Coupled Data Assimilation and Ensemble Initialization with Application to Multiyear ENSO Prediction

We develop and compare variants of coupled data assimilation (DA) systems based on ensemble optimal interpolation (EnOI) and ensemble transform Kalman filter (ETKF) methods. The assimilation system is first tested on a small paradigm model of the coupled tropical–extratropical climate system, then implemented for a coupled general circulation model (GCM). Strongly coupled DA was employed specifically to assess the impact of assimilating ocean observations [sea surface temperature (SST), sea surface height (SSH), and sea surface salinity (SSS), Argo, XBT, CTD, moorings] on the atmospheric state analysis update via the cross-domain error covariances from the coupled-model background ensemble. We examine the relationship between ensemble spread, analysis increments, and forecast skill in multiyear ENSO prediction experiments with a particular focus on the atmospheric response to tropical ocean perturbations. Initial forecast perturbations generated from bred vectors (BVs) project onto disturbances at and below the thermocline with similar structures to ETKF perturbations. BV error growth leads ENSO SST phasing by 6 months whereupon the dominant mechanism communicating tropical ocean variability to the extratropical atmosphere is via tropical convection modulating the Hadley circulation. We find that bred vectors specific to tropical Pacific thermocline variability were the most effective choices for ensemble initialization and ENSO forecasting.

Comparison of Nonlinear Local Lyapunov Vectors and Bred Vectors in Estimating the Spatial Distribution of Error Growth

Instabilities play a critical role in understanding atmospheric predictability and improving weather forecasting. The bred vectors (BVs) are dynamically evolved and flow-dependent nonlinear perturbations, indicating the most unstable modes of the underlying flow. Especially over smaller areas, however, BVs with different initial seeds may to some extent be constrained to a small subspace, missing potential forecast error growth along other unstable perturbation directions. In this paper, the authors study the nonlinear local Lyapunov vectors (NLLVs) that are designed to capture an orthogonal basis spanning the most unstable perturbation subspace, thus potentially ameliorating the limitation of BVs. The NLLVs are theoretically related to the linear Lyapunov vectors (LVs), which also form an orthogonal basis. Like BVs, NLLVs are generated by dynamically evolving perturbations with a full nonlinear model. In simulated forecast experiments, a set of mutually orthogonal NLLVs show an advantage in predicting the structure of forecast error growth when compared to using a set of BVs that are not fully independent. NLLVs are also found to have a higher local dimension, enabling them to better capture localized instabilities, leading to increased ensemble spread.

Analogs on the Lorenz Attractor and Ensemble Spread

Intrinsic predictability is defined as the uncertainty in a forecast due to small errors in the initial conditions. In fact, not only the amplitude but also the structure of these initial errors plays a key role in the evolution of the forecast. Several methodologies have been developed to create an ensemble of forecasts from a feasible set of initial conditions, such as bred vectors or singular vectors. However, these methodologies consider only the fastest growth direction globally, which is represented by the Lyapunov vector. In this paper, the simple Lorenz 63 model is used to compare bred vectors, random perturbations, and normal modes against analogs. The concept of analogs is based on the ergodicity theory to select compatible states for a given initial condition. These analogs have a complex structure in the phase space of the Lorenz attractor that is compatible with the properties of the nonlinear chaotic system. It is shown that the initial averaged growth rate of errors of the analogs is similar to the one obtained with bred vectors or normal modes (fastest growth), but they do not share other properties or statistics, such as the spread of these growth rates. An in-depth study of different properties of the analogs and the previous existing perturbation methodologies is carried out to shed light on the consequences of forecasting the choice of the perturbations.

Brief Communication: Breeding vectors in the phase space reconstructed from time series data

Bred vectors characterize the nonlinear instability of dynamical systems and so far have been computed only for systems with known evolution equations. In this article, bred vectors are computed from a single time series data using time-delay embedding, with a new technique, nearest-neighbor breeding. Since the dynamical properties of the standard and nearest-neighbor breeding are shown to be similar, this provides a new and novel way to model and predict sudden transitions in systems represented by time series data alone.

Brief Communication: Breeding vectors in the phase space reconstructed from time series data

Bred vectors characterize the nonlinear instability of dynamical systems and so far have been computed only for systems with known evolution equations. In this article, bred vectors are computed from a single time series data using time-delay embedding, with a new technique, nearest-neighbor breeding. Since the dynamical properties of the standard and nearest-neighbor breeding are shown to be similar, this provides a new and novel way to model and predict sudden transitions in systems represented by time series data alone.