GEPS5 uses the Global Environmental Multiscale (GEM) atmospheric model . GEPS5 has 45 vertical levels using log-pressure vertical coordinate , and uses the Ying–Yang grid with a horizontal resolution of 39 km . For the ocean boundary condition, GEPS5 uses the persistent anomaly method: on top of the climatological seasonal cycle, the 30 d average SST anomaly preceding the initial date derived from ERA-Interim is added and persists throughout the integration . The sea ice cover is adjusted according to local SST so that the resulting sea ice cover and SST are consistent . The initial conditions are obtained using an Ensemble Kalman-filter EnKF;, with a digital filter and incremental analysis updates to reduce the shock during data assimilation .

GEPS6 is built on top of GEPS5 by replacing the simple statistical SST and sea ice model with a dynamical ocean and sea ice model. The ocean model is NEMO version 3.6 . NEMO uses z-level vertical coordinates, with hydrostatic, Boussinesq approximations and a linear free surface. This version has a horizontal resolution of 0.25° ORCA grid a global tripolar grid configured to remove singularity of poles of a sphere and 50 levels increasing from 1 m at the surface to 500 m at the deepest level. The sea ice model is the Los Alamos multi-category Community Ice Model version 4 CICE4;. The initial conditions are obtained using the EnKF, with European Centre for Medium-Range Weather Forecasts hybrid (ECMWF-hybrid) gain applied to recenter ensemble members around the means of EnKF analysis and 4DEnVar analysis . The 4DEnVar is a 4-dimensional variational data assimilation using the Global Deterministic Prediction System . The SST is initialized with a monthly average Ocean Reanalysis Pilot 5 ORAP5; product. The initial sea ice conditions are obtained from HadISST .

For more detailed documentation, see and . Ensemble methods are described by for GEPS5 and for GEPS6.

The S2S project provides up to 60 lead days hindcasts from 13 different meteorological agencies. ECCC has contributed hindcast data from GEPS5 and GEPS6 from 1998–2017.

The hindcasts are produced operationally on a weekly basis for GEPS5 and GEPS6. For each hindcast date, hindcasts corresponding to the same date were generated for 20 years 1998–2017. Each hindcast has a lead time of 32 d with 4 ensemble members. For GEPS6, the hindcast is generated such that it has twice as many start dates as the GEPS5 hindcast, as documented in Tables S1 and S2 in the Supplement. We subsample the GEPS6 hindcast by choosing the closest start date (underlined in Table S2) to GEPS5. In our focus months, December, January, and February, the resulting start times of GEPS6 are exactly one day earlier than those of GEPS5, and start dates are spaced by 7 d. This strategy minimizes the impact of the start time difference and ensures that the GEPS6 subset has the same amount of data as GEPS5.

As our verification dataset, we use European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 ERA5;. In the Pacific and Atlantic Oceans, it can well capture offshore diurnal SST cycles under various wind conditions . Over Europe, the wind variability is skillfully predicted . Over North America, shows that ERA5 has skills in producing wind and precipitation associated with extra-tropical cyclones, with a tendency to underestimate high winds and overestimate low winds. A study over the Red Sea shows ERA5 is challenged by land–sea induced local dynamics .

Ideally, the impact of using a dynamical ocean model can be revealed by taking the difference between hindcasts of GEPS5 and GEPS6. However, the start dates of these two sets of output differ by exactly 1 d in our time of interests. Therefore, we reference both fields to ERA5 by computing the difference between GEPS and ERA5 data and then sorting the runs by start month. Differences in transient weather systems between the two initializations are not negligible, making the raw differences between GEPS6 and GEPS5 hard to interpret. By taking the difference with ERA5, we effectively remove much of the variance added from the differing transients, thus allowing for a better comparison. We have documented details in the Supplement (Sect. S2).

We first define the pentad bias 1βpdt,Xr,ts,p,γ=Δw-1∫tl=p-1ΔwpΔwXpdt,hcstr,ts,tl,γ-Xrefr,ts+tldtl, where βpdt,X is the bias of the hindcast product “pdt” of the variable X at location r, ts is the start time, tl is the lead time, p is the lead pentad (starting from 1), γ is the ensemble member of a total Nγ members, and Δw=5 d is the size of the pentad. The subscript “hcst” denotes the hindcast, “ref” denotes the reference dataset that is used to verify the hindcast, i.e., ERA5 in this paper. With the 〈⋅〉 being the spatial averaging over a region S, we can separate the bias into a spatial mean 〈βpdt,X〉 and an anomaly βpdt,X′=βpdt,X-〈βpdt,X〉. The averaged bias variance can then be written as the sum of mean and patterned variances. That is, 2〈βpdt,X2〉=〈βpdt,X〉2︷mean+〈β′pdt,X2〉︷patterned. Later in the text for the sake of simplicity, we define bias variance ϵpdt,X=〈βpdt,X2〉, mean bias variance ϵ‾pdt,X=〈βpdt,X〉2, and patterned bias variance ϵ̃pdt,X=〈β′pdt,X2〉, with the decomposition as ϵpdt,X=ϵ‾pdt,X+ϵ̃pdt,X.

The bias and its variance decomposition of variable X of a product pdt grouped by start time set ϕ is 3aBpdt,Xr,ϕ,p=βpdt,Xr,ts,p,γ|ts∈ϕ,γ=1,…,Nγ,3bEpdt,XS,ϕ,p=ϵpdt,XS,ts,p,γ|ts∈ϕ,γ=1,…,Nγ,3cE‾pdt,XS,ϕ,p=ϵ‾pdt,XS,ts,p,γ|ts∈ϕ,γ=1,…,Nγ,3dẼpdt,XS,ϕ,p=ϵ̃pdt,XS,ts,p,γ|ts∈ϕ,γ=1,…,Nγ,

To test the significance, the degrees of freedom are counted by making the following two assumptions: (a) output from different start times or different ensemble members is independent, and (b) the output within the same pentad is not independent. In both GEPS5 and GEPS6, during 1998–2017 there are 4 start times in January with 4 ensemble members. Therefore, for each pentad there are 20×4×4=320 degrees of freedom.

We define the bias change 4ΔBXr,ϕ,p=μBGEPS6,Xr,ϕ,p-μBGEPS5,Xr,ϕ,p, where μ is the averaging operator over a given set, and a significance test is performed with the above-mentioned degrees of freedom. While the ΔBX is a measure of the change in bias, it actually tells us about large-scale property differences between GEPS5 and GEPS6 simulations.

To evaluate the impact of MJO phase, we define three start time groups using the outgoing-longwave-radiation (OLR)-based MJO index OMI;, a two-dimensional vector whose values are normalized principal components. When the magnitude of OMI is less than 1, the MJO is classified as inactive. When the magnitude of OMI is larger than 1, the MJO is active, and the MJO phases 1–8 are defined according to the phase angle of OMI. The MJO phase contains spatial information of the MJO: during MJO phases 1–4, the MJO convection center resides over the Indian Ocean. During MJO phases 5–8, the center is over the Maritime continent and tropical Pacific. The MJO start time groups are defined as 5aϕNonMJO=t|t∈ϕDJF, and the MJO is inactive more than half of the time in the next 15 d.5bϕP1234=t|t∈ϕDJF, the MJO is in phases 1–4 more than half of the time in the next 15 d.5cϕP5678=t|t∈ϕDJF, the MJO is in phases 5–8 more than half of the time in the next 15 d. where ϕDJF is the set of all start times during December–January–February. The remaining start times are ambiguous, meaning that either the MJO is neither consistently inactive nor active, or the phase of MJO cannot be classed in either P1234 or P5678. Out of 1805 d of DJF during 1998–2017, there are 455 d of NonMJO, 331 d of P1234, 321 d of P5678, and 698 d that are ambiguous. (See Fig. S1 for histogram.)

We compute the bias change ΔB, i.e., the difference between GEPS6 and GEPS5, of SST, 850 hPa geopotential height Z850, and 500 hPa geopotential height Z500 of pentads 1–3 and present them in Fig. . The black boxes in Fig. c define the Kuroshio Current Extension (150° E–130° W, 30–50° N) and the Gulf Stream (75–15° W, 35–55° N) regions, and the magenta boxes in Fig. f and i define the Aleutian Low (140° E–130° W, 40–60° N), Icelandic Low (30° W–20° E, 55–70° N), and Atlantic Subtropical High (60° W–20° E, 20–50° N) regions.

The bias of the first pentad shows the impact of SST initialization (Fig. a) on the atmosphere (Fig. d and g). Over the North Pacific, the SST is colder in GEPS6, with the alternating signs around coastal Japan signifying errors in simulating the Kuroshio Current. The Z850 shows that there is a weakening in the Aleutian Low in the middle of North Pacific, which is because of less upward latent heat flux due to a cold SST bias (Fig. a). In the North Atlantic, there is a similar cold bias and a northward shift of the Gulf Stream along 45° N. The impact of this shift extends northward to the edge of Arctic sea ice. The SST bias in the Gulf Stream produces a positive anomaly in Z850 and Z500. In the Northern Hemisphere, the difference in SST initialization strategy introduces a bias variance of about 0.05 K² (Fig. S2).

The weakening of the Aleutian Low continues in the next two pentads (Fig. e and f) and wanes afterward (not shown). The Atlantic basin is less straightforward. In pentad 2, the Atlantic Subtropical High starts to weaken. Meanwhile, a positive anomaly moves westward to the Atlantic (Fig. e and h). By pentad 3, there is a robust weakening of the Icelandic Low and the Atlantic Subtropical High (Fig. f and i).

The Aleutian Low weakening appears to be linked to a similar Icelandic Low weakening through a Rossby wave train . As shown in Fig. f and i, Z850 and Z500 reveal an alternating pattern of high and low centers, extending from the Aleutian Low through the Arctic to the Icelandic Low. This is consistent with , a reanalysis study that links the influence of Aleutian Low on Icelandic Low on a subseasonal time scale, and is also widely noticed in seasonal and longer timescale and reference within.

The large northward shift of the Gulf Stream directly forces Z850 and Z500. Figure d and g show that there are positive geopotential anomalies at 45° N, 75° W. The anomalies persist throughout pentads 1–2.

Here, we define IVT=g-1∫200hPa1000hPaqvdp. Figure  shows the bias change ΔB of the IVT (shading) and Z850 (contours) for pentad 3. Over the North Pacific, the IVT is reduced along the southeastern side of the weakened Aleutian Low toward the Gulf of Alaska. Over the North Atlantic, the reduced IVT lies between the weakened Icelandic Low and the Atlantic Subtropical High, with a more zonal orientation toward western Europe.

The shape of the IVT bias depends on the MJO. Figure a–c show the composite bias changes of IVT (shading) and Z850 (contour) grouped by MJO-inactive, MJO phases 1–4, and MJO phases 5–8 as defined in Sect. . The weakened Aleutian Low remains in the middle of the North Pacific, such that the weakened Pacific IVT is consistently oriented southwest–northeast. In contrast, the Icelandic Low and Atlantic Subtropical High weakening is spatially more variable, such that the Atlantic IVT pattern is less consistent across MJO groups.

Over the North Pacific, the IVT forecast is improved when the MJO is active. Figure a–c show the composited bias variance of IVT over the Kuroshio Current region. The first 3 pentads of non-MJO cases do not show significant differences, while the MJO phases 1–4 and 5–8 show better IVT forecasts starting in pentads 3 and 2, respectively. The lag of the improvement in MJO phases 1–4 by one pentad is reasonable because MJO convection is located over the Indian Ocean during phases 1–4, and it takes some time for the MJO convection to propagate into the Pacific.

Examining the latent heat flux Hlat, we find that both the mean and patterned bias variances of Hlat are improved regardless of MJO phase (Fig. d–f). This does not mean latent heat flux is irrelevant. Rather, it shows that more accurate heat fluxes can positively impact the forecast during a certain window of opportunity, which in our case is MJO phases 5–8. We are also aware that, because using the dynamical ocean model also gives better MJO forecasts , the exact improvement due to local air–sea interaction will be more easily studied using a regional coupled model.

For the North Atlantic, we do not find a similar improvement that depends on MJO phase (not shown).

We use bias variances as functions of lead pentads over the Kuroshio Current Extension and Gulf Stream regions to assess the benefit of using a dynamical ocean model over persistent SST anomaly, as shown in Fig. a–j. In the Kuroshio Current Extension region, GEPS6 performs better than GEPS5 in terms of the mean SST variance, but has poorer performance in patterned SST variance (Fig. a). The patterned SST variance hindcast gradually reaches the mean ERA5 SST variance 0.60±0.16 K (zonally detrended and area weighted variance, years 1998–2017 DJF). By comparison, we find that the SST initialization choice in GEPS6 reduces the mean but increases the patterned bias variances of SST, which together increase about 0.05 K². In the Gulf Stream regions, the initialization in GEPS6 adds 0.5 K² of SST patterned bias variance, and the mean bias variance does not change significantly. The SST patterned bias variance introduced can be due to lack of eddies because GEPS6 initializes the ocean with the monthly mean ORAP5 dataset.

Despite the initial SST error introduced, in the Kuroshio Current Extension region the latent heat flux Hlat, GEPS6 outperforms GEPS5 in both mean and patterned variances (Fig. b), and the bias variance E of GEPS6 is 10 %–20 % smaller than that of GEPS5, as noted in the previous section. Because GEPS6 produces a less accurate SST but a better latent heat flux, this contrast highlights the importance of two-way coupling in correctly predicting air–sea fluxes, especially those associated with extra-tropical cyclones . The improvement of Hlat during MJO active phase, subsequently leads to a better integrated water vapor (IWV, defined as IWV=g-1∫200hPa1000hPaqdp) and therefore better IVT hindcast in GEPS6 (Fig. c–d). In contrast, GEPS6 does not produce a better Z850 hindcast than GEPS5 (Fig. e).

In the Gulf Stream region, GEPS6 simulates a lower mean variance of SST bias in the first three pentads. However, because GEPS6 simulates a northward-shifted Gulf Stream, there is a strong patterned variance of SST bias (Fig. f). This signal propagates into patterned variance of Hlat bias (Fig. g), resulting in little or no improvement in IWV and IVT (Fig. h–i). Moreover, similar to the Kuroshio Current Extension region, we do not see a notable difference in Z850 (Fig. j).

In this section, the goal is to understand the physical mechanisms that cause changes in the Aleutian Low. From Fig. a–c, we know that the weakening bias is first triggered by less than 0.3 K colder SST over the North Pacific in GEPS6 relative to GEPS5, and the weakening continues regardless of MJO phases. This is an indication that local air–sea coupling is an important driver for the Aleutian Low weakening.

To remove the MJO influence, we examine the response of Z850 and latent heat fluxes Hlat composited with non-MJO groups. In the absence of MJO, the Aleutian Low weakens in GEPS6 relative to GEPS5 during pentads 1–2 (contours in Fig. a–d). The SST bias change between 30–60° N is -0.2 K in the first pentad due to difference in SST initialization strategy, and potential issues in model resolution (see Sect. 4). This results in a reduction in Hlat (Fig. c shading), causing a weaker cyclogenesis such that the Z850 is positively biased.

The Aleutian Low experiences a positive feedback loop where its initial weakening leads to further intensification of this weakening, primarily through interactions between circulation and Hlat. In particular, notice that the magnitude of the reduction in Hlat is larger at the southern flank of the Z850 anomaly because its anomalous circulation blows against the mean westerlies (Fig. c). As previously demonstrated, the reduction of Hlat leads to a weaker Aleutian Low, resulting in stronger anomalous circulation in the next pentad (Fig. d). This mechanism is a positive feedback.

Given differences in the initial SST and the use of a global model, further isolation of this feedback is beyond the ability of the present framework. Nonetheless, the results underscore the potential of future regional modeling studies to more directly quantify the strength of the feedback.