Reconciling Non-Gaussian Climate Statistics with Linear Dynamics

Linear stochastically forced models have been found to be competitive with comprehensive nonlinear weather and climate models at representing many features of the observed covariance statistics and at predictionsbeyondaweek.Their success seems atoddswith the factthattheobserved statisticscan besignificantly non-Gaussian, which is often attributed to nonlinear dynamics. The stochastic noise in the linear models can be a mixture of state-independent (‘‘additive’’) and linearly state-dependent (‘‘multiplicative’’) Gaussian white noises. It is shown here that such mixtures can produce not only symmetric but also skewed non-Gaussian probability distributions if the additive and multiplicative noises are correlated. Such correlations are readily anticipated from first principles. A generic stochastically generated skewed (SGS) distribution can be analytically derived from the Fokker‐Planck equation for a single-component system. In addition to skew, all such SGS distributions have power-law tails, as well as a striking property that the (excess) kurtosis K is always greater than 1.5 times the square of the skew S. Remarkably, this K‐S inequality is found to be satisfied by circulation variables even in the observed multicomponent climate system. A principle of ‘‘diagonal dominance’’ in the multicomponent moment equations is introduced to understand this behavior. To clarify the nature of the stochastic noises (turbulent adiabatic versus diabatic fluctuations) responsible for the observed non-Gaussian statistics, a long 1200-winter simulation of the northern winter climate is generated using a dry adiabatic atmospheric general circulation model forced only with the observed long-term wintermean diabatic forcing as a constant forcing. Despite the complete neglect of diabatic variations, the model reproduces the observed K‐S relationships and also the spatial patterns of the skew and kurtosis of the daily tropospheric circulation anomalies. This suggests that the stochastic generators of these higher moments are mostly associated with local adiabatic turbulent fluxes. The model also simulates fifth moments that are approximately 10 times the skew, and probability densities with power-law tails, as predicted by the linear theory.

[1]  Judith Berner,et al.  Linear and Nonlinear Signatures in the Planetary Wave Dynamics of an AGCM: Probability Density Functions , 2007 .

[2]  G. Branstator.  Circumglobal Teleconnections, the Jet Stream Waveguide, and the North Atlantic Oscillation , 2002 .

[3]  David B. Stephenson,et al.  On the existence of multiple climate regimes , 2004 .

[4]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[5]  M. Ghil,et al.  Multiple Flow Regimes in the Northern Hemisphere Winter. Part I: Methodology and Hemispheric Regimes , 1993 .

[6]  R. Khas'minskii.  A Limit Theorem for the Solutions of Differential Equations with Random Right-Hand Sides , 1966 .

[7]  G. White.  Skewness, Kurtosis and Extreme Values of Northern Hemisphere Geopotential Heights , 1980 .

[8]  Jeffrey S. Whitaker,et al.  A Study of Subseasonal Predictability , 2003 .

[9]  George Papanicolaou,et al.  Asymptotic theory of mixing stochastic ordinary differential equations , 2010 .

[10]  S. Swain.  Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences , 1984 .

[11]  M. Newman.  Power laws, Pareto distributions and Zipf's law , 2005 .

[12]  P. Sardeshmukh,et al.  Global Atmospheric Sensitivity to Tropical SST Anomalies throughout the Indo-Pacific Basin , 2002 .

[13]  atthew,et al.  Multiplicative Noise and Non-Gaussianity : A Paradigm for Atmospheric Regimes ? , 2001 .

[14]  S. Saha,et al.  The NCEP Climate Forecast System , 2006 .

[15]  Michael J. Rycroft,et al.  Storms in Space , 2004 .

[16]  Bo Christiansen,et al.  The Shortcomings of Nonlinear Principal Component Analysis in Identifying Circulation Regimes , 2005 .

[17]  Michael Ghil,et al.  Forecasting Northern Hemisphere 700-mb Geopotential Height Anomalies Using Empirical Normal Modes , 1993 .

[18]  K. Hasselmann.  Stochastic climate models Part I. Theory , 1976 .

[19]  Alfonso Sutera,et al.  On the Probability Density Distribution of Planetary-Scale Atmospheric Wave Amplitude , 1986 .

[20]  Adam H. Monahan,et al.  The preferred structure of variability of the northern hemisphere atmospheric circulation , 2001 .

[21]  T. DelSole,et al.  Stochastic Models of Quasigeostrophic Turbulence , 2004 .

[22]  P. Sardeshmukh,et al.  Is the Time-Mean Northern Hemisphere Flow Baroclinically Unstable? , 1998 .

[23]  Jeffrey S. Whitaker,et al.  A Linear Theory of Extratropical Synoptic Eddy Statistics , 1998 .

[24]  D. Stephenson,et al.  Probability-based methods for quantifying nonlinearity in the ENSO , 2003 .

[25]  Brian J. Hoskins,et al.  Rossby Wave Propagation on a Realistic Longitudinally Varying Flow , 1993 .

[26]  P. Ioannou.  Nonnormality Increases Variance , 1995 .

[27]  Michael Ghil,et al.  Multiple Flow Regimes in the Northern Hemisphere Winter. Part II: Sectorial Regimes and Preferred Transitions , 1993 .

[28]  P. Sardeshmukh,et al.  Sensitivity of global warming to the pattern of tropical ocean warming , 2006 .

[29]  Cécile Penland,et al.  Random Forcing and Forecasting Using Principal Oscillation Pattern Analysis , 1989 .

[30]  Kiyosi Itô,et al.  On stochastic processes (I) , 1941 .

[31]  Brian F. Farrell,et al.  Stochastic dynamics of the midlatitude atmospheric jet , 1995 .

[32]  Andrew J. Majda,et al.  Low-Order Stochastic Mode Reduction for a Realistic Barotropic Model Climate , 2005 .

[33]  Tim N. Palmer,et al.  Signature of recent climate change in frequencies of natural atmospheric circulation regimes , 1999, Nature.

[34]  Cécile Penland,et al.  A Balance Condition for Stochastic Numerical Models with Application to the El Niño-Southern Oscillation , 1994 .

[35]  P. Imkeller,et al.  Stochastic climate models , 2001 .

[36]  P. Sardeshmukh,et al.  Another Look at the Annual and Semiannual Cycles of Atmospheric Angular Momentum , 2000 .

[37]  M. Newman,et al.  Tropical and Stratospheric Influences on Extratropical Short-Term Climate Variability , 2007 .

[38]  Cécile Penland,et al.  A stochastic model of IndoPacific sea surface temperature anomalies , 1996 .

[39]  J. Fyfe,et al.  A regime view of northern hemisphere atmospheric variability and change under global warming , 2000 .

[40]  Michael Ghil,et al.  Empirical mode reduction in a model of extratropical low-frequency variability , 2006 .

[41]  R. Stouffer,et al.  Assessment of Twentieth-Century Regional Surface Temperature Trends using the GFDL CM2 Coupled Models , 2006 .

[42]  P. Sardeshmukh,et al.  Barotropic Rossby Wave Dynamics of Zonally Varying Upper-Level Flows during Northern Winter , 1995 .

[43]  K. Vahala.  Handbook of stochastic methods for physics, chemistry and the natural sciences , 1986, IEEE Journal of Quantum Electronics.

[44]  Prashant D. Sardeshmukh,et al.  The Optimal Growth of Tropical Sea Surface Temperature Anomalies , 1995 .

[45]  Detlev Müller,et al.  Bispectra of Sea-Surface Temperature Anomalies , 1987 .

[46]  Adam H. Monahan,et al.  The Spatial and Temporal Structure of ENSO Nonlinearity , 2004 .

[47]  A. Monahan.  A Simple Model for the Skewness of Global Sea Surface Winds , 2004 .

[48]  Prashant D. Sardeshmukh,et al.  A Global View of Non-Gaussian SST Variability , 2008 .

[49]  Andrew J. Majda,et al.  Systematic Strategies for Stochastic Mode Reduction in Climate , 2003 .

[50]  Christopher R. Winkler,et al.  A Linear Model of Wintertime Low-Frequency Variability. Part I: Formulation and Forecast Skill , 2001 .

[51]  Fei-Fei Jin,et al.  Nonlinearity and Asymmetry of ENSO(. , 2004 .

[52]  P. Sardeshmukh,et al.  Multiscale Impacts of Variable Heating in Climate , 2007 .

[53]  L. Bengtsson,et al.  Forcing of Northern Hemisphere Climate Trends , 2003 .

[54]  Michael Ghil,et al.  Multilevel Regression Modeling of Nonlinear Processes: Derivation and Applications to Climatic Variability , 2005 .