On the use of near-neutral Backward Lyapunov Vectors to get reliable ensemble forecasts in coupled ocean\u2013atmosphere systems

Stéphane Vannitsem,Wansuo Duan

doi:10.1007/s00382-020-05313-3

Abstract

The use of coupled Backward Lyapunov Vectors (BLV) for ensemble forecast is demonstrated in a coupled ocean–atmosphere system of reduced order, the Modular Arbitrary Order Ocean–Atmosphere Model (MAOOAM). It is found that overall the most suitable BLVs to initialize a (multiscale) coupled ocean–atmosphere forecasting system are the ones associated with near-neutral and slightly negative Lyapunov exponents. This unexpected result is related to the fact that these BLVs display larger projections on the ocean variables than the others, leading to an appropriate spread for the ocean, and at the same time a rapid transfer of these errors toward the most unstable BLVs affecting predominantly the atmosphere is experienced. The latter dynamics is a natural property of any generic perturbation in nonlinear chaotic dynamical systems, allowing for a reliable spread with the atmosphere too. Furthermore, this specific choice becomes even more crucial when the goal is the forecasting of low-frequency variability at annual and decadal time scales. The implications of these results for operational ensemble forecasts in coupled ocean–atmosphere systems are briefly discussed.

Highlights

An ensemble forecast is an operational procedure developed in the late twentieth century in order to take into account the amplification of uncertainties in the initial conditions and generate a set of potential future outcomes of the atmospheric dynamics (Toth and Kalnay 1993; Molteni et al 1996)
As the Bred modes are empirical modes that are affected by nonlinearities and highly dependent on the breeding time and amplitude, we investigate that problem using the Backward Lyapunov Vectors (BLVs) that are known to correspond to orthogonal Bred modes for small rescaling amplitudes (Feng et al 2016; Duan and Huo 2016)
– A long reference run is performed as displayed in Fig. 1. – For a set of N = 1000 different initial conditions taken at random along this long run, ensemble forecasts are performed with M = 20 ensemble members, including the control forecast. – The initial condition error between the control forecast and the reference trajectory is sampled from a uniform distribution between [− 5 1 0–7, 5 1 0–7] along all variables. – The amplitude of the random perturbations around the initial conditions of control forecast is sampled with the same uniform distribution and projected along the subset of BLVs of interest

Summary

Introduction

An ensemble forecast is an operational procedure developed in the late twentieth century in order to take into account the amplification of uncertainties in the initial conditions and generate a set of potential future outcomes of the atmospheric dynamics (Toth and Kalnay 1993; Molteni et al 1996). Important efforts were devoted to the development of ensemble forecasts based on Bred modes tuned to describe the slow error growth on seasonal to decadal time scales for the ocean dynamics or the coupled ocean–atmosphere dynamics (Cai et al 2003; Vikhliaev et al 2007; Yang et al 2008, 2009; Frederiksen et al 2010; Baehr and Piontek 2014; O’Kane et al 2019). The reasons for this feature are further discussed in the concluding remarks of Sect. 6

The coupled ocean–atmosphere model

The Backward Lyapunov Vectors

Ensemble forecasts: experimental setup

Results

Conclusions