Identifying efficient ensemble perturbations for initializing
subseasonal-to-seasonal prediction
Abstract
The prediction of the weather at subseasonal-to-seasonal (S2S)
timescales is dependent on both initial and boundary conditions. An open
question is how to best initialize a relatively small-sized ensemble of
numerical model integrations to produce reliable forecasts at these
timescales. Reliability in this case means that the statistical
properties of the ensemble forecast are consistent with the actual
uncertainties about the future state of the geophysical system under
investigation. In the present work, a method is introduced to construct
initial conditions that produce reliable ensemble forecasts by
projecting onto the eigenfunctions of the Koopman or the
Perron-Frobenius operators, which describe the time-evolution of
observables and probability distributions of the system dynamics,
respectively. These eigenfunctions can be approximated from data by
using the Dynamic Mode Decomposition (DMD) algorithm. The effectiveness
of this approach is illustrated in the framework of a low-order
ocean-atmosphere model exhibiting multiple characteristic timescales,
and is compared to other ensemble initialization methods based on the
Empirical Orthogonal Functions (EOFs) of the model trajectory and on the
backward and covariant Lyapunov vectors of the model dynamics.
Projecting initial conditions onto a subset of the Koopman or
Perron-Frobenius eigenfunctions that are characterized by time scales
with fast-decaying oscillations is found to produce highly reliable
forecasts at all lead times investigated, ranging from one week to two
months. Reliable forecasts are also obtained with the adjoint covariant
Lyapunov vectors, which are the eigenfunctions of the Koopman operator
in the tangent space. The advantages of these different methods are
discussed.