In this paper,the role of constant optimal forcing(COF) in correcting forecast models was numerically studied using the well-known Lorenz 63 model.The results show that when we only consider model error caused by parameter error,which also changes with the development of state variables in a numerical model,the impact of such model error on forecast uncertainties can be offset by superimposing COF on the tendency equations in the numerical model.The COF can also offset the impact of model error caused by stochastic processes.In reality,the forecast results of numerical models are simultaneously influenced by parameter uncertainty and stochastic process as well as their interactions.Our results indicate that COF is also able to significantly offset the impact of such hybrid model error on forecast results.In summary,although the variation in the model error due to physical process is time-dependent,the superimposition of COF on the numerical model is an effective approach to reducing the influence of model error on forecast results.Therefore,the COF method may be an effective approach to correcting numerical models and thus improving the forecast capability of models.
We use conditional nonlinear optimal perturbation （CNOP） to investigate the optimal precursory disturbances in the Zebiak- Cane El Nino-Southern Oscillation （ENSO） model. The conditions of the CNOP-type precursors are highly likely to evolve into El Nino events in the Zebiak-Cane model. By exploring the dynamic behaviors of these nonlinear El Nino events caused by the CNOP-type precursors, we find that they, as expected, tend to phase-lock to the annual cycles in the Zebiak-Cane model with the SSTA peak at the end of a calendar year. However, E1 Nino events with CNOPs as initial anomalies in the linearized Zebiak-Cane model are inclined to phase-lock earlier than nonlinear E1 Nino events despite the existence of annual cycles in the model. It is clear that nonlinearities play an important role in El Nino＇s phase-locking. In particular, nonlinear temperature advection increases anomalous zonal SST differences and anomalous westerlies, which weakens anomalous upwelling and acts on the increasing anomalous vertical temperature difference and, as a result, enhances E1 Nino and then delays the peak SSTA. Finally, we demonstrate that nonlinear temperature advection, together with the effect of the annual cycle, causes El Nino events to peak at the end of the calendar year.
Most ocean-atmosphere coupled models have difficulty in predicting the E1 Nifio-Southern Oscillation （ENSO） when starting from the boreal spring season. However, the cause of this spring predictability barrier （SPB） phenomenon remains elusive. We investigated the spatial characteristics of optimal initial errors that cause a significant SPB for E1 Nifio events by using the monthly mean data of the pre-industrial （PI） control runs from several models in CMIP5 experiments. The results indicated that the SPB-related optimal initial errors often present an SST pattern with positive errors in the central-eastern equatorial Pa- cific, and a subsurface temperature pattern with positive errors in the upper layers of the eastern equatorial Pacific, and nega- tive errors in the lower layers of the western equatorial Pacific. The SPB-related optimal initial errors exhibit a typical La Ni- fia-like evolving mode, ultimately causing a large but negative prediction error of the Nifio-3.4 SST anomalies for El Nifio events. The negative prediction errors were found to originate from the lower layers of the western equatorial Pacific and then grow to be large in the eastern equatorial Pacific. It is therefore reasonable to suggest that the E1 Nifio predictions may be most sensitive to the initial errors of temperature in the subsurface layers of the western equatorial Pacific and the Nifio-3.4 region, thus possibly representing sensitive areas for adaptive observation. That is, if additional observations were to be preferentially deployed in these two regions, it might be possible to avoid large prediction errors for E1 Nifio and generate a better forecast than one based on additional observations targeted elsewhere. Moreover, we also confirmed that the SPB-related optimal initial errors bear a strong resemblance to the optimal precursory disturbance for E1 Nifio and La Nifia events. This indicated that im- provement of the observation network by additional observations in the identified sensitive areas would also be
With the Zebiak-Cane model and a parameterized stochastic representation of intraseasonal forcing, the impact of the uncertainties of Madden Jullian Oscillation （MJO） on the ＂Spring Predictability Barrier （SPB）＂ for El Nifio-Southern Oscillation （ENSO） prediction is studied. The parameterized form of MJO forcing is added physically to the Zebiak-Cane model to obtain the so-called Zebiak-Cane-MJO model and then the effects of initial error, stochastic model error, and their joint error mode on the SPB associated with El Nifio prediction are estimated. The results show that the model errors caused by stochastic MJO forcing could hardly lead to a significant SPB while initial errors can do; furthermore, the joint error mode of initial error and model error associated with the stochastic MJO forcing can also lead to a significant SPB. These demonstrate that the initial error is probably the main error source of the SPB, which may provide a theoretical foundation of data assimilation for ENSO forecasts.
The authors demonstrate that the E1 Nifio events in the pre- and post-1976 periods show two ampli- tude-duration relations. One is that the stronger E1 Nifio events have longer durations, which is robust for the moderate E1 Nifio events; the other is that the stronger E1 Nifio events have shorter durations but for strong E1 Nifio events. By estimating the sign and amplitude of the nonlinear dynamical heating （NDH） anomalies, the au- thors illustrate that the NDH anomalies are negligible for moderate E1 Nifio events but large for strong E1 Nifio events. In particular, the large NDH anomalies for strong E1 Nifio events are positive during the growth and mature phases, which favor warmer E1 Nifio events. During the decay phase, however, the negative NDH anomalies start to arise and become increasingly significant with the evolution of the E1 Nifio events, in which the negative NDH anomalies dampen the sea surface temperature anomalies （SSTA） and cause the E1 Nifio events to reach the SST normal state earlier. This pattern suggests that the nonlinearity tends to increase the intensities of strong E1 Nifio events and shorten their duration, which, together with the previous results showing a positive correlation between the strength of E1 Nifio events and the signifi- cance of the effect of nonlinear advection on the events （especially the suppression of nonlinearity on the SSTA during the decay phase）, shows that the strong E1 Nifio events tend to have the amplitude-duration relation of the stronger E1 Nifio events with shorter durations. This result also lends support to the assertion that moderate E1 Nifio events possess the amplitude-duration relation of stronger E1 Nifio events with longer durations.
