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Pierre De Mey and Allan R. Robinson

other techniques, suchas optimal estimation or statistical forecasting, whichhave their own limits. To overcome this difficulty, future and operational assimilation schemes in limitedareas can use a hierarchy of models. In addition tomixing data and dynamics, an assimilation schemeshould accommodate noisy inputs, and absence of data(free mode). An open ocean model can meet these requirements if a larger-scale model is used and if thecoupling is monitored by an optimal control. Finally, progress

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Xia Liu, Mu Mu, and Qiang Wang

from one steady state to another owing to nonlinear instability, as shown in Mu et al. (2004 , 2017 ) and Kerswell et al. (2014) . The initial perturbation that can most easily trigger the transition is called an optimal triggering perturbation. It is therefore interesting to look for the triggering perturbation associated with an LM occurrence because we can easily forecast an LM occurrence if we observe the signal of such an initial perturbation. Furthermore, if the triggering perturbation is

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T. P. Barnett

techniques have been used to conduct a study of the relationships between oceanand atmosphere variables in the tropical Pacific Ocean. The results of the study show that the ocean variables can hindcast features of the trade wind field (TWF) variability several months into the future. Theresults are compatible with the notion that the Hadley and Walker cells are associated with east-westand north-south sea surface temperature (SST) gradients as suggested by Bjerknes. However, the levelof skill in even

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Alan D. Fox and Stephen J. Maskell

initial fields are resolved on both the coarse grid and the finegrid in the region of the interface in order to minimize the generation of disturbances. Comparison of the results of the nested model with a fine grid everywhere reference calculation shows thenesting technique to be working successfully over reasonably short periods of time integration ( 16 days) suchas may be used operationally for ocean forecasting.1. Introduction This paper develops the type of technique introducedby Spall and

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E. Joseph Metzger and Harley E. Hurlburt

measure of Kuroshio penetration and, for reference, the four initial states have penetration values of −1.1, 6.5, 8.7, and 15.8 cm.) This provides one of the first insights into the nondeterministic nature of the system. Interannual forcing is by European Centre for Medium-Range Weather Forecasts [ ECMWF (1995) ] 1000-hectopascal (hPa) winds, and in all cases the temporal mean is replaced by the annual mean from HR as discussed in Metzger et al. (1992) . This interannual forcing is referred to as an

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Richard A. Craig, Chester W. Newton, R. Robert Rapp, and Robert O. Reid

; MWR--analysis- and forecast-oriented scientists, including not only forecasters but also scientistswho develop techniques applicable to forecasting problems, and analyses that clarify the structure andbehavior of the atmosphere; JAM--applications-oriented scientists in fields such as instrumentation, weathermodification, atmospheric pollution, agriculture andforestry, transportation and commerce, and otherhuman activities where a substantial meteorologicalinput is required; JPO--scientists in the

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Andrew M. Moore

conditions consistent with the available observations. The distribution in state space of forecasts started from each of these initial states define a time-evolving probability distribution function (PDF) for the system. The PDF is described by the Liouville equations ( Epstein 1969 ; Gleason 1970 ), but direct solutions for the atmosphere and ocean are computationally prohibitive. Monte Carlo techniques offer a means of estimating the PDF by randomly perturbing the forecast initial conditions and

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A. R. Robinson and D. B. Haidvogel

second-order accuracy using the Adams-Bashforth technique. For a complete description of the resulting fully discrete vorticity and Poisson equations and of the extensive testing of the model which is briefly described in the' next paragraphs, the reader is referred to HRS. It is relevant here to point out three specific fea tures of the finite-element model which bear on the efficiency and practicality of its application to ire regional forecasting problems of interest. First, theDECEMBER1980

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Robert N. Miller

; Miller and Robinson, 1984;Robinson and Leslie, 1985) and the California Current.A synoptic study of the initial findings from the currentOPTOMA program in that region was reported inMooers and Robinson (1984). A dynamical predictionexperiment is described in Robinson eta!. (1984).Other investigations are now in progress at a numberof laboratories worldwide. Besides forecasting techniques and studies of ocean physics, these models canbe used for diagnostic purposes, i.e., combined withdata to produce

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Yoichi Ishikawa, Toshiyuki Awaji, and Nobumasa Komori

optimization of ocean forecasting systems. Previous studies have shown that for an adequate forecast, good initial and boundary conditions for the numerical model are necessary and that, in particular, the initial conditions are a key factor in determining the accuracy of the short-range forecast. The four-dimensional data assimilation technique, which incorporates observational data into numerical models, is the most promising approach to obtain suitable initial conditions. It is known, however, that data

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