Ivan Sudakov

Large ecosystems in transition: Bifurcations and mass extinction

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.

Bifurcations of the climate system and greenhouse gas emissions

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.

Infographics and Mathematics: A Mechanism for Effective Learning in the Classroom.

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.Abstract This work discusses the creation and use of infographics in an undergraduate mathematics course. Infographics are a visualization of information that combines data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from undergraduate students on both the general use of infographics and on the specific infographics designed by the authors.

Arctic melt ponds and bifurcations in the climate system

Abstract 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.

The influence of environmental forcing on biodiversity and extinction in a resource competition model

In this paper, we study a model of many species that compete, directly or indirectly, for a pool of common resources under the influence of periodic, stochastic, and/or chaotic environmental forcing. Using numerical simulations, we find the number and sequence of species going extinct when the community is initially packed with a large number of species of random initial densities. Thereby, any species with a density below a given threshold is regarded to be extinct.

Observed winter salinity fields in the surface layer of the Arctic Ocean and statistical approaches to predicting large-scale anomalies and patterns

Abstract Significant salinity anomalies have been observed in the Arctic Ocean surface layer during the last decade. Our study is based on an extensive gridded dataset of winter salinity in the upper 50 m layer of the Arctic Ocean for the periods 1950–1993 and 2007–2012, obtained from ~20 000 profiles. We investigate the interannual variability of the salinity fields, identify predominant patterns of anomalous behavior and leading modes of variability, and develop a statistical model for the prediction of surface-layer salinity. The statistical model is based on linear regression equations linking the principal components of surface-layer salinity obtained through empirical orthogonal function decomposition with environmental factors, such as atmospheric circulation, river runoff, ice processes and water exchange with neighboring oceans. Using this model, we obtain prognostic fields of the surface-layer salinity for the winter period 2013–2014. The prognostic fields generated by the model show tendencies of surface-layer salinification, which were also observed in previous years. Although the used data are proprietary and have gaps, they provide the most spatiotemporally detailed observational resource for studying multidecadal variations in basin-wide Arctic salinity. Thus, there is community value in the identification, dissemination and modeling of the principal modes of variability in this salinity record.

The Geometry of Large Tundra Lakes Observed in Historical Maps and Satellite Images

The climate of the Arctic is warming rapidly and this is causing major changes to the cycling of carbon and the distribution of permafrost in this region. Tundra lakes are key components of the Arctic climate system because they represent a source of methane to the atmosphere. In this paper, we aim to analyze the geometry of the patterns formed by large (> 0.8 km 2 ) tundra lakes in the Russian High Arctic. We have studied images of tundra lakes in historical maps from the State Hydrological Institute, Russia (date 1977; scale 0.21166 km/pixel) and in Landsat satellite images derived from the Google Earth Engine (G.E.E.; date 2016; scale 0.1503 km/pixel). The G.E.E. is a cloud-based platform for planetary-scale geospatial analysis on over four decades of Landsat data. We developed an image-processing algorithm to segment these maps and images, measure the area and perimeter of each lake, and compute the fractal dimension of the lakes in the images we have studied. Our results indicate that as lake size increases, their fractal dimension bifurcates. For lakes observed in historical maps, this bifurcation occurs among lakes larger than 100 km 2 (fractal dimension 1.43 to 1.87 ). For lakes observed in satellite images this bifurcation occurs among lakes larger than ∼100 km 2 (fractal dimension 1.31 to 1.95 ). Tundra lakes with a fractal dimension close to 2 have a tendency to be self-similar with respect to their area–perimeter relationships. Area–perimeter measurements indicate that lakes with a length scale greater than 70 km 2 are power-law distributed. Preliminary analysis of changes in lake size over time in paired lakes (lakes that were visually matched in both the historical map and the satellite imagery) indicate that some lakes in our study region have increased in size over time, whereas others have decreased in size over time. Lake size change during this 39-year time interval can be up to half the size of the lake as recorded in the historical map.