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Anthony T. Weaver
and
David L. T. Anderson

Abstract

A four-dimensional variational method is used to examine the extent to which a time sequence of altimeter measurements can determine the subsurface flow in a linear multilayer model of the tropical Pacific Ocean. The experiments are all of the identical-twin type. Complete maps of sea level extracted from the model in a control integration play the role of the altimeter observations in the assimilation experiments. The results of the experiments indicate that, over timescales of months, the sea level information can be effectively propagated into the subsurface, particularly in the dynamically active equatorial region. Several degrees off the equator, however, where waves propagate more slowly, the recovery of the subsurface flow in models containing more than two vertical modes is significantly more difficult. The sensitivity of these results to the lengths of the data sampling and assimilation periods is discussed.

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Femke C. Vossepoel
,
Anthony T. Weaver
,
Jérôme Vialard
, and
Pascale Delecluse

Abstract

A four-dimensional variational scheme is described in which ocean observations are assimilated into an ocean general circulation model using wind stress forcing fields as control variables. Idealized (“twin”) experiments are performed to evaluate the possibility of reconstructing wind stress variability and its oceanic response from synthetic observations of the ocean state. Two types of wind stress errors are considered: time-varying errors associated with a wind burst and constant errors associated with a wind stress bias. Both sets of experiments demonstrate that the spatial structure of the wind stress variations is well reconstructed, while the estimation of their amplitude and time evolution is less accurate. Sparser equatorial sampling, similar to that of the Tropical Atmosphere–Ocean array, only slightly degrades the analysis. Omitting velocity and salinity observations leads to a less accurate amplitude and time evolution of the wind stress increment. Still, general features are captured in the analysis when only temperature observations are assimilated. Additional twin experiments point out that errors in thermal structure due to errors in the model and initial conditions can only partly be corrected by modifying the wind stress forcing. To change the shape and position of the thermocline through a wind stress correction requires an adjustment time scale of several weeks. The temperature gradient can be changed by the correction of wind stress errors, but controlling model error, initial conditions, or both may be necessary to correct for this type of systematic error more effectively.

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Andrew M. Moore
,
Jérôme Vialard
,
Anthony T. Weaver
,
David L. T. Anderson
,
Richard Kleeman
, and
Jolie R. Johnson

Abstract

In this paper the structure and dynamics of the optimal perturbations of tropical low-frequency coupled ocean–atmosphere oscillations relevant to El Niño–Southern Oscillation (ENSO) are explored. These optimal perturbations yield information about potential precursors for ENSO events, and about the fundamental dynamical processes that may control perturbation growth and limit the predictability of interannual variability. The present study uses a hierarchy of hybrid coupled models. Each model is configured for the tropical Pacific Ocean and shares a common ocean general circulation model. Three different atmospheric models are used: a statistical model, a dynamical model, and a combination of a dynamical model and boundary layer model. Each coupled model possesses a coupled ocean–atmosphere eigenmode oscillation with a period of the order of several years. The properties of these various eigenmodes and their corresponding adjoint eigenmodes are explored.

The optimal perturbations of each coupled model for two different perturbation growth norms are also examined, and their behavior can be understood in terms of the properties of the aforementioned eigenmode oscillations. It is found that the optimal perturbation spectrum of each coupled model is primarily dominated by one member. The dominant optimal perturbation evolves into the most unstable eigenmode of the system. The structure of the optimal perturbations of each model is found to be controlled by the dynamics of the atmospheric model and air–sea interaction processes. For the coupled model with a statistical atmosphere, the optimal perturbation center of action is spread across the entire tropical Pacific in the form of a dipole. For the coupled models that include deep atmospheric convection, the optimal perturbation center of action is primarily confined to the western Pacific warm pool. In addition, the degree of nonnormality of the eigenmodes is controlled by the atmospheric model dynamics. These findings are in general agreement with the results obtained from intermediate coupled models. In particular, the atmospheric models used here have also been used in intermediate coupled models that have been employed extensively in previous studies of the optimal perturbations of El Niño–Southern Oscillation. Thus, a direct comparison of the optimal perturbation behavior of those intermediate models and the optimal perturbations of the hybrid models used here can be made.

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Andrew M. Moore
,
Javier Zavala-Garay
,
Youmin Tang
,
Richard Kleeman
,
Anthony T. Weaver
,
Jérôme Vialard
,
Kamran Sahami
,
David L. T. Anderson
, and
Michael Fisher

Abstract

The optimal forcing patterns for El Niño–Southern Oscillation (ENSO) are examined for a hierarchy of hybrid coupled models using generalized stability theory. Specifically two cases are considered: one where the forcing is stochastic in time, and one where the forcing is time independent. The optimal forcing patterns in these two cases are described by the stochastic optimals and forcing singular vectors, respectively. The spectrum of stochastic optimals for each model was found to be dominated by a single pattern. In addition, the dominant stochastic optimal structure is remarkably similar to the forcing singular vector, and to the dominant singular vectors computed in a previous related study using a subset of the same models. This suggests that irrespective of whether the forcing is in the form of an impulse, is time invariant, or is stochastic in nature, the optimal excitation for the eigenmode that describes ENSO in each model is the same. The optimal forcing pattern, however, does vary from model to model, and depends on air–sea interaction processes.

Estimates of the stochastic component of forcing were obtained from atmospheric analyses and the projection of the dominant optimal forcing pattern from each model onto this component of the forcing was computed. It was found that each of the optimal forcing patterns identified may be present in nature and all are equally likely. The existence of a dominant optimal forcing pattern is explored in terms of the effective dimension of the coupled system using the method of balanced truncation, and was found to be O(1) for the models used here. The implications of this important result for ENSO prediction and predictability are discussed.

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