arXiv subjects

Ivan Sudakov

Publications and source records attributed to Ivan Sudakov.

9 recordsLinked to original sources

arXiv2020

Stochastic physics of species extinctions in a large population

Species extinction is a core process that affects the diversity of life on Earth. Competition between species in a population is considered by ecological niche-based theories as a key factor leading to different severity of species extinctions. There are population dynamics models that describe a simple and easily understandable mechanism for resource competition. However, these models can not efficiently characterize and quantify new emergent extinctions in a large population appearing due to environmental forcing. To address this issue we develop a stochastic physics-inspired approach to analyze how environmental forcing influences the severity of species extinctions in such models. This approach is based on the large deviations theory of stochastic processes (the Freidlin-Wentzell theory). We show that there are three possible fundamentally different scenarios of extinctions, which we call catastrophic extinctions, asymmetric ones, and extinctions with exponentially small probabilities. The realization of those scenarios depends on environmental noise properties and the boundaries of niches, which define the domain, where species survive. Furthermore, we describe a hysteresis effect in species extinction showing that fluctuations can lead to dramatic consequences even if an averaged resource supply is sufficient to support population survival. Our stochastic physics-inspired approach generalizes niche theory by accounting environmental forcing and will be useful to find, by available data, which environmental perturbations may induce extinctions.

q-bio.PE↗

arXiv2020

Stability of a planetary climate system with the biosphere competing for resources

With the growing number of discovered exoplanets, the Gaia concept finds its second wind. The Gaia concept defines that the biosphere of an inhabited planet regulates a planetary climate through feedback loops such that the planet remains habitable. Crunching 'Gaia' puzzle has been a focus of intense empirical research. Much less attention has been paid to the mathematical realization of this concept. In this paper, we consider the stability of a planetary climate system with the dynamic biosphere by linking a conceptual climate model to a generic population dynamics model with random parameters. We first show that the dynamics of the corresponding coupled system possesses multiple timescales and hence falls into the class of slow-fast dynamics. We then investigate the properties of a general dynamical system to which our model belongs and prove that the feedbacks from the biosphere dynamics cannot break the system's stability as long as the biodiversity is sufficiently high. That may explain why the climate is apparently stable over long time intervals. Interestingly, our coupled climate-biosphere system can lose its stability if biodiversity decreases; in this case, the evolution of the biosphere under the effect of random factors can lead to a global climate change.

nlin.CD↗

arXiv2017

Minor climatic fluctuations lead to species extinction in a conceptual ecosystem model

The extinction of species is a core process that affects the diversity of life on Earth. One way of investigating the causes and consequences of extinctions is to build conceptual ecological models, and to use the dynamical outcomes of such models to provide quantitative formalization of changes to Earth's biosphere. In this paper we propose and study a conceptual resource model that describes a simple and easily understandable mechanism for resource competition, generalizes the well-known Huisman and Weissing model, and takes into account species self-regulation, extinctions, and time dependence of resources. We use analytical investigations and numerical simulations to study the dynamics of our model under chaotic and periodic climate oscillations, and show that the stochastic dynamics of our model exhibit strong dependence on initial parameters. We also demonstrate that extinctions in our model are inevitable if an ecosystem has the maximal possible biodiversity and uses the maximal amount of resources. Our conceptual modeling provides theoretical support for suggestions that non-linear processes were important during major extinction events in Earth history.

q-bio.PE↗

arXiv2017

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

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 $\sim$100 km$^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.

nlin.PS↗

arXiv2017

Ising model for melt ponds on Arctic sea ice

Perhaps the most iconic feature of melting Arctic sea ice is the formation of distinctive, complex ponds on its surface during late spring. The evolution of melt ponds and their geometrical characteristics determines the albedo of sea ice, a key parameter in climate modeling. However, a theoretical understanding of this evolution, and predictions of geometrical features, have remained elusive. To address this fundamental problem in polar climate science, here we introduce a two dimensional random field Ising model for melt ponds. The ponds are identified as metastable states of the system, where the binary spin variable corresponds to the presence of melt water or ice on the sea ice surface. With only a minimal set of physical parameters, the model predictions agree very closely with observed power law scaling of the pond size distribution and critical length scale where melt ponds undergo a transition in fractal geometry.

physics.ao-ph↗

arXiv2016

Complex bifurcations in Bénard-Marangoni convection

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.

math-ph↗

arXiv2014

Surface salinity fields in the Arctic Ocean and statistical approaches to predicting anomalies and patterns

Significant salinity anomalies have been observed in the Arctic Ocean surface layer during the last decade. Using gridded data of winter salinity in the upper 50 m layer of the Arctic Ocean for the period 1950-1993 and 2007-2012, we investigated the inter-annual variability of the salinity fields, attempted to identify patterns and anomalies, and developed a statistical model for the prediction of surface layer salinity. The statistical model is based on linear regression equations linking the principal components with environmental factors, such as atmospheric circulation, river runoff, ice processes, and water exchange with neighboring oceans. Using this model, we obtained prognostic fields of the surface layer salinity for the winter period 2013-2014. The prognostic fields demonstrated the same tendencies of surface layer freshening that were observed previously. A phase portrait analysis involving the first two principal components exhibits a dramatic shift in behavior of the 2007-2012 data in comparison to earlier observations.

physics.ao-ph↗

arXiv2014

Arctic melt ponds and bifurcations in the climate system

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.

nlin.PS↗

arXiv2014

Mathematics and Climate Infographics: A Mechanism for Interdisciplinary Collaboration 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.

physics.ed-ph↗