Low-dimensional reduced-order models for statistical response and uncertainty quantification

Two-layer baroclinic turbulence

Research output: Contribution to journalArticle

Abstract

Accurate uncertainty quantification for the mean and variance about forced responses to general external perturbations in the climate system is an important subject in understanding Earth's atmosphere and ocean in climate change science. A low-dimensional reduced-order method is developed for uncertainty quantification and capturing the statistical sensitivity in the principal model directions with largest variability and in various regimes in two-layer quasigeostrophic turbulence. Typical dynamical regimes tested here include the homogeneous flow in the high latitudes and the anisotropic meandering jets in the low latitudes and/or midlatitudes. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. Here a statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. The reduced-order model displays uniformly high prediction skill for the mean and variance response to general forcing for both homogeneous flow and anisotropic zonal jets in the first 102 dominant low-wavenumber modes, where only about 0.15% of the total spectral modes are resolved, compared with the full model resolution of 2562 horizontal modes.

Original languageEnglish (US)
Pages (from-to)4609-4639
Number of pages31
JournalJournal of the Atmospheric Sciences
Volume73
Issue number12
DOIs
StatePublished - 2016

Fingerprint

turbulence
prediction
nonlinearity
damping
energy
perturbation
calibration
climate change
atmosphere
climate
ocean

Keywords

  • Baroclinic models
  • Climate variability
  • Differential equations
  • Numerical analysis/modeling
  • Statistical techniques

ASJC Scopus subject areas

  • Atmospheric Science

Cite this

@article{9ab34ec447364e5180fd81e0c26a4db4,
title = "Low-dimensional reduced-order models for statistical response and uncertainty quantification: Two-layer baroclinic turbulence",
abstract = "Accurate uncertainty quantification for the mean and variance about forced responses to general external perturbations in the climate system is an important subject in understanding Earth's atmosphere and ocean in climate change science. A low-dimensional reduced-order method is developed for uncertainty quantification and capturing the statistical sensitivity in the principal model directions with largest variability and in various regimes in two-layer quasigeostrophic turbulence. Typical dynamical regimes tested here include the homogeneous flow in the high latitudes and the anisotropic meandering jets in the low latitudes and/or midlatitudes. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. Here a statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. The reduced-order model displays uniformly high prediction skill for the mean and variance response to general forcing for both homogeneous flow and anisotropic zonal jets in the first 102 dominant low-wavenumber modes, where only about 0.15{\%} of the total spectral modes are resolved, compared with the full model resolution of 2562 horizontal modes.",
keywords = "Baroclinic models, Climate variability, Differential equations, Numerical analysis/modeling, Statistical techniques",
author = "Di Qi and Majda, {Andrew J.}",
year = "2016",
doi = "10.1175/JAS-D-16-0192.1",
language = "English (US)",
volume = "73",
pages = "4609--4639",
journal = "Journals of the Atmospheric Sciences",
issn = "0022-4928",
publisher = "American Meteorological Society",
number = "12",

}

TY - JOUR

T1 - Low-dimensional reduced-order models for statistical response and uncertainty quantification

T2 - Two-layer baroclinic turbulence

AU - Qi, Di

AU - Majda, Andrew J.

PY - 2016

Y1 - 2016

N2 - Accurate uncertainty quantification for the mean and variance about forced responses to general external perturbations in the climate system is an important subject in understanding Earth's atmosphere and ocean in climate change science. A low-dimensional reduced-order method is developed for uncertainty quantification and capturing the statistical sensitivity in the principal model directions with largest variability and in various regimes in two-layer quasigeostrophic turbulence. Typical dynamical regimes tested here include the homogeneous flow in the high latitudes and the anisotropic meandering jets in the low latitudes and/or midlatitudes. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. Here a statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. The reduced-order model displays uniformly high prediction skill for the mean and variance response to general forcing for both homogeneous flow and anisotropic zonal jets in the first 102 dominant low-wavenumber modes, where only about 0.15% of the total spectral modes are resolved, compared with the full model resolution of 2562 horizontal modes.

AB - Accurate uncertainty quantification for the mean and variance about forced responses to general external perturbations in the climate system is an important subject in understanding Earth's atmosphere and ocean in climate change science. A low-dimensional reduced-order method is developed for uncertainty quantification and capturing the statistical sensitivity in the principal model directions with largest variability and in various regimes in two-layer quasigeostrophic turbulence. Typical dynamical regimes tested here include the homogeneous flow in the high latitudes and the anisotropic meandering jets in the low latitudes and/or midlatitudes. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. Here a statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. The reduced-order model displays uniformly high prediction skill for the mean and variance response to general forcing for both homogeneous flow and anisotropic zonal jets in the first 102 dominant low-wavenumber modes, where only about 0.15% of the total spectral modes are resolved, compared with the full model resolution of 2562 horizontal modes.

KW - Baroclinic models

KW - Climate variability

KW - Differential equations

KW - Numerical analysis/modeling

KW - Statistical techniques

UR - http://www.scopus.com/inward/record.url?scp=85003758536&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85003758536&partnerID=8YFLogxK

U2 - 10.1175/JAS-D-16-0192.1

DO - 10.1175/JAS-D-16-0192.1

M3 - Article

VL - 73

SP - 4609

EP - 4639

JO - Journals of the Atmospheric Sciences

JF - Journals of the Atmospheric Sciences

SN - 0022-4928

IS - 12

ER -