Stochastic diffusive energy balance climate model with a multiplicative noise modeling the Solar variability

2025/09/27 by Gregorio Díaz Díaz, Díaz, Gregorio, Jesús Ildefonso Díaz Díaz +1
Economics, Econometrics and Finance · Energy · Environmental Science · #Analysis of PDEs (math.AP) #Atmospheric and Environmental Gas Dynamics #Complex Systems and Time Series Analysis #FOS: Mathematics #Global Energy and Sustainability Research

paper · pdf · doi:10.48550/arxiv.2509.23153

openalex publication_date 2025/09/27 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We prove the existence, uniqueness, and comparison of solutions for a nonlinear stochastic parabolic partial differential equation that includes the Solar variability in terms of a multiplicative Wiener cylindrical noise in the term of the absorbed radiative energy in a simplified diffusive one-dimensional Energy Balance Model. We introduce a hybrid co-albedo nonlinear term, which has the advantages of both the Sellers model, as it is a continuous function, and the Budyko model, as it has an infinite derivative at u=-10^C (the temperature at which ice is white), allowing the location of the polar ice caps to be easily detected. We show that, despite the lack of differentiability of this function, the method of successive approximations can be satisfactorily applied.

Citations

• Dynamic boundary conditions with noise for energy balance models coupled to geophysical flows
• A non-autonomous framework for climate change and extreme weather events increase in a stochastic energy balance model
• Large solutions of elliptic semilinear equations non-degenerate near the boundary
• Stochastic energy balance climate models with Legendre weighted\n diffusion and a cylindrical Wiener process forcing
• On the exact number of monotone solutions of a simplifed Budyko climate model and their different stability
• On the equations of the large-scale ocean
• A Global Climatic Model Based on the Energy Balance of the Earth-Atmosphere System

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