E3SMv2 is a fully coupled Earth system model that includes the atmospheric, ocean, sea ice, land and river transport components. The atmospheric component (EAMv2) is based on a spectral-element dynamical core with 72 vertical levels and is configured on a cubed-sphere grid with approximately 110 km horizontal resolution (Golaz et al., 2022). The ocean component (MPAS-O) employs an unstructured Voronoi mesh with horizontal spacing of ∼ 60 km in the midlatitudes and ∼ 30 km near the equator and poles, and includes 60 vertical layers using a z-star coordinate (Reckinger et al., 2015). The sea ice component (MPAS-SI) shares the same horizontal mesh with MPAS-O and provides detailed representations of sea ice thermodynamics and dynamics (Turner et al., 2022). The land component (ELMv2) simulates land surface energy and water fluxes, biophysical processes, and soil hydrological processes (Golaz et al., 2019). The river transport component (MOSARTv2) represents streamflow routing across river basins (Li et al., 2013). These five components are dynamically coupled through the CPL7 coupler, which facilitates the exchange of momentum, heat, and mass fluxes among model components (Craig et al., 2012). The detailed description and assessment of E3SMv2 can be found in Golaz et al. (2022).

The 4DEnVar method employed in the WCODA system is based on the dimension-reduced projection four-dimensional variational (DRP-4DVar) algorithm (Wang et al., 2010). In DRP-4DVar, the ensemble-based approach is used to replace the adjoint model traditionally required in standard 4DVar, thereby significantly reducing computational cost. The DRP-4DVar method determines the optimal state in the ensemble subspace by fitting observational data to model-generated ensemble samples within the four-dimensional assimilation window (Liu et al., 2011; Shi et al., 2021). Unlike nudging methods, which typically apply empirical relaxation terms to the model's prognostic equations, the DRP-4DVar scheme obtains the optimal analysis by minimizing the cost function of 4DVar. Specifically, observational information is assimilated along the trajectory of the model solution within the four-dimensional assimilation window, ensuring that the optimal analysis is dynamically consistent with the model physics (He et al., 2017). To mitigate ensemble collapse, the DRP-4DVar algorithm employs an inflation technique that introduces a zero initial condition perturbation sample to reconstruct the ensemble projection space as a full-rank matrix (Wang et al., 2010). Due to its flexibility and efficiency, the DRP-4DVar method has been widely applied in diverse numerical models to improve the initialization of ocean, land, and atmospheric states (He et al., 2020; Shi et al., 2024b; Zhu et al., 2022). In particular, the DRP-4DVar approach has been shown to generate dynamically consistent initial conditions that effectively mitigate the initialization shock during the early years of initialized hindcasts (He et al., 2017).

In this study, monthly mean ocean temperature and salinity from the EN4.2.1 reanalysis (Good et al., 2013) are assimilated into the ocean component of the fully coupled E3SMv2 model within a one-month assimilation window. The observational uncertainty of the EN4.2.1 reanalysis is represented through the observation error covariance matrix, which is statistically derived from the variance of ocean temperature and salinity data. The spatiotemporal density of observations within the EN4.2.1 product modulates the assimilation impact. Regions with dense observational coverage are expected to exhibit more pronounced improvements, whereas in data-sparse areas such as the Indian Ocean, the assimilation constraint is relatively weaker. Each monthly assimilation cycle consists of the analysis and forecast stages. First, the fully coupled E3SMv2 model is run forward for one month using the background initial conditions to generate model-derived monthly means of ocean temperature and salinity. In the analysis stage, the differences between these model outputs and the EN4.2.1 reanalysis are calculated to form the observational innovation. The DRP-4DVar scheme then applies this innovation to compute the optimal initial conditions for the ocean component at the beginning of the assimilation cycle. During the following forecast stage, the fully coupled model is rewound to the start of the month and re-integrated for the same month using the optimized ocean state and the background fields from other components. Through this coupled forecast, ocean observational information is dynamically propagated to influence the state variables of other components (e.g., atmosphere and land) through multi-component interactions. Thus, while the assimilation is confined to the ocean, employing the fully coupled E3SMv2 model in the forecast stage enables the transfer of assimilated ocean information to other Earth system components, classifying this system as a WCDA framework (Zhang et al., 2020). Further technical details of the assimilation system are described in Shi et al. (2025).

Two numerical experiments are conducted to assess the impact of the WCODA system on climate variability: a control experiment (CTRL) and an assimilation experiment (ASSIM). Both experiments are initialized from the same initial condition on 1 January 1950, which is derived from a fully spun-up long-term integration of E3SMv2 (Golaz et al., 2022). Following initialization, the CTRL experiment is integrated freely without re-initialization or further modifications to the model state from 1950 to 2021 under observed historical external forcings. This experiment serves as the reference simulation for evaluating the influence of the assimilation system. Both CTRL and ASSIM experiments are forced with the same historical external forcings prescribed by the CMIP6 protocol (Eyring et al., 2016). The E3SMv2 model had already reached a stable quasi-equilibrium state through a long spin-up and historical integration (Golaz et al., 2022).

The ASSIM experiment assimilates monthly mean ocean temperature and salinity from the EN4.2.1 reanalysis into all 60 layers of the ocean component in the fully coupled E3SMv2 model from 1950 to 2021 using a one-month assimilation window. At the beginning of each month, monthly mean ocean temperature and salinity from the EN4.2.1 reanalysis are assimilated to update the ocean initial conditions, after which the fully coupled model is integrated freely until the end of the month. During this forecast period, the assimilated ocean information is dynamically propagated to other components through multi-component interactions. Unlike the sea surface temperature (SST) relaxation approach used in pacemaker experiments to isolate the ocean influence on climate variability (e.g., Kosaka and Xie, 2016), the assimilation system is implemented to generate initial conditions for hindcast experiments by incorporating full-depth ocean temperature and salinity reanalysis to constrain the complete three-dimensional ocean state. This approach preserves vertical dynamical consistency and retains the subsurface ocean memory necessary for capturing decadal-to-multidecadal variability. For example, Morioka et al. (2018) demonstrated that skillful prediction of decadal variability in the South Atlantic requires the assimilation of subsurface ocean temperature and salinity, as SST-only assimilation fails to accurately represent zonal heat transport. However, the Arctic Ocean is excluded from the assimilation domain due to sparse observational coverage and the current absence of a coupled ice-ocean assimilation scheme. Much of the Arctic Ocean is characterized by pervasive year-round sea ice cover. Without simultaneously updating sea ice variables, assimilating ocean temperature and salinity alone could potentially introduce physical inconsistencies at the ice-ocean interface. Addressing this technical limitation remains a high priority for future system development.

Three types of monthly reanalysis datasets are used for evaluation: (1) ERA5 reanalysis data, including surface air temperature, 850 hPa winds, and 500 hPa geopotential height. ERA5 incorporates a wide range of satellite and in situ observations to produce high-quality global atmospheric fields (Hersbach et al., 2020). (2) Global Precipitation Climatology Project (GPCP) monthly precipitation data. This dataset provides reliable global precipitation estimates based on satellite microwave, infrared measurements, and surface rain gauge data (Adler et al., 2003). (3) Hadley Centre Sea Ice and Sea Surface Temperature (HadISST) data. HadISST provides monthly SST analyses derived from a combination of in situ measurements and satellite-based retrievals (Rayner et al., 2003). Since the HadISST dataset and the assimilated EN4.2.1 reanalysis partially share a common pool of underlying in situ ocean observations, HadISST does not serve as a fully independent validation dataset. Nevertheless, the improved agreement with HadISST still demonstrates the effectiveness of the assimilation system in constraining the ocean states.

The temporal evolution of both non-detrended and linearly detrended annual mean surface air temperature anomalies over the ocean, land, and global domains is shown in Fig. 1. The non-detrended time series (Fig. 1a–c) suggest a long-term warming trend, while the detrended series (Fig. 1d–f) isolate interannual variability by removing the linear trend from each domain-averaged time series. In both cases, ASSIM better captures the observed interannual surface air temperature variability compared to CTRL across all domains. For the non-detrended global annual mean surface air temperature, the correlation of ASSIM with observations is 0.92, slightly higher than the value of 0.85 reported by Douville et al. (2015) in their tropical Pacific pacemaker experiment. After linear detrending, the correlation coefficient between ASSIM and observations reaches 0.47 over the ocean, much higher than that of CTRL (0.09). Over land and global domains, the correlation coefficients for ASSIM are 0.44 and 0.49, respectively, again exceeding those of CTRL (land/global: 0.26/0.18). All three detrended correlations from ASSIM pass the 95 % confidence level, indicating statistically significant improvements in simulating interannual surface temperature variability. The improvement is most pronounced over the ocean, where the assimilated ocean state exerts a direct influence on near-surface atmospheric conditions. Notably, the improved correlations over land suggest that the benefits of ocean data assimilation extend beyond oceanic regions, reflecting its broader influence on global surface temperature variability. However, compared with pacemaker experiments in which SST is directly nudged within the tropical Pacific, the relatively weaker atmospheric response to certain ENSO events in ASSIM may be related to the competing influence of global ocean constraints beyond the tropical Pacific, as well as the smoothing effect introduced by the monthly assimilation window.

Figure 2 displays the spatial distribution of climatological mean differences in surface air temperature. Compared to observations, CTRL exhibits widespread cold biases over the tropical and subtropical oceans, as well as notable warm biases at high latitudes. In contrast, these biases are significantly reduced in ASSIM, particularly over the North Pacific, North Atlantic, and the midlatitude Southern Ocean. Specifically, the cold bias in the North Pacific decreases from -1.81 °C in CTRL to -0.76 °C in ASSIM, and from -3.23 to -1.09 °C in the North Atlantic. The warm bias over the midlatitude Southern Ocean is notably reduced from 1.07 °C in CTRL to 0.13 °C in ASSIM. Improvements are also evident over land regions, such as eastern China, northern Eurasia, northern Africa, and parts of North America. The spatial pattern of reduced surface air temperature bias closely aligns with the reduction in SST bias reported by Shi et al. (2025), highlighting the strong coupling between the ocean surface and the atmosphere. However, the current assimilation experiment does not explicitly isolate the respective contributions of SST and subsurface ocean states. Future SST-only assimilation experiments would be needed to disentangle their individual effects on surface air temperature. The climatological warm biases over the Arctic Ocean appear slightly enhanced in ASSIM compared with CTRL. Since the Arctic Ocean state is not directly constrained by assimilation, it may respond indirectly to remote adjustments introduced elsewhere, potentially leading to a redistribution of temperature biases. Despite this localized degradation, the assimilation maintains the overall stability of the coupled system. As shown in Fig. A1, key global mean diagnostics, including top-of-atmosphere net energy flux, surface air temperature, ocean temperature and salinity, remain stable throughout the ASSIM integration.

The interannual variability of linearly detrended precipitation anomalies over the ocean, land, and global domains is illustrated in Fig. 3. Compared with CTRL, ASSIM shows markedly improved agreement with the observed interannual precipitation variability across all three domains. Specifically, the temporal correlations with observations increase from 0.11 in CTRL to 0.52 in ASSIM over the ocean and from 0.27 in CTRL to 0.60 in ASSIM over land. At the global scale, the correlation rises from 0.04 in CTRL to 0.55 in ASSIM. All three correlations from ASSIM are statistically significant at the 95 % confidence level. These results suggest that assimilating observed ocean states enhances the simulation of interannual precipitation variability over both ocean and land, with the latter improvement possibly related to atmospheric circulation and moisture transport.

Figure 4 shows the spatial distribution of climatological mean precipitation and associated model biases. In the observations (Fig. 4a), major precipitation maxima are located along the Intertropical Convergence Zone (ITCZ) in the equatorial Pacific, the South Pacific Convergence Zone (SPCZ) extending southeastward from the western Pacific, and over the tropical Indian Ocean. A dry zone is also evident along the west coast of South America. Compared with observations, CTRL overestimates precipitation over the central Pacific and the southern equatorial Atlantic, and significantly underestimates rainfall over the tropical eastern Indian Ocean and the northern equatorial Atlantic (Fig. 4b and d). In contrast, these biases are substantially reduced in ASSIM (Fig. 4c and e). Precipitation in the tropical eastern Indian Ocean is enhanced, resulting in better agreement with observations. Moreover, in the tropical Atlantic, the dry bias over the northern equatorial Atlantic is reduced from -1.27 mm d⁻¹ in CTRL to -0.34 mm d⁻¹ in ASSIM, while the wet bias over the southern equatorial Atlantic decreases from 1.81 to 0.62 mm d⁻¹. These reductions in systematic biases bring the climatological precipitation in ASSIM into better agreement with observations. Over some regions, particularly the tropical Pacific, the residual differences are no longer statistically significant. The improvement in tropical precipitation is closely linked to changes in the large-scale meridional circulation. As illustrated in Fig. A2, CTRL exhibits an anomalously strong ascending branch of the Hadley circulation in the northern tropics, which sustains a pronounced wet bias over the tropical Pacific. In contrast, this anomalous ascent is effectively suppressed in ASSIM, contributing to a more realistic precipitation distribution across the tropical and subtropical regions.

ENSO is the dominant mode of interannual climate variability in the tropics and exerts profound impacts on global atmospheric circulation (Chiang and Sobel, 2002). ENSO variability is commonly monitored by the Niño 3.4 index, defined as the SST anomalies averaged over the equatorial central Pacific (5° S–5° N, 170–120° W) (Trenberth and Stepaniak, 2001). To evaluate the representation of ENSO variability, we analyze the temporal evolution of the monthly and winter Niño 3.4 indices (Fig. 5). As expected, CTRL exhibits very weak correlations with observations, with correlation coefficients of only 0.02 for the monthly and 0.07 for the winter Niño 3.4 index, indicating poor phase agreement with the observed Niño 3.4 index. Compared with CTRL, ASSIM exhibits markedly improved phase agreement with the observed ENSO variability. The temporal evolution of the Niño 3.4 index in ASSIM closely matches observations, with correlations increasing to 0.87 for the monthly and 0.95 for the winter index. These results demonstrate that ocean data assimilation provides an effective constraint on tropical Pacific SST variability.

Figure 6 further evaluates ENSO characteristics through the power spectra and seasonal cycle of the monthly Niño 3.4 index. The observed spectrum exhibits a pronounced peak in the 3–5 year band, consistent with typical ENSO periodicities (Fig. 6a). This spectral feature is reasonably well reproduced in ASSIM (Fig. 6b). By comparison, CTRL underestimates the variance in this band and produces an unrealistically amplified peak at 2–3 years (Fig. 6c). Beyond its frequency characteristics, ENSO also exhibits a strong seasonal cycle. The observed Niño 3.4 index shows minimum variance in April and peak amplitude in December, reflecting the well-known phase-locking behavior of ENSO (Fig. 6d). ASSIM captures this seasonal cycle well, although the minimum occurs one month later (Fig. 6e). In contrast, CTRL exhibits a flatter seasonal cycle with markedly weaker variance during the winter peak, and its seasonal minimum is delayed by two months (Fig. 6f).

To further assess the representation of ENSO-related atmospheric variability, we examine the Southern Oscillation Index (SOI), which reflects the east–west seesaw pattern in sea level pressure (SLP) between the western and eastern tropical Pacific. The SOI is commonly defined as the normalized difference in SLP anomalies between Tahiti and Darwin, and serves as the atmospheric counterpart to the Niño 3.4 index (Hanley et al., 2003). Figure 7 presents the temporal evolution of the monthly and winter SOI from the observation, ASSIM, and CTRL. The observed SOI exhibits pronounced interannual fluctuations associated with ENSO phases. Consistent with its poor simulation of the Niño 3.4 index, CTRL fails to capture the observed SOI variability, with correlations of -0.02 for the monthly and -0.04 for the winter index. In contrast, ASSIM reproduces the SOI variability more realistically, with correlations increasing to 0.40 for the monthly and 0.62 for the winter index. These results indicate that assimilating ocean reanalysis not only constrains SST but also enhances the phase agreement of ENSO-related atmospheric variability with observations in coupled models.

The Indian Ocean Dipole (IOD) is a prominent mode of interannual variability in the tropical Indian Ocean that strongly influences surrounding climate systems (Saji et al., 2006). It typically begins to develop in boreal summer and reaches its peak during autumn. A widely used metric for quantifying IOD variability is the Dipole Mode Index (DMI), defined as the difference in SST anomalies between the western (50–70° E, 10° S–10° N) and eastern (90–110° E, 0–10° S) equatorial Indian Ocean (Saji et al., 1999). The temporal evolution of the autumn DMI is further shown in Fig. 8. The observed DMI exhibits pronounced interannual variations associated with alternating positive and negative IOD phases. The CTRL simulation substantially overestimates the IOD amplitude and shows a weak correlation of -0.11 with observations. Such overestimation is a common bias in coupled climate models, as noted in previous studies (Ju et al., 2025). In contrast, ASSIM shows notable improvements in both the amplitude and temporal variability of the DMI, with the correlation increasing to 0.56 and passing the 95 % confidence level. These results highlight the effectiveness of ocean data assimilation in improving the temporal agreement of IOD variability with observations. Nevertheless, the lower DMI correlation in ASSIM compared with that of the Niño 3.4 index is partly attributable to known limitations of the assimilated EN4.2.1 dataset in the Indian Ocean. As noted by Good et al. (2013), the EN4.2.1 reanalysis exhibits regional deficiencies in this basin due to the limited availability of near-surface observations that meet quality-control standards, thereby limiting the assimilation effectiveness in the Indian Ocean.

The Pacific Decadal Oscillation (PDO) is the leading mode of decadal SST variability in the North Pacific, characterized by basin-scale SST anomalies that typically persist for one to two decades. The PDO index is derived as the leading empirical orthogonal function (EOF) mode of detrended SST anomalies over the North Pacific (20–70° N, 110° E–100° W) (Mantua et al., 1997). The EOF analysis is performed separately for the observations and each model experiment. Prior to the EOF calculation, all observational datasets and model outputs are interpolated onto a common horizontal grid and linear trends are removed at each grid point. Figure 9 illustrates both the temporal evolution and spatial pattern of the annual PDO index from 1965 to 2016. The observed PDO index displays a canonical sequence of phase transitions: a cool phase before the late 1970s, a persistent warm phase extending into the late 1990s, and a return to negative values thereafter (Fig. 9a). These decadal transitions are reasonably captured by ASSIM, yielding a temporal correlation of 0.67 with observations (Fig. 9b). In contrast, CTRL fails to reproduce the observed phase transitions, with a much lower correlation of 0.19 (Fig. 9c). Besides the temporal evolution, the spatial structure of the PDO index is also analyzed. The observed pattern exhibits a horseshoe-shaped structure with cold anomalies in the central North Pacific and warm anomalies along the western coast of North America (Fig. 9d). This spatial pattern is well reproduced in ASSIM, with a spatial correlation of 0.90 (Fig. 9e). However, the PDO pattern from CTRL exhibits a distorted structure, and its spatial correlation decreases to 0.68 (Fig. 9f). These improvements in both the temporal evolution and spatial structure of the PDO underscore the potential of the assimilation system to enable more skillful decadal climate predictions by providing improved initial states.

Beyond the North Pacific, another major mode of decadal variability affecting the entire Pacific basin is the Interdecadal Pacific Oscillation (IPO). Similar to the PDO, the IPO index is obtained from the leading EOF mode of detrended SST anomalies, but computed over the whole Pacific (50° S–50° N, 100° E–70° W) (Doblas-Reyes et al., 2013). The annual evolution of the IPO index is shown in Fig. 10, indicating the basin-wide coherence of Pacific decadal variability. The observed IPO index undergoes distinct decadal shifts, including a negative phase prior to the late 1970s, a prolonged positive phase extending through the 1980s and 1990s, and a return to negative values in the early 2000s. These phase transitions are closely reproduced by ASSIM, which achieves a high temporal correlation of 0.80 with observations. On the other hand, CTRL fails to track the decadal evolution of the observed IPO and shows a much weaker correlation of 0.20. These results indicate that ocean data assimilation serves as an effective pathway for constraining Pacific-basin SST variability and enhancing phase alignment with observed Pacific SST variability on decadal timescales.

In addition to the Pacific, the North Atlantic also exhibits notable low-frequency SST variability characterized by the Atlantic Multidecadal Oscillation (AMO). The AMO index is computed as the linearly detrended SST anomalies averaged over the North Atlantic (0–60° N, 0–80° W) (Trenberth and Shea, 2006). Figure 11 presents the temporal evolution of the annual AMO index from 1965 to 2016. The observed AMO index shows a pronounced negative phase in the 1970s and 1980s, followed by a persistent positive phase beginning in the mid-1990s. These phase transitions are more accurately reproduced in ASSIM than in CTRL, particularly with respect to the timing and amplitude of the warm shift after the mid-1990s. The temporal correlation with observations is 0.71 in ASSIM, much higher than 0.17 in CTRL. This improved phase agreement of AMO variability in ASSIM reinforces its potential for better predicting related climate impacts over the North Atlantic and adjacent regions.

Building on the improved representation of tropical SST variability through ocean data assimilation, we extend our analysis to assess its impact on regional climate over land via teleconnections. Given the well-established influence of ENSO on US winter climate variability (Ropelewski and Halpert, 1986; Higgins et al., 2000), we evaluate model performance in simulating interannual temperature and precipitation variability over the contiguous US during boreal winter (Figs. 12 and 13). For winter surface air temperature (Fig. 12), ASSIM exhibits widespread increases in temporal correlation with observations across large portions of the northern and western US, particularly over the Intermountain West and Great Lakes regions. In these areas, correlation improvements commonly exceed 0.3 and locally surpass 0.4. Consistent with the correlation patterns, RMSE reductions in ASSIM are also evident across the northern and central US, with decreases of up to 0.6 °C over the central Great Plains.

In contrast to temperature, improvements in winter precipitation simulations are more localized but remain pronounced across the southern US (Fig. 13). Compared with CTRL, ASSIM shows higher correlations with observed precipitation over the Southwest, southern Great Plains, and Southeast. In particular, significant enhancements are evident in parts of California, Texas, and Alabama, where correlation increases exceed 0.4 and locally approach 0.5. These correlation improvements are accompanied by consistent reductions in RMSE across similar regions. Notably, the largest RMSE reductions, exceeding 0.45 mm d⁻¹, are found over coastal California. The spatial coherence of these improvements suggests that incorporating realistic ocean states can better capture US winter precipitation variability.

To further investigate the mechanisms underlying the improved simulation of US winter climate, we examine the regression of surface air temperature and precipitation onto the Niño 3.4 index during boreal winter (Fig. 14). Boreal winter is the focus of this analysis because ENSO teleconnections to North America are strongest and most coherent during winter, while ENSO-related impacts in other seasons are generally weaker and less spatially coherent over the US (Ropelewski and Halpert, 1986; Higgins et al., 2000). The Niño 3.4 index is calculated separately using each corresponding dataset, and all regressions are performed using simultaneous winter averages. The observed patterns reveal that ENSO exerts a pronounced influence on US winter climate through large-scale atmospheric responses. During El Niño events, positive geopotential height anomalies dominate the northern part of the continent, which may suppress the southward intrusion of cold air masses. This circulation pattern could lead to anomalous warming across the northern US, producing significant positive correlations with ENSO in these regions (Fig. 14a). Meanwhile, strengthened subtropical westerlies enhance moisture transport into the southern US, favoring increased precipitation and yielding strong positive correlations with ENSO across the southern tier of the country (Fig. 14d).

These ENSO-related spatial structures are well reproduced in ASSIM (Fig. 14b and e). In particular, the regression patterns of temperature and precipitation in ASSIM closely resemble those in the observations, especially across the northern and southern US, respectively. The spatial pattern correlation between ASSIM and observations is 0.86 for surface air temperature, much higher than that of CTRL (0.35). For precipitation, the spatial correlation increases from 0.67 in CTRL to 0.72 in ASSIM. Furthermore, the regions with robust ENSO-related signals in ASSIM largely overlap with areas showing improved correlation and reduced RMSE in Figs. 12 and 13. The stippled regions in these figures denote statistically significant differences at the 95 % confidence level. Specifically, for winter surface air temperature, statistically significant increases in correlation and concurrent reductions in RMSE are primarily found in parts of Arizona and Iowa (Fig. 12), while for winter precipitation, such improvements are mainly located over parts of California and Alabama (Fig. 13). To account for the potential delayed impact of ENSO, a one-month lagged regression analysis is also presented in Fig. A3. The resulting lagged patterns are highly consistent with the simultaneous winter regression results (Fig. 14), reinforcing the linkage between ENSO variability and US winter climate anomalies. These results demonstrate that the improved phase alignment of ENSO variability enhances the simulation of US winter surface air temperature and precipitation.