Minimal impact of model biases on northern hemisphere ENSO teleconnections

Abstract. Correctly capturing the teleconnection between the El Niño–Southern Oscillation (ENSO) and Europe is of importance for seasonal prediction. Here we investigate how systematic model biases may affect this teleconnection. A two– step bias–correction process is applied to an atmospheric general circulation model to reduce errors in the climatology. The bias–corrections are applied to the troposphere and stratosphere independently and jointly to produce a range of climates. ENSO type sensitivity experiments are then performed to reveal the impact of differing climatologies on the ENSO–Europe teleconnections. The bias–corrections do not affect the response of the tropical atmosphere nor the Aleutian Low to the strong ENSO anomalies imposed in our experiments. However, in El Niño experiments the anomalous upward wave flux and the response of the northern hemisphere polar vortex differ between the climatologies. We attribute this to a reduced sensitivity of the upward wave fluxes to the Aleutian Low response in the bias-correction experiments, where the reduced biases result in a deepened Aleutian Low in the base state. Despite the differing responses of the polar vortex, the NAO response is similar between the climatologies, implying that for strong ENSO events the stratospheric pathway may not be the dominant pathway for the ENSO–North Atlantic teleconnection.


Introduction
The El Niño-Southern Oscillation (ENSO) has been shown to influence European climate via tropospheric and stratospheric teleconnections. Although ENSO is a key driver of global variability on seasonal to annual timescales it's effect on Europe is less robust (Brönninman 2007), and exhibits decadal variability (Rodríguez-Fonseca et al., 2016). The large seasonal variability in the mid-latitude Northern hemisphere, and relatively low number of observed ENSO events create some difficulty in measuring the effect in observational data. The ENSO-Europe teleconnection begins with anomalous convection in the tropical Pacific, and during El Niño events this leads to increased divergence in the upper troposphere, creating a Rossby wave source (Hoskins and Karoly, 1981). The anomalous Rossby waves propagate to the Northern Pacific where they strengthen the wintertime Aleutian Low. There are multiple possible connections between the North Pacific anomalies and the North Atlantic (Jiménez-Esteve and Domeisen, 2018), with a tendency for a negative North Atlantic Oscillation during El Niño event. For the stratospheric connection, as reviewed by Domeisen et al., (2019), the deepened Aleutian low can lead to upward propagating waves, particularly of wavenumber 1, which travel into the stratosphere and weaken the wintertime stratospheric polar vortex. For strong vortex weakening events, such as sudden stratospheric warmings, anomalies can propagate down to the troposphere and project onto the Northern Annular Mode, and the North Atlantic Oscillation (NAO) (Butler et al., 2014). The result is also a tendency for a negative NAO during El Niño events.
The opposite is approximately true for La Niña events, but the anomalous response is weaker (e.g. Jiménez-Esteve and . Mezzini et al. (2020) suggest the NAO-like patterns that result from ENSO variability are distinct from the NAO, and result from a Rossby wave train from the tropics to the North Atlantic which does not affect NAO variability.
Both the tropospheric and stratospheric teleconnection pathway can be simulated with climate models of sufficient resolution (Cagnazzo andManzini, 2009, Bell et al. 2009). Models also allow for large numbers of ENSO events to be simulated, which has revealed non-linearities in teleconnections (Frauen, et al. 2014, Jiménez-Esteve and Domeisen, 2019. However, for confidence in modelling results, we need an understanding of the deficiencies of models. A fully coupled model needs to correctly represent both the complex dynamics of the ENSO ocean-atmosphere interactions to generate the convective anomalies that drive the teleconnections, and the mean climatology so the anomalies interact with the base state correctly. For example, the convective response of tropical Pacific is dependent on the mean state of the Walker circulation (Bayr et al. 2018). The location and strength of the convective response is then important in controlling the location of the extratropical pressure response (Bayr et al., 2019), and can lead to non-linearities. In addition to the patterns of climatological SSTs, the state of the tropical (e.g. Quasi-Biennial Oscillation (QBO)QBO phase) and extratropical atmosphere can influence the response of the NAO and polar vortex (Garfinkel et al., 2007).
The technique of flux correcting SSTs has been used to study the effect of model biases on ENSO dynamics (Spencer et al., 2007, Magnello and Huang, 2009, DomengetDommengetDomenget et al., 2014 or seasonal forecasting (Magnusson et al., 2013a, Magnusson et al., 2013b. Empirical corrections are added to the coupling between the ocean and atmosphere to push 2 20 25 30 35 40 45 the model towards the observed climatology. It is possible to use a similar technique on the prognostic atmospheric variables of a model. This bias-correction technique was used by Kharin and Scinocca (2012), and artificially decreased biases were associated with an increase in predictive skill on seasonal timescales. Simpson et al., (2013aSimpson et al., ( , 2013b used the technique to study the impact of jet latitude bias on the Southern Annular Mode (SAM), although they did not see improvements in the persistence of the SAM when they reduced biases in the jet. When Chang et al. (2019) used a similar bias-correction technique they found an improvement in the North Pacific jet and North American rainfall climatology, and a modest improvement in seasonal forecast skill. Tyrrell et al., (2020) investigated how climatological biases effect the relationship between the Eurasian snow extent and the wintertime polar vortex. The strength of the vortex was found to have only a small effect on itsit's response to a tropospheric forcing, however the downward propagation of stratospheric anomalies was sensitive to the tropospheric circulation.
In this study we have used a similar bias correction technique to probe the impact of climatological biases on the communication of ENSO anomalies from the tropical Pacific to the North Atlantic and European sector. The technical details of the model and experiments are described in section 2, the results of the bias corrections and ENSO experiments are described in section 3, and a discussion and conclusions are presented in section 43.

Data and Methods
We use the ECHAM6 spectral atmospheric model (Stevens et al., 2013), run with a horizontal truncation of T63 and 95 vertical levels with a model top at 0.02 hPa. The bias correction technique follows Kharin and Scinocca, 2012, and is similar to that described in Tyrrell et al., 2020 (T20). It is a two-step process; first, the bias correction terms are calculated in a nudged training stage. The model's prognostic variables -divergence, vorticity, temperature, and log of surface pressureare nudged towards ERA-Interim for 30 years and the nudging tendencies are recorded every 6 hours. Then the nudging tendencies are used to create a climatology of correction terms. This climatology is then smoothed in time with a Gaussian filter with a 25 day window, and it represents the inherent bias in the model's prognostic variables. Secondly, the climatology of correction terms is added to the free running model as an additional tendency term at each time step. An important difference between the nudged and bias corrected runs is that the bias correction terms are independent of the current model state, so the model can respond to perturbations, whereas during the nudged run the model is tightly constrained to the reanalysis. The technical details of the bias correction are outlined in T20, with two differences for the current experiments. For the training step the model was nudged to ERA-Interim data from 1979-2009, whereas in T20 only the years 1979-1989 werewas used. This did not impact the results, with the resulting bias correction terms being very similar. The second difference to T20 was that the only bias correction terms used for this study were the divergence and temperature, rather than the divergence, vorticity, temperature and log of surface pressure. During the training stage all the model's prognostic variables were nudge towards ERA Interim, but it was found that using only two of the temperature, divergence and vorticity of the bias correction terms gave the best results for reducing the biases in the winds and 3 55 60 65 70 75 temperature. Through testing differentdifference combinations we found that bias correcting only the divergence and temperature lead to the biggest decreases in the climatological biases of the control run.
The bias corrections were applied on model levels between approximately 850 hPa and 2.6 hPa, and three types of bias correction runs were performed; the troposphere and stratosphere were corrected in FullBC, the stratosphere only in StratBC, and the troposphere only in TropBC (see Table 1 for details). Then ENSO SST forcing experiments were conducted with each of these bias corrected climatologies. To generate the SST pattern we used a regression of the Niño3.4 timeseries and HadISST SSTs from 1979-2009. Only positive regression values between 30°S and 30°N and east of 150°E in the Pacific Ocean were used for the pattern, and the regression values were multiplied by 1.5 to strengthen the response, which corresponds to an El Niño or La Niña forcing magnitude of 1.5K. Climatological SSTs, using HadISST data from 1979-2009, were used for the CTRL run. The ENSO The pattern was then added to (El Niño), or subtracted from (La Niña) the SST climatology in the tropical Pacific, with climatological SSTs used everywhere else. The ENSO and the pattern was kept constant in time, i.e., the anomaly did not vary seasonally. Each experiment was run for 100 years. It should be noted that using a regression to generate ENSO patterns results in symmetric El Niño/La Niña magnitudes, whereas from observations El Niño anomalies tend to be larger than La Niña. This simplification, along with a constant ENSO forcing and climatological SSTs outside the Pacific Ocean basin, has the advantage of reducing the number of controlling parameters when analysing the results of the bias-corrections, which was the main aim of the research. However, the simplifications should be considered when comparing the results with observations, particularyparticularly in relation to the intra-seasonal and early winter ENSO-Atlantic connection (e.g. King et al., 2018) that may be driven by SSTs and rainfall away from the Pacific (Ayarzagüena et al., 2018, Abid et al., 2021. To calculate the root-mean-mean square error and biases between the model and reanalysis (Fig. 1) we use ERA Interim 1979-2009, since that data was used for our bias correction scheme. However, when analysing the response to El Niño and La Niña runs, the newer ERA5 data is used (Hersbach et al., 2020), since it is a longer time series. To divide the data the NINO3.4 index was used for DJF (https://origin.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ONI_v5.php). El Niño years defined as NINO3.4 above 0.9 K (8 years), La Niña years NINO3.4 below -0.9 K (8 years) and the years between -0.5 K and 0.5 K were defined as neutral years (13 years). The slightly stricter threshold of +/-0.9 K was used to define the El Niño/La Niña years to include only stronger events.

Reduced model biases
The climatological biases of the model's wind and temperature vary with latitude and height. In Fig. 1  that the control run (green dashed line) performs very well in many regions, particularly the tropics, with UZ RMSE values below 2 m s -1 . The errors are small in the lower troposphere, and tend to increase with height. In Fig. 1 panels d-e we show the percentage change in the UZ RMSE, between the CTRL run and the three bias-corrected runs. These figures demonstrate the effectiveness of the different height-dependent bias correction experiments. For example in Fig. 1e, in the mid-latitudes the corrections in the TropBC experiment reduce the UZ RMSE by around 40% in the troposphere. Although the corrections stop at around 100 hPa their effect continues into the stratosphere, but weakens. As the tropospheric corrections weaken, the corrections in StratBC lead to around a 25% decrease in UZ RMSE in the upper stratosphere. In the mid-latitudes FullBC the UZ RMSE is reduced throughout the atmosphere with reductions of over 50% in the upper troposphere-lower stratosphere region. The same is somewhatbroadly true for the tropics and polar regions, although with some exceptions such as the tropical stratosphere, where errors are increased in the FullBC and TropBC, which may be related to the QBO. In the polar atmosphere, the improvements in the FullBC are mostly seen between 100-200 hPa and in the upper stratosphere. The TropBC also leads to increased errors in the polar stratosphere, hence, tropospheric bias-corrections may degrade the midstratosphere. Additionally, in the StratBC experiment there is no significant improvement below 20hPa (midlat) & 50hPa (polar), even though the bias corrections are applied from 100hPa.
The SLP bias is shown in Fig. 1 g-j. Here we see similarities between the CTRL and StratBC, with a large bias in the Aleutian Low, and the FullBC and TropBC, where that Aleutian low bias is reduced. The reduced bias in surface pressure, and structure of the pressure field is a barotropic feature, as shown in the geopotential height at 300hPa in Supplementary

Teleconnection response to ENSO
We trace the path of ENSO anomalies from the tropical Pacific to the northern hemisphere polar regions and the North Atlantic. Following from Rossby wave that leads to a deepening (El Niño) or weakening (La Niña) of the Aleutian low. We measure this using an Aleutian Low Index (ALI), defined as the SLP between 35°-60°N, 180°-240°E, indicated by the green box in Fig. 1 g. The response of the ALI is proportional to the tropical divergence, with the anomalous negative El Niño response being greater than the positive La Niña response. Again, there are no clear differences in the anomalous response between the different climatologies. However, in contrast to the tropical regions, the FullBC and TropBC runs have reduced Aleutian Low biases compared to the CTRL and StratBC runs (Fig. 1 g-j), implying that the response of the Aleutian Low to an ENSO signal is not dependant on model biases. The modelled ALI anomalies are very similar to ERA5. The next step in the teleconnection is the response of heat flux at 100 hPa, 45°-75°N (HF). The anomalous HF for both El Niño and La Niña shows a differences between the climatologies. For an El Niño forcing the CTRL and StratBC runs show an increase in HF with significant values (indicated by black dots) for the DJF and JFM three-month means, whereas the FullBC and TropBC anomalies are about half as strong and have no significant values. The results are almost opposite for the La Niña forcing, except the CTRL and TropBC anomalous HF was around half the value of the StratBC and FullBC runs, and no there were no significant HF values for any of the La Niña experiments. The lack of significance could be partly due to the weaker Rossby wave source associated with a La Niña, and the high variability of the HF . All El Niño model runs underestimate HF relative to ERA5, however, the La Niña HF anomalies are actually positive, which is not the canonical response,. It may be due to the low number of events in the observational record.
We measure the response of the stratospheric polar vortex with the zonal mean zonal wind at 60N and 10 hPa (UZ60). UZ60 is well predicted by the HF values. Namely, for anthe El Niño forcing the CTRL and StratBC experiments show a significant weakening, whereas the response of FullBC and TropBC only show a slight weakening of the vortex (Fig. 2d). . Likewise with the La Niña forcing the FullBC and StratBC show a greater strengthening than the CTRL and TropBC. These results are also true for the lower stratosphere as measure with the zonal mean zonal wind at 60N and 100hPa (Fig. 2e). We also show the seasonal mean of the full zonal mean wind response in Supplementary figure 4. As with the ALI response, the response of the polar vortex does not appear to be affected by biases in the strength of the vortex, and is instead fully explained by the heat flux response, , which is discussed further in the next section. Comparing the late-winter response in ERA5 to the models, the CTRL and StratBC anomalies are similar to ERA5 at 10hPa, but the FullBC and TropBC anomalies are similar at 100hPa.
The differences in the stratospheric response are not mirrored in the response of the NAO, despite the well-known connection between the vortex and the NAO and the importance of a realistic stratosphere for the ENSO-North Atlantic teleconnection (for example, as shown by Cagnazzo and Manzini, 2009 with a similar model to our study). There is a weaker FullBC response in early winter UZ60 to La Nina, and correspondingly weaker NAO response in early winter. However, for the other runs the strength of the polar vortex anomaly has no clear connection withimpact on the response of the NAO. This is evident when comparing the El Niño response of the CTRL and StratBC, to FullBC and TropBC, where the latter two have a weak UZ60 response but a strong NAO response. Hence, there is weak correspondence, but overall the stratosphere plays only a minor role in the NAO response. To determine the reason for the weak connection between the stratospheric anomalies and the NAO, we investigate scatter plots of uz 60N 10hPa and the NAO index, as shown in Figure 3. For this figure we chose to show the variability within each experiment (i.e. 100 years of DJF means for El Niño, Neutral and La Niña) to better understand the time-mean sensitivity of ENSO teleconnection as well as the sensitivity of the stratosphere-troposphere couplings to different climatologies. The figure shows that there is the expected relationship between UZ60 and the NAO within each experiment -that is, a weaker vortex is associated with a more negative NAO. There is an indication that this relationship is also apparent between the El Niño, and Neutral/La Niña years, with a much smaller signal between the Neutral and La Nina experiments. However, the large variability within each experiment means that the forced difference is relatively small. Although causality is not explained, the figure demonstrates that the stratosphere-troposphere coupling does not play an important role in the ENSO-EU teleconnection in our experiments. The effect is relatively small compared to variability, and hence, the different polar vortex responses between the bias correction experiments do not translate neatly into different magnitudes of the NAO response. One could also hypothesize that a weakened polar vortex response to El Niño in FullBC and TropBC can cause a NAO response of similar magnitude to that in CTRL and StratBC because of an increased sensitivity of NAO to the stratospheric variability. However, the similarity of the UZ60-NAO correlation coefficients between the experiments does not support this hypothesis. Instead, it reveals that the sensitivity of NAO to the stratospheric variability remained unchanged. Overall, for our experiments the stratosphere plays only a minor role in the NAO response.

Difference in polar vortex El Niño response
To investigate the cause of the different HF response between the experiments it is necessary to consider the effect of the bias corrections. To do that we must consider the absolute values and anomalous response together. In Figure 4Fig. 3 we show the DJF ALI, HF and UZ60, for La Niña, Neutral and El Niño conditions. ERA5 is included to demonstrate the biases. other words, in the model the HF is less sensitive to the deepening of the AL in the climatologies where the AL is already deeper due to the reduced bias. The same is not true in ERA5, although we caution against using this to dismiss the model results, due to the low number of events (around 8-9 per ENSO phase).
As shown in Fig. 2d, the response of the polar vortex is controlled by the HF response in the different climatologies. Figure   4c3c reiterates this, and also demonstrates that the biases in the polar vortex do not impact its response to anomalous wave forcing. In neutral conditions the UZ60 biases in the StratBC and FullBC are around 5 m s -1 less than the CTRL and TropBC biases. However, for El Niño conditions the FullBC (less bias, stronger vortex) and TropBC (more biased, weaker vortex) have a weak response, and the StratBC (less bias, stronger vortex) and CTRL (more biased, weaker vortex) have a strong response.
We have shown that the stratospheric response to an El Niño forcing is partially dependant on model biases, and seems to be related to the sensitivity of the HF to the AL. In Fig. 54 we use regressions of HF onto SLP to show how the effectiveness of wave forcing by the Aleutian low changes between neutral and El Niño conditions. Similar to Figure 3, we again consider the variability within each bias-correction and ENSO experiment, to understand the time-mean response. Figure 5 Figure 4 a-d shows the regression of monthly HF onto monthly SLP for the extended winter months (November-March) in neutral ENSO conditions. The areas of SLP that are most strongly associated with HF are the Aleutian low region and Siberia, with weaker connections over Greenland and North America. In neutral years these features are very similar between the control and the bias corrected runs, which means the deeper Aleutian low has not affected it's association with wave driving. Figure   54 e-h is the same regression in years with an El Niño forcing. Rather than testing the difference between neutral and El Niño years, this is now a measure of variability during El Niño years. The connection between SLP in the Aleutian low and HF is lower in the CTRL and StratBC El Niño runs, but is now absent in the FullBC run and very weak in the TropBC runs.
Therefore, for an equally large AL anomaly, there would be less wave forcing in the FullBC and TropBC. There appears to be a threshold for the depth of the Aleutian Low, below which any additional anomalies do not result in additional wave forcing. During La Niña years the regression values over the AL region are slightly stronger in the FullBC and TropBC, but this did not lead to differences in the response of the HF (i.e.

Discussion and Conclusions
By applying a bias-correction technique to the divergence and temperature tendencies of an atmospheric model we have reduced biases in the tropospheric and stratospheric mean states troposphere and stratosphere to create various climatologies.
With the different climatologies we have performed idealized ENSO forcing experiments to test the role of biases in ENSO teleconnections. There were only small reductions in the bias in the tropics, and there was no difference in the convective response to ENSO between the experiments. Likewise, the anomalous response of the Aleutian low to El Niño and La Niña forcing was similar between the experiments, despite the reduced biases in the Northern hemisphere troposphere. Reduced biases in the Aleutian low SLP did, however, lead to differences in the anomalous upward wave flux associated with a deepened low due to an El Niño forcing. A stronger polar vortex in the experiments with stratospheric bias correction did not 8 affect the anomalous response of the vortex. Hence, we find that reducing certain climatological biases in the surface pressure and wind speed does do not significantly affect the response of the Aleutian low to Rossby wave forcing . The response of , or the polar vortex was also shown to be dependent on the to upward planetary wave forcing, and not affected by local biases in the strength of the vortex. However, the model's ability to generate a planetary wave flux may be dependent on biases in surface pressure. Because the NAO response is not sensitive to the stratospheric representation or response, we conclude that in our experiments with SST forcing corresponding to large ENSO events it is dominated by tropospheric teleconnections. This result appears consistent with that by Bell et al. (2009) who also found that for strong ENSO events the tropospheric teleconnections dominate.
Although one motivation behind artificially bias-correcting the model was to investigate how the response to various forcings might improve if the biases were reduced, it should be noted that the ECHAM atmospheric model has already been shown to have a realistic response to an ENSO forcing (Manzini et al. 2006, Cagnazzo andManzini, 2009). The ENSO teleconnection, and the Siberian snow-polar vortex connection investigated in Tyrrell et al. (2020), are both relevant to seasonal forecasting, but the bias correction technique is unlikely to be used for operational forecasting. Hence, for these experiments the bias corrections are a tool that is used not to improve the response relative to observations, but rather to explore the sensitivity of the response to climatological biases.
It was interesting to find that response of the Aleutian low and the stratospheric polar vortex was not affected by the climatological biases that we reducedclimatological biases. These two features are important in the ENSO-to-Europe teleconnection and had large reductions in bias due to the corrections. These features are also both forced by planetary waves; horizontally propagating waves from anomalous convection in the tropical Pacific, or vertically propagating waves from the northern hemisphere troposphere to the stratosphere. Hence, model biases in the depth of the Aleutian low, or the magnitude of the polar vortex winds, do not appear to strongly affect their response to wave forcing.
The control and bias corrected runs differed in the magnitude of wave forcing caused by the deepening Aleutian low due to the El Niño forcing. We theorize that this was due to the relationship between the depth of the Aleutian low and itsit's effectiveness at wave forcing. The two experiments with bias corrections in the troposphere both had a deeper Aleutian low, which was closer observations. Although the magnitude of ALI anomaly was the same, the runs with a deeper Aleutian low had reduced wave forcing for El Niño conditions. Regressions between SLP and HF showed that lower Aleutian low SLP was associated with a decreasing correlation between Aleutian low SLP and HF. Therefore, we speculate that the reduced wave forcing when the troposphere was bias corrected in the FullBC and TropBC, was due to the lower climatological SLP values in the Aleutian low area. It appears that at some threshold of low values of SLP, further anomalies in the Aleutian low do not result in anomalous upward waves. The opposite was not true for the La Niña conditions, since there appears to be no maximum values where the relationship between HF and Aleutian low SLP changes. Additionally, the non-linearity in the El Niño/La Niña atmospheric response (e.g. Frauen et al., 2014) means that the La Niña response is smaller, making it more difficult to distinguish robust differences between the climatologies. By artificially bias correcting an atmospheric model, we have shown that some aspects of ENSO teleconnections are very robust to the specific model biases we correctedmodel 9 245 250 255 260 265 270 biases, while more subtle interactions of anomalies with the basic state can impact the overall response. A deeper understanding of the influence of inherent model biases on teleconnections can guide future model development, and also aid in the physical understanding of these important teleconnections.

Data availability
The climatological means of all model experiments, for the variables used in this paper are available at: https://figshare.com/articles/dataset/ECHAM6_Bias_Correction_ENSO/13311623. The full timeseries is available upon request to Nicholas Tyrrell. ERA-Interim and ERA5 data Copernicus Climate Change Service Climate Data Store (CDS, https://climate.copernicus.eu/climate-reanalysis). The ECHAM6 model is available to the scientific community under a version of the MPI-M license http://www.mpimet.mpg.de/en/science/models/license/. The HadISST SST and sea ice data are available from the U.K. Met Office https://www.metoffice.gov.uk/hadobs/hadisst/.

Author contributions
NLT conducted the model runs, analysis, and wrote the first draft. AYK contributed to the interpretation of the results, and improving the final manuscript.

Competing interests
The authors declare that they have no conflict of interest.