Atmospheric Weather Variability

  • Rex J. Fleming


The atmosphere is proven to be a chaotic system. Two classes of solutions from a simple model of baroclinic instability are examined – one is chaotic. The power of the chaos is determined with Monte Carlo samples. The results for the 40,000 deterministic chaotic solutions were all different. This weather diversity would expand with the seasons due to different heating characteristics – and would exist in any climate regime (warm or cold). This model actually underestimates atmospheric variability – and can be extreme, but it is not climate-change.


Baroclinic instability Chaos 


  1. 1.
    Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20, 130–141.CrossRefGoogle Scholar
  2. 2.
    Fleming, R. J. (2015). Analysis of the SDE/Monte Carlo approach in studying nonlinear systems. Saarbrücken: Lambert Academic Publishing, 136 pp.Google Scholar
  3. 3.
    Salazar, J. M., & Nicolis, C. (1988). Self-generating aperiodic behavior in a simple climate model. Climate Dynamics, (2), 105–114.Google Scholar
  4. 4.
    Peixoto, J. P., & Oort, A. H. (1992). Physics of climate. New York: American institute of Physics, 522 pp.CrossRefGoogle Scholar
  5. 5.
    Thompson, P. D. (1987). Large-scale dynamic response to differential heating: Statistical equilibrium states and amplitude vacillation. Journal of the Atmospheric Sciences, 44, 237–1248.CrossRefGoogle Scholar
  6. 6.
    Webster, P., & Keller, J. L. (1975). Atmospheric variations: Vacillation and index cycles. Journal of the Atmospheric Sciences, 44, 1238–1300.Google Scholar
  7. 7.
    Fleming, R. J. (2014). Explosive baroclinic instability. Journal of the Atmospheric Sciences, 71, 2155–2168.CrossRefGoogle Scholar
  8. 8.
    Finding the roots of the characteristic equation of a nonlinear system, provides the eigenvalues. The sum of the real parts of these roots is the “trace”. If the trace is negative (as is the case for the model in the text which produces explosive baroclinic instability (EBI), there will never be runaway EBI – the chaos is constrained).Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Rex J. Fleming
    • 1
  1. 1.Global Aerospace, LLC (Retired)BoulderUSA

Personalised recommendations