Valerio Lucarini

TL;DR: In this article, a modified Kramers-Kronig Relations in Nonlinear Optics and Sum Rules for Data Analysis for Harmonic Generation Processes are presented. But the Sum Rules are not suitable for data analysis in nonlinear systems.

TL;DR: In this article, the authors make a case that the use of stochastic representation of unresolved processes in the atmosphere, oceans, land surface, and cryosphere of comprehensive weather and climate models gives rise to more reliable probabilistic forecasts of weather, and reduces systematic model bias.

TL;DR: In this article, the authors highlight recent developments from different research groups which show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface and cryosphere of comprehensive weather and climate models (a) gives rise to more reliable probabilistic forecasts of weather, and (b) reduces systematic model bias.

TL;DR: Numerical bifurcation analysis of high-dimensional dynamical systems has been extensively studied in the literature as discussed by the authors, where the authors provide an overview of current techniques and typical applications of such problems in fluid dynamical problems.

TL;DR: This paper reviewed the observational evidence on climate phenomena and the governing equations of planetary-scale flow, as well as presenting the key concept of a hierarchy of models as used in the climate sciences.