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A dynamically motivated statistical forecasting scheme for eastern Mediterranean winter rainfall is presented. The scheme is based on North Atlantic sea level pressure precursors. The resulting forecasts are robust and statistically significant at ∼13 months lead time, and improve at ∼7 months lead. It is suggested that these forecasts form a foundation for an operational early-warning system for eastern Mediterranean droughts.

A finite-difference scheme for solving the linear shallow water equations in a bounded domain is described. Its time step is not restricted by a Courant–Friedrichs–Levy (CFL) condition. The scheme, known as Israeli–Naik–Cane (INC), is the offspring of semi-Lagrangian (SL) schemes and the Cane–Patton (CP) algorithm. In common with the latter it treats the shallow water equations implicitly in y and with attention to wave propagation in x. Unlike CP, it uses an SL-like approach to the zonal variations, which allows the scheme to apply to the full primitive equations. The great advantage, even in problems where quasigeostrophic dynamics are appropriate in the interior, is that the INC scheme accommodates complete boundary conditions.

The fastest perturbation growth (optimal growth) in forecasts of El Nino–Southern Oscillation (ENSO) with the Zebiak and Cane model is analyzed by singular value decomposition of forward tangent models along forecast trajectories in a reduced EOF space. The authors study optimal growth in forecast runs using two different initialization procedures and discuss the relationship between optimal growth and forecast skill. Consistent with Part I of this work, one dominant growing singular vector is found. Most of the variation of optimal growth, measured by the largest singular value, for warm events and mean condition is seasonal, attributable to the seasonal variations in the background states. For cold events the seasonal optimal growth is substantially suppressed. The first singular vector is approximately white in EOF space, while its final pattern after a 6-month evolution is dominated by the first EOF. The energy norm amplifies between 5- and 24-fold in 6 months. This indicates that small-scale...

The skill of a coupled ocean‐atmosphere model in predicting ENSO has recently been improved using a new initialization procedure in which initial conditions are obtained from the coupled model, nudged toward observations of wind stress. The previous procedure involved direct insertion of wind stress observations, ignoring model feedback from ocean to atmosphere. The success of the new scheme is attributed to its explicit consideration of ocean‐atmosphere coupling and the associated reduction of ‘‘initialization shock’’ and random noise. The so-called spring predictability barrier is eliminated, suggesting that such a barrier is not intrinsic to the real climate system. Initial attempts to generalize the nudging procedure to include SST were not successful; possible explanations are offered. In all experiments forecast skill is found to be much higher for the 1980s than for the 1970s and 1990s, suggesting decadal variations in predictability.

The Kalman filter is the optimal linear assimilation scheme only if the first- and second-order statistics of the observational and system noise are correctly specified. If not, optimality can be reached in principle by using an adaptive filter that estimates both the state vector and the system error statistics. In this study, the authors compare the ability of three adaptive assimilation schemes at estimating an unbiased, stationary system noise. The adaptive algorithms are implemented in a reduced space linear model for the tropical Pacific. Using a twin experiment approach, the algorithms are compared by assimilating sea level data at fixed locations mimicking the tropical Pacific tide gauges network. It is shown that the description of the system error covariance matrix requires too many parameters for the adaptive problem to be well posed. However, the adaptive procedures are efficient if the number of noise parameters is dramatically reduced and their performance is shown to be closed to optimal, that is, based on the true system noise covariance. The link between those procedures is elucidated, and the question of their applicability and respective computational cost is discussed.

In Part II of this study on the application of the interactive Kalman filter to higher-dimensional systems, a modification suited to periodically forced systems is introduced. As in Part I, the object of study here is the ENSO model of Zebiak and Cane, but here the technique of quasi-fixed points is applied to certain Poincare maps of that system that are related to the forcing period of I year. As a result, it is possible to search the model systematically for possible periodic orbits, no matter whether they are stable or unstable. An unstable 4-year cycle is found in the model, and it is argued that this cycle can be traced back to a 4-year limit cycle, which is known to exist under weak atmosphere-ocean coupling. All other quasi-fixed points are related to orbits that do not appear to be periodic. The findings are applied to the modified version of the interactive Kalman filter, which deals with cycles as regimes. Comparing these results with the findings in Part I, it is found that the filter performances improve using, in the following order, the extended filter, the interactive filter with cycles, a seasonal average filter, and the original interactive Kalman filter from Part I.

In an effort to apply the interactive Kalman filter to higher-dimensional systems, the concept of a quasi-fixed point is introduced. This is defined to be a system state where the tendency, in a suitable reduced space, is at a minimum. It allows one to use conventional search algorithms for the detection of quasi-fixed points. In Part I quasi-fixed points of the ENSO model of Zebiak and Cane are found when run in a permanent monthly mode, the reduced space being defined via a multiple EOP projection. The stability characteristics of the quasi-fixed points are analyzed, and it is shown that they are significantly different from the (in)stabilities of the average monthly models. With these quasi-fixed points, assimilation experiments are carried out with the interactive Kalman filter for the Zebiak–Cane model in the reduced space. It is demonstrated that the results are superior to both a seasonal Kalman filter and the extended Kalman filter.

A reduced gravity, primitive equation, ocean GCM with an isopycnal vertical coordinate is developed. A “buffer” layer is introduced to allow the mixed layer to detrain mass at arbitrary densities without the coordinate drift or the heat loss suffered by other isopycnal models. The diapycnal velocity is derived from the thermodynamic equation. Negative layers are removed by a heat- and mass-conserving convective adjustment scheme. The model formulation on a β plane employs an A grid and allows irregular coastlines and local grid stretching. Simulations with climatological winds and surface heat fluxes based on observed sea surface temperatures (SSTs) are presented for the Atlantic, the Pacific, and the Indian Oceans. The surface mixed layer is modeled as a constant depth layer, and salinity effects are neglected in this version. The surface heat flux parameterization used here leads to errors in model SSTs, which are reasonable in the Tropics but are higher in the western boundary current regions....

A scheme is presented for solving the equation for barotropic ocean circulation, taking into account the special character of the problem: nearly inviscid motion following f/H contours in the ocean interior, with viscous effects closing the flow near western boundaries. Using a special compact finite-difference discretization, the scheme generates boundary layers without spurious oscillations and without demanding very high resolution. Sharp changes in topography and closed f/H contours (e.g., in the vicinity of high sea mounts) are also handled by the scheme in a way that localizes errors due to underresolved topographic features. Strategies are formulated for simplifying the connectedness of the domain by “sinking” the islands.

A coupled atmosphere-ocean model is developed and used to study the ENSO (El Ni&ntilde/Southern Oscillation) phenomenon. With no anomalous external forcing, the coupled model reproduces certain key features of the observed phenomenon. including the recurrence of warm events at irregular intervals with a preference for three to four years. It is shown that the mean sea surface temperature, wind and ocean current fields determine the characteristic spatial structure of ENSO anomalies. The tendency for phase-locking of anomalies is explained in terms of a variation in coupling strength associated with the annual cycle in the mean fields. Sensitivity studies reveal that both the amplitude and the time of scale of the oscillation are sensitive to several parameters that affect the strength of the atmosphere–ocean coupling. Stronger coupling implies larger oscillations with a longer time scale. A critical element of the model oscilliation is the variability in the equatorial heat content of the upper o...