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Atmosphere 2016, 7(12), 157; doi:10.3390/atmos7120157

Sensitive versus Rough Dependence under Initial Conditions in Atmospheric Flow Regimes

1
Department of Soil, Environmental, and Atmospheric Sciences, University of Missouri, Columbia, MO 65211, USA
2
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
3
Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Robert W. Talbot
Received: 5 October 2016 / Revised: 28 November 2016 / Accepted: 30 November 2016 / Published: 5 December 2016
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Abstract

In this work, we will identify the existence of “rough dependence on initial conditions” in atmospheric phenomena, a concept which is a problem for weather analysis and forecasting. Typically, two initially similar atmospheric states will diverge slowly over time such that forecasting the weather using the Navier-Stokes equations is useless after some characteristic time scale. With rough dependence, two initial states diverge very quickly, implying forecasting may be impossible. Using previous research in atmospheric science, rough dependence is characterized by using quantities that can be calculated using atmospheric data and quantities. Rough dependence will be tested for and identified in atmospheric phenomena at different time scales using case studies. Data were provided for this project by archives outside the University of Missouri (MU) and by using the MU RADAR at the South Farm experiment station. View Full-Text
Keywords: rough dependence on initial conditions; sensitive dependence on initial conditions; RADAR; blocking rough dependence on initial conditions; sensitive dependence on initial conditions; RADAR; blocking
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Lupo, A.R.; Li, Y.C.; Feng, Z.C.; Fox, N.I.; Rabinowitz, J.L.; Simpson, M.J. Sensitive versus Rough Dependence under Initial Conditions in Atmospheric Flow Regimes. Atmosphere 2016, 7, 157.

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