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

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.

Identifying efficient ensemble perturbations for initializing subseasonal-to-seasonal prediction

“…Indeed, it was shown by Vannitsem et al (2015) that the strength of the wind stress controls the presence and the amplitude of a low-frequency variability (LFV) typically found in the real atmosphere at midlatitude. Following Vannitsem (2017) and Vannitsem and Duan (2020), we shall consider two cases: one with weak LFV (C = 0.01 kg m −2 s −1 ) and another with much more pronounced LFV (C = 0.016 kg m −2 s −1 ). Solutions of the models for both cases are depicted in Figure 1, where the difference in the amplitude of LFV between the left and right panels is clear.…”

“…This introduces the additional difficulty of building appropriate perturbations for the different components of such multi-scale systems (O'Kane et al, 2019). Several approaches consisting of appropriately tuning the bred modes to capture the long time scales of the dynamics have for instance been proposed (Peña & Kalnay, 2004; S.-C. Yang et al, 2008;O'Kane et al, 2019), and the use of backward Lyapunov vectors (BLV), closely related to the bred modes, have been used to build reliable ensemble forecasts in idealized scenarios (Vannitsem & Duan, 2020).…”

“…The usefulness of the Perron-Frobenius and Koopman operators for producing ensemble forecasts will be analyzed in a reduced order coupled ocean-atmosphere model, previously demonstrated for a similar purpose by Vannitsem and Duan (2020). The model will be briefly described in Section 2.…”

“…In Section 4, the different bases onto which the perturbed initial conditions are projected will be presented: first, the EOFs that are often used in initializing climate models and their ensemble integrations, e.g. Polkova et al (2019); second, the Lyapunov vector approach used by Vannitsem and Duan (2020), which is closely related to the bred modes and ensemble Kalman filters; and third, the eigenfunctions of the Koopman and Perron-Frobenius operators. The Koopman and Perron-Frobenius operators are extensively discussed, as important clarifications on their link with DMD is needed.…”

qgs: A flexible Python framework of reduced-order multiscale climate models

“…This coupling consists in both mechanical and heat exchange interactions between the two components. The model has already been used in different contexts, in particular for data assimilation (Penny et al, 2019;Tondeur et al, 2020), and predictability studies (Vannitsem et al, 2019;Vannitsem & Duan, 2020) • In the case of a land surface coupling, it emulates the model proposed in Reinhold & Pierrehumbert (1982) and Cehelsky & Tung (1987) with a simple thermal relaxation toward a climatological temperature and a mechanical coupling due to the friction between the land and the atmosphere. It can also emulate the model proposed in Li et al (2018), with mechanical coupling and heat exchange.…”