Pangu-Weather, NeuralGCM, and UFS forecasts are all initialized from the same ensemble of data assimilations (EDA) from the ERA5 reanalysis data set . The EDA includes 10 ensemble members that account for uncertainties in the observations and the underlying model by perturbing model physical tendencies in the short forecasts that link subsequent analysis windows. It contains all atmospheric variables to initialize the models of this study and is available on a regular latitude–longitude grid with 0.5° × 0.5° grid spacing. The EDA data is regridded with bilinear interpolation to match each model's grid spacing.

The subseasonal forecasts for the 2 cases are initialized on 15 December 2022 and 2 February 2023, respectively. The initialization of the subseasonal forecasts is achieved through a time-lagged combination of ensemble members from EDA following the approach of . For example, the forecast initialized on 15 December 2022, 00:00 UTC incorporates ensemble members from forecasts issued on 14 December 2022, 12:00 UTC, 15 December 2022, 00:00 UTC and 15 December 2022, 12:00 UTC. With 10 ensemble members at each time, this yields a 30 member time-lagged ensemble. This methodology is applied consistently for the February case study.

This study evaluates subseasonal prediction skill using 3 distinct modeling approaches: (1) an experimental version of the National Oceanic and Atmospheric Administration (NOAA) UFS, a state-of-the-art NWP model , (2) NeuralGCM, a hybrid neural network-based general circulation model , and (3) Pangu-Weather, a purely data-driven MLWP model .

All forecasts are relaxed and evaluated against ERA5 reanalysis data . This dataset provides analyses of atmospheric conditions at 0.25° grid spacing . ERA5 data are remapped using bilinear interpolation to each model's native resolution. Daily climatological means from the ERA5 for 1990–2019 were used to compute anomalies of all atmospheric variables. A sliding window is applied around each day-of-year and time-of-day combination, with weights that decrease linearly from the center to zero. This approach smooths the climatology by reducing sample noise, though it slightly diminishes the seasonal amplitude. These climatological means, obtained from the WeatherBench2 dataset, are calculated following the method of . All models generate 30 d ensemble forecast using the method mentioned in the Sect. . For each case, we examine the subseasonal prediction of the large-scale circulation over the North Pacific and western North America at 3–4 weeks lead time. Forecasts are averaged daily during the validation periods ranging from 30 December 2022–13 January 2023 and 17 February–3 March 2023, respectively.

For the first event, lasting from 26 December 2022 to mid-January 2023, the total rainfall accumulation of ERA5 exceeds 450 mm in California (Fig. a). In some regions, the observed accumulated precipitation even reached values up to 1000 mm . This extreme precipitation event led to at least 21 fatalities and caused property damage estimated between USD 5–7 billion . Additionally, operational forecasts from both NOAA and ECMWF exhibited relatively large forecast errors during this event .

The synoptic situation during this 2-week period was characterized by a Rossby wave pattern featuring a positive geopotential height anomaly over the subtropical North Pacific, a negative height anomaly over the eastern North Pacific and a positive height anomaly over eastern North America. The anomalous, quasi-stationary upper-level trough over the northeastern Pacific (Fig. b) created a prolonged southwesterly flow along the US West Coast. It was associated with enhanced cyclone and atmospheric river (AR) activity that impacted an area extending from California to British Columbia (not shown). During the 2-week period, the mean water vapour flux (Sect. ) at 850 hPa reached values of 40 gkg-1ms-1 at the coastline (black contours in Fig. b) favouring the enormous rainfall amounts in California and Oregon. From 21 to 28 December 2022, the MJO progressed through phases 4–5 in the real-time multivariate MJO (RMM; ) phase space. This earlier MJO activity may have influenced the midlatitude circulation pattern linked to the precipitation event. The 2-week period of the event itself co-occurred with an active MJO phase 6–7 from 29 December 2022 to 9 January 2023. Though MJO phases 6–7 are on average followed by a positive geopotential height anomaly over western North America, this event featured a negative geopotential height anomaly illustrating the enormous variability in the extratropical response to the MJO as also documented by . Recent studies suggest that the Rossby wave pattern was enhanced by the active MJO with convection over the western Pacific, promoting the ridge-trough-ridge tripole extending from the subtropical North Pacific to eastern North America .

Forecasts initialized on 15 December 2022 and valid during weeks 3–4 (30 December–13 January) are shown in Fig. . The CRL experiments across all models fail to adequately capture the dipole pattern of negative and positive geopotential height anomalies extending from the northern Pacific to eastern North America (Fig. a–c). Notably, the UFS model exhibits the lowest prediction skill for 500 hPa geopotential height, with a regional mean ACC of 0.07 and the highest MAE of 93 m (Fig. a). Pangu-Weather shows a similar prediction skill with an ACC of 0.07 and MAE of 92 m in the target region (Fig. b). The low forecast skill from CRL in Pangu-Weather might be associated with a systematic negative temperature bias , likely stemming from limitations in its model architecture and training procedure . In contrast, NeuralGCM demonstrates a comparative better representation of the large-scale circulation (Fig. c). The 500 hPa trough extends further east and a weak positive geopotential height anomaly exists over eastern North America. This contributes to a higher subseasonal forecast skill for this case – not only in terms of geopotential height, but also regarding the representation of 850 hPa water vapour flux.

The WTR (Fig. d–f) and NTR (Fig. g–i) experiments show marked improvements in reproducing the anomalous 500 hPa geopotential height pattern over the Pacific in all 3 models. All models better represent the positive geopotential height anomaly over the subtropical North Pacific. Pangu-Weather and NeuralGCM improve the representation of the deep trough over the eastern North Pacific leading to higher ACC values. The presence of this trough is the key distinguishing feature compared to CRL in all 3 models.

The associated enhanced westerly flow leads to a band of strong 850 hPa water vapour flux exceeding 40 gkg-1ms-1 (the magnitude highlighted by the bold black solid line in Fig. ). This moisture transport extends closer to the west coast of North America in the WTR and NTR experiments compared to the CRL configuration. Its proximity to the coast also better matches the verification data (Fig. b), indicating an improved representation of the precipitation event.

The similarity between the WTR and NTR forecasts for all models suggests that a better representation of the tropics would have improved the subseasonal forecast skill for this event. came to a similar conclusion based on forecast experiments with altered initial conditions in the tropics using a fully data-driven MLWP model. Note that examined impacts of the tropics for experiments initialized later, on 26 December, and thus focused on shorter forecast lead times.

To further understand how the relaxation in the tropics impacts the extratropical Rossby wave forcing, we analyze the RWS (Sect. ) at 200 hPa averaged from 23–30 December 2022 (during week 2; Fig. ), which is 1 week earlier than the validation period (week 3–4). The focus here is to analyze the establishment of the large-scale flow pattern associated with this extreme precipitation in December in the forecast. Noting that MAEs of RWS are calculated between forecasts and ERA5 in the red box (20–38° N, 75–155°E) ranging from the Maritime Continent to the western Pacific.

UFS CRL predictions consistently overestimate the divergent outflow and the resulting negative vorticity advection to the north of the MJO-related convection over the Maritime Continent and western Pacific, in the days preceding the precipitation events . Here, results are only shown for the NTR experiments because WTR experiments are qualitatively similar. In NTR and CRL, all models represent the band of negative RWS values over eastern Asia and an area of positive RWS over the western Pacific (Fig. a–f). This indicates that the 2 MLWP models of this study are physically consistent with the UFS model in representing tropical–extratropical teleconnections.

The NTR experiments in UFS exhibits large differences in terms of RWS relative to CRL (Fig. a, d, and g) over eastern Asia and the western Pacific. UFS NTR shows an improved RWS with a smaller forecast error (MAE: 0.59). The differences in Rossby wave source emerge as a negative–positive couplet in 200 hPa relative vorticity in this region indicating a slight eastward shift of the broad trough–ridge pattern over eastern Asia and the western Pacific (Fig. j, ).

Pangu-Weather and NeuralGCM CRL exhibit a better prediction of the RWS associated with the divergent outflow with an MAE of 0.80 and 0.90, respectively (Fig. b and c). In NTR, RWS is strengthened in the northeastern Indian ocean for both MLWP models (Fig. e and f). Overall, the reduction of the MAE through tropical relaxation is considerably smaller than in UFS (Fig. d, e, and f). The differences in RWS manifest as dipoles of vorticity differences along the strongest vorticity gradient (Fig. k and l). However, the dipoles are considerably weaker than between CRL and NTR in UFS.

To further understand the role of the tropical forcing for the predictability of the event, we specifically focus on the representation of the velocity potential (VP) associated with the MJO. As outgoing long-wave radiation (OLR) is not available from the models used here, we use 200 hPa VP anomalies as a proxy for the convective activity associated with the MJO. Time–longitude Hovmöller diagrams averaged between 10° S–10° N are shown in Fig. .

Starting with ERA5 (black contours in Fig. ), the period is characterized by suppressed convection over the Indian Ocean after day 10 and slightly enhanced convection over the Maritime continent most noteworthy between 5 to 15 d lead time. Though the suppressed convection and its eastward propagation can be seen in the CRL experiment with UFS, the convective activity is substantially overestimated over the Maritime Continent (Fig. a) which is consistent with the too strong RWS. Pangu-Weather and NeuralGCM are both characterized by a weaker dipole pattern in 200 hPa VP with the magnitude of the negative VP over the Maritime Continent being closer to that in ERA5 (Fig. b and c).

All NTR experiments clearly represent the suppressed convective activity over the Indian Ocean from day 10 onwards (Fig. d–f). Likewise, all 3 models show error reduction and better represent the 200 hPa VP anomaly over the Maritime Continent (Fig. g–i). Most notable is the reduced magnitude of the VP in UFS between 5 and 30 d forecast lead time. For Pangu-Weather and NeuralGCM, the negative 200 hPa VP is of similar magnitude as in CRL, but the representation of the occurrence of local and temporal maxima is improved after relaxation. Overall, the changes in 200 hPa VP indicate an improved representation of the MJO envelope, which likely contributes to a better representation of the tropical–extratropical teleconnection.

For the second event from mid February to the beginning of March 2023, the ERA5 accumulated precipitation over California reaches approximately 200 mm (Fig. c). Though the MJO entered simultaneously its active phases 6–7, the midlatitude geopotential height anomalies are very different from case 1. For case 2 (valid from 17 February–3 March), a persistent positive geopotential height anomaly is located over the eastern North Pacific (Fig. d). ARs are deflected around the associated high pressure anomaly and reach the west coast of North America in a northwesterly flow. There, the precipitation is connected to the passage of several upper-level troughs (as manifested by a negative geopotential height anomaly in Fig. ) associated with Rossby wave breaking on the eastern flank of the Pacific ridge.

All 3 models exhibit greater subseasonal forecast skill in the CRL experiment (Fig. a–c) with higher ACCs and lower MAEs than for Case 1. Pangu-Weather especially depicts the positive geopotential height anomaly over the eastern North Pacific and the surrounding moisture transport, whereas UFS and NeuralGCM underestimate the anomaly amplitude, resulting in lower ACC and higher MAE.

In the UFS model, both the WTR (Fig. d) and NTR (Fig. g) experiments yield a substantially stronger ridge over the eastern North Pacific, resulting in a considerably improved representation of the large-scale circulation compared to the CRL experiment (Fig. a). This finding is consistent with . Pangu-Weather shows modest improvements for the WTR (Fig. e) and NTR (Fig. h) experiments, particularly in capturing the positive and negative geopotential height anomaly patterns. NeuralGCM predicts a pattern similar to the UFS model, yet with overall higher forecast skill than UFS in this case (cf. Fig. a, d, and g vs. Fig. c, f, and i). The bands of highest moisture transport around the ridge over the eastern North Pacific, with magnitudes around 40 gkg-1ms-1, are consistently well represented. Independent of the relaxation configuration, the forecasts for Pangu-Weather and NeuralGCM with relaxation yield significantly improved representation of the location, amplitude and positive tilt of the trough near the west coast of North America, which may affect precipitation. The UFS forecasts only show a modest improvement regarding the location of the trough.

The improvements in large positive geopotential height anomalies in the UFS for both WTR and NTR indicate that tropical forecast errors in this model exert a strong influence on predicting the blocking ridge over the eastern North Pacific, even if they did not strongly constrain predictions of downstream wave breaking and trough amplification near the west coast of North America. In the UFS WTR experiment, positive height anomalies are well captured, but negative anomalies near the west coast of North America remain misrepresented. Interestingly, MLWP models better capture the positive geopotential height anomaly over the eastern North Pacific in the CRL without relaxation, possibly due to superior representation of tropical conditions and Rossby wave forcing even without nudging.

Overall, the differences in forecast skill between the WTR and NTR experiments are remarkably small across all 3 models (cf. Fig. d–f and g–i). This similarity suggests that forecast skill is not highly sensitive to the width of the tropical nudging region. In other words, extending the nudging region beyond the core tropics does not substantially influence the forecast evolution, implying that forecast errors originating in the deep tropics likely play the dominant role in this event. However, this result does not imply that subtropical or extratropical processes are unimportant, but rather that constraining the large-scale tropical state appears sufficient to capture the key sources of predictability in this case.

We also examine the RWS to assess the impact of the tropical relaxation during week 2 on the forcing of the extratropical wave response. The UFS overestimates the RWS over eastern Asia and the western Pacific in CRL (Fig. a; ) relative to NTR (Fig. d), reflecting an overprediction of the divergent outflow and negative vorticity advection in that region. The error in the RWS is reduced when NTR is applied, with the MAE decreasing from 0.55 to 0.38.

Results of suggest that an improved representation of the RWS in NTR relative to CRL led to a better representation of the extratropical pattern over the North Pacific in this case. Pangu-Weather and NeuralGCM exhibit a dipole pattern in terms of RWS over Eastern Asia in the CRL experiment with lower MAEs (Fig. b and c). Meanwhile, in the NTR experiments, the RWS in both MLWP models is even slightly deteriorating (Fig. e and f). Higher MAEs in NTR than in CRL are aligned with the hypothesis above that the divergent outflow from the tropics in Case 2 is likely better represented in the MLWP models than in UFS. Finally, there is a noteworthy area of intense positive RWS and divergent winds over the eastern Pacific, which is possibly linked to enhanced warm conveyor belt activity in this mid-latitude region following MJO phases 6 and 7 .

NeuralGCM reaches the lowest RWS MAE in the CRL experiment (0.10). This indicates that the model already captures most of the contributing RWS during the early stage without any nudging. Moreover, the differences in RWS and ζ between the CRL and NTR are comparably small (Fig. i and l), indicating that NeuralGCM's representation of the relevant dynamical fields is less sensitive to the relaxation procedure.

To investigate potential changes in the tropics through the relaxation, we analyze anomalies of the 200 hPa VP (Fig. ). As for Case 1, the situation is characterized by a dipole of VP anomalies over the Indian Ocean and the Maritime Continent (black contours). The negative 200 hPa VP anomaly (Fig. a) is overestimated and longer lived in the UFS CRL relative to ERA5. The magnitude and timing of the negative 200 hPa VP anomaly are considerably better represented in Pangu-Weather and NeuralGCM already in the CRL (Fig. b and c). Accordingly, the improvements of the negative 200 hPa velocity potential anomalies in NTR in Pangu-Weather and NeuralGCM are rather small (Fig. e, h, f, and i). In contrast, relatively large improvements are found in the NTR experiments of UFS near the western and eastern Pacific (Fig. d and g). This is consistent with the large improvements in the representation of 200 hPa RWS and geopotential height anomalies when tropical relaxation is applied in UFS.

Given the different impacts of relaxation in the 2 cases and the varying contribution of individual members to the ensemble mean, we further examine forecast skill per ensemble member. This provides a more detailed view of forecast performance and model uncertainty across the ensemble for each case.

Both MLWP models demonstrate on average a higher forecast skill in the CRL experiment for the December case compared to UFS (Figs. a–c; ). Still, individual ensemble members in Pangu-Weather and NeuralGCM show negative ACC and thus no forecast skill for this particular event. The application of tropical relaxation (WTR) in December leads to a clear improvement over the control experiment, suggesting a strong influence of tropical forecast errors in all 3 models on the mid-latitude prediction skill. The substantially reduced range of ACC values between the different ensemble members can be attributed to the reduced variability in the tropics through tropical relaxation.

In contrast to the December case, the February case shows less sensitivity to tropical relaxation (Fig. d–f) and is better captured by all 3 models in CRL, especially for the MLWP models. Though a large improvement in terms of ACC can be seen for UFS, the median ACC of Pangu-Weather and NeuralGCM increases only marginally when tropical relaxation is applied. Also, the smaller range of ACC values between the different ensemble members suggest a higher confidence in the predictions of the 2 MLWP models. The rather small improvement through tropical relaxation compared to the December case further suggests that tropical forecast errors in MLWP models are less critical for the predictability of the February precipitation event, especially during weeks 1–2 (Fig. ). Errors in the tropics in UFS seem relatively large and might be associated with parameterization of physical processes that affect the representation of tropical convection.

Another possible explanation for the weaker impact of the relaxation in the February event is the different state of tropical variability at initialization. In the December case, the MJO is not active at initialization, whereas in the February case the MJO is already active in phase 3 . An active MJO provides a coherent large-scale tropical signal that can enhance subseasonal predictability and may already be reasonably represented in the initial conditions. As a result, the February forecasts may contain higher intrinsic predictability in the tropics, reducing the additional benefit from relaxation. Overall, our result indicates that other regions provided predictability for the February case, which could be further investigated with additional nudging experiments in a future study.