Abstract
This article is a first attempt to develop a numerical approach to solving differential equations based on Galerkin projections and extensions of polynomial chaos to analyze the sensitivity of input parameters in the Lorenz–Stenflo climate model (Leonov in Commun Pure Appl Anal 16(6):2253–2267, 2017). The sensitivity analysis was undertaken to measure the influence of key parameters (chemical properties of the atmosphere, rotation, temperature gradient, convection motion). In addition, we do simulations of the climate model in the non-chaotic case and in the chaotic case and we calculate the Sobol indices when the parameters follow the uniform law.
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