  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
best set of BLVs to initialize a (multiscale) coupled ocean-atmosphere
forecasting system are the ones associated with near-neutral or slightly
negative Lyapunov exponents. This unexpected result is related to the fact that
these sets 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.
