The problem of climate change is that of a chaotic system subject to time-dependent forcing, such as anthropogenic greenhouse gases and natural volcanism. To solve this problem, we describe the mathematics of dynamical systems with explicit time dependence and those of studying their behavior through topological methods. Here, we show how they are being applied to climate change and its predictability.

A hybrid weighted particle swarm optimization (wPSO) and gravitational search algorithm (GSA) is compared with individual PSO and GSA methods to assess 1-D resistivity models from magnetotelluric data across diverse geological terrains. This involved creating numerous models to match apparent resistivity and phase curves, selecting the best-fit models, and conducting posterior PDF, correlation matrix, and stability analysis to improve the mean model's accuracy with minimized uncertainty.

This study aimed to enhance weather and hydrological forecasts by integrating soil moisture data into a global weather model. By assimilating atmospheric observations and soil moisture data, the accuracy of forecasts was improved, and certain biases were reduced. The method was found to be particularly beneficial in areas like the Sahel and equatorial Africa, where precipitation patterns vary seasonally. This new approach has the potential to improve the precision of weather predictions.

Many systems in nature are characterized by the coexistence of different stable states for given environmental parameters and external forcing. Examples can be found in different fields of science, ranging from ecosystems to climate dynamics. Perturbations can lead to critical transitions (tipping) from one stable state to another. The study of these transitions requires the development of new methodological approaches that allow for modeling, analyzing and predicting them.

Statistical post-processing is necessary to generate probabilistic forecasts from physical numerical weather prediction models. To allow for more flexibility, there has been a shift in post-processing away from traditional parametric regression models towards modern machine learning methods. By fusing these two approaches, we developed model output statistics random forests, a new post-processing method that is highly flexible but at the same time also very robust and easy to interpret.

An increasing amount of data allows us to move from low-order moments of fluctuating observations to their PDFs. We found the analytical fat-tailed PDF form (a combination of Gaussian and two-exponential convolutions) for 2 years of sea surface current increments in the Gulf of Trieste, using superstatistics and the maximum-entropy principle twice: on short and longer timescales. The data from different wind regimes follow the same analytical PDF, pointing towards a universal behaviour.

Our paper tours powerful methods of finding the effective behavior of complex systems, which can be applied well beyond the initial setting of sea ice. Applications include transport properties of porous and polycrystalline media, such as rocks and glacial ice, and advection diffusion processes that arise throughout geophysics. Connections to random matrix theory establish unexpected parallels of these geophysical problems with semiconductor physics and Anderson localization phenomena.

Forecasting near-surface winds over complex terrain requires high-resolution numerical weather prediction models, which drastically increase the duration of simulations and hinder them in running on a routine basis. A faster alternative is statistical downscaling. We explore different ways of calculating near-surface wind speed and direction using artificial intelligence algorithms based on various convolutional neural networks in order to find the best approach for wind downscaling.

Effusive–explosive volcanic energy emissions are a complex and dynamic physical phenomenon. The complexity of this process for the Volcán de Colima along the years 2013–2015 is analysed by means of the reconstruction theorem being determined by the persistence, complexity and “loss of memory” of the physical mechanism. The results suggest that appropriate forecasting algorithms could be applied to determine forthcoming high-energy emissions.

In semi-arid regions, hydric stress affects plant growth. In these conditions, vegetation patterns develop and effectively allow for vegetation to persist under low water input. The formation of patterns and the transition between patterns can be studied with small models taking the form of dynamical systems. Our study produces a full map of stable and unstable solutions in a canonical vegetation model and shows how they determine the transitions between different patterns.