Steady-State Solutions of a Diffusive Energy-Balance Climate Model and Their Stability

Abstract

A diffusive energy-balance climate model is considered, governed by a nonlinear parabolic partial differential equation. Three positive steady-state solutions of this equation are found; they correspond to three possible climates of our planet: an interglacial (nearly identical to the present climate), a glacial, and a completely ice-covered earth. Also considered are models similar to the main one studied, and the number of their steady states are determined. All the models have albedo continuously varying with latitude and temperature, and entirely diffusive horizontal heat transfer. The diffusion is taken to be nonlinear as well as linear. The stability under small perturbations of the main model's climates are investigated. A stability criterion is derived, and its application shows that the 'present climate' and the 'deep freeze' are stable, whereas the model's glacial is unstable.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1975
Accession Number
ADA011673

Entities

People

  • Michael Ghil

Organizations

  • New York University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Climate Change
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Eigenvalues
  • Equations
  • Equations Of State
  • Fluid Dynamics
  • Greenhouse Effect
  • Grids
  • Heat Flux
  • Latitude
  • Optical Properties
  • Radiation
  • Solar Radiation
  • Steady State

Fields of Study

  • Environmental science
  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Polar and Arctic Studies