Seeding Chaos: The Dire Consequences of Numerical Noise in NWP Perturbation Experiments

Brian C. Ancell Texas Tech University, Lubbock, Texas

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Allison Bogusz Texas Tech University, Lubbock, Texas

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Matthew J. Lauridsen Texas Tech University, Lubbock, Texas

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Christian J. Nauert Texas Tech University, Lubbock, Texas

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Abstract

Perturbation experiments are a common technique used to study how differences between model simulations evolve within chaotic systems. Such perturbation experiments include modifications to initial conditions (including those involved with data assimilation), boundary conditions, and model parameterizations. We have discovered, however, that any difference between model simulations produces a rapid propagation of very small changes throughout all prognostic model variables at a rate many times the speed of sound. The rapid propagation seems to be due to the model’s higher-order spatial discretization schemes, allowing the communication of numerical error across many grid points with each time step. This phenomenon is found to be unavoidable within the Weather Research and Forecasting (WRF) Model even when using techniques such as digital filtering or numerical diffusion.

These small differences quickly spread across the entire model domain. While these errors initially are on the order of a millionth of a degree with respect to temperature, for example, they can grow rapidly through nonlinear chaotic processes where moist processes are occurring. Subsequent evolution can produce within a day significant changes comparable in magnitude to high-impact weather events such as regions of heavy rainfall or the existence of rotating supercells. Most importantly, these unrealistic perturbations can contaminate experimental results, giving the false impression that realistic physical processes play a role. This study characterizes the propagation and growth of this type of noise through chaos, shows examples for various perturbation strategies, and discusses the important implications for past and future studies that are likely affected by this phenomenon.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

CORRESPONDING AUTHOR: Brian C. Ancell, brian.ancell@ttu.edu

ADDITIONAL AFFILIATIONS: Lauridsen—Fleet Numerical Meteorology and Oceanography Center, Monterey, California; Nauert—Rockhill Group, Lubbock, Texas

Abstract

Perturbation experiments are a common technique used to study how differences between model simulations evolve within chaotic systems. Such perturbation experiments include modifications to initial conditions (including those involved with data assimilation), boundary conditions, and model parameterizations. We have discovered, however, that any difference between model simulations produces a rapid propagation of very small changes throughout all prognostic model variables at a rate many times the speed of sound. The rapid propagation seems to be due to the model’s higher-order spatial discretization schemes, allowing the communication of numerical error across many grid points with each time step. This phenomenon is found to be unavoidable within the Weather Research and Forecasting (WRF) Model even when using techniques such as digital filtering or numerical diffusion.

These small differences quickly spread across the entire model domain. While these errors initially are on the order of a millionth of a degree with respect to temperature, for example, they can grow rapidly through nonlinear chaotic processes where moist processes are occurring. Subsequent evolution can produce within a day significant changes comparable in magnitude to high-impact weather events such as regions of heavy rainfall or the existence of rotating supercells. Most importantly, these unrealistic perturbations can contaminate experimental results, giving the false impression that realistic physical processes play a role. This study characterizes the propagation and growth of this type of noise through chaos, shows examples for various perturbation strategies, and discusses the important implications for past and future studies that are likely affected by this phenomenon.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

CORRESPONDING AUTHOR: Brian C. Ancell, brian.ancell@ttu.edu

ADDITIONAL AFFILIATIONS: Lauridsen—Fleet Numerical Meteorology and Oceanography Center, Monterey, California; Nauert—Rockhill Group, Lubbock, Texas

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