The Rectification Effect Of ENSO Events Into The Time-mean State Of Tropical Pacific

Sea surface temperature (SST) in eastern tropical Pacific has obviously become warming since the year 1976, while during the same time the level of El Nino/La Nina-Southern Oscillation (ENSO) activity is anomalously higher. The causal relationship between them has become a hot research topic in the world in recent years. To better understand this issue, we use a low-order nonlinear ENSO theoretical model in our study to simulate the coupled tropical atmosphere and ocean. By comparing the differences between the time-mean state of the system and its corresponding equilibrium state, we study the influence of ENSO on the time-mean state of tropical Pacific. Based on the definition of "Rectification" in Physics, we define the influence of ENSO (interannual variability) on the time-mean state of tropical Pacific (decadal variability) as the conception of "Rectification effect".The low-order analytical model in our study characterizes well the air-sea coupling in the tropic Pacific, and encapsulates the essential physics of the ENSO system. In the experiment, the equilibrium state of the system is obtained analytically; the realized time-dependent state is calculated numerically. Results show that the simulated ENSO events resemble the observations well, also with the diversity and complexity of ENSO reflected. The equilibrium state of the system is found to change with the variation of external forcing, and has an oscillatory regime within which we can observe the ENSO oscillation. In this oscillatory regime, the amplitude of ENSO becomes first increased then decreased when we continuously enhance the external forcing. Meanwhile, the time-mean state of the system and the equilibrium state become different obviously; their difference is in direct proportion to the amplitude of ENSO, following the same variation. The differences between the time-mean state and the equilibrium state in sea surface are that the time-mean SST is found to be always warmer than the corresponding equilibrium SST, especially in eastern equatorial Pacific. In addition, the zonal SST contrast of the time-mean state is found to be less sensitive to increases in external forcing than that of the equilibrium state, due to warming effect of ENSO events on the eastern Pacific. Differences between the time-mean subsurface ocean temperature and its equilibrium in the presence of ENSO oscillation are similar to those in eastern Pacific SST, but are more pronounced, consistent with the observations. The time-mean upwelling is less strong than that in the equilibrium state. In the presence of ENSO, the depth of the thermocline in the eastern Pacific is deeper in the time-mean state than that in the equilibrium state. The reverse is true for the thermocline in the western Pacific.Further analysis shows that the rectification effect of ENSO events into time-mean state of tropical Pacific is not determined by the choice of value of the parameters used in the model, and also has no relationship with the diversity and complexity of ENSO characteristics. This rectification effect seems to be an "inherent" property of the oscillatory system itself. We further point out that the rectification effect of ENSO events stems from the nonlinear effect of the system. And there are two sources of nonlinearity in the model:one is from the nonlinear parameterization of the subsurface ocean temperature; the other owns to the nonlinear advection term in the heat budget equation. By the comparison of differences between the nonlinear and linear parameterizations of the subsurface ocean temperature, we prove that the first source of nonlinearity has no relationship with the rectification effect of ENSO events. Through the derivation of mathematical equations, we prove that the difference between the time-mean SST in eastern Pacific and its corresponding equilibrium SST can be attributed to an item of nonlinear heating (always positive), and its value is proportional to the variance of ENSO. The derivation directly shows that it is the warming effect of nonlinear items in the system that makes the warming effect of ENSO into the time-mean state.The rectification effect of ENSO into the time-mean state can also be shown by the asymmetry between the two phases of ENSO. In the regime with regular oscillation, the main asymmetry is in the duration of the warm and cold events; while in the regime with irregular ENSO oscillation, the main asymmetry is in the magnitude of the warm and cold events. It is found that the system of ENSO mostly stays on the warmer side of its phase space-leading to a warmer eastern Pacific and a reduced zonal SST contrast-on average, because the system feels less "warm stress" and becomes more stable in the side of warm events.Our study reveals the rectification effect of ENSO events into the time-mean state of tropical Pacific, and elucidates the role of ENSO events in shaping the tropical mean climate state and also suggests that decadal warming in the recent decades in the eastern tropical Pacific may be more a consequence than a cause of the elevated ENSO activity during the same period. The results also provide a simple explanation for why it is difficult to detect an anthropogenically forced trend in the zonal SST contrast in the observations.