1. Introduction
The Pacific decadal oscillation (PDO) is characterized by anomalous cold (warm) sea surface temperature (SST) in the midlatitude North Pacific and opposite SST anomalies in its surrounding areas, including the tropical central and eastern Pacific and along the west coast of North America, during the positive (negative) phase (Mantua et al. 1997; Newman et al. 2016). The time evolution of the PDO, which is referred to as the PDO index, is defined as the normalized time series of the leading mode of North Pacific SST (Mantua et al. 1997). The PDO index has undergone several phase changes in approximately 1925, 1947, 1977, and the late 1990s in the past century (Mantua et al. 1997; Ding et al. 2013; Meehl and Teng 2014; Meehl et al. 2016). These phase transitions have substantial influences on the global climate, agriculture, fisheries, marine ecosystems, and human health (Mantua et al. 1997; Power et al. 1999; McCabe et al. 2004; Osgood 2008; Vera et al. 2010; Kosaka and Xie 2013; Meehl et al. 2014a; Yu et al. 2015; Zhu et al. 2015; Fyfe et al. 2016). For example, the 1930s Dust Bowl, the 1950s Great Plains drought, and the Southern Flood and Northern Drought in China from the late 1970s to the late 1990s gave rise to serious social and economic losses and threatened people’s lives. In this regard, predicting the PDO phase transitions a few years in advance successfully can provide a valuable basis for decision-making in various socioeconomic industries (Vera et al. 2010).
Some studies have shown that the PDO index is predictable in an initial few years (Mochizuki et al. 2010) or some periods by case studies (Ding et al. 2013; Meehl and Teng 2014; Meehl et al. 2016). More recent studies have also made some progress in predicting the PDO. For example, PDO trends are skillfully predicted up to 10 years in advance based on the decadal prediction system of the Max Planck Institute Earth System Model (MPI-ESM) (Wiegand et al. 2019). The multimodel ensemble mean of phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6) retrospective decadal predictions have high skill in predicting the PDO at the first two lead years and lead years 5–9 (Choi and Son 2022). The NorCPM1 prediction system participating in the CMIP6 decadal prediction experiments can skillfully predict the early warning signals of the late-1970s and late-1990s regime shifts 5–7 years ahead (Ma et al. 2022). However, predicting the PDO index accurately is still a challenge (Guemas et al. 2012; Kim et al. 2012; van Oldenborgh et al. 2012; Doblas-Reyes et al. 2013; Li et al. 2020). By analyzing the retrospective prediction (hindcast) results from the available decadal prediction systems, which are initiated every year in CMIP5 and CMIP6 (Taylor et al. 2012; Eyring et al. 2016) (Table 1), the PDO index is skillfully predicted 1 and 2 years in advance and on the decadal time scale (i.e., averaged over forecast years 1–10 or 2–10) by most systems (Fig. 1a). The predictions of the PDO index fail to show statistically significant correlations with observations for annual variations 3 or more years in advance for a majority of the systems. The poor PDO index prediction skills are probably limited by initialization schemes (Yuan and Lu 2020), which do not take into account the PDO mechanisms (Kushnir et al. 2002). Another major limitation is model error, which produces bias and drift (Taylor et al. 2012; Eyring et al. 2016).
Decadal prediction systems contributing to CMIP5 and CMIP6, which are initiated every year; i1 and i2 represent different initialization schemes. IAU = incremental analysis update; EnKF = ensemble Kalman filter.
(a) Correlation and (b) RMSE (°C) of the predicted PDO index vs the HadISST. The y axis is the prediction year from 1 to 10 and the average predictions for 1–10 and 2–10 years in advance. The correlation that is significant at a 95% confidence level is marked by a five-pointed star. Gray squares denote that the model lacks the prediction results of lead year 1 and lead years averaged over 1–10. Here i1 and i2 represent different initialization strategies. Only the hindcast by HadCM3 is plotted in the CMIP5 multimodel ensemble mean hindcasts in lead year 1 due to the lack of data for the other CMIP5 hindcasts. The hindcasts by BCC-CSM1.1, CanCM4, GFDL-CM2.1, MIROC5, MPI-ESM-LR, BCC-CSM2-MR, CanESM5, and IPSL-CM6A-LR are excluded in the lead years averaged over 1–10 years due to a lack of data in the first lead year.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
Although the PDO mechanisms are still under debate (Mantua and Hare 2002), it is widely accepted that the midlatitude air–sea interaction (ASI) over the North Pacific and tropical–midlatitude interactions play important roles in PDO formation, maintenance, and phase transitions (Latif and Barnett 1994, 1996; Barnett et al. 1999; Meehl and Hu 2006; Fang and Yang 2011; Farneti et al. 2014; Zhang and Delworth 2015; Fang and Yang 2016; Newman et al. 2016). The role of the midlatitude ASI found by these studies includes the influence of the meridional gradient of SST on atmospheric circulation, which in turn changes oceanic circulation, inducing the PDO to oscillate (Barnett et al. 1999). The current initialization methods, such as the widely used simple restoration of model states to observational states (Meehl et al. 2014b) and other more sophisticated methods (Zhang et al. 2007; Wang et al. 2017), rarely include the ASI constraint in the initialization. Taking one commonly used simple restoration method called nudging as an example, it directly restores the modeled ocean state to the observational state at every model time step and thus resists any feedback from other components of the coupled model. In this case, the interactions between the ocean and other components of the climate system (especially the ASI) are limited. Whether the initialization constrained by the ASI is beneficial to the PDO index prediction skills remains unclear. If so, how does it influence the PDO index prediction?
In this study, we use a novel weakly coupled data assimilation (CDA) method (He et al. 2017, 2020a,b), named dimension-reduced projection four-dimensional variational (DRP-4DVar) data assimilation (Wang et al. 2010, 2018). Global oceanic observations are incorporated under the constraint of ASI during initialization with a climate model, gridpoint version 2 of the Flexible Global Ocean–Atmosphere–Land System Model (FGOALS-g2) (Li et al. 2013). Detailed descriptions of the DRP-4DVar CDA method and experiments are described in section 2. In section 3, we evaluate the PDO prediction skills based on the DRP-4DVar initialization, compared with those based on the initialization without the ASI constraint and the decadal prediction systems in CMIP5 and CMIP6. Then possible reasons for the prediction skills are investigated. A summary and discussion are provided in section 4.
2. Methods and data
a. Initialization methods
The initialization method is based on DRP-4DVar (He et al. 2017, 2020a,b), which is a kind of 4DVar method. Before describing the DRP-4DVar-based initialization method, several specialized terms are defined. The “assimilation window” is a time window used in 4DVar, where all the observations at different times and even averaged observations in this time window are assimilated. In this study, the assimilation window is one month. Monthly mean ocean temperature and salinity data of the ds285.3 dataset (Ishii et al. 2005, 2006) are assimilated as averaged observations in the one-month assimilation window. The “analysis” is the optimal estimation of IC at the beginning of the assimilation window after incorporating observations. The “background” is the a priori estimation of IC, which is produced by a one-month integration (or prediction) by the coupled model with the previous analysis as the IC. The “adjoint model” is the transpose of the tangent linear model that is the linear perturbation model of the nonlinear forecast model, and is used in calculating the gradient of the 4DVar cost function and integrates backward from the end of the assimilation window to the beginning of the assimilation window (Kalnay 2003). The “adjoint technique” means computing the gradient of the 4DVar cost function using the adjoint model. The “observational innovation” is the difference between the observation (i.e., the monthly mean ocean temperature and salinity of the ds285.3 dataset) and the projection of the background onto the observation space through the observation operator (Wang et al. 2010). In this study, the observation operator is an interpolation of the monthly mean model data, which is produced from the one-month coupled model integration of FGOALS-g2, to the observation grid. Due to the complexity of the coupled climate model, the tangent linear of the coupled model and its adjoint model are also very complex and hard to obtain, requiring huge costs for development and computing. To overcome this difficulty, DRP-4DVar uses historical prediction samples to form a dimension-reduced space and minimize the 4DVar cost function in this space without the adjoint technique. Thus, both the development and computing costs of 4DVar are greatly reduced.
The DRP-4DVar-based initialization is performed under the FGOALS-g2 coupled climate model (Li et al. 2013) using a weakly coupled data assimilation (WCDA) method that directly incorporates ocean observations into the ocean variables only but indirectly influences the variables of other components of the coupled model in the next assimilation window through the coupled integration. It consists of the following three steps (Fig. 2).
Schematic of the DRP-4DVar-based initialization method with the FGOALS-g2 climate model. It contains a one-month assimilation window. The term xb stands for the background fields of ICs, including the atmosphere (
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
First, FGOALS-g2 runs freely for a month starting from the background (xb) of all the components at the beginning of the assimilation window. This background is obtained from the second member of the twentieth-century simulation experiment of FGOALS-g2 on 1 January 1945, for all the components for the first assimilation window and is provided by the third step of the previous assimilation analysis for the following assimilation windows. The purpose of this step is to produce the observational background by FGOALS-g2 (
Third, a one-month free coupled integration of FGOALS-g2 is conducted again to prepare the background (xb) of all the components for the next assimilation analysis, starting from the optimal ocean IC (
DRP-4DVar-based initialization is a long-term coupled data assimilation cycle from 1945 to 2006 consisting of many data assimilation analyses with the above three steps. The ICs of all the components are improved continuously following the assimilation cycle. These improved ICs most likely benefit the prediction of climate variations.
For comparison, the nudging-based initialization method, which excludes the ASI constraint, is applied as well (Wang et al. 2013). It is also a weakly coupled data assimilation method but does not have an assimilation window like the DRP-4DVar method. The same monthly mean ocean observational data (i.e., the ds285.3 dataset) are linearly interpolated to every time step in the ocean component model, and then the model ocean states are directly restored to the interpolated observational field at each model time step (i.e., 1 h). In this way, the states of the atmosphere, sea ice, and land components are almost controlled by one-way forcing from the ocean with very little feedback on the ocean state. Consequently, the multicomponent interactions (e.g., ASI and ocean–land–atmosphere interaction) are greatly limited, leading to an imbalance or inconsistency between the ocean state and the states of the other components (e.g., the atmosphere). Other initialization methods used in the decadal prediction experiments of CMIP5 and CMIP6 have similar characteristics to the nudging-based initialization, thereby substantially limiting the multicomponent interactions.
Quite different from the one-way forcing of the ocean to the atmosphere in the nudging-based ocean initialization, the DRP-4DVar method allows feedback from the atmosphere to the ocean during the one-month free coupled integration in the first and third steps. The ocean is constrained only by the a priori (background) and optimal (observation) estimations at the beginning of each month in the first and third steps, respectively. However, the nudging method greatly limits the atmospheric feedback to the ocean because the ocean is constrained by the observations at every time step so that the atmosphere has little opportunity to influence the ocean. Therefore, the DRP-4DVar-based initialization produces better-balanced ICs between the ocean and atmosphere than the nudging-based initialization.
b. Experiments
The initialization experiment includes a climate model run from 1945 to 2006, in which the monthly mean ocean temperature and salinity of the ds285.3 analysis dataset (Ishii et al. 2005, 2006) are assimilated into the ocean component of FGOALS-g2 using full-field DRP-4DVar-based and nudging-based initialization methods (ASSM-DRP and ASSM-Nudging). The ICs of 1 January 1945 are from the second ensemble member of the twentieth-century simulation of FGOALS-g2. The uninitialized simulation (UNINIT) from 1945 to 2006 contains a five-member ensemble from the twentieth-century simulations and one member from the climate change projections following the representative concentration pathway (RCP) 4.5 scenario from CMIP5.
Using the initial conditions (ICs) provided by ASSM-DRP (ASSM-Nudging), we conduct decadal prediction experiments following the CMIP5 and CMIP6 decadal prediction experiment protocols, which are referred to as HCST-DRP (HCST-Nudging). During decadal predictions, only the ICs contain the observed information; the coupled model runs freely for the rest of the time. Note that there is usually an initial shock problem due to the rapid model adjustment during the first several years of decadal prediction (Meehl et al. 2014b). When we assimilate the full-field observations during initialization, the climatology of the initial conditions is often close to that of the observation. Due to the model deficiency, there is often a climatological bias in the model simulation relative to the observation. The initial shock happens when the model rapidly drifts from the observationally constrained initial conditions toward the model climate. If we directly use the initial conditions obtained during initialization, serious initial shock happens (Fig. S1a in the online supplemental material). When we replace the partial (75%) climatology of the initial conditions with that of the model, the initial shock is greatly reduced (Figs. S1b,c). The revised ocean initial conditions, including seawater temperature, salinity, sea surface height, and zonal current, are obtained as follows. We first compute the multiyear mean annual cycles of both the ocean initial conditions and the uninitialized simulations from 1955 to 2006. Then the revised ocean initial conditions are acquired by the original ocean initial conditions subtracting 75% of their mean annual cycle and then plus 75% of the mean annual cycle from the uninitialized simulation (He et al. 2020b). Each decadal prediction experiment consists of 10-yr-long 10-member hindcasts initiated every year over the 1961–2006 period. The 10 ensemble members are generated using a time-lagged method (i.e., from 1 February to November each month of the year before each starting year). HCST-Nudging is performed the same way as HCST-DRP. The external forcings, including the greenhouse gases, solar cycle, and aerosol concentrations, of all the experiments follow the CMIP5 protocol (Taylor et al. 2012).
c. Indices
The PDO index is computed based on SST anomalies. We first compute the boreal winter mean SST at each forecast lead year from 1 to 10. Then, the climatology of each lead year is calculated by averaging all boreal winter mean SSTs in the same lead year. The anomalies in each lead year are calculated by subtracting the climatology from the boreal winter mean SST in this lead year. The PDO index is defined as the normalized time series of the first leading empirical orthogonal function (EOF) mode for the North Pacific (20°–70°N, 110°–260°E) boreal winter mean SST anomalies (Mantua et al. 1997). The global mean and the linear trend of the SST anomalies are subtracted to remove the global warming signal and the variabilities on a longer time scale (van Oldenborgh et al. 2012; Zhang et al. 1997).
The activity of atmospheric transient eddies can be measured by the Eady growth rate, which is calculated as
d. Prediction skill assessment
Various datasets have been used as references to assess prediction skill. The HadISST v1.1 dataset (hereafter simply HadISST; Rayner et al. 2003) is used to verify the SST. The NCEP–NCAR Reanalysis (hereafter simply NCEP; Kalnay et al. 1996) and the NOAA–CIRES–DOE Twentieth Century Reanalysis V3 (20CRv3; Slivinski et al. 2019) are used for sea level pressure, geopotential height, air temperature, and wind stress. To cancel out random errors, we combine the NCEP and 20CRv3 reanalyses into a single blended product by arithmetically averaging the two. The ECMWF Ocean Reanalysis System 4 (ORAS4; Balmaseda et al. 2013) is used for seawater temperature. The HadCRUT4 dataset from the Met Office Hadley Centre is used for surface air temperature anomalies (Morice et al. 2012).
The prediction skill of the PDO index is assessed in terms of correlation and RMSE. The ensemble mean of each model is computed first by equally weighted averaging of all the ensemble members. The CMIP5 (CMIP6) multimodel ensemble mean is provided by equally weighted averaging of the 6 (10) selected CMIP5 (CMIP6) models based on their multimember ensemble means. The correlation and RMSE of the PDO index are calculated based on the multimember ensemble mean for each CMIP model and the multimodel ensemble mean for the CMIP5 or CMIP6 ensemble mean.
The statistical significance test is performed using a nonparametric moving block bootstrap method (Mignani and Rosa 1995; Mudelsee 2010; Wilks 2019). The significance of the correlation is based on the time series of observational data and ensemble mean hindcasts of each model, which are randomly resampled while blocks of five consecutive years are maintained to take into account the serial correlation (Goddard et al. 2013; Smith et al. 2013). The resampling process is repeated 10 000 times, and each pair of bootstrap-generated time series yields a bootstrap correlation. Then, all the bootstrap correlations are sorted in ascending order. The correlation that lies above the 95th percentile is significant at the 95% confidence level (one-tailed). The significance of the composite difference of the variable between the PDO positive and negative phases is computed using 10 000 bootstrapped time series of the variable with 5-yr blocks. The difference that lies outside the 2.5th (5th) and 97.5th (95th) percentiles is significantly different from zero at a 95% (90%) confidence level (two-tailed).
e. Estimation of seawater temperature tendency
The seawater temperature tendencies induced by horizontal advection and Ekman pumping are computed as
3. Results
a. Prediction skill of the PDO index
The prediction skill of the PDO index on interannual and decadal time scales is computed based on the SST anomalies at each lead year from 1 to 10 and the 9-yr or 10-yr mean, respectively. The SST anomalies are calculated as the boreal winter mean SST in each lead year minus the climatology of this lead year. The 9- or 10-yr mean SST anomalies are obtained by averaging the SST anomalies over lead years 2–10 or 1–10. Figure 1 shows the interannual and decadal prediction skills of the PDO index. HCST-DRP shows statistically significant skills at predicting the interannual variations of the PDO index 1 to 10 years in advance in terms of the correlations with the observed data (0.32–0.57) and root-mean-square errors (RMSEs) ranging from 0.91° to 1.15°C (Fig. 1). In particular, the hindcasts of all the leading years capture the observed phase transitions (i.e., the late 1970s and 1990s) (Figs. S2a–j). In contrast, HCST-Nudging rarely exhibits significant skill in the predictions 3–10 years in advance, although it has a higher correlation (0.8) and a lower RMSE (0.62°C) for the 1-yr prediction than HCST-DRP (Fig. 1 and Fig. S2). Note that the predicted PDO index on the interannual time scales in HCST-DRP only has a low-frequency variability, which may be due to be the direct assimilation of the monthly mean data under the strong coupled model constraint in one-month assimilation windows that filters a lot of signals in the ICs at time scales less than one month. The use of a shorter assimilation window (say one or two weeks) may probably alleviate the problem, which requires further study. The reason that HCST-DRP has a lower correlation coefficient with the observation at lead year 1 than HCST-Nudging is the differences between the DRP-4DVar and nudging methods in absorbing the observed information. When incorporating observations, the DRP-4DVar method uses the background error covariance and observational error covariance as the weightings of both the background and observations, while the nudging method adopts a simple nudging coefficient rather than these two covariances. Therefore, the nudging method may excessively include the observed information into ICs in general and thus may result in relatively high prediction skills in its initialized hindcasts. The higher correlation (0.95) of the ASSM-Nudging against the observation than that of the ASSM-DRP (0.75) in Fig. S3 verifies the excessive incorporation of the observed information in the ICs by the ASSM-Nudging. However, this excessive incorporation may lead to the inconsistency between ICs and the coupled model, thus degrading the prediction skills in the following lead years. On the contrary, the ICs from the ASSM-DRP are more consistent with the coupled model by reasonably considering the background information that contains dynamic and physical constraints, and thereby lead to high prediction skills in each lead year from 2 to 10. This implies that the high interannual prediction skills of the PDO index are not dependent on the excessive incorporation of observed information in the analysis data into the oceanic ICs. The performance of HCST-DRP is more striking on the decadal time scale than HCST-Nudging, with a correlation of up to 0.92 (0.90) and an RMSE of 0.41°C (0.44°C) for lead years averaged over 1–10 (2–10) (Fig. 1).
The PDO index prediction skill of HCST-DRP is also well above the CMIP5 and CMIP6 multimodel ensemble mean hindcasts at each forecast year from 2 to 10 and averaged over 1–10 (2–10) years (Fig. 1). Apart from the first two lead years, the CMIP5 and CMIP6 multimodel ensemble mean hindcasts hardly have correlation skills and present high RMSEs (Fig. 1). HCST-DRP also has higher skill in predicting the interannual and decadal PDO index than individual CMIP5 and CMIP6 hindcast (Fig. 1). None of these CMIP hindcasts has significant correlation skills in all lead years, although some hindcasts have high prediction skills in the first two lead years.
Since the oceanic ICs used in HCST-DRP are not as good as those in HCST-Nudging (Fig. S3), they should not be a key factor contributing to the higher PDO prediction skill of HCST-DRP. According to the ASI mechanism of the PDO, the consistent ICs between the ocean and atmospheric components might be more vital.
b. PDO-related atmospheric ICs coordinated with oceanic ICs
Previous studies have found that the atmospheric states over the North Pacific are closely tied to the PDO (Davis 1976; Trenberth and Hurrell 1994; Kushnir et al. 2002). These atmospheric states are characterized by vertical structures of lower geopotential height in the troposphere as well as colder (warmer) air temperature in the low (high) troposphere during the PDO positive phase (Fang and Yang 2016; Luo et al. 2020; Tao et al. 2020). The atmospheric states linked to the PDO are defined as the differences in the linearly detrended atmospheric circulations and air temperature in boreal winter between the positive and negative phases of the PDO (Table S1).
The blended reanalyses show a negative sea level pressure anomaly centered over the North Pacific, indicating a strengthened Aleutian low during the PDO positive phase (Fig. 3a). ASSM-DRP reproduces the Aleutian low much closer to the reanalyses than ASSM-Nudging does in terms of its location, intensity, and horizontal distribution (Figs. 3b,c). The Aleutian low in ASSM-Nudging is located southeastward with weak intensity. It shows an east–west distribution that differs from the southeast-northwest distribution in the reanalyses and ASSM-DRP.
The difference in boreal winter sea level pressure between the PDO positive and negative phases in (a) the blended reanalyses, (b) ASSM-Nudging, and (c) ASSM-DRP. The black dots correspond to the points where the difference is significant at a 90% confidence level.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
The geopotential height anomalies in the lower, middle, and upper troposphere in the reanalyses (Figs. 4a–c) exhibit patterns similar to the sea level pressure anomalies, with negative anomalies over the Aleutian low area. These patterns are captured better by ASSM-DRP (Figs. 4g–i) than by ASSM-Nudging (Figs. 4d–f). In addition, the blended reanalyses show positive geopotential height anomalies over the tropical Pacific, especially in the western part at 850 hPa and the eastern part at 500 and 200 hPa, which are well represented by ASSM-DRP and ASSM-Nudging.
The differences in boreal winter geopotential height between the PDO positive and negative phases. (a)–(c) The blended reanalyses, (d)–(f) ASSM-Nudging, and (g)–(i) ASSM-DRP at (left) 850, (center) 500, and (right) 200 hPa. The black dots correspond to the points where the difference is significant at a 90% confidence level.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
The air temperature displays cold anomalies in the lower and middle troposphere and warm anomalies in the upper troposphere in the reanalyses, with negative sea level pressure and geopotential height anomalies in the same horizontal region (Figs. 5a–c). This vertical structure is captured reasonably well by ASSM-DRP despite the intensity underestimation in the upper troposphere (Figs. 5g–i). In comparison, ASSM-Nudging produces cold anomalies in the upper troposphere that are inconsistent with those in the reanalyses, although it reproduces the cold anomalies in the lower and middle troposphere in the reanalyses to some extent (Figs. 5d–f). In the tropical Pacific, ASSM-DRP and ASSM-Nudging resemble the blended reanalyses, which present warm air temperature anomalies in the eastern part at all levels.
The differences in boreal winter air temperature between the PDO positive and negative phases. (a)–(c) The blended reanalyses, (d)–(f) ASSM-Nudging, and (g)–(i) ASSM-DRP at (left) 850, (center) 500, and (right) 200 hPa. The black dots correspond to the points where the difference is significant at a 95% confidence level.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
More reasonable PDO-related atmospheric states in ASSM-DRP benefit from the coupled model constraint that DRP-4DVar employs so that the atmospheric and oceanic ICs are coordinated and accurate. In contrast, the nudging method does not include the coupled model constraint, which may lead to inconsistency between the atmospheric and oceanic ICs. A better balance of accurate ICs from ASSM-DRP between the ocean and atmosphere components can represent more realistic ASIs during predictions. This may promote higher interannual and decadal prediction skills of the PDO index in HCST-DRP than in HCST-Nudging. The possible mechanism will be explored and identified below.
c. Positive atmospheric feedback to sea surface temperature changes
The PDO-related atmospheric states are mainly maintained by midlatitude ASI over the North Pacific (Fang and Yang 2016; Luo et al. 2020). In this mechanism, the transition zone of different seawater properties (i.e., oceanic front) and the atmospheric disturbances on the mean flow (i.e., transient eddies) are indispensable. The observed meridional SST gradient is intensified in the Kuroshio and its extension region and weakened in the northern North Pacific when the PDO phase transitions from negative to positive. These observed SST gradient changes are well represented by HCST-DRP on the decadal time scale but mispresented by HCST-Nudging (Fig. S4). The intensified SST gradient enhances the subtropical oceanic front, which further influences midlatitude atmospheric circulations (Nakamura et al. 2004; Small et al. 2008). As a result, the low-level meridional air temperature gradient is increased south of 40°N in the blended reanalyses (Fig. 6a). HCST-DRP correctly predicts the vertical structure of the meridional air temperature gradient shown in the reanalyses despite the weak intensity, but HCST-Nudging fails to reproduce it (Figs. 6b,c). As the increased meridional air temperature gradient can enhance the vertical shear of the zonal wind (Lindzen and Farrell 1980), atmospheric transient eddies become more active in the lower and middle troposphere between 20° and 40°N. HCST-DRP reproduces the activities of the transient eddies in the blended reanalyses much better than HCST-Nudging (Fig. 7).
The differences in zonal mean boreal winter meridional air temperature gradient, geopotential height, and air temperature between the PDO positive and negative phases averaged over forecast years 1–10. Latitude–altitude sections of (a)–(c) meridional air temperature gradient, (d)–(f) geopotential height, and (g)–(i) air temperature averaged between 150°E and 150°W are computed using the (left) blended reanalyses, (center) HCST-Nudging, and (right) HCST-DRP. The black dots correspond to the points where the difference is significant at a 95% confidence level.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
The difference of zonal mean (150°E–150°W) boreal winter Eady growth rate between the PDO positive and negative phases averaged over forecast years 1–10 in (a) the blended reanalyses, (b) HCST-Nudging, and (c) HCST-DRP. The black dots correspond to the points where the difference is significant at a 90% confidence level.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
Due to the transient eddy feedback on the atmospheric mean flow, the North Pacific exhibits a strengthened Aleutian low, a lower geopotential height vertical structure across the whole troposphere (Figs. S5a–d). Meanwhile, air temperature in the lower and middle troposphere becomes colder and the upper troposphere turns warmer during the PDO positive phase (Figs. S6a–c). In the blended reanalyses, the vertical distributions are more evident when averaging between 150°E and 150°W. Negative geopotential height anomalies can be seen throughout the troposphere from 30° to 60°N (Fig. 6d) accompanied by cold air temperature anomalies in the lower and middle troposphere and warm anomalies in the upper levels (Fig. 6g). HCST-DRP well predicts these distributions (Figs. 6f,i; see also Figs. S5i–l and S6g–i), although the intensities are underestimated. In contrast, HCST-Nudging misrepresents the geopotential height and air temperature structures in the midlatitude North Pacific. It shows a weakened Aleutian low, positive geopotential height anomalies in the lower troposphere, and very weak negative anomalies in the middle and upper levels (Fig. 6e; see also Figs. S5e–h), as well as cold anomalies at all vertical levels (Fig. 6h and Figs. S6d–f).
The geopotential height vertical structure leads to a similar wind vertical structure in light of the midlatitude atmospheric feature (Marshall and Plumb 2008), with westerly winds strengthened in the whole troposphere from 20° to 40°N and reaching maximum values in the upper troposphere in the reanalyses (Fig. 8a). Thus, the midlatitude westerly jet (Fig. 9a) and the surface westerly are intensified, which are favorable for SST cooling in the midlatitude North Pacific through surface turbulent heat flux and wind stress, suggesting positive feedback. HCST-DRP successfully captures the zonal wind structure, although the maximum center is slightly south compared to the reanalyses (Figs. 8c and 9c). HCST-Nudging, however, incorrectly represents the westerly winds (Figs. 8b and 9b). In the tropical Pacific, HCST-DRP captures intensified easterlies, as shown in the reanalyses, while HCST-Nudging shows incorrect westerly wind anomalies (Fig. 9).
The difference of zonal mean (150°E–150°W) boreal winter zonal wind between the PDO positive and negative phases averaged over forecast years 1–10 in (a) the blended reanalyses, (b) HCST-Nudging, and (c) HCST-Nudging. The black dots correspond to the points where the difference is significant at a 95% confidence level.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
The difference in boreal winter 200-hPa zonal wind between the PDO positive and negative phases averaged over forecast years 1–10 in (a) the blended reanalyses, (b) HCST-Nudging, and (c) HCST-DRP. The black dots correspond to the points where the difference is significant at a 95% confidence level.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
HCST-DRP reproduces the positive ocean–atmosphere feedback well in the averages of 1–10-yr predictions. It also reasonably reproduces this mechanism in the predictions averaged over 2–10 years (figures not shown). The observed interannual variability of the PDO index is also the result of the interactions between the ocean and atmosphere (Figs. S7–S9). HCST-DRP also reproduces the observed mechanism in the interannual predictions (figures not shown). The North Pacific also has a time-delayed negative response to the overlying atmosphere, which may contribute to the PDO phase transitions (Latif and Barnett 1994, 1996; Jin et al. 2001; Primeau and Cessi 2001; Zhang and Delworth 2015). The intensified Aleutian low (Fig. S5a) and the strengthened midlatitude westerlies (Fig. 8a) are associated with a dipole structure of wind stress curl anomalies over the North Pacific. The blended reanalyses present cyclonic wind stress anomalies and positive wind stress curl anomalies over the subpolar and midlatitude regions on the decadal time scale. Moreover, anticyclonic wind stress anomalies and negative wind stress curl anomalies occur over the subtropics (Fig. 10a). HCST-DRP is more advantageous than HCST-Nudging, as it accurately depicts the patterns of wind stress anomalies and their curl anomalies with intensities weaker than those of the reanalyses (Figs. 10b,c). The better performance of HCST-DRP may result from the improvement of ASSM-DRP compared to ASSM-Nudging in describing the anomalies of wind stress and its curl (Fig. S10), although ASSM-DRP is not as good as HCST-DRP due to more sufficient ASI in HCST-DRP than ASSM-DRP.
The differences in the boreal winter wind stress and its curl anomalies averaged over forecast years 1–10 between the PDO positive and negative phases in (a) the blended reanalyses, (b) HCST-Nudging, and (c) HCST-DRP. Wind stress and its curl anomalies are indicated by arrows and shadings, respectively. The black dots correspond to the points where the difference in the wind stress anomalies is significant at a 95% confidence level.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
d. Negative oceanic feedback to wind stress changes
The changes in wind stress can induce changes in the upper ocean, which involve horizontal circulation adjustment of subpolar and subtropical gyres, vertical motions of seawater (i.e., Ekman pumping or suction), and oceanic Rossby waves (Latif and Barnett 1994; Schneider et al. 2002). The westerly wind stress anomaly at approximately 30°N is intensified at a lag of 0–3 years in HCST-DRP and the blended reanalyses (Figs. 11a,b,g,h), causing subpolar and subtropical gyres to adjust. Their adjustments lag behind the wind stress anomaly changes and last for 6 years (Figs. 12a–c,g–i).
Lagged regression of boreal winter wind stress anomalies (arrows) and wind stress curl anomalies (shadings) in (a)–(f) the blended reanalyses and (g)–(l) HCST-DRP on the PDO index averaged over forecast years 1–10.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
Lagged regression of boreal winter sea surface height anomalies (shadings) and geostrophic current anomalies (vectors) averaged over forecast years 1–10 on the PDO index for (a)–(f) the ORA reanalysis and (g)–(l) HCST-DRP. The zonal and meridional geostrophic currents are estimated as
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
In the western boundary, there are cold (warm) advection anomalies north (south) of 35°N in HCST-DRP (Figs. 13a–c) resulting from the Oyashio (Kuroshio) transporting cold (warm) water from the north (south) to south (north) (Figs. 12g–i). The westerly wind stress anomaly then decreases after 6–9 years and turns to an easterly anomaly after 12 years (Figs. 11c–f,i–l). The resulting gyre circulations spin down at a lag of 9–15 years (Figs. 12d–f,j–l), and cold (warm) advection anomalies in the north (south) of the gyres are reduced (Figs. 13d,e). After 15 years, the vertical distribution of the advection anomalies (Fig. 13f) is opposite to that at the beginning.
Lagged regression of zonal mean western boundary (120°–160°E) boreal winter seawater temperature tendencies on the PDO index averaged over forecast years 1–10 in HCST-DRP for (a)–(f) seawater temperature tendencies induced by horizontal advection of the oceanic gyres and (g)–(l) seawater temperature tendencies induced by Ekman pumping.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
In the central North Pacific, cold advection anomalies exist in the upper water at a lag of 0–6 years and are gradually replaced by warm advection anomalies after 9 years (Figs. 14a–f). Similar changes in horizontal advection are found in the ORAS4 reanalysis (Figs. S11a–f and S12a–f).
Lagged regression of zonal mean central North Pacific (160°E–140°W) boreal winter seawater temperature tendencies on the PDO index averaged over forecast years 1–10 in HCST-DRP for (a)–(f) seawater temperature tendencies induced by horizontal advection of the oceanic gyres and (g)–(l) seawater temperature tendencies induced by Ekman pumping.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
For the vertical motion of seawater, in the central North Pacific, the anticlockwise (clockwise) wind stress anomalies produce Ekman divergence (convergence), which results in upward (downward) vertical motion, that is, Ekman suction (pumping) in HCST-DRP at a lag of 0–3 years (Figs. 14g,h). The Ekman suction brings cold water to the surface and reinforces the negative SST anomalies in the midlatitude North Pacific, while the Ekman pumping warms the tropical Pacific. After 6 years, Ekman suction in the north and Ekman pumping in the south both weaken, and the induced seawater temperature anomalies become opposite to those at the beginning after 15 years (Figs. 14i–l). The patterns in HCST-DRP resemble those in the ORAS4 reanalysis (Figs. S12g–l). Note that the role of vertical motion is smaller than that of horizontal advection in HCST-DRP, while the difference between the roles of these two processes in the ORAS4 reanalysis is not as significant as in HCST-DRP. In the western boundary, the contribution of vertical motion is smaller than that of horizontal advection in both HCST-DRP (Fig. 13) and ORAS4 reanalysis (Fig. S11). In addition, the westward propagation of oceanic Rossby waves is not evident in HCST-DRP and ORAS4 reanalysis (Fig. S13). Therefore, the horizontal advection of the oceanic gyres is the main process in the North Pacific in HCST-DRP and ORAS4 reanalysis except that both horizontal advection and vertical motions are important in the central North Pacific in the ORAS4 reanalysis.
Horizontal advection and vertical motions play essential roles in seawater temperature changes. In the western boundary, most water is cold north of 35°N and warm south of 35°N in HCST-DRP at a lag of 0–6 years (Figs. 15g–i). After 9 years, the seawater increasingly becomes warm in the north and cold in the south and shows an opposite pattern to that at the beginning after 15 years in HCST-DRP (Figs. 15j–l). The ORAS4 reanalysis has similar changes (Figs. 15a–f). In the central North Pacific, cold water is widely distributed at the surface and subsurface, and warm water occurs at the subsurface south of 35°N at a lag of 0–6 years (Figs. 16a–c,g–i). After 9 years, the water warms at the surface and subsurface, and warm SST anomalies occur in most areas at a lag of 15 years (Figs. 16d–f,j–l). These seawater temperature changes facilitate the PDO phase transition, denoting negative ocean–atmosphere feedback. The time scale of the PDO in HCST-DRP is largely determined by the advection time scale in the subpolar and subtropical gyres of the climate model (Barnett et al. 1999; Schneider et al. 2002).
Lagged regression of zonal mean western boundary (120°–160°E) boreal winter seawater temperature anomalies averaged over forecast years 1–10 on the PDO index for (a)–(f) ORA reanalysis and (g)–(l) HCST-DRP.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
Lagged regression of zonal mean central North Pacific (160°E–140°W) boreal winter seawater temperature anomalies averaged over forecast years 1–10 on the PDO index for (a)–(f) ORA reanalysis and (g)–(l) HCST-DRP.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
The much higher skill of HCST-DRP at predicting the PDO index and its related mechanism (Fig. 17) compared to HCST-Nudging is attributed to the more realistic and well-balanced atmospheric and oceanic ICs that ASSM-DRP provides for the climate model, which demonstrates the crucial role of the ASI constraint in the initialization process. During decadal predictions in HCST-DRP, the compatible PDO-related atmospheric and oceanic states in the ICs evolve in coordination through the ASI under the framework of the climate model.
Schematic of the mechanism contributing to high PDO prediction skills. When the PDO enters the positive phase, cooling in the midlatitude North Pacific intensifies the SST gradient along the Kuroshio and its extension region, which excites positive atmospheric feedback. The overlying atmosphere exhibits negative geopotential height anomalies throughout the troposphere (contours with a 2-m interval) as well as colder air temperature in the lower troposphere and warmer air temperature in the upper troposphere (shadings), leading to intensified westerlies (purple arrows). The atmospheric response of wind stress anomalies influences the subpolar and subtropical oceanic gyre circulations (red arrows), which force the warm ocean upper water to be transported to the midlatitude North Pacific mainly through the western boundary current (i.e., the Kuroshio). The initial cold SST anomaly is thus weakened in the midlatitude North Pacific, suggesting delayed negative oceanic feedback.
Citation: Journal of Climate 36, 17; 10.1175/JCLI-D-22-0635.1
4. Summary and discussion
The DRP-4DVar method has been applied to the initialization of decadal predictions with the FGOALS-g2 climate model and achieved high interannual and decadal prediction skills of the PDO index. The prediction skills are higher than those based on the nudging initialization method with the same climate model and a majority of the decadal prediction systems in CMIP5 and CMIP6. The reason for the high prediction skills is possibly due to the accurate and coordinated oceanic and atmospheric ICs obtained over the North Pacific under the constraint of ASI during initialization. Thus, accurate predictions of the PDO ASI mechanisms including the positive atmospheric feedback to SST changes and the negative oceanic feedback to wind stress changes are achieved, leading to high PDO prediction skills.
In addition to the skillful prediction of the PDO index, high prediction skills of surface air temperature anomalies in the tropics on the decadal time scale have also been achieved (Fig. S14). Significantly positive correlation skills are present in almost the entire tropical regions (Fig. S14a). After linearly detrending, there are still high correlation skills in the tropical central and eastern Pacific and the tropical Atlantic (Fig. S14b). In particular, the Niño-3.4 index on the decadal time scale is skillfully predicted (Fig. S15), with a high correlation of 0.59 with observations.
The DRP-4DVar initialization method has also been applied to other successful decadal or interannual predictions, such as the decadal and interannual predictions of precipitation over the Tibetan Plateau (Yang et al. 2020; Li et al. 2021) and East Asian summer monsoon (Shi et al. 2021). These studies have also demonstrated the crucial role of the constraints of the multicomponent interactions (e.g., ASI and air–sea–land interaction) in achieving high prediction skills. Our study suggests that using an advanced initialization scheme with constraints of multicomponent interactions (particularly ASI) to initialize a climate model probably produces skillful decadal and interannual climate predictions. This type of initialization also has significant potential for further improving subseasonal to seasonal prediction skills. Other new methods such as strongly coupled data assimilation, which offer promising approaches to reduce the initialization shock and imbalance in the model compared to weakly coupled data assimilation, may potentially further improve the prediction skills (Penny and Hamill 2017).
Acknowledgments.
This research was supported by the National Natural Science Foundation of China (Grants 42230606, 42005030, and 12241105) and National Key Research and Development Program of China (Grant 2021YFC3101505).
Data availability statement.
The ds285.3 ocean temperature and salinity analyses can be accessed online at https://rda.ucar.edu/datasets/ds285.3/. The CMIP5 data are available from http://www.ipcc-data.org/sim/gcm_monthly/AR5/Reference-Archive.html. The CMIP6 data can be obtained at https://pcmdi.llnl.gov/CMIP6/. HadISST v1.1 is available at https://www.metoffice.gov.uk/hadobs/hadisst/. The NCEP–NCAR Reanalysis 1 dataset can be downloaded from https://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.pressure.html. The ORAS4 reanalysis is obtained from https://climatedataguide.ucar.edu/climate-data/oras4-ecmwf-ocean-reanalysis-and-derived-ocean-heat-content. The NOAA–CIRES–DOE 20th Century Reanalysis V3 dataset is available at https://psl.noaa.gov/data/gridded/data.20thC_ReanV3.html. The model results for the initialization and decadal prediction experiments are available from the corresponding author upon reasonable request.
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