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.
Highlights
In atmospheric sciences, weather forecasters today rely on numerical models in order to make predictions, and these can be made reliably out to about seven days, sometimes quite well (e.g., Winter Storm Jonas 22–23 January 2016—impacted the Eastern USA) but the absolute limit is about 10–14 days
sensitive dependence on the initial conditions (SDOIC) occurs in a system where at least one Lyapunov Exponent is positive, and as stated above is a measure of divergence for the trajectories of two systems that are initially close
Exponent in the atmosphere can be expressed as the area integrated regional enstrophy (IRE):
Summary
Weather forecasters today rely on numerical models in order to make predictions (synoptic-scale), and these can be made reliably out to about seven days, sometimes quite well (e.g., Winter Storm Jonas 22–23 January 2016—impacted the Eastern USA) but the absolute limit is about 10–14 days. Numerical weather forecasts at the same time and spatial scale can fail in the one-to-two-day time frame, or even more quickly Error in the initial and/or boundary conditions can yield model forecasts as quickly as a few days [3], and this behavior, which is inherent in the Navier. Stokes equations, is called sensitive dependence on the initial conditions (SDOIC) [4]. Predictability has improved greatly in the last 20 years, which has saved lives and property. Smaller-scale systems can change radically over very small time scales (e.g., 5–10 min) as detected by RADAR
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