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Integrated Regional Enstropy as a Measure of Kolmogorov Entropy
* 1 , 2
1  Department of Soil, Environmental, and Atmospheric Sciences, University of Missouri, Columbia, MO, USA
2  Department of Mathematics and Meteorology, Northland College, Ashland, WI, USA


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 Lypunov 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. 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 Entropy (KolE) 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 KolE as well. This study will show that relatively low (high) values of IRE derived from atmospheric flows correspond to more stable (transitioning) large-scale flow a greater (lesser) degree of predictability and KolE. The transition is least predictable and should be associated with higher IRE and KolE.

Keywords: enstrophy; entropy; Lyapunov Exponents; blocking
Comments on this paper
Arthur Zakinyan
Different views exist about the blocking formation mechanism. Nonlinear instability and breaking of Rossby waves are considered the principal cause of blocking. But, for example, N.S. Sidorenkov considered that the 2010 blocking event was caused by beatings, i.e., the interacting temperature fluctuations with close frequencies. It seems that not all clear in this subject. In your opinion, what is the physical mechanism of blocking?

In this work the integrated regional enstrophy (IRE) has been proposed for the blocking analysis. What is the value of inaccuracy of IRE measurements? Can the reanalysis inaccuracy influence on the prediction of blocking?

Anthony Lupo

Good afternoon. thank you for your comment. Some of our earlier work implied that blocking is the result of the proper phasing of the synoptic-scale waves with the planetary, This view agrees with the Sidorenkov view, as repeated cyclone action will sustain blocking (see some of the references in the conference paper). These theories do not preclude Rossby wave breaking, which is a signature of the process described.

We have not investigated the inaccuracy of IRE, or the influence of reanalysis inaccuracy. Thus, the following answer is speculation. IRE is of course calculated from the observed wind field. This means there will be some error, since wind measurements contain larger error than say, temperature or height. But, often, the geostrophic values of vorticity are close to the observed values. This may not be as true in areas where these quantities are maximum. However, what is of interest in our work thus far is the relative value of IRE during the onset and decay periods of blocking. Investigating inaccuracies is a good topic of study for the immediate future.