Tropical Atlantic rainfall drives bias in extratropical seasonal forecasts

We investigate the impact of seasonal forecast biases in the Tropical Atlantic on the North Atlantic. The analysis uses a novel ensemble‐based method to estimate the impact of tropical rainfall bias on forecasts of the Extratropical North Atlantic. The inter‐ensemble spread of the forecast model is used to estimate the impact of the bias in Tropical Atlantic rainfall on the North Atlantic by selecting model members that happen to produce forecast anomalies that most closely resemble the tropical rainfall bias and using these as a proxy for the model error. The Tropical Atlantic rainfall bias impacts Rossby wave sources over the Subtropical Atlantic and there is a clear Rossby wave pattern originating from this area which is comparable to the mean bias in hindcasts. We argue that Tropical Atlantic rainfall errors explain a significant amount of the bias in seasonal forecasts over the Extratropical North Atlantic.


| INTRODUCTION
The North Atlantic Oscillation (NAO) is a key source of predictability for European and North American seasonal forecasts (Athanasiadis et al., 2017;Baker et al., 2018;Scaife et al., 2014) and is the single largest factor governing inter-annual rainfall and temperature.Much of the forecast skill for the NAO emanates from the Tropical West Pacific and Tropical Atlantic via Rossby waves (Scaife et al., 2017).As a result, the tropics is a key region for seasonal forecasting for the extratropics (Scaife et al., 2018).
Previous studies have also shown biases in climate models in the Tropical Atlantic region.These focus on the lack of development of the cold tongue in the Boreal Spring and Summer season (Ding et al., 2015;Grodsky et al., 2012;Harlaß et al., 2015;Richter & Xie, 2008) and the development of a double ITCZ (Lin, 2007;Tian, 2015& Tian & Dong, 2020).Research into the biases in seasonal forecast systems is more limited, but Hermanson et al. (2018) show that the bias in the GloSea seasonal forecast system in the Tropical Atlantic region sea surface temperature in Boreal Spring/Summer is of opposite sign to the bias that eventually develops in long simulations with most climate models.
Furthermore, despite skillful winter NAO forecasts, there is a systematically opposite teleconnection between Equatorial Atlantic rainfall variability and forecast winter NAO compared to the relationship seen in observations (Scaife et al., 2017).In addition, correcting mean biases in the Tropical Atlantic can also increase seasonal rainfall prediction skills (Ding et al., 2015).These studies, along with evidence of increasing variability in future Tropical Atlantic rainfall (Liu et al., 2022), motivate further investigation of the role of the Tropical Atlantic in seasonal forecasts.
We investigate the importance of the Equatorial Atlantic rainfall bias for forecasting at seasonal timescales.In this study, we use the internal variability present in the model as a proxy to investigate the impact of the bias by subsetting ensemble members to infer the impact of the tropical rainfall bias.

| DATA
We use seasonal hindcast data from the GloSea system (Maclachlan et al., 2015).GloSea is initialised using a lagged ensemble method, with members starting on 4 dates (1, 9, 16, and 25) each month.For each start date, we initialize 7 members making a total of 28 members for the month.For this study, we use boreal winter hindcasts with start dates on October 25, November 1, and November 9. Boreal winter start dates, which are the dates used to calculate the winter forecast, from the lagged ensemble (Maclachlan et al., 2015), are taken for all available hindcast years, 1993-2016.Seasonal means (December-February) are used throughout.
Seasonal forecast system hindcast data is taken from Copernicus Climate Change Service (Buontempo et al., 2022) for CMCC, DWD, Meteo France & ECMWF.

| TROPICAL ATLANTIC RAINFALL BIAS
In this study, we focus on winter (DJF) as the season for which there is currently more skill in seasonal forecasting in the northern extratropics (see above references).This results at least in part from it being the peak season of ENSO which links to the extratropics (e.g., Hu et al., 2021) and the dynamically active stratospheric teleconnections in this season (e.g., Scaife et al., 2022).
We first calculate the mean bias in the GloSea5 hindcast members by comparing the hindcast mean, averaged over all years  and all members, to the GPCP data set mean.We plot the bias averaged over longitude across the Atlantic basin (Figure 1).A clear dry bias centered on the equator, a wet bias to the North of the equator, and smaller magnitude wet bias to the south of the equator are found relative to observed rainfall.Given the large number of ensemble members, both the dry slot and the wet areas to the north and south of the equator are statistically significant at the two-standard error (95%) level.Figure 2a shows the two wet areas very clearly with the dry slot along the equator.This so-called "double ITCZ pattern" is common in climate models (e.g., Lin, 2007) and clearly appears in these seasonal forecasts despite the initialization with realistic analyses of initial atmospheric and oceanic conditions.
The mean bias in the forecast Rossby wave vorticity source (RWS, Sardeshmukh & Hoskins, 1988) is shown in Figure 2b.This shows a dipolar bias a little further north than the bias in rainfall.There is a positive bias in the RWS near Cuba and the Caribbean, and an area of negative bias stretching eastwards from the northern part of South America.This is likely due to the bias in trade winds from the bias in convection over the equator associated with the rainfall bias.It also occurs in a region that has been highlighted as a key source for tropical teleconnections to the Extratropical Atlantic in other studies (e.g., Maidens et al., 2021;Manola et al., 2013;Scaife et al., 2017).
The 200 hPa stream function bias (Figure 2c) shows clear wave trains, roughly symmetric about the equator, apparently emanating from the Tropical Atlantic region toward the North and South Atlantic.The great symmetry between the two hemispheres is consistent with our interpretation of a tropical source of this pattern and its propagation from the tropics to the extratropics (Hoskins & Karoly, 1981).Mean sea level pressure anomalies (Figure 2d) show a corresponding pattern with strong centers in the North Atlantic.We use a novel method to infer the impact of the bias in the Tropical Atlantic that exploits the internal variability of the ensemble hindcasts.Figure 2 demonstrates the full bias in the model enabling us to examine the full extent of bias present in GloSea.In order to investigate the impact of the Tropical Atlantic specifically, we first regress out the effects of ENSO to avoid aliasing of this highly predictable and dominant signal which is present in all ensemble members and projects onto the Tropical Atlantic (Nicholson, 1997).To regress out ENSO from each variable field we first calculate the regression coefficients between the ENSO 3.4 values and the given variable.We then multiply these coefficients by the ENSO values and subtract the result from the original fields.After regressing ENSO out, we then create a rainfall index using 3 regions of the Tropical Atlantic (Figure 2a) that correspond to the extremes of the mean rainfall bias.Our central box is positioned over the equator collocated with the dry bias (À15 to 45W, À3 to 3N), the northerly and southerly boxes are positioned equidistant from the equator in opposite hemispheres where there are wet biases (northerly box 55 to 25W, 5 to 10N; southerly box 25 to 5W, 5 to 10S).Boxes are staggered in longitude to take account of the shape of the South American continent and ensure we only use ocean points for our analysis.We calculate an index by subtracting the average of the mean rainfall in the outer two boxes from the mean value of the central box.Taking each ensemble member for each year and each start date gives a total of 504 values.We form two sub-ensembles, the first using the bottom 10% of members (50 members with negative indices).We find the other sub-ensemble, by taking member numbers 18-68 rather than the actual top 10% which would be member numbers 1-50.This is to account for the skewness in the data, and taking this approach means the mean of the top 10% sub-ensemble we use is the same as the mean of the bottom 10% subensemble mean multiplied by À1.It should be noted that using the actual top 10% with skewness included does not change the findings of the study.We subtract the average of the positive members away from the average of the negative members.The difference between these two ensembles is then used to infer the impact of the mean tropical rainfall bias in the seasonal hindcast.The ensemble member difference according to this simple index and the highest/lowest 10% threshold, captures the northerly wet bias and the dry bias on the equator (Figure 3a).This shows that there is sufficient internal variability in the system to use as a proxy for the mean model bias.

| EXTRATROPICAL IMPACTS
To investigate the impact of tropical rainfall bias on the extratropics, we show other global variables for the same differences of ensemble subsets.The ratio of the tropical rainfall bias in hindcasts to the tropical rainfall difference in the ensemble subsetting is 0.9, we, therefore, scale by 0.9 to make the ensemble subsetting equivalent to the model bias.All fields in Figure 3 again have ENSO regressed out prior to analysis.
Figure 3b again shows a negative RWS just to the north of the equator.Comparing this to the original RWS bias plot (Figure 2b) we can see the difference in tropical rainfall rate in Figure 3b is of comparable size to account for a large portion of the mean hindcast bias in RWS shown in Figure 2b.
Figure 3c shows the inferred impact of the bias in Tropical Atlantic rainfall rate on the wider stream function field.From this we can again see evidence of a Rossby wave train emanating from the Tropical Atlantic close to where the Rossby wave source features were seen in Figure 3b and as might be expected given earlier identifications of this region as an important wave source (see references above).There is some symmetry about the equator but in this case, the pattern is stronger in the Northern hemisphere than the Southern hemisphere.This is perhaps due to our index representing the Equatorial and Northern hemisphere rainfall biases more effectively than those in the Southern hemisphere.The pattern we see in the Northern hemisphere has a low zonal wave number, consistent with its path almost directly northwards with only a small degree of refraction eastwards.We conclude that there is evidence of the tropical rainfall variability driving wavelike errors in the extratropics.Mean sea level pressure (Figure 3d) also shows a similar pattern to that of the model bias in Figure 2d.
In summary, this analysis shows that the ensemble member variability in tropical rainfall can be used to infer the impact of ensemble mean errors and that the patterns of circulation between ensemble members with different Tropical Atlantic rainfall can be used to understand the origin of a significant component of extratropical seasonal forecast bias which therefore originates in the Tropical Atlantic.

| OTHER SEASONAL FORECAST SYSTEMS
To ensure our results are not specific to a single forecasting system, which is key to solving wider model error issues (Saurral et al., 2021), we expand it to other seasonal forecast systems from ECMWF, DWD, CMCC, and Meteo France.We found a similar tropical rainfall rate bias present in all four seasonal forecast systems (Figure 4) and these closely resembled the bias in GloSea that was shown in Figure 2a.All centers show a wet bias to the north of the equator and a dry slot on the equator.The extent to which they show a wet bias in the Southern hemisphere is more variable.
The geopotential height fields reveal a clear impact on the North Atlantic as a result of the bias in Tropical Atlantic rainfall.All models show a negative bias over the North Atlantic.We can also see a wavelike bias pattern over the North Atlantic in the different models.The extent and pattern of the bias varies between the models with CMCC showing a more tripolar pattern than other models, and Meteo France exhibiting a stronger bias.Other models therefore show similar Atlantic mean biases that are likely driven, at least in part, by tropical rainfall biases.

| CONCLUSION
We have shown that there is a significant rainfall bias present in seasonal forecasts in the Tropical Atlantic during the boreal winter season.We also found that there were biases present in the Rossby wave source field over the Northern Tropical Atlantic which relate to the dry bias we saw over the equator.The stream function and pressure at mean sea level over the wider Atlantic region also contained related biases.
We used the internal variability in the model as a proxy to relate these tropical and extratropical mean biases.We have shown that a substantial portion of the biases in the circulation over the North Atlantic can be attributed to the bias in the Tropical Atlantic rainfall.We find mean biases in the stream function field that form a wave train emanating from the Tropical Atlantic region, consistent with mean errors in the Rossby wave source.We also showed that this bias was not limited to the Glo-Sea system and found that it also affects other seasonal forecast systems.
Finally, we note that mean biases are linearly removed in most seasonal predictions by subtracting the hindcast mean and so biases do not therefore project directly onto the skill of anomaly forecasts.Similarly, biases are not always directly related to prediction skill (Scaife et al., 2019).However, there is at least some evidence that the mean state errors in the Tropical Atlantic can have a significant impact on seasonal prediction skill (e.g., Ding et al., 2020) and so the skill of seasonal forecasts for the Atlantic sector would likely benefit from more accurate model simulation of tropical rainfall over the Atlantic.

F
I G U R E 1 Forecast rainfall bias in the Tropical Atlantic.The zonal average of the rainfall rate bias is plotted for winter (DJF) GloSea5 hindcasts compared to GPCP rainfall data for the same Atlantic region: 15W-45W.The bias is calculated over 1993-2016.AS A PROXY FOR MODEL BIAS

F
I G U R E 2 Biases in seasonal hindcasts.(a) Rainfall Rate (mmd-1), with surface winds shown on the zoomed-in section (b) Rossby wave source (S-1), (c) Stream Function (m 2 =s) and (d) pressure at mean sea level (hPa).Each plot is stippled where the bias is larger than 2 standard errors in the observations.

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I G U R E 3 Impact of tropical rainfall bias.(a) Rainfall rate, (b) Rossby wave source, (c) stream function, and (d) pressure at mean sea level.Differences between the highest and lowest 10% of ensemble member tropical rainfall cases are shown.ENSO has been regressed out.Stippling shows where the bottom and top datasets are significantly different using a t-test.

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I G U R E 4 Rainfall and geopotential height bias at 200 hPa from multiple seasonal forecast systems.(a) ECMWF, (b) Meteo France, (c) DWD, and (d) CMCC.The zonal mean has been removed.Note the similar tropical Atlantic rainfall bias in all cases.