Sensitivity of Nonlinearity on the ENSO Cycle in a Simple Air-Sea Coupled Model

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1 ATMOSPHERIC AND OCEANIC SCIENCE LETTERS, 2009, VOL. 2, NO. 1, 1 6 Sensitivity of Nonlinearity on the ENSO Cycle in a Simple Air-Sea Coupled Model LIN Wan-Tao LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing , China Received 2 June 2008; revised 3 September 2008; accepted 17 September 2008; published 16 January 2009 Abstract In this paper, the influence of the El Niño- Southern Oscillation (ENSO) cycle on the sensitivity of nonlinear factors in the numerical simulation is investigated by conducting numerical experiments in a simple air-sea coupled model for ENSO prediction. Two sets of experiments are conducted in which zonal nonlinear factors, meridional nonlinear factors, or both are incorporated into the governing equations for the atmosphere or ocean. The results suggest that the ENSO cycle is very sensitive to the nonlinear factor of the governing equation for the atmosphere or ocean. Thus, incorporating nonlinearity into air-sea coupled models is of exclusive importance for improving ENSO simulation. Keywords: simple air-sea coupled model, sensitivity, nonlinearity, ENSO cycle Citation: Lin, W. T., 2009: Sensitivity of nonlinearity on the ENSO cycle in a simple air-sea coupled model, Atmos. Oceanic Sci. Lett., 2, Introduction The complexity and nonlinearity of the ocean-atmosphere interaction poses great difficulties for theoreticians attempting to create a simple model of the ENSO. Consequently, numerical modeling becomes a popular approach to predict the ENSO. Researchers over past two decades have demonstrated some success with the use of simple to intermediate coupled models (McCreary and Anderson, 1984; Cane and Zebiak, 1985; Anderson and McCreary, 1985; Zebiak and Cane, 1987; Schopf and Suarez, 1988), general circulation models (GCMs) (Philander et al., 1989; Latif et al., 1993), and hybrid models (Neelin, 1989, 1990). These models have considerably advanced our understanding of the physics involved in the ENSO. Despite improvements in the ENSO numerical simulation, it is still a difficult task to provide a theoretical explanation of the physical mechanisms of the ENSO cycle. Furthermore, it is of substantial importance to estimate the impact of nonlinearity on the ENSO because the motions of atmosphere and ocean in nature are intrinsically nonlinear. Only by clarifying the impact of any nonlinear effects can the mechanisms for the ENSO cycle be fully revealed and the ability for accurate prediction be improved. Consequently, many previous studies have been devoted to comprehensively investigating the local and overall properties of the equations governing the ENSO based on simple coupled ocean-atmosphere models (Wang and Fang, 1996; Wang et al., 1999; Eccles and Tziperman, Corresponding author: LIN Wantao, linwt@lasg.iap.ac.cn 2004; Lin and Mo, 2004, 2008; Lin et al., 2008). In this paper, the influence of nonlinear factors on numerical simulations of the ENSO cycle is investigated by incorporating a zonal factor, a meridional factor, or both into the governing equations for the atmosphere or ocean in a simple air-sea coupled model for ENSO prediction. The ENSO prediction model used in this work is the ZC model (Zebiak and Cane, 1987). 2 The nonlinear extension of the governing equations and numerical experiment The original governing equations for the atmosphere and ocean in the ZC model are linear. Through incorporating an additional nonlinear term,the equations can be written as follows: εua + δ uauax + δ vauay βyva = px, (1) εv + δ u v + δ v v βyu = p, (2) a a ax a ay a y ε p + δ u p + δ v p + c 2 ( u + v ) = Q, (3) a x a y a ax ay τ ut + δ uux + δ vuy βyv = gh x + γu, ρh (4) s τ y β yu+ δ uvx + δ vvy = gh y + γv, ρh (5) h + δ uh + δ vh + H( u + v ) = γh. (6) t x y x y where δ is a small parameter that is referred to as the nonlinear coefficient. For other variables and parameters of the equations, where u a and v a are the components of surface wind anomaly, p is the surface pressure anomaly, β is the Coriolis parameter, ε is the damping coefficient, c a is the characteristic speed, Q is the specified heating anomaly, u and v are the zonal and meridional velocity s x fields, τ and τ s y are the zonal and meridional components of the wind stress, ρ is the density of the upper layer, H is the depth of the upper layer, γ is the Rayleigh friction, h is the thickness of the upper layer, g = g( Δ ρ / ρ) and g is the acceleration of gravity (Zebiak and Cane, 1987). To estimate the impact of nonlinearity, a series of numerical experiments are carried out in which the nonlinear coefficient values varies from 0 to 1 in the Niño-3 area (5 N-5 S, W). 3 The influence of sensitivity on the nonlinear factor in the equation governing the atmosphere Three sets of typical numerical results are chosen for analysis. These results are shown in Figs s x

2 2 ATMOSPHERIC AND OCEANIC SCIENCE LETTERS VOL. 2 Figure 1 The temporal evolution of the mean SSTA (Sea Surface Temperature Anomaly) over a 480-year model interval (solid line is for a zonal nonlinear factor with a δ of ; dashed line is for a zonal nonlinear factor with a δ of ). Figure 2 The temporal evolution of the mean SSTA over a 480-year model interval (solid line is for a meridional nonlinear factor with a δ of ; dashed line is for a meridional nonlinear factor with a δ of ).

3 NO.1 LIN: SENSITIVITY OF NONLINEARITY ON THE ENSO CYCLE 3 Figure 3 The temporal evolution of the mean SSTA over a 480-year model interval and comparison by a model using both zonal and meridional nonlinear factors (solid line is for zonal and meridional nonlinear factors with a δ of ; dashed line is for zonal and meridional nonlinear factors a δ of ). Figure 1 demonstrates how the ENSO cycle is sensitive to the zonal nonlinear factor in the governing equation for the atmosphere. Over the first 20-year period covered by this model, there is no difference between the two δ values, indicating little influence of nonlinearity. Beyond that initial period, the difference becomes quite distinct. The amplitude of the ENSO cycle is amplified for the case where the δ value is increased by 10%; however, the ENSO phase lags behind that of the case with a smaller δ value after the 90th model year. The ENSO model cycle for the larger δ case appears to become unstable after the 220th model year, but maintains a consistent periodicity. Figure 2 demonstrates the sensitivity of the ENSO cycle to the meridional nonlinear factor. As with the zonal model, no difference is seen for the two δ values over the first 20 years. After that, for the case with the δ increased by 10%, the amplitude of the ENSO increases from the 80th to the 290th model year, but decreases after the 290th model year. In particular, the phase tends to lag, even becoming out-of-phase relative to the case with a smaller δ, in conjunction with the decrease in amplitude. In comparison, this latter period appears insensitive to the meridional nonlinear factor, much like the zonal nonlinear case. Figure 3 shows the sensitivity of the ENSO cycle to the combined zonal and meridional nonlinear factors. For the case with the δ increased by 10%, the amplitude increases from the 90th to the 190th model year, but does not significantly change after the 190th year. The ENSO cycle phase is sensitive to the combined zonal and meridional nonlinear factors. The increasing nonlinearity causes the phase to lag; however, the period of the ENSO seems to be insensitive to the nonlinear factors, as seen in the individual zonal or meridional cases. The above analyses clearly suggest that the variation of the nonlinear factor does not change the period of the ENSO cycle in spite of its substantial changes to the ENSO phase and amplitude. The ENSO cycle appears to be more sensitive to the zonal nonlinear factor, which is demonstrated by the instability after the 220th year in Fig The influence of sensitivity on the nonlinear factor in the equation governing the ocean Similar to the method seen in Section 3, three sets of results from typical numerical experiments with nonlinearity in the ocean governing equation are chosen to further study the influence of the nonlinear factor. These results are shown in Figs Figure 4 suggests that the ENSO cycle is sensitive to the zonal nonlinear factor in the governing equation for the ocean, although little influence is seen over first 200

4 4 ATMOSPHERIC AND OCEANIC SCIENCE LETTERS VOL. 2 Figure 4 The temporal evolution of the mean SSTA over a 480-year model interval (solid line: zonal nonlinear factor ;dashed line: zonal nonlinear factor ). Figure 5 The temporal evolution of the mean SSTA over a 480-year model interval (solid line: meridional nonlinear factor ; dashed line: meridional nonlinear factor ).

5 NO.1 LIN: SENSITIVITY OF NONLINEARITY ON THE ENSO CYCLE 5 Figure 6 The temporal evolution of the mean SSTA over a 480-year model interval and comparison by a model using both zonal and meridional nonlinear factors (solid line: zonal and meridional nonlinear factors ; dashed line: zonal and meridional nonlinear factors ). years. For this case, with strengthened nonlinearity, from the 200th to the 250th model year, the ENSO cycle becomes weakened, but is intensified from the 250th to the 360th model year. Beyond the 360th model year, it becomes weakened again and this persists for the following 90 years. Figure 5 demonstrates the sensitivity of the ENSO cycle to the meridional nonlinear factor in the governing equation for the ocean. From the 140th to the 200th model year, the ENSO cycle becomes weakened. After the 200th model year the cycle is then enhanced. Figure 6 displays the sensitivity of the ENSO cycle to combined zonal and meridional nonlinear factor in the governing equation for the ocean. From the 170th to the 210th model year, the ENSO cycle becomes intensified. After that, it becomes weakened, and this weakening persists until the end of the model run. Meanwhile, a large phase change is seen. The above results illustrate that both the amplitude and phase of the ENSO cycle are sensitive to nonlinearity in the governing equation for the ocean. This implies that the zonal nonlinear factor, meridional nonlinear factor, or the combined factors can considerably change the amplitude and phase of the ENSO. 5 Conclusions In this study, the influence of nonlinearity on the ENSO cycle is explored by conducting numerical experiments on a simple air-sea coupled model in which an additional nonlinear term is incorporated into the atmospheric or oceanic governing equation of the model. The results suggest that the nonlinearity exerts substantial influence on the ENSO cycle and this influence increases with model s integration period. In particular, on interdecadal timescales, any tiny change of nonlinearity in the atmospheric or oceanic governing equation can significantly influence ENSO cycle. In comparison, the nonlinearity in the ocean governing equation appears to have a more significant effect. These effects imply a vital role of nonlinearity in predicting the ENSO and provide a candidate explanation for previous prediction failures. Since numerical models are the primary approach to predicting the ENSO, incorporating nonlinearity into these models is important for improving ENSO simulations. Acknowledgments. The author is grateful to Dr. Shuanglin Li for his help in preparing this manuscript. This work was supported by the National Natural Science Foundation of China (Grant No ). References Anderson, D. L. T., and J. P. McCreary, 1985: Slowly propagating disturbances in a coupled ocean-atmosphere model, J. Atmos. Sci., 42,

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