A possible bias of simulating the post-2000 changing ENSO

Since the late 1990s, a climate shift has occurred over the tropical Paciﬁc that is characterized with a La Nin˜a-like mean state. Coincident with this climate shift, climate models’ skills in predicting the El Nin˜o Southern Oscillation (ENSO) events in the 2000s are sig-niﬁcantly lower than in the 1980s–1990s. A common bias is likely to exist in contemporary ENSO models that got ampliﬁed after the climate shift. In this study, we identify this model bias to be the wind–sea surface temperature coupling processes over the tropical Paciﬁc. Evidence is presented to show that this coupling process experienced an obvious shift around year 2000 in its coupling strength and coupling center. A simple ENSO coupled model is used to demonstrate that the changing properties of the post-2000 ENSO events can be more realistically simulated if this model bias is alleviated.


Introduction
The El Nin ˜o Southern Oscillation (ENSO) is one of the important sources of climate variability on seasonal to interannual scales and has been extensively studied in the past few decades.Since the Zebiak-Cane (ZC) model first reproduced the main observed features of ENSO [1], models with various complexities of atmosphere-ocean coupling have been developed to simulate and predict ENSO events.Contemporary coupled models have now reached a stage at which accurate predictions can be made 6-12 months in advance [2][3][4][5][6].However, the ENSO prediction skill was noticed to decline since around year 2000 [7,8], which is about the time when a shift in the climate regime took place in the tropical Pacific that is characterized by a prominent La Nin ˜a-like mean state and enhanced trade winds [9][10][11].Barnston et al. [7] suggested that decadal variations in ENSO properties may be a skill-determining factor.
It has been noticed that the central Pacific (CP) ENSO [12,13] occurred more frequently in recent decades [14,15].This type of ENSO has its sea surface temperature (SST) anomaly center in the central equatorial Pacific and is distinct from the traditional eastern Pacific (EP) ENSO that has its SST anomaly center in the eastern equatorial Pacific.The CP type of ENSO is believed to be produced by a mechanism distinct from that of the traditional ENSO [16] and its increased occurrence is possibly linked to the mean state change after the year 2000 [17][18][19].It is likely that the changing ENSO property (i.e., the ENSO type) after the climate shift in year 2000 causes the decline of ENSO prediction skills.This hypothesis is supported by Xue et al. [8] who analyzed the ENSO simulations in the Climate Forecast System, version 2 (CFSv2), model and noticed biases in simulating the Nin ˜o3.4 index [average SST anomalies over the area (5°S-5°N, 170°-120°W)] and the maximum standard deviation (SD) of SST anomalies shifted along with the change of ENSO properties around the year 2000.Meanwhile, it is noticed that the CP ENSO pattern cannot be adequately simulated in the phase 5 of the Coupled Model Intercomparison Project (CMIP5) [20].
The climate shift near the year 2000 appears to have amplified some specific biases in contemporary ENSO models [21] and thus degrades their performances in simulating and predicting the changing ENSO events in the twenty-first century.Models that were turned for or trained with the observations before 2000 may not be able to reasonably simulate the post-2000 ENSO characteristics.Biases in a model can be attributed to imperfect physical formulation and/or improper parameterizations, among other errors.In this study, we examined the impacts of the year-2000 climate shift on ENSO simulation skills using a simple ENSO coupled model (i.e., the GMODEL, version 3.0) [22].We show with evidence that a model bias associated with the air-sea interaction over the tropical Pacific can get amplified after the year-2000 climate shift.A bias correction scheme is developed to improve the model performance in simulating the changing ENSO events after the year-2000 climate shift.

Data and model
Several monthly observational/reanalysis datasets were used for the study period 1982-2013: SST data from the National Oceanic and Atmospheric Administration Extended Reconstructed SST (ERSST, v3b) dataset [23]; sea surface height (SSH) data, which are used to represent the variations in thermocline depth, from the National Centers for Environmental Prediction/Global Ocean Data Assimilation System (NCEP/GODAS); and zonal wind stress (TAUX) data from European Center Hamburg Atmospheric Model, version 4.5 (ECHAM4.5),ensemble simulations [24].
A simple linear coupled model is used in this study, which is the GMODEL, version 3.0 [22].Its atmospheric component is a statistical atmosphere model that was trained by the observed monthly wind stress anomalies from Florida State University and the observed Nin where T represents the SST anomaly field, h is the thermocline anomaly field, and s x is the zonal wind stress (TAUX) forcing anomaly field.The parameters a, b, and c correspond to the thermocline feedback, Ekman pumping feedback, and heat flux feedback, respectively.These parameters can be determined by regressing the time rate of changes of SST anomalies onto the anomalies of thermocline depth, zonal wind stress, and SST.All three variables (i.e., T, h, and s x ) in Eq. ( 1) are two-dimensional, and the three parameters (i.e., a, b, and c) in Eq. ( 1) are one-dimensional, which are only varying considerably along the equator [22].
3 Climate shift in the wind-SST coupling process As described in the introduction, the year-2000 shift in the tropical Pacific means climate may affect atmosphereocean couplings to alter ENSO properties.In order to examine the changes of tropical Pacific coupling across the year-2000 climate shift, we separate the analysis period into two sub-periods: 1982-1999 and 2000-2013.Figure 1a shows the longitudinal distributions of zonal wind stress (s x ) anomalies along the equatorial (5°S-5°N) Pacific during the two sub-periods.The center of the anomalous TAUX is noticed to shift from 170°W in 1982-1999 to 165°E in 2000-2013.This westward shift of the wind stress anomaly center together with the change of ENSO from the EP type to the CP type [13] indicates that the wind-SST coupling center of ENSO events has displaced westward after year 2000.We further examined the wind-SST coupling strength during the two sub-periods by finding the regression coefficient between the Nin ˜o4 TAUX and the Nin ˜o3.4 SST anomalies.As shown in Fig. 1b, the regression coefficient decreased from 4.49 in 1982-1999 to 3.77 in 2000-2013, suggesting that the coupling strength weakened after the year-2000 climate shift.The difference between these two regression coefficients is statistically significant at the 95 % confidence level using a Student's t test.Figure 1a, b together indicates that, associated with the climate shift, the wind-SST coupling in the equatorial Pacific was observed to shift westward and became weaker after 2000.

Impacts of wind-SST coupling on ENSO characteristics
We next used the GMODEL to examine how the changes in the center and strength of the tropical Pacific wind-SST coupling can together and separately impact ENSO characteristics and simulations.This coupling process is represented in GMODEL by the parameter b of Eq. ( 1).As shown in Sect.3, the year-2000 climate shift displaced the wind-SST coupling center westward by about 20°and weakened the coupling strength by about 16 %.Four experiments were conducted with the GMODEL to evaluate the importance of the wind-SST parameter (i.e., b) in affecting the model simulation of the post-2000 ENSO (Table 1).In the control experiment, all the three parameters (a, b, and c) of Eq. ( 1) were determined by conducting regression analyses with the 1982-1999 observations.We refer to this experiment as the Schemeoriginal experiment.In the second experiment, we updated the b parameter with a regression analysis of the 2000-2013 observations.This experiment is referred to as the Scheme-new experiment.To further identify the individual impacts of changing the center and the strength of the wind-SST coupling on ENSO simulations, we updated b parameter in the control experiment to the values in the 2000-2013 period only for its coupling strength in a bstrength experiment and only for its coupling center in a b-center experiment.Table 1 summarizes the detailed setups of these four GMODEL experiments.All the four experiments were integrated for 60 years from a same initial condition, and the last 50-year results (i.e., avoiding the effects of the initial conditions) were used for the following analysis.
We compared in Table 2 the SDs of the SST anomalies calculated from the two sub-periods of the observations and the four GMODEL experiments over the Nin ˜o3, Nin ˜o3.SST coupling parameter in reproducing the changing ENSO characteristics in the past three decades.Figure 2 further compares the power spectra of the Nin ˜o3.4 SST anomalies between the two sub-periods of the observations (Fig. 2a) and between the Scheme-original and Scheme-new experiments (Fig. 2b). Figure 2a shows that the dominant ENSO frequency decreases from once every 4.1 years in 1982-1999 to about once every 2.3 years in 2000-2013.Figure 2b shows a similar frequency decrease from the Scheme-original experiment (about 3.4 years) to the Scheme-new experiment (about 2.0 years).Table 2 and Figure 2 together show that, by updating the wind-SST coupling parameter (b) to the observed values in each sub-period, the same GMODEL model is able to realistically simulate the changing El Nin ˜o amplitude and frequency before and after the year-2000 climate shift.These results also indicate that the wind-SST coupling is a key process to cause the different characteristics between the post-2000 and the pre-2000 ENSOs.
To further understand why an updated wind-SST coupling parameter can produce a more realistic simulation of the post-2000 ENSO, we examined the main differences in the simulated TAUX, thermocline depth, and SST between the Scheme-original and of Scheme-new experiments.The differences were identified by applying an empirical orthogonal function (EOF) analysis to the differences of their simulations in each of the analyzed fields.The first EOFs of the structure differences are displayed in Fig. 3.The figures indicate that the main structure differences under the decadal changes of the interannual wind-SST coupling (i.e., the parameter b) are characterized by strengthened easterly wind stresses over the central Pacific; higher thermocline over the western Pacific and lower thermocline over the eastern Pacific; and La Nin ˜a-like SSTs over the eastern-to-central Pacific.These patterns depict the following wind-SST coupling process: First, the strengthened easterly winds over the central Pacific provide a mechanism to deepen the thermocline in the western Pacific and shoal the thermocline in the eastern equatorial Pacific.Colder seawater emerges in the eastern Pacific can then propagate to the west through the action of coastal upwelling and advection to produce a cold SST state (i.e.,   The main differences of simulated fields show a high degree of similarity with the observed mean state changes (i.e., 2000-2013 period minus 1982-1999 period) of TAUX, SSH, and SST (i.e., Fig. 3d-f), except for a weaker magnitude.This similarity further proves the critical role played by the wind-SST coupling parameter in improving the simulation of the post-2000 ENSO.This also suggests that the weakened ENSO cycle (i.e., decreased SD values of Nin ˜o3 and Nin ˜o3.4 SST simulated by the Scheme-new experiment) is related to the enhancement of easterly mean winds over the tropical Pacific (Fig. 3a), which hinders the transportation of warm water anomalies (Fig. 3b) from west to east to amplify ENSO events.Significantly, the observed cooling mean state over the tropical Pacific has been previously alluded to as the facilitator of the CP El Nin ˜o [10,17,25].
We next focused on isolating the individual roles of the coupling strength and the coupling center of b in influencing the ENSO characteristics in the GMODEL simulations.We first compared in Table 2 (columns 4 and 5) the SD values of SST between the b-strength experiment and the b-center experiment over the Nin ˜o regions.We noticed that the observed decrease in the SD values across the 2000 over the Nin ˜o3 and Nin ˜o3.4 regions can only be produced when the b-strength is updated from the pre-2000 value (i.e., the Scheme-original experiment) to the post-2000 values (i.e., the b-strength experiment).However, the observed increase in the SD value across the climate shift over the Nin ˜o4 region can only be produced when the bcenter is updated from the pre-2000 location (i.e., the Scheme-original experiment) to the post-2000 location (i.e., the b-center experiment).Therefore, the observed change in ENSO pattern (i.e., from the EP ENSO before the year-2000 climate shift to the CP ENSO afterward) involves changes in not only the strength but also the center of the wind-SST coupling in the tropical Pacific.
We repeated the EOF analysis of Fig. 3a-c  ), e SSH (m), and f SST (°C) from the observed data original experiment to the b-strength experiment (Fig. 4a), the main simulation changes (Fig. 4b-d) between these two experiments are consistent with those from the Schemeoriginal to the Scheme-new experiments (Fig. 3a-c) and are also similar to the mean state changes observed from the pre-to post-2000 climate shift eras (Fig. 3d-f).This robust weakened relationship between the atmospheric winds and the tropical SST in the post-2000 era has been explored in many previous studies [17,[25][26][27][28].And one possible reason for inducing this weakened air-sea interaction at the interface might be from the variations in the background state of the tropical Pacific [10,11,26].For example, cooler mean SST in the eastern and central equatorial Pacific results in reduced convection there together with a westward shift in the ascending branch of the Walker circulation [10,11].And this shift leads to a weakening in the relationship between eastern Pacific SST and longitudinally averaged equatorial zonal wind stress [26,29].However, the asymmetry of interannual variabilities can also modulate the mean state conditions, which will in turn affect the interannual variabilities, but this mechanism has been less investigated [11].As demonstrated in Fang and Zheng [11], the interannual variabilities also can significantly affect the climate mean state, and the predominance of the EP and CP El Nin ˜o can be modulated by relationships between anomalous wind stresses and SST.
In this study, we further found that changing the strength and center of the wind-SST coupling can give rise to changes in the tropical Pacific mean state: A weakening of the coupling strength gives rise to a La Nin ˜a-like mean state, while shifting the coupling center westward gives rise to an El Nin ˜o-like mean state.And a common parameter bias exists in representing the changed relationship between wind and SST in ENSO models around 2000.Our GMODEL experiments conclude that weakening the wind-SST coupling strength dominates the westward shift of the wind-SST coupling center in controlling the cooling pattern over the tropical Pacific in the post-2000 era, and the changing properties of the post-2000 ENSO events can be more realistically simulated if this bias is reasonably reduced.Although the findings reported here are based on a simple coupled model, they can be used to understand and to alleviate biases of other more complex coupled models in simulating/predicting the changing El Nin ˜o observed in the twenty-first century [6,[30][31][32].It should be noted that the possible impacts of the other two coupling parameters [i.e., a and c of Eq. ( 1)] remain a matter of major interest and merit further studies [33,34].

Fig. 1 Table 1
Fig. 1 Observed shift in the wind-SST coupling progress.a The zonal structure for the anomalous TAUX averaged over 5°S-5°N in the period 1982-1999 (red lines/points) and 2000-2013 (blue lines/points).b Scatter diagram and the corresponding linear fitting lines (with the values of slopes plus and minus 1.96 standard errors, namely 95 % confidence for a Student's t test) between the Nin ˜o4 TAUX and Nin ˜o3.4 SST anomalies during the two sub-periods(1982-1999 and 2000-2013)

Table 2
Standard deviation (SD) of the SST anomalies over the three Nin ˜o (Nin ˜o3, Nin ˜o3.4,and Nin ˜o4) regions, estimated from the four different schemes (Scheme-original, Scheme-new, b-strength, and b-center) and from the observations in two sub-periods (1982-1999 and 2000

Figure 4 Fig. 4
Fig.4Leading EOF modes of the simulation differences in TAUX (dyn cm -2 ; second row), thermocline depth (m; third row), and SST (°C; bottom row) between b-strength and Scheme-original (left column), and between b-center and Scheme-original (right column).And the top row is sketching the scheme differences between b-strength and Scheme-original (left), and between b-center and Scheme-original (right), respectively