Preprints
https://doi.org/10.5194/egusphere-2024-287
https://doi.org/10.5194/egusphere-2024-287
09 Feb 2024
 | 09 Feb 2024

Prognostic Assumed-PDF (DDF) Approach: Further Generalization and Demonstrations

Jun-Ichi Yano

Abstract. A methodology for directly predicting the time evolution of the assumed parameters for the distribution densities based on the Liouville equation, as proposed earlier, is extended to multi–dimensional cases as well as when the systems are constrained by integrals over a part of the variable range. The extended methodology is tested against a convective energy cycle system as well as the Lorenz’s stranger attractor. As a general tendency, the variance tends to collapse to a vanishing value over a finite time regardless of the chosen assumed distribution form. This general tendency is likely due to the common cause as collapse of the variance commonly found in ensemble–based data assimilation.

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Jun-Ichi Yano

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2024-287', Anonymous Referee #1, 03 Apr 2024
    • AC1: 'Reply on RC1', Jun-Ichi Yano, 15 Apr 2024
  • RC2: 'Comment on egusphere-2024-287', Anonymous Referee #2, 08 Apr 2024
    • AC2: 'Reply on RC2', Jun-Ichi Yano, 15 Apr 2024
Jun-Ichi Yano
Jun-Ichi Yano

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Short summary
A methodology for directly predicting the time evolution of the assumed parameters for the distribution densities based on the Liouville equation, as proposed earlier, is extended to multi–dimensional cases as well as when the systems are constrained by integrals over a part of the variable range. The extended methodology is tested against a convective energy cycle system as well as the Lorenz's stranger attractor.