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Dynamics and Practical Predictability of Extratropical Wintertime Low-Frequency Variability in a Low-Dimensional System

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  • 1 Graduate School of Science, Hokkaido University, Sapporo, Japan
  • 2 Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto, Japan
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Abstract

Dynamics and practical predictability of extratropical low-frequency variability (LFV) in Northern Hemisphere winter are examined in the framework of a two-dimensional (2D) stochastic differential equation (SDE) on the phase space spanned by two leading empirical orthogonal function modes of low-pass-filtered 500-hPa geopotential height variations. The drift vector and diffusion tensor of the 2D SDE with multiplicative noise are theoretically connected with deterministic and stochastic error growth, respectively; both are statistically estimated from a reanalysis dataset. Projected onto the 2D phase space is the practical predictability of the LFV estimated by the 10-day forecast spread based on the 1-month ensemble prediction operationally conducted by the Japan Meteorological Agency (JMA). It is shown that the forecast spread of the LFV prediction by the JMA model for a relatively shorter prediction period when the model bias does not hamper the forecast is primarily explained by the stochastic error growth associated with the diffusion tensor and the deterministic error growth due to the Jacobian of the drift vector plays a secondary role. A non-Gaussian PDF of the LFV is also related to the norm of the diffusion tensor. Hence, the stochastic processes mostly control the dynamics and predictability of the LFV in the 2D phase space.

Corresponding author address: Dr. Masaru Inatsu, Graduate School of Science, Hokkaido University, Rigaku Bldg. 8, N10W8, Kita, Sapporo 0600810, Japan. E-mail: inaz@mail.sci.hokudai.ac.jp

Abstract

Dynamics and practical predictability of extratropical low-frequency variability (LFV) in Northern Hemisphere winter are examined in the framework of a two-dimensional (2D) stochastic differential equation (SDE) on the phase space spanned by two leading empirical orthogonal function modes of low-pass-filtered 500-hPa geopotential height variations. The drift vector and diffusion tensor of the 2D SDE with multiplicative noise are theoretically connected with deterministic and stochastic error growth, respectively; both are statistically estimated from a reanalysis dataset. Projected onto the 2D phase space is the practical predictability of the LFV estimated by the 10-day forecast spread based on the 1-month ensemble prediction operationally conducted by the Japan Meteorological Agency (JMA). It is shown that the forecast spread of the LFV prediction by the JMA model for a relatively shorter prediction period when the model bias does not hamper the forecast is primarily explained by the stochastic error growth associated with the diffusion tensor and the deterministic error growth due to the Jacobian of the drift vector plays a secondary role. A non-Gaussian PDF of the LFV is also related to the norm of the diffusion tensor. Hence, the stochastic processes mostly control the dynamics and predictability of the LFV in the 2D phase space.

Corresponding author address: Dr. Masaru Inatsu, Graduate School of Science, Hokkaido University, Rigaku Bldg. 8, N10W8, Kita, Sapporo 0600810, Japan. E-mail: inaz@mail.sci.hokudai.ac.jp
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