Articles | Volume 12, issue 2
Nonlin. Processes Geophys., 12, 257–267, 2005
Nonlin. Processes Geophys., 12, 257–267, 2005

  09 Feb 2005

09 Feb 2005

Data assimilation for plume models

C. A. Hier Majumder4,1, E. Bélanger2, S. DeRosier3,4,*, D. A. Yuen3,4, and A. P. Vincent2 C. A. Hier Majumder et al.
  • 1Computational Physics Group, Earth Science Division, Lawrence Livermore National Laboratory, Livermore, CA, USA
  • 2Département de Physique, Université de Montréal, Montréal, Québec, Canada
  • 3Department of Geology and Geophysics, University of Minnesota, Minneapolis, Minnesota, USA
  • 4Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota, USA
  • *now at: Department of Earth and Space Sciences, University of Washington, Seattle, Washington, USA

Abstract. We use a four-dimensional variational data assimilation (4D-VAR) algorithm to observe the growth of 2-D plumes from a point heat source. In order to test the predictability of the 4D-VAR technique for 2-D plumes, we perturb the initial conditions and compare the resulting predictions to the predictions given by a direct numerical simulation (DNS) without any 4D-VAR correction. We have studied plumes in fluids with Rayleigh numbers between 106 and 107 and Prandtl numbers between 0.7 and 70, and we find the quality of the prediction to have a definite dependence on both the Rayleigh and Prandtl numbers. As the Rayleigh number is increased, so is the quality of the prediction, due to an increase of the inertial effects in the adjoint equations for momentum and energy. The horizon predictability time, or how far into the future the 4D-VAR method can predict, decreases as Rayleigh number increases. The quality of the prediction is decreased as Prandtl number increases, however. Quality also decreases with increased prediction time.