Breeding and predictability in the baroclinic rotating annulus using a perfect model

Abstract

Abstract. We present results from a computational study of predictability in fully-developed baroclinically unstable laboratory flows. This behaviour is studied in the Met Office/Oxford Rotating Annulus Laboratory Simulationa model of the classic rotating annulus laboratory experiment with differentially heated cylindrical sidewalls, which is firmly established as an insightful laboratory analogue for certain kinds of atmospheric dynamical behaviour. This work is the first study of "predictability of the first kind" in the annulus experiment. We devise an ensemble prediction scheme using the breeding method to study the predictability of the annulus in the perfect model scenario. This scenario allows one simulation to be defined as the true state, against which all forecasts are measured. We present results from forecasts over a range of quasi-periodic and chaotic annulus flow regimes. A number of statistical and meteorological techniques are used to compare the predictability of these flows: bred vector growth rate and dimension, error variance, "spaghetti plots", probability forecasts, Brier score, and the Kolmogorov-Smirnov test. These techniques gauge both the predictability of the flow and the performance of the ensemble relative to a forecast using a climatological distribution. It is found that in the perfect model scenario, the two quasiperiodic regimes examined may be indefinitely predictable. The two chaotic regimes (structural vacillation and period doubled amplitude vacillation) show a loss of predictability on a timescale of hundreds to thousands of seconds (65-280 annulus rotation periods, or 1-3 Lyapunov times).

Low-dimensional nonlinearity of ENSO and its impact on predictability

“…Recently, Tang et al [18] found that an ensemble size of 15-20 might be sufficient to measure ENSO prediction uncertainty. Also, considering the computational cost, we used 15 pairs of random perturbations for each initial condition, i.e., 15 The cumulative growth rate for bred vector m after cycle k is defined below, as in [6]:…”

“…It was proposed by Patil et al [4] and has been applied to study the local predictability of some dynamical systems (e.g. [10,5,11,6]); however, the BV-dimension is not effective in measuring the * Corresponding author.…”

“…While the BV has been widely used in weather forecasts and geophysical fluid dynamics (e.g. [3][4][5][6]), it has relatively few applications in climate predictions. Cai et al [7] first used the breeding method to investigate the ENSO predictability in the ZC model [8].…”

The onset of convection in rotating circular cylinders with experimental boundary conditions

“…Motivated by the wish to understand the fundamental dynamics taking place in planetary fluid interiors and atmospheres, convection in rotating cylindrical geometry has been extensively studied both experimentally and theoretically (see, for example, Daniels 1980;Zhong, Ecke & Steinberg 1991;Herrmann & Busse 1993;Kuo & Cross 1993;Aurnou et al 2003;Plaut 2003;Young & Read 2008). In particular, careful numerical studies of convective instabilities in a fluid contained in a circular cylinder uniformly heated from below and rotating about its vertical axis (Goldstein et al 1993(Goldstein et al , 1994 reveal an exceedingly complicated and seemingly incomprehensible behaviour at small and moderate Prandtl numbers.…”

Data assimilation in the laboratory using a rotating annulus experiment

“…Here we have only used real data but it would certainly be possible to use simulated morals data in this way for experiments comparing assimilation systems, or to investigate the effects of including or omitting certain types of observation. Indeed, we have already used this 'perfect model' paradigm with morals in work involving breeding vectors (Young and Read, 2008a).…”