Sudden stratospheric warmings during El Niño and La Niña: sensitivity to model biases

Abstract. The number of sudden stratospheric warmings (SSWs) per year is affected by the phase of the El Niño–Southern Oscillation (ENSO), yet there are discrepancies between the observed and modeled relationship. We investigate how systematic model biases may affect the ENSO-SSW connection. A two-step bias-correction process is applied to the troposphere, stratosphere or full atmosphere of an atmospheric general circulation model. ENSO type sensitivity experiments are then performed to reveal the impact of differing climatologies on the ENSO–SSW teleconnection. The number of SSWs per year is overestimated in the control run, and this statistic is improved when stratospheric biases are reduced. The seasonal cycle of SSWs is also improved by the bias corrections. The composite SSW responses in the stratospheric zonal wind, geopotential height and surface response are well represented in both the control and bias corrected runs. The model response of SSWs to ENSO phase is more linear than in observations, in line with previous modeling studies, and this is not changed by the reduced biases. However, the trend of more wave-1 events during El Niño years than La Niña years is improved in the bias corrected runs.


Introduction
The El Niño-Southern Oscillation (ENSO) can impact the northern hemisphere wintertime stratospheric variability, and the prevalence of sudden stratospheric warmings (SSWs). Understanding the ENSO-SSW link can help interpreting seasonal model predictions and improve seasonal forecasts. The increased convection in the tropical east Pacific during an El Niño event triggers a Rossby wave train that strengthens and deepens the Aleutian low (Bell et al. 2009;Cagnazzo and Manzini 2009). This leads to constructive linear interference of the planetary waves and an increased wave flux into the stratosphere, and hence, a weakened stratospheric polar vortex. During El Niño years the polar vortex is, on average, weaker than in neutral years, and El Niño is also associated with an increase in the number of SSWs .
Although La Niña is the opposite phase to El Niño, the negative SST anomalies tend to be weaker, more westward, and have a different time evolution (Hoerling et al., 1997, Larkin & Harrison, 2002, Frauen et al., 2014. The decrease in convection in the topical east Pacific associated with La Niña still leads to a shallower Aleutian low, decreased wave flux and a stronger polar vortex (Iza et al., 2016, Jiménez-Esteve, B., & Domeisen, D. I. V., 2019. The anomalous La Niña response is weaker than El Niño due in part to the weaker response of the tropical convection and Rossby wave forcing (Trascasa-Castro et al., 2019). The changes to the vertical wave activity flux seem a valid dynamical argument as to why El Niño might lead to more SSWs and La Niña lead to less SSWs, however, the observational record is not so clear. There is a higher chance of an SSW during El Niño years, but there is also an increase in SSW frequency associated with La Niña years . However, there may be sampling errors due to the relatively short observational record , and the La Niña-SSW relationship is sensitive to the SSW definition (Song & Son 2018). Modeling studies show the increased likelihood of an SSW during an El Niño, and show a decrease likelihood of SSWs during La Niña years (Polvani et al., 2017, Song & Son, 2018. It is unclear if the discrepancy between models and observations is due to the low number of observed ENSO and SSW events in observations, or non-linearities in the ENSO teleconnections which the models are unable to simulate . The role of mean state model biases has been investigated for some aspects of the ENSO-SSW teleconnection. Biases in the tropical Pacific SSTs can lead to different ENSO dynamics (Bayr et al., 2018), and affect the position of the North Pacific sea level pressure response (Bayr et al., 2019). Mean state biases in the extratropical circulation can affect the propagation of Rossby waves (Li et al., 2020), and their impact on North Pacific SSTs (Dawson, et al., 2011). The impact of climatological biases on the mean ENSO-to-northern hemisphere teleconnection was discussed in Tyrrell and Karpechko (2021), using output from the same modeling experiments as in this paper (see Section 2). It was found that mean state of the Aleutian low changed the response of the polar vortex to an El Niño forcing by modulating the upward wave flux to the stratosphere.
Biases in the strength of the polar vortex did not impact its anomalous response to ENSO, and the NAO response was not impacted by biases.
In this paper we investigate how the climatological biases affect the relationship between ENSO and northern hemisphere SSWs. We use a bias correction technique to reduce atmospheric biases at specific levels to create different climates, within which we can run ENSO-like SST perturbation experiments. The bias correction technique and data are described in Section 2, in Section 3 we present the bias reductions and mean ENSO response (3.1), the statistics of SSWs (3.2), downward propagation and the surface response (3.3), and the heatflux response (3.4). A discussion and conclusions are presented in Section 4.

Bias corrections
We used the ECHAM6 atmospheric model (Stevens et al., 2010), with a horizontal truncation of T63 and 95 levels in vertical with a model top at 0.02 hPa. It was run in bias-corrected and biased modes and with SST perturbation experiments.
The bias correction process follows Kharin and Scinocca (2012), and has been used to study the effects of model biases on the Eurasian snow extent-polar vortex connection (Tyrrell et al., 2020), Quasi-Biennial Oscillation teleconnections  and the ENSO-northern hemisphere winter teleconnections ) and involves two steps: first, the dynamic variables of the model (divergence, vorticity, temperature, and log of surface pressure) are nudged towards ERA-Interim reanalysis. During this step the nudging tendencies are recorded every 6 hours. Forty years of nudging tendencies are then composited and smoothed to create an annual climatology of the nudging tendencies. This climatology represents the inherent biases in the model. In the second step, the nudging tendency climatology is added to the model as an additional tendency at each timestep, in order to correct the biases in the model's climatology. For the second step it was found that the biggest reduction in biases occurred when only the divergence and temperature were corrected. The dynamic variables of ECHAM6 are solved using a spectral decomposition of the globe, which allows for nudging and bias correcting on specific wavenumbers. Wavenumbers below n = 21 were nudged and corrected, which means features below about 1000km were not corrected. The bias corrections can also be applied at different height levels, and three experiments were performed with bias corrections in the troposphere only, TropBC, stratosphere only, StratBC, and full atmosphere, FullBC (details in Table 1). The critical difference between the nudged and bias corrected runs is that when the model is nudged it is very tightly constrained towards observations, whereas when the bias corrections are applied the model can still respond realistically to perturbations. Additional details of the bias correction scheme are available in Tyrrell et al., (2020) and Tyrrell and Karpechko, (2021).

El Niño and La Niña experiments
Simplified ENSO SST sensitivity experiments were performed using the bias corrected climatologies as described in Tyrrell and Karpechko, (2021). For the ENSO SST pattern we used a regression of the Niño3.4 time series and HadISST SSTs from . Only the positive regression values between 30°S and 30°N and east of 150°E in the Pacific Ocean were used, and the regression values were multiplied by 1.5 to strengthen the response, corresponding to an El Niño or La Niña forcing magnitude of 1.5K. Climatological SSTs using HadISST data from 1979-2009 were used outside the tropical Pacific, and for the control run (CTRL). The ENSO anomaly was kept constant in time, i.e., the anomaly did not vary seasonally, and each experiment was run for 100 years.
The ERA5 Reanalysis data from 1979-2019 (Hersbach et al., 2020)  that few of the reanalysis ENSO results have statistically significance, and they may be dependent on the temperature threshold for defining ENSO events. As such, the reanalysis is included as a reference, but a more in depth analysis focusing on ERA5 -and other observational data sets -would be required to fully verify and explain those results.
The SSW central date is defined using the Charlton-Polvani criteria (Charlton and Polvani, 2007), defined as the first day when zonal mean zonal wind at 60N and 10hPa (uz60) is easterly (i.e. uz60 < 0 m/s). The reversal has to occur during 1st November -31st March. After an SSW has been detected, winds must return to westerlies for 20 consecutive days before another SSW is detected (as in Butler et al. 2017), and uz60 must return to westerlies for at least 10 consecutive days before 30 April.

Reduced model biases and mean ENSO response
The bias corrections are applied globally at different pressure levels. The reductions in biases have a three-dimensional structure which has relevance to the ENSO teleconnection to the stratospheric vortex and the Northern hemisphere, and this was explored in Tyrrell and Karpechko (2021). As this paper focuses on SSWs, the reduced model biases in the wintertime polar vortex are of particular interest. In Figure 1a we show the seasonal progression of uz60 using the mean daily values for the 100 year model runs, and 41 years of ERA5 data. The standard deviation for ERA5 and CTRL is also shown as shading.
The CTRL run (blue) has a too weak vortex compared to ERA5 from October to January, and this bias is reduced by approximately half in the FullBC and StratBC runs. The bias corrections in TropBC actually increase the bias in the polar vortex in November-December. All model runs effectively capture the polar vortex strength during February and March. As shown in Figure 1 b the interannual variability of the vortex strength is relatively well simulated in CTRL, and the bias corrections do not significantly change the variance. The largest difference between the reanalysis and the model is in January when ERA5 exhibits increased variance, which is not simulated by any of the model runs. The mean difference in daily uz60 between El Niño and neutral years, and La Niña and neutral years is shown in Figure 1 c  Before analyzing SSW responses we assess the ability of the model to capture the timescales of variability. This is explored in Figure 2 Figure   3, which plots the DJF UZ 60N 10hPa against the DJF timescales of variability averaged from 150hPa to 50hPa. Figure 3a shows each ENSO phase for each model separately, so a weaker or stronger vortex strength may be due to the ENSO phase or the bias corrections. A stronger vortex corresponds to longer timescales of variability, and a weaker vortex corresponds to shorter timescales, with a correlation coefficient of r = 0.62. We examine this more closely in Figure 3b  therefore, application of the bias correction technique may have affected the timescales of the variability.

SSW statistics
The statistics of SSWs are detailed in The seasonal evolution of SSWs frequency is shown in Figure 4. To explore the differences in seasonal evolution more clearly, the number of SSWs in each month is divided by the total number of SSWs for each experiment, similarly for ERA5.
This gives the percentage of the annual total SSWs in each month. Compared to ERA5 there is not enough seasonal variation in CTRL, with too many SSWs in November, December, and March, and too few in January and Feb. The seasonal variation is improved slightly in FullBC, although the seasonal cycle is still underestimated. In StratBC and TropBC the SSW seasonal statistics are not improved as much as in FullBC. In particular, TropBC almost has an inverse of the seasonal relationship of SSWs compared to ERA5, with the most SSWs in November. There are no consistent changes to the seasonality of SSWs with El Niños or La Niñas. response (relative to neutral years) before SSW events, with a slightly stronger stratospheric response and weaker tropospheric response after SSW events. Whereas during La Niña years the normalized Zcap response is weaker before, and stronger after SSW events.

SSW downward propagation and surface response
The sea level pressure response to SSWs is well represented in all model experiments and is similar across different climatologies, i.e. bias correction does not greatly affect the surface response. Figure 6 shows the composites of absolute sea level pressure anomalies averaged over 30 days after the central dates of SSWs, and the differences between this quantity in El Niño minus neutral years (middle column), and La Niña minus neutral years (right column). A negative Arctic Oscillation (AO) pattern following SSWs is seen in all runs. The negative AO pattern is stronger in La Niña experiments for the FullBC and StratBC runs, which relates to the stronger stratospheric Zcap response in Figure 4 i and o. The weaker Zcap response in Figure 4 during El Niño years can also be seen in the weaker negative AO response in CTRL and TropBC, but not FullBC or StratBC (Figure 6 e, h, k, n). The 2-meter temperature response was expected to be quite weak in the model runs, since the same climatological SSTs were used for all runs (except SST anomalies prescribed in tropical Pacific in El Niño and La Niña experiments) which dampens the near surface temperature anomalies, however, there was a La Niña -El Niño difference of 0.4K across Eurasia in the monthly averaged 2-meter temperature (not shown).

Heatflux and wave 1/wave 2 response
We now look at the wave forcing that causes SSWs. Figure 7 shows the SSW composite anomalies for the heat flux at 100hPa, 45N-75N. The black lines show all wave numbers, the red lines are wave 1, and the blue lines are wave 2. Solid lines indicate significance at the 90% confidence level. The ratios of wave 1 to wave 2 SSW events are also listed in Table 1, where each event is defined based on the average heat flux for the 10 days preceding an SSW. The CTRL run has too small wave1/wave2 flux ratio of 62/38 compared to the ERA5 ratio of 77/23, i.e. there are too many wave 2 events in CTRL; ERA5 has 0.15 wave 2 SSWs per year, and CTRL has 0.41 wave 2 SSWs per year. This ratio is improved in the bias correction experiments, with the FullBC (76/24) being most similar to ERA5, and a smaller improvement in StratBC (67/33) and TropBC (68/32). As expected, in ERA5 the wave 2 flux is weaker in El Niño years and stronger in La Niña years, hence, La Niña events have a smaller wave 1/wave 2 ratio than El Niño events (e.g. Garfinkel & Hartmann, 2008). This is simulated reasonably well in the experiments, but the relationship is weaker. For all climatologies the El Niño years have a larger wave 1/wave 2 ratio than La Niña years, however, in CTRL the La Niña experiment has a larger wave 1/wave 2 ratio than the neutral experiment. The total heat flux anomaly before an SSW is smallest in El Niño and largest in La Niña in all climatologies. Since the anomalies are calculated with respect to each experiment's own background flux, which is largest in El Niño and smallest in La Niña experiments, the result explains the larger frequency of SSWs in El Niño and small frequency in La Niña. It happens because during El Niños, an SSW can be induced by a weaker wave activity pulse which happen more frequently; however, a larger wave activity pulse that occurs more rarely is required to induce an SSW during La Niñas. Note that in all experiments as well as in ERA5 the larger flux during La Niñas is due to increased wave 2 contribution; however, only in StratBC the wave 2 increase is larger than that of wave 1, which is also seen in ERA 5.

Discussion and Conclusions
The ECHAM6 atmospheric model was run with bias-correcting tendencies added to the temperature and divergence at each timestep. The bias corrections were added at different levels -the stratosphere (StratBC), troposphere (TropBC), or the full atmosphere (FullBC) -to create a range of climates with reduced biases. SST forcing experiments were conducted within these climates by applying a positive or negative ENSO pattern in the tropical Pacific. The seasonal mean response is explored in Tyrrell and Karpechko (2021) and in this paper we have focused on the relationship between the ENSO forcing and SSWs.
For the years without an ENSO forcing the number of SSWs is overestimated in our control run in comparison with ERA5. This is largely due to the polar vortex being too weak in the CTRL run. When the strength of the vortex is improved in the FullBC the SSW statistics also improve. There is a smaller improvement in the StratBC runs, despite the improvement in the strength of the vortex being similar to FullBC. The polar vortex remains weak in the TropBC run, and there is no significant improvement in the number of SSWs. The lack of stratospheric bias correction in TropBC indicates that the stratospheric biases do not originate in the tropospheric circulation biases but are more likely resulting from parameterizations. The seasonal variation of SSWs is too small in the CTRL run compared to ERA5, with too many SSWs in November and March.
This is slightly improved in FullBC, but not in StratBC or TropBC. The duration of an SSW is well simulated, i.e. the number of days that UZ < 0 m/s after an SSW is not significantly different from ERA5 in any of the model runs suggesting that it is controlled by basic processes such as radiative relaxation, well represented in the model. Likewise, the downward propagation and surface response is similar between ERA5 and the control run, and not affected by the bias corrections. The ratio of wave 1 to wave 2 events is too small in CTRL, and this is improved in FullBC, and to a lesser extent in StratBC and TropBC.
The ERA5 reanalysis data suggests that there is an increase in SSWs in both La Niña and El Niño years, when compared to neutral years (Table 1). This is based on a fairly low number of events; depending on the threshold used to define ENSO there are around 10-15 El Niño or La Niña years, with around 0.6 -0.