The Importance of Accounting for the North Atlantic Oscillation When Applying Observational Constraints to European Climate Projections

Variability in the North Atlantic Oscillation (NAO) has contributed to the recent multidecadal trends observed in European climate, especially to trends in winter precipitation over Northern Europe. However, the current generation of coupled climate models struggle to reproduce the NAO's contribution to multidecadal trends, which has important implications for deriving constraints based on the comparison of observed and modeled trends. An observational constraint based on attribution results, both with and without the contribution of variability associated with the NAO, is applied to projections of Northern European precipitation and temperature, and observed NAO variability is shown to lead to a constraint that overestimates future forced changes. Only after removing the NAO variability is the observed climate change consistent with model simulations, and a tighter, unbiased observational constraint based on the forced signal (without the NAO) can be applied to future projections.

• Variability in the North Atlantic Oscillation (NAO) has contributed to the recent multidecadal trends observed in European climate • The suite of current comprehensive global models (CMIP6) struggle to reproduce the NAO's contribution to multidecadal trends • Removing the NAO from both observations and models provides a tighter, unbiased constraint, which can then be applied to model projections

Supporting Information:
Supporting Information may be found in the online version of this article.
By estimating the forced component of change from observations, a constraint can be derived and applied to future projections based on the assumption that any relationship between observations and models can be extrapolated into the future. For example, if past forced changes simulated by climate models underestimate the observed changes over the same time period, future projected changes by the same climate models may also underestimate the true forced signal in the future. One such approach, hereafter the Allen-Stott-Kettleborough "ASK" method (Allen et al., 2000;Allen & Stott, 2003;Shiogama et al., 2016;Stott & Kettleborough, 2002) has been used for constraining global projections, including for the Intergovernmental Panel on Climate Change (Knutti et al., 2008), and was recently employed in a multi-method study of constrained European climate projections (Brunner et al., 2020). The strength of the ASK method is that it uses well-understood patterns of response to external forcings to determine from observations the magnitude of the response. ASK allows a magnitude of response outside the model range, and also lends itself to estimating the transient and equilibrium climate sensitivity (Frame et al., 2005;A. Schurer et al., 2018;Tokarska et al., 2020). However, regional climate change is strongly influenced by internal variability. ASK accounts for this, but cannot do so correctly if the climate model decadal circulation variability is smaller than observed, as appears to be the case for the NAO (e.g., O'Reilly et al., 2021;A. P. Schurer et al., 2023). This study demonstrates that NAO variability can strongly influence observational constraints on European climate, particularly in winter. In order to evaluate its effect, we remove the influence of the NAO from the time series of regional mean precipitation and temperature change by linear regression and then apply the ASK method. Here we use two different sets of fingerprints and samples of variability, one with and one without the NAO. Focusing on winter precipitation and temperature over Northern Europe, we show the NAO has a marked influence on the magnitude (and uncertainty estimate) of the derived observational constraints, with important ramifications for their application to future climate projections. Similar concerns may arise for observational constraints in other regions influenced by the NAO, such as Mediterranean temperature and precipitation (not shown).

Observations and Climate Model Simulations
Gridded observations of European precipitation and surface air temperature over land were retrieved from the E-OBS v19.0e data set (Cornes et al., 2018;Haylock et al., 2008), with monthly values computed from the daily data . The observed NAO was computed from gridded sea level pressure (SLP) (see Section 2.2) retrieved from HADSLP2 (Allan & Ansell, 2006). The study analyzes CMIP6 global climate model simulations run with historical forcings (1850-2014). The common period from 1950 to 2014 was used for analysis of monthly precipitation (a total of 163 ensemble members from 41 CMIP6 models) and surface air temperature (178 ensemble members, 49 models), see Table S1 of Supporting Information S1. To facilitate comparison with observations, the monthly precipitation and temperature fields (for each of the model ensemble members) were spatially regridded to a regular 2.5° × 2.5° latitude-longitude grid, and masked to retain only the gridboxes over land, matching the E-OBS data availability. In order to explore the impact on future projections, historical simulations were extended with CMIP6 Scenario-MIP Shared Socioeconomic Pathway (SSP; Gidden et al., 2019) simulations (2015-2100), thus only the subset of model ensemble members common to both the historical and scenario experiments have been used for the observational constraint (see Table S1 in Supporting Information S1).

Removing the NAO Variability
For this study, we characterize the NAO variability by the first Empirical Orthogonal Function (EOF) of SLP over the North Atlantic sector (20°-90°N; 90°W-40°E). The EOF and first principal component time series is computed for each month's  anomalous SLP, separately, in order to construct a monthly time series of the NAO. The spatio-temporal European precipitation is then regressed against the NAO time series, separately for each month, in order to compute the component of observed precipitation associated with the NAO, accounting for seasonal variations in the response. This is repeated for the observed temperature field, identifying the component of European temperature anomalies associated with NAO variability. The individual NAO time series for each of the CMIP6 models is computed from its own SLP field, followed by a regression of each model ensemble member's European temperature and precipitation fields on its own NAO time series (1950-2014, month by month). The resulting multi-model mean EOF and regression patterns are similar to the corresponding observed patterns (Figures S1 and S2 in Supporting Information S1; see also Deser et al., 2017;Iles & Hegerl, 2017). The residual spatio-temporal fields provide an estimate of the monthly European precipitation and temperature anomalies after the component linearly related to the NAO variability has been removed. We acknowledge that this approach is limited to removing the linear response and will miss any nonlinear aspects of the NAO's influence on European climate. However, Iles and Hegerl (2017) found that aggregated NAO temperature trend responses in models (allowing for nonlinearity) were similar to estimates using a linear assumption; and results from Deser et al. (2017) suggests this is also broadly the case for precipitation.

Allen-Stott-Kettleborough (ASK) Method
The ASK method (Allen & Stott, 2003;Allen et al., 2000;Stott & Kettleborough, 2002) assumes that the true observed climate response (y obs ) to historical forcing(s) is a linear combination of one or more (n) individual forcing fingerprints (X j ). The fingerprints are scaled to best fit the observed change by their respective scaling factors (β j ), accounting for noise/uncertainty in both the observations (ɛ obs ), and in the modeled response to each of the forcings (ɛ j ): When applied to global-scale temperature, ASK estimates the contribution from the greenhouse gas fingerprint against that of other forcings, and then uses this to constrain future warming. However, the climate change signal for winter precipitation and temperature in a small region is expected to have a much lower signal-to-noise ratio. We therefore use fingerprints of the total forcing response. This approach is supported by the finding that anthropogenic forcing is dominant against natural forcing (see Gillett et al., 2021), and that anthropogenic forcing provides reasonable future constraints (Tokarska et al., 2020).
Thus, we employ a one-signal all-forcing application of Equation 1, y obs = β All X Hist + ɛ, constructing the model fingerprint (X Hist ) by taking an unweighted average of the individual historically forced model-ensemble means from the CMIP6 historical simulations, spatially averaged over the region of interest. This results in a time-dependent fingerprint of the regional forced change. The scaling factor is estimated (̂A ll ) by computing a total least squares (TLS) regression of the observed time series on the model fingerprint. We assume that the internal variability of the multi-model mean is reduced by a factor of √ ∑ =1 2 due to ensemble averaging, where m k is the number of ensemble members belonging to each of the N models. Random samples from the pre-industrial control simulations are added to both the noise-reduced model fingerprints and observations, recomputing the TLS regression (10,000 times) in order to build a distribution of scaling factors and estimate their 5th-95th percentile range. This results in a range of model response that is consistent with the observations given internal variability. This approach is applied to both raw observations, and forced and control simulations; and to those from which the NAO influence has been removed from all components.
When applied as an observational constraint on the forced component of future climate model projections (following Kettleborough et al., 2007), the best estimate of the scaling factor (̂A ll ) , along with the 5th-95th percentile range, is multiplied by the CMIP6 multi-model mean anomaly that was used as a fingerprint. This provides a constrained estimate of the range of the forced response in future model projections, with anomalies in reference to a 1950-2014 baseline, the period over which the scaling factor is also calculated. Similar implementations of the ASK approach have recently been applied to constrain future projections of temperature and precipitation across European regions (Brunner et al., 2020;Hegerl et al., 2021), with a particular focus on summer temperature. The results will focus on Northern European precipitation and temperature, particularly in winter, given the well-known influence of the NAO.

The NAO's Contribution to Variability and Trends
The contribution of NAO variability to recent multidecadal trends in Northern European winter climate is illustrated for both the observations (Figures 1a-1d) and model simulations (Figures 1e and 1f). As expected, removing the influence of the NAO reduces the interannual variability of the observed time series of precipitation ( Figure 1a) and temperature (Figure 1b). The corresponding panels below (Figures 1c and 1d) show the distributions of multi-year linear trends, with the distribution for a trend duration of n years formed from all possible n-yr periods within 1950-2014. The 30-year trends in winter precipitation (i.e., 36 trends throughout the 1950-2014 period) range from a minimum of a ∼5 mm decrease to a maximum of ∼60 mm increase, with the majority of 30-year trends showing an increase of ∼20-40 mm (Figure 1c). The estimated contribution to the trends over the same 1950-2014 period that is associated with the observed variability of the NAO (green shading) indicates that for trends longer than ∼35-40 years the NAO has contributed positively to observed annual precipitation trends, irrespective of the starting year of the trend (see also Blackport & Fyfe, 2022). An increase of ∼20 mm in Northern European winter precipitation, and an increase of ∼1°C in winter temperature, can be attributed to the influence of the NAO over a period of ∼40-60 years. Once the impact of NAO variability has been regressed out of the raw time series, the residual trends over the same period are markedly reduced. In fact, the residual ∼40-60-year trends are less than (for temperature), or comparable to (for precipitation) the magnitude of the trends owing to variability in the NAO alone.
In contrast to the impact of removing the NAO on observed trends, the primary impact of removing the NAO from simulations is to reduce the variability and thus narrow the range of residual trends modeled over the historical period (Figures 1e and 1f). While a multi-model mean range of ∼±20 mm is estimated for the component of all 30-year winter precipitation trends associated with the NAO (e.g., in Figure 1e), there are rare individual ensemble members that have NAO trends that are as much as twice this magnitude. Nevertheless, the long-term increasing trend in winter precipitation is substantially weaker (a factor of 3-4) in the multi-model mean than observed, consistent with the models having smaller trends associated with the NAO, and smaller multidecadal NAO variability,as discussed above. Removing the NAO from long-term precipitation trends (blue shading, Figures 1c and 1e) reduces the difference between simulations and observed, whereas for temperature (Figures 1d  and 1f) the difference increases.

The NAO's Impact on the Regional Constraint
The ̂A ll scaling factors derived for Northern European precipitation are shown in Figure 2, computed using the annual (Figures 2a and 2b) and winter (Figures 2c and 2d) time series, retaining the NAO variability (Figures 2a  and 2c), and with the NAO removed (Figures 2b and 2d; note the reduced variability in the observed time series and the control simulations). The scaling factors show that there has been a detectable change in Northern European annual and winter precipitation (̂A ll > 0 ) . However, unless the NAO is removed, the magnitude of the model fingerprint is not consistent with observations (i.e., the range in ̂A ll does not include unity), and needs to be scaled by a factor of 1.4-3.8 in annual data (Figure 2a), and even more in the winter (2.2-6.0; Figure 2c), to reproduce observed changes. After removing the NAO (Figures 2b and 2d) the best estimate scaling factors are reduced, especially in winter, and the constraint also tightens (i.e., the spread in scaling factors narrows) due to the increased signal-to-noise in the modeled response once the NAO is removed. The scaling factors for temperature are shown in Figure S3 of Supporting Information S1, and similarly indicate a reduction and tightening of the constraint, especially in winter, once the NAO is removed.
Past changes in Northern European winter temperature and precipitation are shown together in Figure 3, with individual climate model simulations from CMIP6 historical model ensemble members (small squares; large square for multi-model mean) compared to observed changes (circles). The change displayed is between 1950-1969 and 1995-2014, but  . The multi-model mean change in winter temperature is slightly less than the observed change (∼0.28°C per decade), while for precipitation the mean change (∼1% per decade) is significantly lower than observed, consistent with the earlier comparison of trend distributions and scaling factors. The purple shaded region depicts the externally forced change in the observations, as estimated from the range of scaling factors (5th-95th percentile spread of ̂A ll , recalling Figure 2c and Figure S3c in Supporting Information S1) multiplied by the historical change in the multi-model mean for temperature and precipitation separately. Only a small fraction of individual simulations (∼10%) show a past change that is consistent with the observational constraint in both variables and indicates that there is only a modest chance of internal variability or model uncertainty explaining the discrepancy. Thus, without removing the NAO the multi-model mean is inconsistent with the observed precipitation change. CMIP6 , separately for temperature and precipitation.
simulated changes in winter precipitation are unlikely to be consistent with the estimates of the forced change, even when accounting for model uncertainty and internal variability.
Once the NAO has been removed from the historical time series (Figure 3, right panel), the observed wintertime temperature and precipitation change are each reduced by ∼50%. There is also a slight tightening in the spread of individual model ensemble members while the multi-model mean remains relatively unchanged. Compared to the constraint including the NAO, there is a clear shift in the estimate of the forced component (blue shaded region), and a narrowing of the uncertainty range. The observed increase in Northern Europe winter precipitation that is attributed to anthropogenic forcing reduces from ∼2.3%-6.4% to ∼0.8%-3.2% (relative to climatology, per decade), with more than half of the ensemble members now within this observationally constrained range. The uncertainty range for the forced component of precipitation change narrows and the wintertime past wettening change remains detectable. There is also a reduction in the forced component of winter warming without the NAO, from ∼0.09-0.68°C to ∼-0.03-0.41°C per decade. Thus a forced signal of winter warming is no longer detectable at the p > 0.05 level (one-sided tail, note the scaling factor in Figure S3d of Supporting Information S1). Once the NAO variability is removed, several CMIP6 model members show stronger warming than the forced estimate range. While internal variability can help to explain individual simulations having trends outside of the forced range, the presence of these higher-warming models is also consistent with various analyses showing some of the CMIP6 models have a higher climate sensitivity (Forster et al., 2021). The question remains to what extent the observed NAO evolution may have been influenced by external forcing in a way not captured by the CMIP6 ensemble (Smith et al., 2020).

The NAO's Impact on the Future Constraint
The results presented here also have implications for constraints on future projections, particularly for regional climate change as illustrated in Figure 4. For this example, winter precipitation from the CMIP6 high-emissions scenario (SSP5-85) was used as the raw future projection time series, extending the historical simulations previously analyzed. Note that the increasing trend in NEU winter rainfall is only projected to emerge from the variability in the pre-industrial control simulations (±2σ) during the 2050s (Figure 4, left panel). The constrained projection (thick purple line and shading) is computed by multiplying the raw CMIP6 multi-model mean anomaly time series with the best estimate and 5th-95th percentile spread of ̂A ll (Figure 2c). The large scaling factor has a marked impact on the future projection of NEU winter precipitation, both in terms of the magnitude of trend, and in anticipating an earlier emergence of the forced change in precipitation beyond the pre-industrial climatology. For the 20-year period centered on 2050, for example, (Figure 4, right panel), an increase in the forced component of winter precipitation of ∼30%-80% is projected. Note that the constraint reflects forcing only, and estimated future changes would need to also account for natural (and other) forcings and internal variability. Figure 4 (middle panel) illustrates the impact of accounting for the NAO on observational constraints to future projections. The trend in the CMIP6 multi-model mean of precipitation once the NAO has been removed is very similar (thin gray lines) to the raw simulations, thus there is little indication of a forced trend in the future NAO within the CMIP6 model projections (see also the historical multi-model mean changes in Figure 3). However, as shown in the previous section, the ̂A ll scaling factor is reduced substantially after removing the NAO, and thus when applied as an observational constraint on the CMIP6 projection produces a markedly different estimate of the forced change in future NEU winter precipitation. The magnitude of the forced component of future change over the 2041-2060 period is significantly reduced after removing the NAO (more than halving, from a ∼50% to ∼22% increase), and the uncertainty in the forced component narrows. Note that we only consider the forced component of the change, and are neglecting forced changes in the NAO, which are an additional source of uncertainty in estimates of future climate projections beyond the scope of the current study.

Summary
The NAO provides a clear example of a large-scale mode of climate variability that can have non-negligible impacts on the detection and attribution of forced trends in observations, as exemplified by its influence on Northern European climate. Past variability in the NAO has contributed to the recent multidecadal trends in winter temperature and precipitation over Northern Europe. The suite of current comprehensive global models underestimate the NAO's multidecadal variability and do not reproduce its contribution to multidecadal trends. The influence of the NAO can distort the estimate of the magnitude of past forced changes, with important ramifications for the application of observation-based constraints on future model projections, and can lead to an overestimate of future changes in Northern European winter precipitation, which could have important implications for adaptation planning decisions. If the NAO is removed before deriving the constraint, the estimated magnitude of the forced signal is lower and the uncertainty range is smaller.
For both detection and attribution, and in order to estimate an observational constraint based on the externally-forced signal, we suggest assessing and, if necessary, removing the influence from major modes of internal variability, particularly if these show poorly understood trends. This will reduce the potential that these modes bias the estimated magnitude of past forced changes, and also helps narrow the uncertainty. Various storylines describing the future progression of large-scale variability could then be superimposed on the forced-only estimate, allowing consideration of an unforced or forced evolution of this variability.