Research On ENSO Ensemble Predictions

In the past two decades, ENSO (El Ni?o-Southern Oscillation) studies have made remarkable progress, reaching the stage where reasonable predictions can be made 6 to 12 months in advance, and the ENSO prediction is the most successful one in current short-range climate predictions. Several forecast systems have been used routinely in real time to do so. These include statistical models and physical coupled models of varying degree of complexity, ranging from intermediate coupled models (ICMs), to hybrid coupled models (HCMs), and to coupled general circulation models (GCMs). However, the forecast results from these statistical models and physical coupled models are significantly different (which indicts that there are large uncertainties for model predictions). Indeed, there is considerable uncertainty in ENSO predictions even at relatively short lead times, which is due to the chaotic or irregular aspects of climate variability. To minimize or reduce the forecast uncertainty for ENSO predictions, the ENSO forecasts should be probabilistic.The ensemble prediction methods have been made quiet great researches and applications. But there is the initiative stage for the ENSO probabilistic forecast, and most current researches are focusing on the effects of the initial perturbations on ENSO predications. However, the model uncertainties for the model physical process are also an important factor of working on the ENSO predication skills, and still less for considering. In this work, we attempted to use an intermediate coupled model to discuss the methods of ENSO ensemble forecast, and synthetically considered and analyzed the effects of the accuracy of the initial conditions, the initial and model uncertainties during the prediction process on ENSO ensemble predictions.1. Through reasonably considering the effects of the model errors, the'filter divergence'for the ensemble Kalman filter (EnKF) is effectively prevented. Comparing to some current, simpler data assimilation schemes, which assume that the background error is known a priori and does not vary in time, the EnKF can optimize the background to newly available observations by providing flow- and location-dependent estimates of the background error, and produce more accurate analyses and forecasts. However, the EnKF depends on a set of ensemble forecasts to calculate the background error covariance. Without model perturbations and the inflation of forecast ensembles, the spread of the ensemble forecasts will collapse rapidly (i.e.,'filter divergence').In this work, we focused on the"adding some error terms to the right-hand-side of the model equations"approach, and utilized a first-order Markov chain model that allows for modeling the errors. This approach was convenient for those unforced models, such as the coupled atmosphere-ocean models. Under the assumption of that the model errors of the coupled model are mainly caused by the model imperfections and defined as departures of forecast tendencies from the observations without considering the observational errors. We focused on the simulated sea surface temperature (SST) anomaly field of the model, which is the key variable for coupled air-sea interactions. So we embed the stochastic component into the SST anomaly model to perturb the modeled SST anomaly field randomly by applying the first-order, linear Markov stochastic model. To improve assimilation effects of the EnKF, this stochastic model has been validated to be effective and feasible to prevent the filter divergence during the assimilation process by controlling the ensemble members of model variables in a reasonable spread.2. For the ensemble predictions, we presented a new approach to generate the initial ensemble members and representing model uncertainties during the simulation procedure. Firstly, we used the EnKF data assimilation system to provide initial condition ensemble for the ICM with 100 members. The initial model background error covariance between state variables after a series of assimilation cycles is compliant with the observation error covariance. The horizontal distribution of the model uncertainties has the same shape as that of the observation errors. So each ensemble member after assimilation might represent one kind of realistic conditions, and the initial ensemble state variables can be dynamically consistent with both the model and the observations.Secondly, the linear, first-order Markov stochastic model used in the assimilation process was modified and extended to twelve months by the empirical orthogonal function (EOF) approach, and embedded within the SST anomaly model of the ICM to represent and simulate model uncertainties in twelve-month ensemble forecasting procedures. We implemented this ensemble method into the ICM to predict SST anomalies over the tropical Pacific Ocean. The retrospective forecasts experiments covering the period 1975-2004 were performed and compared to available observations and the original deterministic hindcast results, and a 12-month hindcast is initialized each month during this 30-yr period.Lastly, the deterministic verification, including correlation and root mean square (RMS) error, and the probabilistic verification, including the Talagrand probability distribution, gaussian distribution, spread, brier score (BS), and the relative operational character (ROC) were applied to verifying the prediction skills of the ensemble prediction system (EPS). The verification results showed that the ensemble prediction method was feasible; the deterministic prediction skills of the ICM was improved by the ensemble technique, and the probabilistic forecast information and skill assessment for the SST anomalies provided additional information that could not be gleaned from a purely deterministic approach.3. Based on the 30-year ensemble hindcast results, we focused on the two pop research subjects on ENSO predictions ("spring predictability barrier"and the effects of forecast errors on ENSO predictions), further discussed the seasonal predictability of our EPS, and the impacts of the forecast error scheme (including initial errors and model errors) adopted in the EPS on the ENSO prediction skills. For the seasonal predictability, the deterministic ensemble-mean forecast presented obvious seasonal variations, while the probabilistic prediction skills of the EPS did not conspicuously change along the seasons.For the forecast errors, the ensemble mean provided by the EnKF assimilation results for the deterministic initialization was the optimal estimation, and the initial perturbations did not work on improving the deterministic prediction skill. The improvement of the prediction skill occured because the advanced EnKF assimilation method can provide more dynamically consistent and accurate initial conditions than the original initialization method, and the model errors during the forecast process can make ensemble mean remove some unpredictable stochastic information and further improve the prediction skill of the ensemble mean. Without considering the model uncertainties during the forecast process, the initial uncertainties provided by the EnKF would be collapse and decrease rapidly in short lead times, and the distributions (spread) of the ensemble members could not represent the model forecast uncertainties. While considering the model errors can conquer the problem, and further improve the probabilistic prediction skills of the EPS significantly.4. The El Ni?o is evident in instrumental observations dating back to the mid-nineteenth century. We explored the ensemble forecast method using only reconstructed SST anomaly data for ensemble initialization into the past 120-year hindcast experiment, to verify the predictability of the EPS in a much longer period (lager freedom), and to analyze its decadal predictability in different periods. The hindcast results indicated that the skill scores for the ensemble-mean hindcast were still better than that of the original deterministic forecast scheme, and the ensemble-mean forecast was able to predict the observed strong El Ni?o 12 months in advance. The deterministic analysis (correlation and RMS error) and the probabilistic analysis (Talagrand distribution and ROC area) indicted that the EPS presented obvious decadal variations, and the probabilistic predictability did not conspicuously change along the seasons.5. To assimilate more than one kind of observation into the model, and provide more accurate initial conditions for the EPS, we made further improvements on the previous study by extending the stochastic model error model from a univariate one to a bivariate one that contains model errors of SST and the sea level (SL) anomalies. The data assimilation scheme was also extended to assimilate both SST and SL anomaly observations. A multivariate empirical orthogonal functions (MEOFs) approach was adopted to analyze the properties of the model errors of SST and SL anomalies in order to obtain the balanced parameters in the stochastic model. An improved, linear, first-order, multivariate Markov stochastic model was embedded within the dynamical ocean model of the ICM to represent and simulate model uncertainties in the EnKF data assimilation procedure. We used the developed ensemble assimilation scheme to provide more accurate and dynamically balanced initial ensemble conditions for the EPS with 100 members. Comparing to the original ensemble hindcast results, the ensemble prediction skills of the new hindcast results were significantly improved out to a 12-month lead time by improving SL initial conditions for better parameterization of subsurface thermal effects. This improvement suggests that the ENSO predictability is, to a larger degree, limited by the growth of initial errors than by stochastic forcing and great improvements in prediction skill can be expected by improving the accuracy and compatibility of the initial conditions via comprehensive ensemble data assimilation techniques.