Ensemble ENSO prediction based on various perturbation methods

Abstract

Inaccurate initial conditions, along with imperfect models, bring errors in prediction. Initial conditions are constructed by adding small perturbations to the analysis. For decades a number of perturbation methodologies have been developed such as the breeding method (Toth and Kalnay, 1993

Cai et al., 2003

Yang et al., 2006, 2008

Tang and Deng, 2010, 2011), the singular vector (SV) method (Farrell, 1989

Palmer et al., 1994) and the ensemble Kalman filter (EnKF) method (Evensen, 1994). All the initialization methods aim to satisify two conditions. One is to capture the uncertainties in the analysis

another is to grow the perturbation spanning the probable range of truth (Magnusson et al., 2008

Houtekamer and Derome, 1995). The breeding method was previously used by the National Centers for Environmental Prediction (NCEP) until May 2006. This method is based on the idea that small but fast-growing perturbations saturate earlier (Yang et al., 2006). Therefore, by changing rescaling interval and rescaling amplitude, dominant perturbations of interest can be isolated from faster growing perturbations which are no more than noise (Peña and Kalnay, 2004

Yang et al., 2006, 2008). Peña and Kalnay (2004) suggested that frequent rescaling of the order of 10 minutes can separate storm-scale signals. For larger-scale weather forecast, however, rescaling interval of 6 to 48 hours are recommended to create baroclinic initial perturbations. Cai et al. (2003) first showed that the BVs generated with 3 and 6-month rescaling intervals can successfully separate ENSO-related variabilities from weather and other shorter timescale variabilities. Yang et al. (2006, 2008) further asserted that rescaling period longer than two weeks can keep the slow, coupled instabilities in bred perturbations. However, few studies have been conducted concerning the effect of rescaling periods on prediction skill. It is well known that there are a variety of time scales in tropical climate system (Kang and Kug, 2004

Lau and Weng 1999

Jin et al., 2003). In addition to 3-5 year ENSO cycle, near annual variability of 12-18 month period, decadal-interdecadal variability of more than 10-year period and even linear trend are superimposed on the tropical phenomena. Therefore, it is important to take into consideration these various frequency modes to improve seasonal prediction skill over the tropical Pacific. Ham et al. (2012, in press) showed that BV1 (BV6) is driven by zonal advection feedback (thermocline feedback) and similar to high-frequency (typical ENSO) mode. Motivated by this result, the characteristics and the predictabilities of breeding methods with 3 different rescaling intervals (1, 3 and 6 months) are investigated in this study. Along with BV, SV is another widely used initialization method. While breeding method keeps integrating model dynamics to filter out noisy modes, the singular vector method uses a mathematical technique to directly pick out optimal perturbations (Magnusson et al., 2008). The singular vector method performs singular value decomposition on a linear model using a linearized version of the dynamics to obtain a singular vector corresponding to the largest singular value. In this way, SV maximizes the growth over a fixed time interval and is consequently expected to dominate forecast errors (Buizza et al., 2005). The European Centre for Medium-Range Weather Forecasts (ECMWF) has applied the singular vector method to weather forecast system. On a seasonal basis, however, SV method has some difficulties. Because this method requires a linearized version of a coupled model, it is problematic to capture variability associated with long-term timescale because the linearized system has a difficulty in capturing a nonlinear behavior when the lead time is long (Kug et al., 2010, 2011). In an effort to apply the SV method to a nonlinear model, Kug et al. (2010) introduced empirical SV method. In ESV method, the operator (L) is estimated not by linearizing the governing equation but by using historical data from the long-term model integration. Kug et al. (2010, 2011) applied ESV method to both hybrid coupled model and sophisticated CGCM and showed the forecast skill for ENSO was improved. This study further investigates the effects of variables used to generate the empirical operator. Based on the understanding of the characteristics of BVs and ESVs, the two methods are compared each other, and finally ensemble seasonal prediction skills are studied using SNU CGCM. There has been several studies to compare the initialization methods (Buizza et al. 2005

Magnusson et al. 2008a,b

Bowler 2006

Smith et al. 1999

Trevisan et al. 1995

Anderson 1996). Nonetheless, many studies derived conclusions using simple models (Magnusson et al. 2008a,b

Anderson 1996) or not excluding different model effects (Buizza et al. 2005). Also, there have been few studies focusing on seasonal prediction. The study is structured as follows. In section 2 the description of the model, data, initialization methods used and prediction experimental design are provided. The characteristics and prediction results of the breeding method and the empirical singular vector method are presented in section 3 and 4, respectively. The comparison of the methods and the ensemble results are explored in section 5, and conclusions are drawn in section 6.