us to obtain an expression for the greenhouse gas flux via the temperature and fluid fields. We show that there is a possible tipping point in atmospheric dynamics resulting from greenhouse gas emissions, where the climate system becomes bistable under sufficiently intensive greenhouse gas emissions.

Abstract. We study the dynamics of a system defined by the Navier-Stokes equations for a non-compressible fluid with Marangoni boundary conditions in the two dimensional case. We show that more complicated bifurcations can appear in this system for a certain nonlinear temperature profile as compared to bifurcations in the classical Rayleigh-Bénard and Bénard-Marangoni systems with simple linear vertical temperature profiles. In terms of the Bénard-Marangoni convection, the obtained mathematical results lead to our understanding of complex spatial patterns at a free liquid surface, which can be induced by a complicated profile of temperature or a chemical concentration at that surface. In addition, we discuss some possible applications of the results to turbulence theory and climate science.

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Understanding how sea ice melts is critical to climate projections. In the Arctic, melt ponds that develop on the surface of sea ice floes during the late spring and summer largely determine their albedo -- a key parameter in climate modeling. Here we explore the possibility of a conceptual sea ice climate model passing through a bifurcation point -- an irreversible critical threshold as the system warms, by incorporating geometric information about melt pond evolution. This study is based on a bifurcation analysis of the energy balance climate model with ice - albedo feedback as the key mechanism driving the system to bifurcation points