# 4. Statistical Physics of Environment, Climate and Ecosystems

**Statistical Physics, Environment and Climate**

**P. Ditlevsen, D. Hristopulos**

The aim of this workshop is to bring together contributions on theoretical, experimental, and computational approaches to climate and environmental modeling which are inspired by statistical physics.

The workshop will focus on applications of statistical physics in the modeling of environmental systems and climate as well the analysis of environmental and climate data. Statistical physics has traditionally centered on the behavior of the microscopic systems. Environmental and climate processes, on the other hand, typically involve macroscopic systems. In spite of the difference in physical scales, statistical physics and environmental/climate modeling both investigate partially determined systems and require a stochastic approach, thus creating the potential for interdisciplinary transfer of knowledge.

The climate is governed by the interchange of energy and mass between atmosphere, oceans, icecaps, land masses and biosphere. From a dynamical systems perspective the climate can be seen as the long term mean of the state of the system, while from a statistical point, the climate can be seen as the equilibrium state as response to the external forcing and boundary conditions. In recent years the problem of understanding and determining the state of the climate has been attacked with different approaches, such as maximum entropy principles, scaling theories, networks, system reduction theories, bifurcations and critical transitions, just to mention some. These different approaches are rooted in statistical physics. Statistical physics also influenced subsurface hydrology which adapted and incorporated methods and ideas from the theory turbulence (structure functions, perturbation expansions, closure schemes), statistical field theory (Feynman diagrams, Renormalization Group theory, replica variational approach), and classical statistical mechanics (Liouville’s theorem, fractional Brownian motion). To date, statistical physics concepts are also used in seismology and other environmental processes. In addition, statistical and machine learning methods originating in statistical physics are used to analyze and process complex patterns in environmental data. This workshop aims to highlight such contributions and to present novel ideas and methods motivated by statistical physics that can lead to new environmental applications and insights into the Earth's climate.

A non-exclusive list of topics of interest includes novel computational and theoretical tools for the analysis of large spatiotemporal data sets, innovative approaches to complex environmental processes and climate that combine nonlinear and stochastic components, methods that address the interaction of multiple scales, approaches for the reconstruction and simulation of non-Gaussian natural or artificial media, applications of stochastic differential equations to environmental processes, higher-order upscaling methods, applications of complex network theory, statistical and stochastic models of extreme events, and estimation of long-range correlations in environmental systems. Physical phenomena of interest include (but are not limited to) the flow and transport of pollutants in the atmosphere, the ocean and the subsurface, natural hazards (earthquakes, fires, avalanches, and landslides), precipitation, global circulation and climate.

**Modelling of Ecosystems: Role of Chaos and Noise**

**D. Valenti**

During the last decades, theoreticians worked to devise deterministic models able to describe ecosystems in which spatial patterns and chaotic phenomena are present, such as (i) sudden switching, in marine ecosystems, from Deep Chlorophyll Maximum to Upper Chlorophyll Maximum, (ii) fast passage from coexistence to exclusion regime in the dynamics of two competing species, (iii) quick decline of predator for slight modifications of initial conditions in prey-predator systems.

Natural systems however are open structures subject to continuous, both deterministic and stochastic, perturbations coming from the environment. As a consequence, deterministic models can not explain some effects due to the intrinsic stochastic nature of real ecosystems. To fill this gap of knowledge, noise induced phenomena in population dynamics have been recently investigated in several theoretical studies, so that nowadays the role of random fuctuations is a well established subject in physics, mathematics, biology, and in their interdisciplinary applications. The goal of the current workshop is to report on very recent results obtained in fundamental issues of population dynamics by both deterministic approaches and stochastic modelling, while highlighting on the one hand the role of chaos, on the other hand the effects of random uctuations, in the dynamics of real ecosystems. Because of its interdisciplinary characteristics, the Workshop constitutes a forum suitable to favour the dialogue and the collaboration among scientists of different areas, such as mathematicians, physicists and biologists, in view of a further development and progress in the modelling of population dynamics and theoretical ecology.