Integrated regional enstrophy and block intensity as a measure of Kolmogorov entropy

Enstrophy in a fluid relates to the dissipation tendency in a fluid that has use in studying turbulent flows. It also corresponds to vorticity as kinetic energy does to velocity. Earlier work showed that the integrated regional enstrophy (IRE) was related to the sum of the positive Lyapunov exponents. Lyapunov exponents are the characteristic exponent(s) of a dynamic system or a measure of the divergence or convergence of system trajectories that are initially close together. Relatively high values of IRE derived from an atmospheric flow field in the study of atmospheric blocking was identified with the onset or demise of blocking events, but also transitions of the large-scale flow in general. Kolmogorv–Sinai Entropy (KSE), also known as metric entropy, is related to the sum of the positive Lyapunov exponents as well. This quantity can be thought of as a measure of predictability (higher values, less predictability) and will be non-zero for a chaotic system. Thus, the measure of IRE is related to KSE as well. This study will show that relatively low (high) values of IRE derived from atmospheric flows correspond to a more stable (transitioning) large-scale flow with a greater (lesser) degree of predictability and KSE. The transition is least predictable and should be associated with higher IRE and KSE.

[1]  P. Chylek,et al.  The Dissipation Structure of Extratropical Cyclones , 2014 .

[2]  K. Haines,et al.  Vacillation cycles and blocking in a channel , 1998 .

[3]  A. Lupo,et al.  Scale Analysis of Blocking Events from 2002 to 2004: A Case Study of an Unusually Persistent Blocking Event Leading to a Heat Wave in the Gulf of Alaska during August 2004 , 2010 .

[4]  F. Sanders,et al.  Synoptic-Dynamic Climatology of the “Bomb” , 1980 .

[5]  I. Mokhov,et al.  Assessment of the impact of the planetary scale on the decay of blocking and the use of phase diagrams and enstrophy as a diagnostic , 2007 .

[6]  M. Matsueda Predictability of Euro‐Russian blocking in summer of 2010 , 2011 .

[7]  A. Jensen The Nonequilbrium Thermodynamics of Atmospheric Blocking , 2016 .

[8]  X. Zeng,et al.  Estimating the fractal dimension and the predictability of the atmosphere , 1992 .

[9]  V. I. Oseledec A multiplicative ergodic theorem: Lyapunov characteristic num-bers for dynamical systems , 1968 .

[10]  I. Mokhov,et al.  Blockings in the Northern hemisphere and Euro-Atlantic region: Estimates of changes from reanalysis data and model simulations , 2013, Doklady Earth Sciences.

[11]  David P. Baumhefner,et al.  Numerical prediction of the onset of blocking : A case study with forecast ensembles , 1998 .

[12]  S. Colucci,et al.  Large-Scale Dynamics, Anomalous Flows, and Teleconnections , 2014 .

[13]  Y. Pesin CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY , 1977 .

[14]  Phillip Smith,et al.  Climatological features of blocking anticyclones in the Northern Hemisphere , 1995 .

[15]  I. Mokhov,et al.  A Dynamic Analysis of the Role of the Planetary- and Synoptic-Scale in the Summer of 2010 Blocking Episodes over the European Part of Russia , 2012 .

[16]  A. Lupo A Diagnosis of Two Blocking Events That Occurred Simultaneously in the Midlatitude Northern Hemisphere , 1997 .

[17]  Nicholas A. Bond,et al.  Causes and impacts of the 2014 warm anomaly in the NE Pacific , 2015 .

[18]  I. Mokhov,et al.  Studying Summer Season Drought in Western Russia , 2014 .

[19]  David Ruelle,et al.  Ergodic Theory of Chaos , 1985, Topical Meeting on Optical Bistability (OB3).

[20]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[21]  Y. C. Li,et al.  Sensitive versus Rough Dependence under Initial Conditions in Atmospheric Flow Regimes , 2016 .

[22]  A. Lupo,et al.  The Predictability of Northern Hemispheric Blocking Using an Ensemble Mean Forecast System , 2017 .

[23]  A. Lupo,et al.  The role of deformation and other quantities in an equation for enstrophy as applied to atmospheric blocking , 2014 .

[24]  Ralph Shapiro,et al.  Smoothing, filtering, and boundary effects , 1970 .

[25]  David Ruelle,et al.  An inequality for the entropy of differentiable maps , 1978 .

[26]  R. Reynolds,et al.  The NCEP/NCAR 40-Year Reanalysis Project , 1996, Renewable Energy.

[27]  United Kingdom,et al.  Dynamical analysis of blocking events: spatial and temporal fluctuations of covariant Lyapunov vectors , 2015, 1508.04002.

[28]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[29]  Zhijun Zhang,et al.  Exact boundary behavior of solutions to singular nonlinear Dirichlet problems , 2014 .

[30]  I. Mokhov Specific features of the 2010 summer heat formation in the European territory of Russia in the context of general climate changes and climate anomalies , 2011 .

[31]  The distinction of turbulence from chaos — rough dependence on initial data , 2013, 1306.0470.

[32]  A. Lupo,et al.  Using enstrophy advection as a diagnostic to identify blocking‐regime transition , 2014 .

[33]  E. Ott Chaos in Dynamical Systems: Contents , 1993 .

[34]  I. Mokhov,et al.  The Climatology of Blocking Anticyclones for the Northern and Southern Hemispheres: Block Intensity as a Diagnostic. , 2002 .

[35]  A. Jensen A Dynamic Analysis of a Record Breaking Winter Season Blocking Event , 2015 .