Sensitive versus Rough Dependence under Initial Conditions in Atmospheric Flow Regimes

Abstract

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.

The Predictability of Northern Hemispheric Blocking Using an Ensemble Mean Forecast System

“…Also, the study by [18] describes blocking as a quasistationary atmospheric state with quasi-barotropic structure, and in a quasi-barotropic flow the sum of the positive Lyapunov exponents is related to IRE. A Lyapunov exponent is the measure of the divergence or convergence of system trajectories that are initially close, and can be approximated by integrating enstrophy over a finite region known as IRE, which is vorticity squared [10,29]. The work of [29] used this technique to determine the stability or predictability within a planetry flow regime.…”

“…Since numerical models are reliable out to about seven days or so, but limited to 10-14 days at a maximum (e.g., [8,9]) the failure of these models in operational forecasting is a problem for anticipating blocking. Model predictions are subject to fail for various reasons, several being: parameterization errors, lack of data, measurement errors and errors in initial conditions (e.g., [10] and references therein).…”

“…As opposed to previous studies that examined climatological data sets with numerous blocking event, this study will be similar to [10] and analyze four quasi-randomly chosen blocking events during the period May 2016-2017 and representing Pacific and Atlantic Region as well as strong and weak blocking events. The National Meteorological Center (NMC-now NCEP) started operational ensemble forecasting during December 1992 [19].…”

Integrated Regional Enstrophy and Block Intensity as a Measure of Kolmogorov Entropy

“…Enstrophy in a geophysical fluid relates to the dissipation tendency, and this quantity has use in studying turbulent flows (e.g., [14][15][16][17]). Many studies have shown that IRE is related to the sum of the positive Lyapunov exponents as discussed first by [2] and later by the work cited above and by [12] flow stability.…”

The Utility of the Bering Sea and East Asia Rules in Long-Range Forecasting

“…Limitations for dynamic weather are due also to the lack of data, knowledge of the physical processes, and measurement error (e.g., [9,10]). Error in the initial and/or boundary conditions can render model forecasts useless in as quickly as a few days [8], or alternatively two forecasts with slight difference in the initial conditions could evolve in radically different ways over the course of time (e.g., [11,12]). This problem is referred to 2 Advances in Meteorology as sensitivity to the initial conditions (SDOIC).…”