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Benyang Tang

Abstract

The results of the POP (principal oscillation pattern) analysis of the tropical Pacific wind stress data are presented. The wind stress data are smoothed and detrended in the same way as that used by Lamont's coupled ocean-atmosphere model to initialize EJ Niño forecasts. Thus, the present wind stress POP model serves as an indicator of prediction skill of the data alone, without the use of the coupled model. The POP results show that predictions of warm and cold events can be obtained at lead times of about two seasons, which is much shorter than the lead time of more than one year achieved by Lamont's coupled ocean-atmosphere model.

It is shown that during the period of about two to three seasons before the peak of a warm/cold event, the ENSO system evolves in a linear, low-dimensional way. This properly allows a precursor of a warm/cold event to be identified around May of the event year. In other periods of the ENSO cycle, the POP model does not perform well.

The author performed a cross-validation experiment, in which the data of two years following the month of the initial condition are withheld in both the EOF calculation and the POP model construction. It was found that the skill (measured by correlation coefficient) of the cross-validation model is 0.05–0.15 lower than that of the hindcast model. The ability of the cross-validation model to pick up the precursor of a warm/cold event is also slightly lower than that of the hindcast model.

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Benyang Tang

Abstract

A model is presented for the fluctuating flow through a strait of nonuniform depth connecting two semi-infinite oceans.

An analytical solution is found. The solution is applied to several depth profiles to study the effect of the topography on the volume flux through the strait. A nondimensional number σ = (∂h/∂x)fW/2ωh is found to determine the importance of the topography of the strait, where f, ω, W, L and h are the Coriolis parameter, fluctuating frequency, and the width, length and depth of the strait, respectively. If σ < 0.6, the effect of the variation of strait depth is negligible; if σ increases, the effect of the depth variation is to shorten the length of the strait, thus allowing more flux through the strait; at the value of about σ = π/2, the strait is almost invisible to the open oceans as far as the flux is concerned.

The mechanism of the geostrophic control of the flux through the strait is studied. A model of energy balance clearly shows that the flux is limited by the amount of the energy which the two outgoing Kelvin waves can carry: the flux through the strait can not be greater than the flux at the geostrophic-control limit, otherwise it will generate in the open oceans such big Kelvin waves that they would carry away more energy than the strait system can receive from the incoming Kelvin waves.

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William W. Hsieh and Benyang Tang

Empirical or statistical methods have been introduced into meteorology and oceanography in four distinct stages: 1) linear regression (and correlation), 2) principal component analysis (PCA), 3) canonical correlation analysis, and recently 4) neural network (NN) models. Despite the great popularity of the NN models in many fields, there are three obstacles to adapting the NN method to meteorology–oceanography, especially in large-scale, low-frequency studies: (a) nonlinear instability with short data records, (b) large spatial data fields, and (c) difficulties in interpreting the nonlinear NN results. Recent research shows that these three obstacles can be overcome. For obstacle (a), ensemble averaging was found to be effective in controlling nonlinear instability. For (b), the PCA method was used as a prefilter for compressing the large spatial data fields. For (c), the mysterious hidden layer could be given a phase space interpretation, and spectral analysis aided in understanding the nonlinear NN relations. With these and future improvements, the nonlinear NN method is evolving to a versatile and powerful technique capable of augmenting traditional linear statistical methods in data analysis and forecasting; for example, the NN method has been used for El Niño prediction and for nonlinear PCA. The NN model is also found to be a type of variational (adjoint) data assimilation, which allows it to be readily linked to dynamical models under adjoint data assimilation, resulting in a new class of hybrid neural–dynamical models.

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Benyang Tang and Benoit Cushman-Roisin

Abstract

In Part I of this series, generalized geostrophic equations were formulated for the two-layer system on a beta plane and over a flat bottom. Here numerical experiments with these equations are carried out to study freely evolving geostrophic turbulence. In contrast with the classical quasigeostrophic analysis, the emphasis is placed on the finite amplitude of the vertical displacement (the frontal effect).

A previous study with a reduced-gravity, generalized geostrophic equation has shown that geostrophic turbulence of finite amplitude (frontal geostrophic turbulence) evolves toward a statistical equilibrium state dominated by large, coherent anticyclones. The present study reveals that, in the presence of baroclinicity, this statistical equilibrium state can only be reached if the finite-amplitude turbulent flow evolves from scales smaller or equal to the baroclinic deformation radius. Although the emerging anticyclones should be unstable according to the classical quasigeostrophic theory of baroclinic instability, they nonetheless appear to be stable within the present, generalized-geostrophic formalism. By their stability, they prevent potential energy from being released by baroclinic instability to the barotrophic flow.

Finally, similarities and differences between the evolution of two-layer geostrophic turbulence in the quasi-geostrophic regime, on one hand, and the frontal (finite-amplitude) geostrophic regime, on the other, are discussed and summarized.

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Benoit Cushman Roisin and Benyang Tang

Abstract

Geostrophic turbulence has traditionally been studied within the framework of the classical, quasi-geostrophic equation. This equation, valid only when vertical displacements are weak, possesses a symmetry between cyclonic and anticyclonic vortices that is not present in the primitive equations. Moreover, previous studies were restricted by length scales not in excess of the deformation radius. In an attempt to advance the study of unforced geostrophic turbulence, we address here the following questions: How is the energy cascade toward longer length scales affected beyond the deformation radius? And, what is the result of the cyclonic-anticyclonic asymmetry brought on by finite vertical displacements?

Some answers are provided by numerical experiments using a generalized geostrophic equation. The energy cascade is found to come to a halt beyond the deformation radius. There, a statistical equilibrium is reached at a length scale prescribed as a combination of the deformation radius, the beta effect and the energy level of the system. Also, over the long run, one witnesses the emergence of few, large eddies, which all are anticyclonic and drift in a weaker, shorter-scale, quasi-geostrophic background. A simple theory capturing the essence of this bimodal distribution correctly predicts the bulk characteristics of the statistical equilibrium. Finally, some arguments are outlined to explain the selection of anticyclonic eddies and its relation to the statistical equilibrium.

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Tong Lee, Ichiro Fukumori, and Benyang Tang

Abstract

Local advection of temperature is the inner product of vector velocity and spatial gradient of temperature. This product is often integrated spatially to infer temperature advection over a region. However, the contribution along an individual direction can be dominated by internal processes that redistribute heat within the domain but do not control the heat content of the domain. A new formulation of temperature advection is introduced to elucidate external heat source and sink that control the spatially averaged temperature. It is expressed as the advection of interfacial temperature relative to the spatially averaged temperature of the domain by inflow normal to the interface. It gives a total advection of temperature that is identical to the spatial integration of local temperature advection, yet the contributions along individual directions depict external processes. The differences between the two formulations are illustrated by analyzing zonal advection of near-surface temperature in the eastern equatorial Pacific during the 1997–98 El Niño and the subsequent La Niña by an ocean general circulation model. The new formulation highlights the advection of warmer water at the western side of the Niño-3 region into (out of) the region to create part of the warming (cooling) tendency during El Niño (La Niña). In contrast, the traditional formulation is dominated by the effect of tropical instability waves within the region that redistribute heat internally. The difference between the two formulations suggests a need for caution in discerning mechanisms controlling heat content of a region. Spatial integration of local temperature advection does not explain external processes that control a domain's heat content. The conclusion applies not only to the advection of oceanic temperature, but also to that of any property in any medium.

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Benoit Cushman-Roisin, Benyang Tang, and Eric P. Chassignet

Abstract

Since the pioneering work of Nof, the determination of the westward drift of mesoscale eddies under the planetary (beta) effect has been a recurrent theme in mesoscale oceanography, and several different formulae have been proposed in the literature. Here, recpatiulation is sought, and, within the confines of a single-layer model, a generalized formula is derived. Although it is similar to Nof's, the present formula is established from a modified definition and with fewer assumptions. It also recaptiulates all other formulae for the one-layer model and applies to a wide variety of situations, including cases when the vortex develops a wake of Rossby waves or undergoes axismmetrization.

Following the derivation of the formula, a physical interpretation clarifies the migration mechanism, which can be divided between a self-induced propulsion and a reaction from the displaced ambient fluid. Numerical simulations with primitive and geostrophic equations validate the formula for a variety of length scales and amplitudes. The work concludes with an attempt to extend the result to systems with two moving layers.

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Benoit Cushman-Roisin, G. G. Sutyrin, and Benyang Tang

Abstract

Although the quasigeostrophic formalism has been a cornerstone in oceanographic modeling for over four decades, studies have shown time and time again that other geostrophic, but non-quasigeostrophic, regimes can also exist. These include a particular class of regimes representative of oceanic fronts and frontal eddies. The task undertaken here is the clarification and investigation of the possible geostrophic regimes, quasigeostrophic and otherwise, of a two-layer mean. To simplify the analysis, attention is restricted to a system on the midlatitude beta plane, above a flat bottom and below a rigid lid.

Under the assumption of a small Rossby number, geostrophic regimes are sought, and the set of primitive equations is reduced to two prognostic equations, one for each of the barotropic and baroclinic pressure fields. These equations share with the quasigeostrophic equations the absence of inertia-gravity waves, but their greater range of validity allows order-one variations in the upper-layer depth. The various dynamical regimes are investigated, including a frontal geostrophic regime of particular importance. Finally, invariant properties are determined and discussed.

As part of the analysis, the conditions under which the one-layer, reduced-gravity model is a valid approximation of the two-layer system are also considered.

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Benyang Tang, William W. Hsieh, Adam H. Monahan, and Fredolin T. Tangang

Abstract

Among the statistical methods used for seasonal climate prediction, canonical correlation analysis (CCA), a more sophisticated version of the linear regression (LR) method, is well established. Recently, neural networks (NN) have been applied to seasonal climate prediction. Unlike CCA and LR, NN is a nonlinear method, which leads to the question whether the nonlinearity of NN brings any extra prediction skill.

In this study, an objective comparison between the three methods (CCA, LR, and NN) in predicting the equatorial Pacific sea surface temperatures (in regions Niño1+2, Niño3, Niño3.4, and Niño4) was made. The skill of NN was found to be comparable to that of LR and CCA. A cross-validated t test showed that the difference between NN and LR and the difference between NN and CCA were not significant at the 5% level. The lack of significant skill difference between the nonlinear NN method and the linear methods suggests that at the seasonal timescale the equatorial Pacific dynamics is basically linear.

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Fredolin T. Tangang, Benyang Tang, Adam H. Monahan, and William W. Hsieh

Abstract

The authors constructed neural network models to forecast the sea surface temperature anomalies (SSTA) for three regions: Niño 4, Niño 3.5, and Niño 3, representing the western-central, the central, and the eastern-central parts of the equatorial Pacific Ocean, respectively. The inputs were the extended empirical orthogonal functions (EEOF) of the sea level pressure (SLP) field that covered the tropical Indian and Pacific Oceans and evolved for a duration of 1 yr. The EEOFs greatly reduced the size of the neural networks from those of the authors’ earlier papers using EOFs. The Niño 4 region appeared to be the best forecasted region, with useful skills up to a year lead time for the 1982–93 forecast period. By network pruning analysis and spectral analysis, four important inputs were identified: modes 1, 2, and 6 of the SLP EEOFs and the SSTA persistence. Mode 1 characterized the low-frequency oscillation (LFO, with 4–5-yr period), and was seen as the typical ENSO signal, while mode 2, with a period of 2–5 yr, characterized the quasi-biennial oscillation (QBO) plus the LFO. Mode 6 was dominated by decadal and interdecadal variations. Thus, forecasting ENSO required information from the QBO, and the decadal–interdecadal oscillations. The nonlinearity of the networks tended to increase with lead time and to become stronger for the eastern regions of the equatorial Pacific Ocean.

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