Journal Article

Identifying Efficient Ensemble Perturbations for Initializing Subseasonal‐To‐Seasonal Prediction

Penny, Stephen G., Vannitsem, Stéphane, Demaeyer, Jonathan

2022

Overview

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 (CLVs) 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 CLVs, which are the eigenfunctions of the Koopman operator in the tangent space. The advantages of these different methods are discussed. Plain Language Summary Weather forecasts often reach their limit of predictability at one to two weeks. In order to extend forecast skill beyond this two week limit, the weather prediction community has begun transitioning to the use of coupled models that include both atmosphere and ocean dynamics, with the slower ocean dynamics enabling an extended forecast horizon. Due to uncertainties in the accuracy of the initial conditions and the model itself, such forecasts must be probabilistic. The primary approach for probabilistic weather prediction is to generate ensemble forecasts that integrate multiple copies of the model started from slightly different initial conditions. Here we show that the method used to determine the ensemble of initial conditions has a significant impact on the probabilistic forecast skill at horizons ranging from a few weeks to a few months. We show that many of the existing techniques used for short forecasts are suboptimal for longer forecast horizons. We introduce a new perspective and corresponding techniques that permit the initialization of these ensemble forecasts using information that is intrinsic to the nature of the evolution of the coupled system dynamics, and present data‐driven methods that allow this information to be estimated directly from historical data. Key Points Several methods for initializing ensemble forecasts with long lead times are tested in the context of an ocean‐atmosphere coupled model The methods providing the most reliable ensembles are the adjoint Lyapunov vectors and the adjoint modes of the Dynamic Mode Decomposition These vectors are related to the eigenfunctions of the Koopman and Perron‐Frobenius operators of the system

• Publisher: John Wiley & Sons, Inc,American Geophysical Union (AGU)
• Subject: Atmosphere / Atmospheric models / Boundary conditions / Data assimilation / Dynamics / Eigenfunctions / Empirical orthogonal functions / Ensemble forecasting / Experiments / Forecasting / koopman operator / lyapunov vectors / Mathematical models / Methods / Modelling / Numerical models / Ordinary differential equations / Oscillations / Partial differential equations / Probability theory / S2S / subseasonal‐to‐seasonal prediction / Vectors