RISE: Undergraduates Find That Regime Changes in Lorenz's Model are Predictable

Abstract

The summer of 2002 marked the beginning of the Research Internships in Science and Engineering (RISE) program. RISE worked to build an extensive network of women faculty, science and engineering researchers, graduate students, and undergraduates. The program built this network through an eight-week summer research experience for "rising" junior and senior undergraduates. The goal was to encourage all participants to remain in science and engineering and to pursue graduate degrees. By engaging twenty undergraduate junior and senior RISE scholars in teams with research projects coordinated by female faculty, the program introduced female students to women mentors and role models while providing high-quality opportunities to enhance their research knowledge and skills. RISE interns received advanced training in team skills, interpersonal communication,

Ensemble clustering in deterministic ensemble Kalman filters

“…Miller et al, 1994;Evans et al, 2004;Kalnay et al, 2007). The system of nonlinear coupled ODEs describing its evolution is The standard values for the parameters are p 010, r 028 and b 08/3, which result in a chaotic behaviour with two regimes in a very well-known butterfly-shaped fractal attractor in the phase space.…”

Brief Communication: Breeding vectors in the phase space reconstructed from time series data

“…As pointed out by Evans et al (2004) and apparent in the right column of Fig. 1, high bred vector growth rate, marked in red, is a very good predictor of regime change in the standard breeding in the Lorenz model.…”

“…periment (a) is the standard breeding in the 3-D model phase space using Eq. (3) as in Evans et al (2004). Experiment (b) is the nearest-neighbor breeding applied to a discrete time series data in the model phase space, i.e., x i = {x(t i ), y(t i ), z(t i )}.…”

“…1 shows the growth rates along the respective controls in the three experiments. The magni-E. Lynch: Breeding vectors in the phase space reconstructed from time series data tudes of the growth rate are represented by colors using the same empirical thresholds as in Evans et al (2004): negative growth points (g i < 0) in blue, low-growth points (0 ≤ g i < 3.2) in green, medium-growth points (3.2 ≤ g i < 6.4) in yellow, and high-growth points (g i ≥ 6.4) in red. As shown in Evans et al (2004) for the standard breeding, all experiments show high growth at points concentrated in the regime transition region, while the regions with different growth rates are well separated.…”

“…Breeding is a technique to generate an ensemble of such perturbations, developed for operational ensemble forecasting of the numerical weather prediction Kalnay, 1993, 1997;Kalnay, 2003), and the resulting perturbations are called "bred vectors". Evans et al (2004) demonstrated that the growth rate of the bred vectors could be used as a means of predicting the regime changes in the chaotic Lorenz (1963) system (Lorenz, 1963). They found that the appearance of high growth rate typically indicated that a regime change would occur upon completion of the current orbit and that the longer the duration of the high growth rate, the longer the next regime would last.…”