1. Introduction
Westerly wind events or bursts (WWEs/WWBs) are anomalously strong, synoptic to intraseasonal (3–30 day) westerlies occurring over the Pacific or Indian Oceans with a high frequency of occurrence over the western Pacific warm pool (e.g., Luther and Harrison 1984; Hartten 1996; Harrison and Vecchi 1997; Lengaigne et al. 2004a; Seiki and Takayabu 2007; Lian et al. 2018). We use the WWE term in this paper while other works use the WWB nomenclature to refer to the same phenomena (e.g., Hartten 1996; Seiki and Takayabu 2007; Tziperman and Yu 2007; Seiki et al. 2011; Levine et al. 2016). Equatorial wind stress imparted on the ocean by WWEs is capable of exciting oceanic wave modes including eastward-propagating downwelling Kelvin waves and westward-propagating upwelling equatorial Rossby (ER) waves (e.g., Delcroix et al. 1991; Kessler and McPhaden 1995; McPhaden et al. 1988; Battisti 1988; Seiki and Takayabu 2007; Webber et al. 2012). The ocean waves in turn help modulate the ocean’s thermocline depth, heat content, sea surface temperature, and height (SST and SSH, respectively), and currents (e.g., Harrison and Schopf 1984; Giese and Harrison 1990; Delcroix et al. 1991; Kutsuwada and McPhaden 2002; Wakata 2007; Farrar 2008; Pujiana and McPhaden 2020; Rydbeck et al. 2023). Through their modifications of upper-ocean thermodynamic structure, the WWE-generated ocean waves can have important ramifications on the evolution of coupled atmosphere–ocean phenomena such as tropical cyclones (e.g., Boucharel et al. 2016), intraseasonal (30–90 day) Madden–Julian oscillation (MJO; Madden and Julian 1972; Zhang 2005) events (Webber et al. 2010; Rydbeck and Jensen 2017; West et al. 2020), the Indian Ocean dipole (e.g., Rao and Yamagata 2004; Han et al. 2006; Yuan and Liu 2009), and El Niño–Southern Oscillation (ENSO; e.g., Luther et al. 1983; Latif et al. 1988; Kirtman 1997; Perigaud and Cassou 2000; Boulanger et al. 2004; Lengaigne et al. 2004a; Fedorov et al. 2015; Chen et al. 2017; Puy et al. 2019).
The link between WWEs, oceanic Kelvin waves, and ENSO evolution has, in particular, been studied extensively (e.g., Luther et al. 1983; McPhaden et al. 1988; McPhaden and Yu 1999; McPhaden 1999; Moore and Kleeman 1999; Fedorov 2002; Lengaigne et al. 2003, 2004a; Hu et al. 2014; Lian et al. 2014; Chen et al. 2015; Hu and Fedorov 2019; Puy et al. 2019). WWEs can initiate Kelvin waves and eastward surface jets that work together to extend the eastern edge of the western Pacific warm pool eastward through the advection of warm waters (e.g., Picaut and Delcroix 1995; Matsuura and Iizuka 2000; Boulanger et al. 2001; Lengaigne et al. 2004a,b; Drushka et al. 2015; Puy et al. 2019; Jauregui and Chen 2024). Often warming in the central and eastern Pacific follows as the downwelling Kelvin wave traverses the Pacific and deepens the thermocline (e.g., Kessler and McPhaden 1995; McPhaden 2004; Lengaigne et al. 2002). The positive Bjerknes feedback ensues (Bjerknes 1969) where the eastward displacement of the western Pacific warm pool edge encourages convection to develop further eastward and enhance the fetch of WWEs, which initiates more Kelvin waves and further pushes the warm pool edge eastward (McPhaden 1999; Lengaigne et al. 2003, 2004a,b). Sometimes the multiplicative effect of the series of WWE-generated Kelvin waves sustains a suppressed east Pacific thermocline (e.g., Lopez and Kirtman 2013) and helps the evolution of El Niño. Because of these feedbacks, WWEs are state dependent with WWEs generally shifting eastward and occurring more frequently during anomalously warm SST conditions (e.g., El Niño) than neutral or La Niña conditions (Lengaigne et al. 2003; Yu et al. 2003; Eisenman et al. 2005; Gebbie et al. 2007; Tziperman and Yu 2007).
WWEs have an important impact on the evolution of extreme El Niño events though exactly how is still an open question. Several works emphasize the role of early year WWEs in the development of extreme El Niño events (Luther et al. 1983; Latif et al. 1988; McPhaden 1999; Perigaud and Cassou 2000; Fedorov 2002; Lengaigne et al. 2004b; Fedorov et al. 2015; Hu and Fedorov 2019; Puy et al. 2019). More recent work, however, shows that midyear WWEs are more important for extreme El Niño development compared to early year WWEs (Yu and Fedorov 2020). There does appear to be agreement that successive WWEs increase the likelihood of an extreme El Niño event developing (e.g., Vecchi and Harrison 2000; Levine et al. 2016; Chiodi and Harrison 2017; Feng and Lian 2018; Yu and Fedorov 2020).
Given WWEs important role in coupled tropical atmosphere–ocean phenomena, numerous studies have focused on their characteristics. The detailed description of WWEs is somewhat dependent on WWE classification metrics, but in general, WWEs are associated with convective activity and occur approximately six times per year in the Pacific with a higher frequency of occurrence during the boreal winter and spring. They typically extend 20°–40° zonally and 5°–15° meridionally with an amplitude of 5–7 m s−1 (e.g., Harrison and Vecchi 1997; Puy et al. 2016). WWEs originate from a variety of sources including extratropical intrusions (e.g., Chu 1988; Kiladis et al. 1994), the Indian monsoon (e.g., Seiki and Takayabu 2007), single or twin cyclones (e.g., Keen 1982; Harrison and Vecchi 1997), the MJO (Madden and Julian 1972; Zhang 2005; Seiki and Takayabu 2007; Puy et al. 2016; Feng and Lian 2018), convectively coupled Rossby waves (Puy et al. 2016), and a combination of the aforementioned sources (Yu and Rienecker 1998; Liang and Fedorov 2021).
The MJO is the dominant mode of tropical intraseasonal variability with alternating convective and suppressed phases that usually initiate in the Indian Ocean before moving slowly eastward (∼5 m s−1) to the Maritime Continent and west Pacific before convection wanes in the central Pacific (e.g., Madden and Julian 1972; Hendon and Salby 1994; Zhang 2005). Anomalously strong low-level westerly winds are associated with the MJO convective phases (e.g., Madden and Julian 1972; Zhang 2005) and can therefore increase the likelihood of WWEs, especially strong, long-lasting ones (Fasullo and Webster 2000; Seiki and Takayabu 2007; Puy et al. 2016; Feng and Lian 2018). However, not all works show increased WWE production associated with the MJO (Chiodi et al. 2014). The differing conclusions appear to be tied to the metrics used to define MJO events and WWEs (Puy et al. 2016). More recent work that aimed to reconcile the opposing conclusions tested a variety of MJO and WWE definitions and found that regardless of MJO and WWE definition, WWEs were significantly more likely during the convective phases of the MJO than random chance alone would predict (Feng and Lian 2018). However, despite the increased likelihood of WWEs during MJO convective phases, Feng and Lian (2018) emphasized that the MJO is not the major source of WWEs.
Despite the wealth of observationally based studies characterizing WWEs, the number of studies evaluating the characteristics of WWEs in climate models is somewhat limited. A comprehensive evaluation of WWE fidelity across generations of CMIP models is lacking with only Seiki et al. (2011) and Feng and Lian (2018) evaluating WWEs in an array of CMIP models. In 18 CMIP3 models, Seiki et al. (2011) found that most models correctly associated WWEs with organized convection and twin cyclonic circulation straddling the equator though the intensity and spatial structure of the convection and winds differed among models and from observations. More recent analysis showed that the mean frequency of occurrence of WWEs across 23 CMIP5 models was similar to observations though overestimation and underestimation occurred with varying degrees for individual models (Feng and Lian 2018). The analysis focused on WWEs in CAM4.0 and Community Climate System Model, version 4 (CCSM4), showed an underestimation in the frequency and intensity of WWEs while overestimating WWE zonal extent and duration (Lian et al. 2018). In a 70-yr present-day forcing simulation using CESM version 1.2.2, WWEs occurred more frequently than in observations, especially over the western Pacific (Tan et al. 2020).
Model biases in WWE characteristics can lead to biases in ocean wave modes. For example, biases in the meridional structure of intraseasonal WWEs in the Pacific can lead to the misrepresentation of the preferred latitude and phase speed of westward-propagating oceanic ER waves, which impact the period of ENSO (Capotondi et al. 2006; Neale et al. 2008; Deser et al. 2012). El Niño events were shown to have more realistic time scales when the off-equatorial wind response became more accurate after the inclusion of cumulus momentum transport in NCAR’s CCSM3 cumulus parameterization (Neale et al. 2008).
This work aims to bolster WWE evaluation in climate models by examining the fidelity of WWE characteristics in several CMIP6 models (Eyring et al. 2016) against observations and contribute a suite of WWE model diagnostics to the Model Diagnostic Task Force (MDTF) diagnostic framework package provided by NOAA (Maloney et al. 2019; Neelin et al. 2023). This work is part of a broader goal to assess the fidelity of WWE-forced oceanic waves in climate models. A complementary study evaluates the realism of oceanic Kelvin waves in a subset of CMIP6 models as used here (Cui et al. 2023). Future work will bring the WWE and oceanic Kelvin wave analysis together to evaluate how the ocean responds via Kelvin waves to a given WWE forcing.
The following section details the observations and model simulations used in this study as well as the methods we used to identify and characterize WWEs. Section 3 compares the characteristics of observed and simulated WWEs. Section 4 relates biases in simulated WWEs to biases in atmospheric and oceanic variability. Section 5 summarizes our results and highlights the conclusions of this work.
2. Data and methods
a. Observations and models
TropFlux daily zonal wind stresses τx from 1980 to 2014 on a 1° × 1° grid (Praveen Kumar et al. 2013) were used to identify WWEs. TropFlux wind stresses are computed using the COARE version 3.0 bulk flux algorithm (Fairall et al. 2003) with ERA-Interim (ERA-I) variables as input, where the ERA-I biases have been corrected based on global tropical moored buoy observations (Praveen Kumar et al. 2013). Among other wind stress products, QuikSCAT, NCEP, NCEP2, ERA-I, TropFlux, and ERA-I had the best agreement with in situ buoy data with TropFlux best at capturing significant WWEs in late 1996 and 1997 that were vital to the evolution of the 1997/98 El Niño. NOAA daily-interpolated OLR on a 1° × 1° grid from 1980 to 2014 (Liebmann and Smith 1996) was used to link MJO and convectively coupled Rossby wave (CRW) activity to observed WWEs. Finally, SSTs from NOAA’s Extended Reconstructed SST, version 5 (ERSST.v5; Huang et al. 2021), were used to relate ENSO conditions to WWE activity. ERSST5 provides global monthly SSTs on a 2° × 2° grid from 1854 to the present. ERSST5 data are based on ship and buoy measurements from the International Comprehensive Ocean–Atmosphere Data Set (ICOADS), release 3.0 (Woodruff et al. 2011), Argo floats above 5 m (Riser et al. 2016), and Hadley Centre Sea Ice and SST dataset, version 2 (HadISST2), and ice concentration (Titchner and Rayner 2014). The ERSST5 was regridded from their native 2° × 2° grid to a 1° × 1° grid using bilinear interpolation to match the TropFlux data.
Analysis of simulated WWEs was done for 30 CMIP6 simulations forced with historical greenhouse gas concentrations (Eyring et al. 2016). These 30 simulations provided the required daily output of τx for WWE identification and represented 14 different model families (Table 1). For 22 of the 30 simulations, the first ensemble member was used (i.e., r1i1p1f1), while for the remaining eight simulations, the physics (p) and forcing (f) corresponding to the first realization (r1) and initialization (i1) that provided the daily output of τx were used (Table 1). The period of analysis was the same as the observations from 1980 to 2014 for all but three of the simulations whose daily τx output terminated before 2014 (i.e., CNRM-CM6-1, CNRM-ESM2-1, and GFDL CM4). To maintain a 35-yr analysis period, the years 1975–2009 were used for the two CNRM simulations, while 1966–2000 was used for GFDL CM4. In addition to τx, daily OLR and monthly SST were used to relate WWE activity to MJO and CRW activity and ENSO conditions, respectively. The GFDL-ESM4, NorESM2-LM, and NorESM2-MM simulations did not provide daily OLR for the analogous ensemble member that provided daily τx. Model τx and OLR were interpolated to the 1° × 1° TropFlux grid using conservative interpolation. Prior to regridding τx, values over land were masked out to be consistent with missing values over land in the observations. Using the conservative, as opposed to bilinear, interpolation avoided exaggeration of the land mask when going from coarser to finer resolution, while also retaining global sums before and after regridding. SST was regridded to match the 1° × 1° TropFlux grid using bilinear interpolation.
The list of CMIP6 simulations and their ensemble member used in this study and the statistics for their WWEs identified using a 120-day high-pass filter and a common τx threshold of 0.04 N m−2. Each simulation’s 2σ τx threshold is also shown. When the simulation’s 2σ τx threshold is different than 0.04 N m−2, the total WWE count and average number per year are shown in parentheses. Statistics for both observations and simulations are based on the period 1980–2014, except for the two CNRM simulations, which used 1975–2009, and the GFDL CM4 simulation, which used 1966–2000.
b. WWE detection method
WWEs are identified in the Pacific Ocean (120°–280°E) using τx criteria following Puy et al. (2016). Our analysis region is similar to Feng and Lian (2018) who looked at WWEs between 120° and 260°E. Wind stress is used, as opposed to wind speed, since wind stress is directly related to the surface momentum flux and therefore a better indicator of the wind’s ability to force ocean waves, whereas wind speed is nonlinearly related to the surface momentum flux. As in Puy et al. (2016), we are interested in strong WWEs that impact equatorial oceanic wave modes. Therefore, our analysis uses equatorially averaged (2.5°S–2.5°N) τx with a 120-day high-pass filter applied. The filtering ensures that the identified WWEs are stronger than low-frequency variations in τx, such as during El Niño when westerly wind anomalies occur (Puy et al. 2016), and are capable of exciting ocean waves. At time scales longer than ∼90 days, the τx and zonal pressure gradient are in balance making it harder to generate an ocean wave response (McPhaden and Taft 1988; Yu and McPhaden 1999).
To qualify as a WWE, τx must meet certain magnitude, zonal extent, and duration criteria similar to previous studies (Hartten 1996; Harrison and Vecchi 1997; Seiki and Takayabu 2007; Chiodi et al. 2014; Puy et al. 2016). Similar to Puy et al. (2016), patches of equatorially averaged 120-day filtered τx anomalies must have a magnitude of at least 0.04 N m−2 and last for at least 5 days with a zonal extent at or above 10° longitude to be considered a WWE. The 0.04 N m−2 threshold is approximately two standard deviations (0.038 N m−2) above the equatorially averaged τx in the TropFlux observations, indicating that very conservative strength criterion was used to detect only the strongest wind events capable of exciting oceanic waves. WWEs identified using the above three criteria that occurred within 3 days and 3° of each other were considered one event (Puy et al. 2016). Another criterion, not used in Puy et al. (2016), is that the maximum zonal extent of a WWE must extend to at least 140°E. This additional requirement ensures that the WWEs are extending sufficiently away from the Maritime Continent and shallow seas and are therefore capable of exciting oceanic waves. The same metrics are used to identify WWEs in each model as in the observations despite variations in the standard deviation of τx from model to model and observations. The 0.04 N m−2 threshold was the 2σ value for 23 of the 30 simulations (Table 1). The 2σ threshold for five simulations is 0.03 N m−2 while 0.05 N m−2 for two of the simulations (Table 1). While using a common τx threshold differs from prior work (Feng and Lian 2018; Seiki et al. 2011), which used a common standard deviation threshold of wind speed magnitude to identify WWEs in models and observations, we use the same wind stress magnitude threshold as the oceanic Kelvin wave response is dependent on not only the wind stress forcing but also the stability of the ocean (Long and Change 1990; Benestad et al. 2002; Roundy and Kiladis 2006). Using a magnitude threshold based on the standard deviation of wind stress would, therefore, not necessarily convey how appropriately the ocean responded to wind events. There is at least one study, Tan et al. (2020), that used the same thresholds in observations and models to identify WWEs. This choice in threshold is important for future work that will examine how the ocean responds to a given WWE strength. Details on how the Puy et al. (2016) WWE-detection method compares to previous methods are available in Table 1 of Puy et al. (2016). Table 1 lists the number of WWEs detected in observations and each simulation and their average frequency per year. Figure 1 provides examples of WWEs in TropFlux observations during 1997, which was before and during one of the strongest observed El Niño events.
Time–longitude evolution of equatorially averaged and 120-day high-pass filtered τx (shading) during the strongest El Niño year or year preceding the strongest El Niño if the ONI peaked in the first half of the strongest El Niño year, in observations and indicated simulations. The y axis is months. WWEs are outlined in black where a common τx threshold of 0.04 N m−2, which is 2σ of the observed filtered τx, was used to isolate WWEs. Overlaid is the monthly evolution of the 28.5°C SST isotherm (black line).
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0629.1
We also identified WWEs by removing the mean annual cycle from the equatorial-averaged τx as in some previous studies (e.g., Harrison and Giese 1991; Harrison and Vecchi 1997; Seiki and Takayabu 2007; Chiodi et al. 2014; McGregor et al. 2016). A common 0.05 N m−2 threshold, representing 2σ of the observed τx, was used in observations and simulations to identify strong WWEs. As before, the WWE patches had to last at least 5 days and span 10° longitude, and WWEs within 3 days and 3° of each other were considered as one event. Figure 2 shows the WWEs in observations for 1997 using this alternative method. The WWEs last much longer, sometimes exceeding a month, than the WWEs identified using 120-day high-pass filtered τx (cf. Figs. 1 and 2). These extremely long WWEs have been called “super bursts” and occur during strong El Niño events when the background zonal wind becomes anomalously westerly (Liang and Fedorov 2021). Applying a 120-day high-pass filter avoids these spuriously long-lasting WWEs and ensures we are detecting WWEs that are sufficiently stronger than the background winds and capable of exciting Kelvin waves. The results based on WWEs identified by removing the mean annual cycle are discussed, however, to show the robustness of our conclusions using an alternative WWE detection method. The results shown will be for WWEs identified using the 120-day high-pass filtered τx unless otherwise noted since this method isolates strong WWEs capable of inducing oceanic Kelvin waves.
As in Fig. 1, but for the anomaly with respect to the mean annual τx shown and used to identify WWEs.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0629.1
For each WWE, several attributes were recorded to compare observed and simulated WWE characteristics. The attributes include the WWE’s duration, zonal extent, central longitude and central date, and integrated wind work (IWW), where IWW is simply the sum of τx over the entire WWE patch in time–longitude space and is a measure of the WWEs total forcing to the ocean. The IWW serves as an indicator of how the ocean will respond to a WWE as the oceanic response is generally proportional to the magnitude of the wind stress forcing and its zonal extent and duration (Giese and Harrison 1990). Our IWW metric is similar to Harrison and Vecchi’s (1997) “wind measure index” and Puy et al.’s (2016) “wind event index.” The central longitude and day of occurrence were based on the surface stress-weighted average longitude and the date of each time-longitude WWE patch (see equations in section 2.2 of Puy et al. 2016). An example of the central longitude and time for WWEs is shown for observations by the white dots in Figs. 1 and 2.
c. Atmospheric variability detection method
MJO and CRW events are detected in observations and simulations by filtering global OLR averaged between 15°S and 15°N following Wheeler and Kiladis (1999). The MJO is defined in the symmetric wavenumber–frequency spectrum as wavenumbers 1–5 with a period between 30 and 96 days, while CRWs are bounded by wavenumbers −1 to −10 with a period between 10 and 40 days and the theoretical dispersion curves corresponding to 8- and 90-m equivalent depths. The filtered OLR for each wave type was then normalized by its standard deviation between 130°E and 160°W following Puy et al. (2016) and Feng and Lian (2018). As in Puy et al. (2016), this longitude band represents where nearly 90% of the WWEs occur. Convective MJO and CRW phases were then defined as regions in time–longitude space where the normalized filtered OLR had anomalies less than or equal to −1. Figure 3 provides an example of the MJO and CRW convective phases in the observations during 1997.
Time–longitude evolution of WWEs during 1997 (gray shading). These are the same stresses outlined in black in the top-left plot of Fig. 1. Overlaid are the convective phases of MJO events in blue and convectively CRWs in orange. See the text for how the convective phases were defined. Dots indicate the time–longitude center of each WWE. Blue, orange, and green dots indicate WWE overlap with MJO, CRW, or both MJO and CRW convection, respectively. White dots indicate WWE time–longitude centers that do not overlap with either MJO or CRW convection.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0629.1
El Niño and La Niña events were identified when Niño-3.4 SST anomalies (5°S–5°N, 120°–170°W) defined by the oceanic Niño index (ONI) were ≥0.5°C or ≤0.5°C, respectively, for at least five consecutive overlapping 3-month seasons (NOAA CPC 2024). Figure 1 shows the 120-day high-pass filtered τx and WWEs during the strongest El Niño or the year preceding the strongest El Niño if the ONI peaked in the first half of the year during the strongest El Niño year, for observations and each simulation. Figure 2 is analogous to Fig. 1, except showing wind stress and WWEs after removing the mean annual cycle. In each figure, the evolution of the 28.5°C SST isotherm is overlaid to indicate the position of the eastern edge of the west Pacific warm pool (EEWP). The MIROC-ES2L panels are not shown to simplify the figure format; however, its wind stress and WWEs are very similar to MIROC-ES2H and MIROC6. When WWEs are identified by removing the mean annual cycle, the MIROC simulations produce long-lasting “super burst” WWEs like the observations (Fig. 2). In the TropFlux observations, the WWEs and EEWP move eastward in tandem as the El Niño event develops. Several models capture this harmonious eastward progression well during their respective strongest El Niño event (i.e., the CESM, CMCC, GFDL, and MIROC simulations and the HadGEM3-GC31-MM; Figs. 1 and 2), while others show that the EEWP moves eastward independent of WWE activity (i.e., CNRM-ESM2-1, HadGEM-GC31-LL, and the IPSL simulations). Still, other models show a stagnant EEWP despite El Niño conditions (e.g., the INM simulations). The relationship between the EEWP and WWE activity will be discussed below.
3. WWE characteristics in observations and models
a. WWE location and frequency
The distribution of observed WWE location, as measured by each WWE’s surface stress-weighted central longitude, is generally unimodal with a peak in the west Pacific near 140°E that mostly tapers toward the east with minor local peaks around the date line and 205° (Fig. 4a). This distribution is similar to the location histogram in Puy et al. (2016), which showed WWE location peaking in the west Pacific at 150°E and decreasing to the east (their Fig. 5b). The simulations capture the distribution of WWE locations with varying degrees of success (Fig. 4). Most simulations have a unimodal peak in WWE location in the west Pacific that then tapers to the east like the observations. However, for several simulations, the WWE location distribution is biased westward; the exceptions to this are CMCC-CM2-SR5 (Fig. 4h), CMCC-ESM2 (Fig. 4i), CNRM-CM6-1 (Fig. 4j), EC-EARTH3 (Fig. 4l), the two HadGEM and INM simulations (Figs. 4o–r), IPSL-CM6A-LR (Fig. 4t), IPSL-CM6A-LR-INCA (Fig. 4u), and NorESM2-MM (Fig. 4cc). A few simulations show a strong bimodal distribution with peaks in the west Pacific and central Pacific (i.e., INM-CM5-O; Fig. 4r) or eastern Pacific [i.e., IPSL-CM6A-LR and IPSL-CM6A-LR-INCA (Figs. 4t–u) and NorESM2-MM (Fig. 4cc)]. The INM-CM4-8 distribution is unimodal, but the peak is shifted to the central Pacific (Fig. 4q), while the distributions for the two HadGEM simulations are relatively flat.
Histograms of the central longitude of WWEs in TropFlux observations (blue shading in each panel) and CMIP6 simulations (red shading in each panel). Bin spacing is 5° longitude.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0629.1
The central longitude histograms are useful for showing the fidelity of the location of the WWEs in each simulation; however, the distribution is normalized by the number of WWEs in each simulation, which means the histograms do not indicate how accurately each simulation captures the frequency of WWEs across the Pacific. Therefore, we define the frequency of WWE occurrence by longitude as the likelihood of a given longitude experiencing a WWE per day, calculated as the total number of unique events at each longitude divided by the total number of days in each dataset. For the frequency calculation, all unique longitude points in a WWE are considered and not just the central longitude of the WWE, which was used to determine WWE location (Fig. 4). The reciprocal of the frequency is the average return rate of a WWE per longitude or the average number of days between WWEs at each longitude. The WWE frequency of occurrence by longitude in observations (gray shading Fig. 5) is shaped similar to the WWE-location distribution (blue bars Fig. 4) with the shortest return rate (or highest frequency) around 120 days in the west Pacific near 140°E that increases in return rate (or decreases in frequency) toward the east Pacific. A 120-day return rate equates to roughly three WWEs per year and a 0.8% chance of experiencing a WWE on any given day.
The probability per day of a WWE occurring at each 1° longitude in the Pacific in TropFlux observations (gray shading in each panel) and each simulation (blue shading in each panel). The probability per day is calculated as the number of unique WWEs occurring at each longitude divided by the total number of days in the dataset. The inverse of the probability per day indicates the average return rate (right y axis) of a WWE at each longitude or the amount of time in between unique WWEs impacting a given longitude.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0629.1
The frequency of occurrence of WWEs in each simulation (blue shading in Fig. 5) generally has a pattern similar to their respective WWE-location distribution (red shading in Fig. 4). However, now peaks are emphasized or mitigated relative to the observations based on how frequently WWEs occur. For example, the peak in the central longitude distribution for the two CNRM simulations is nearly the same as observations (∼14% at 135°E), but the frequency of occurrence in the two simulations falls well below the observations (cf. Figs. 4j,k and 5j,k). Nearly all simulations underestimate the frequency of WWEs in the west Pacific 140°E–180° though there are varying degrees of underestimation with the INM and IPSL simulations egregiously incorrect (Figs. 5q–u), while the EC-EARTH3 and GFDL-ESM4 simulations compare quite well to the observations (Figs. 5l,n). Not all simulations underestimate WWE frequency in the west Pacific including the MIROC-ES2H, MPI-ESM-1-2-HAM, and MPI-ESM1-2-LR (i.e., Figs. 5v,y,aa), which tend to overpredict the frequency of WWEs in the west Pacific and have strong westward biases. Finally, as mentioned in the central longitude histograms, several models produce WWEs in the east Pacific too frequently giving the frequency of occurrence distribution a bimodal structure (i.e., AWI-ESM-1-1-LR, IPSL-CM6A-LR, MIROC-ES2H, MIROC6, and the two Nor simulations, shown in Figs. 5a,t,v,x,bb,cc, respectively). The central longitude and frequency of occurrence by longitude distributions are qualitatively similar when WWEs are identified by removing the mean annual cycle (not shown) from the distributions using the 120-day high-pass filter (Figs. 4 and 5).
WWE frequency can also be evaluated as the number of WWEs per year (Table 1) as previous works have been done (Feng and Lian 2018; Harrison and Vecchi 1997; Puy et al. 2016; Seiki and Takayabu 2007). This diagnostic, though, is dependent on whether a standard deviation or absolute threshold is used to define WWEs (Table 1). For example, in the INM-CM4-8 simulation, when the common 0.04 N m−2 threshold is used for WWE detection, the annual WWE frequency is 1.8 WWEs per year but jumps to 8.49 when 0.03 N m−2 is used, which is the simulation’s 2σ τx value. For TropFlux observations, there are approximately six WWEs per year, similar to Puy et al. (2016), while the multimodel mean is 4.6 WWEs per year. Extreme examples of WWE rate per year include IPSL-CM5A2-INCA, which only has 0.77 WWE per year, while MPI-ESM1-2-LR has nearly 9 yr−1 (Table 1). CESM2(WACCM)-FV-2 and GFDL-ESM4 have annual WWE rates closest to observations (6.23 and 6.29, respectively), but their distribution of WWE frequency per longitude is different from observations as previously mentioned (Figs. 5f,i). Our findings are similar to the WWE analysis performed with CMIP5 simulations that showed a slight underestimation of the rate of WWEs per year between the multimodel mean and observations with a wide variation among individual simulations (Feng and Lian 2018, their Table 5). Note that Feng and Lian (2018) used different metrics than we did to define WWEs, but the comparison of WWEs per year in the multimodel mean versus observations is consistent.
b. WWE duration, zonal extent, and intensity
Figure 6 examines the fidelity of WWE IWW as a function of duration and zonal extent in model simulations relative to observations. From such plots, we can determine if models produce the correct IWW for a given WWE duration and zonal extent. Black downward-pointing triangles and red upward-pointing triangles indicate where the simulation-mean IWW is significantly less than or greater than observations, respectively, at the 90th percentile using a Student’s t test. Differences were only calculated for bins that contained WWEs in both the observations and simulation.
Average IWW per duration and zonal extent bins in (a) observations and (b)–(ee) simulations. Black downward-pointing triangles indicate that the simulation’s average IWW is statistically less than the observations at the 90th percentile using a Student’s t test, while the red upward-pointing triangles indicate the simulation’s average IWW is statistically more than the observations. Differences were only calculated for bins that had data in both the simulation and the observations. Bin size is 10 days for duration and 10° longitude for zonal extent.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0629.1
In observations, the maximum duration a WWE can have for a given zonal extent generally increases with increasing zonal extent (Fig. 6a). For example, WWEs in the zonal extent bin centered on 25° last ≤15 days, while those in the bin centered at 55° can last up to 25 days. Additionally, in observations, mean IWW tends to increase as WWEs lengthen in extent and duration as indicated by the saturation of IWW values going from the shortest WWEs to the longest in both duration and zonal extent (Fig. 6a).
The simulations mimic the observations with varying degrees of success. Most simulations show that WWE-mean IWW increases as WWE duration and zonal extent increases, which at least indicates a correct relationship between IWW, zonal extent, and duration. However, the zonal extent and duration at which a simulation’s IWW saturates vary widely among simulations. AWI-ESM-1-1-LR, CESM2, and CESM2-FV2 match the observations well (Figs. 6b,d,e), while simulations like the CNRM-ESM2-1, GFDL CM4, and HadGEM3-GC31-MM (Figs. 6l,n,q) have their strongest WWEs at durations and zonal extents less than the observations as the WWEs in these simulations and several others are bound to smaller zonal extents and durations than the observations. The MIROC and MPI simulations, except for MPI-ESM1-2-HR, produce very strong WWEs that last longer than observations despite being more zonally confined (Figs. 6w–z,bb). Interestingly, for the bins where model–observation mean IWW values are significantly different from one another, the simulation’s mean IWW is usually lower (i.e., most triangles are black downward pointing) indicating models tend to produce WWEs that are weaker than observations across a variety of durations and zonal extents. The exceptions are the MIROC and MPI simulations, except for MPI-ESM1-2-HR, which show just as many or more bins with stronger mean IWW, as opposed to weaker mean IWW (Figs. 6w–z,bb).
The fidelity of the WWE characteristics in a simulation is generally linked to how well the simulation represents the WWE frequency by longitude distribution (cf. Figs. 5 and 6). Models that decently represent WWE frequency by longitude also do a better job replicating IWW in duration–zonal extent space (i.e., AWI-ESM-1-1-LR, CESM2, CESM2-FV2, EC-EARTH3, GFDL CM4, and GFDL-ESM4), while simulations that grossly under- or overestimate WWE frequency also strongly over- or underestimate WWE IWW, zonal extent, and duration (i.e., the INM and IPSL simulations and MIROC-ES2H, MPI-ESM-1-2-HAM, and MPI-ESM1-2-LR).
4. WWE relationship to atmospheric and oceanic variability
a. WWE relationship to MJO and CRW variability
To further understand model biases in WWE frequency and characteristics, WWE activity is related to MJO and CRW convective activity. Figure 3 provides an example of the overlap between observed WWEs and MJO or CRW convection or both during 1997 (blue, orange, and green dots, respectively). WWEs sometimes occur simultaneously in the MJO and CRW, such as the observed WWE in early October 1997 just west of the date line (Fig. 3). Figure 7 shows the percentage of observed and simulated WWEs whose central time and longitude fall exclusively within the MJO (blue bars) or CRW (orange bars) convective phase or overlap with both the MJO and CRW convective phase (green bars). In observations, 31.1% of the WWEs occur exclusively within MJO convection, while 23.6% of the WWEs occur only with CRW convective phases. A total of 12.7% of the WWEs overlap with both MJO and CRW convection. These percentages of MJO and CRW overlap are different from those in Puy et al. (2016) who found that 16% and 29% of their identified WWEs overlapped solely with MJO or CRW convective phases, respectively, while 29% of their WWEs occurred in both (their Fig. 7b). Our results are more aligned with Feng and Lian (2018) who found that 32%–38% of WWEs overlap with MJO convection depending on how MJO convective phases were identified though they did not evaluate how many of their identified WWEs overlapped with both MJO and CRW convection. Discrepancies may be due to how WWEs and convective phases of the MJO and CRW are defined. In Puy et al. (2016), filtered τx was used to identify the convective phases instead of OLR. Additionally, Feng and Lian (2018) calculated the overlap of WWEs and MJO convection based on WWEs defined by anomalies of zonal wind speed relative to the mean annual cycle.
Fraction of WWEs that overlap with the convective phase of the MJO only (blue bars), CRW only (orange bars), and both MJO and CRW convection (green bars) for observations (far left), the multimodel mean, and each simulation. Simulations are ordered from the largest to smallest percentage of the combined percentage in MJOs and CRWs. The color scheme matches the dots in Fig. 3 that were used to indicate WWE overlap with each or both wave types.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0629.1
The multimodel mean falls well below the observed overlap between WWEs and MJO or CRW convection or both with an average of 22.8% and 16.3% of WWEs associated with MJO and CRW convective phases, respectively, and 8% overlapping with convection in both the MJO and CRW. Only the MIROC-ES2L simulation has a larger percentage of WWE overlap with MJO or CRW convection or both, indicating that most models underestimate the importance of the MJO or CRW or both.
Most models at least accurately show an appropriate split between WWEs associated with the MJO, CRW, or both. Observations show that of the 143 out of 212 WWEs that occur in the MJO, CRW, or both, 46% and 35% are solely in the MJO and CRW, respectively, and 19% in both; the multimodel mean has a similar distribution with 48% and 36% exclusively in the MJO and CRW, respectively, and 16% in both (not shown). This suggests that in observations and most simulations, MJO and CRW activities are both important to WWE activity despite their overall connection to the MJO and CRW being underestimated in most simulations. Exceptions include the MPI-ESM1-2-HR, CNRM-ESM2-1, GFDL CM4, IPSL-CM6A-LR-INCA, and IPSL-CM6A-LR, which are highly skewed to have WWE overlap with the MJO than CRW. The IPSL-CM5A2-INCA and INM-CM4-8 are oppositely skewed with a much larger proportion of WWEs in CRWs versus MJOs. Biases in WWE-wave activity overlap are similar when WWEs are identified by removing the mean annual cycle of τx (not shown).
Figure 8 more directly shows the relationship between MJO and CRW activity and the percentage of WWEs associated with each wave type (left panels) and the total IWW between 150°E and 180° (right panels). Results were insensitive to using a wider longitude band of 130°E–200°W to measure total IWW. Wave activity was measured as the wave type’s OLR variance between 130°E and 160°W, which as stated above is the region where nearly 90% of the observed WWEs occur. The total IWW between 150°E and 180° is simply the sum of all τx values associated with WWEs in that longitude band and represents the total WWE forcing upon the ocean in observations and simulations.
Scatterplot of MJO OLR variance between 130° and 200°E vs (a) the percentage of WWEs that occur within the convective region of the MJO and (b) the total IWW between 150°E and 180° in observations and simulations. (c),(d) As in (a) and (b), but for CRWs.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0629.1
There is a strong relationship between MJO variance and both the percentage of WWEs within convective phases of the MJO and the total IWW in the west Pacific with a correlation coefficient greater than 0.6 for both (Figs. 8a,b). Almost all simulations underestimate the fraction of WWEs associated with the MJO, as previously seen in Fig. 7, while also underestimating the total IWW in the west Pacific. Two-thirds of the simulations also underestimate MJO OLR variance. Simulations with the weakest MJO variance tend to severely misrepresent the number of WWEs associated with the MJO and the total IWW in the west Pacific [i.e., simulations in the bottom quadrant of panels (a) and (b), such as CanESM5, CMCC-CM2-SR5, the INM simulations, IPSL-CM6A-LR, and IPSL-CM6A-LR-INCA]. These simulations with extremely deficient MJO variance underestimate the frequency of WWEs across the Pacific (Figs. 5b,g,q,r,t,u) and produce WWEs that are generally shorter lasting, more zonally confined, and weaker than observed WWEs (Figs. 6c,h,r,s,u,v).
CRW variance shows a similar, yet weaker, relationship as MJO variance to WWE overlap with CRW convective phases and the total IWW between 150°E and 180° (i.e., R = 0.53 and 0.39, respectively; Figs. 8c,d). As with MJO activity, simulations that severely underestimate CRW activity also severely underestimate WWEs associated with CRWs and the total IWW in the west Pacific. Unlike the MJO variance, the observed CRW variance is in the middle of the spread of variance values associated with the simulations.
MJO and CRW OLR variances are themselves tightly linked with a correlation coefficient of 0.74 (Fig. 9). In general, total IWW increases as both MJO and CRW variances increase as indicated by the saturation of color in Fig. 9 going from the bottom left to the top right of the plot. Observations (marked by the number 1) fall within the middle of the plot yet have more total IWW than several simulations with higher MJO and CRW variance. This relationship reiterates that both the MJO and CRW are important for WWE representation in models.
Scatterplot of MJO vs CRW variance in observations and simulations. Dot shading indicates the total IWW between 150°E and 180°.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0629.1
WWE representation in simulations that fall at either extreme of the relationship between wave activity and total IWW in the west Pacific would likely benefit from the improved representation of the MJO and/or CRW. However, improving the MJO and CRW is not a cure-all for WWE representation as there are other sources of WWE production (i.e., not all WWEs overlap with MJO and CRW activity; Fig. 7). There are also the simulations that accurately represent MJO and CRW variance yet still underestimate both the fraction of WWEs occurring in MJO and CRW convective phases and the total IWW in the west Pacific (e.g., CESM2-FV2, GFDL CM4). The WWEs in CESM2-FV2 and GFDL CM4 occur with reasonable frequency relative to observations (Figs. 5d,m and Table 1) but are generally weaker than observations and limited to slightly smaller durations and zonal extents (Figs. 6e,n). Further analysis of the MJO and CRW near-surface zonal winds could inform why the WWEs in the CESM2-FV2 and GFDL CM4 simulations are weaker and more confined zonally and temporally than observed, which leads to overall underestimation of total IWW in the west Pacific. The relationship between the MJO and CRW and WWE activity is robust to identifying the WWEs by removing the annual cycle (not shown).
b. WWE relationship ENSO variability
We next evaluate how well models represent the dependency of WWE occurrence on ENSO conditions since previous works have shown that WWEs occur more frequently during El Niño than La Niña events (e.g., Eisenman et al. 2005; Gebbie et al. 2007; Lengaigne et al. 2003; Tziperman and Yu 2007; Yu et al. 2003). Figure 10 shows the annual frequency of WWEs separately during El Niño (red bars) and La Niña (blue bars) for observations and each simulation. Similar to previous works, the frequency of observed WWEs is higher during El Niño versus La Niña—7.0 versus 5.0 WWEs per year, respectively. Twenty-two of the thirty simulations correctly have a higher annual rate of WWEs during El Niño versus La Niña. The eight models that fail to produce more WWEs during El Niño have a black dot on the bottom of the La Niña bar in Fig. 10. These eight simulations greatly underpredict the frequency of WWEs across all times (i.e., <3.7 WWEs per year). The multimodel mean underpredicts the annual rate of WWEs in both El Niño and La Niña conditions.
Annual frequency of WWEs for observations, the multimodel mean, and individual simulations during El Niño (red bars) and La Niña (blue bars). Simulations are ordered from largest to smallest annual frequency within El Niño. The black dots indicate simulations which have a higher annual WWE frequency during La Niña vs El Niño.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0629.1
Previous works have indicated that the occurrence of WWEs is modulated by ENSO conditions. A feedback exists wherein warm underlying ENSO conditions and the eastward extension of the EEWP support more WWEs, which in turn push the EEWP eastward and warm SSTs through Kelvin wave excitation and deepening of the thermocline (e.g., Eisenman et al. 2005; Tziperman and Yu 2007). Given this feedback, a possible reason simulations underpredict WWE forcing is due to an underprediction of ENSO warm conditions.
However, comparing the fraction of time observations and each simulation spent in El Niño conditions to their annual frequency of WWEs showed very little relationship (R = 0.13; not shown). Observations spent ∼23% of the time in El Niño conditions with an annual WWE frequency of 6.06, whereas two-thirds of the simulations spent 26%–40% of their time in El Niño with WWE rates ranging from less than 1 to nearly 9 WWEs per year. Interestingly, most simulations spend more time in El Niño than the observations yet have a lower WWE frequency. The results above suggest that MJO and CRW activity within the simulations is more strongly linked to WWE frequency and characteristics than to ENSO conditions.
c. WWE relationship to biases in the eastern edge of the west Pacific warm pool
A possible cause for the westward bias in WWE frequency in some of the simulations (i.e., AWI-ESM-1-1-LR, GFDL CM4, MIROC-ES2H, MPI-ESM-1-2-HAM, and MPI-ESM1-2-LR; Fig. 5) is the mean position of the EEWP or a cold tongue bias in those models (e.g., Brown et al. 2020; Jiang et al. 2021; Wu et al. 2022). Under this hypothesis, simulations with a strong westward bias in WWE activity would also have a mean westward bias to the EEWP since the WWEs are primarily located over warm SSTs and help push the EEWP eastward (e.g., Lengaigne et al. 2003, 2004a,b; Drushka et al. 2015; Puy et al. 2019). We found that the mean position of the EEWP, as defined as the longitude of the temporally and equatorially averaged (2.5°S–2.5°N) 28.5°C SST isotherm, had no relationship to total IWW in the far west Pacific (120°–140°E) [R = −0.11 (not shown)]. Instead, several simulations with strong westward biases in the mean position of their EEWP showed no westward bias in WWE activity [i.e., the CNRM and INM simulations, IPSL-CM6A-LR-INCA, and IPSL-CM6A-LR (not shown)]. Further work is needed to understand the westward biases in WWE activity in several of the CMIP6 simulations.
5. Summary and conclusions
The fidelity of WWE characteristics in 30 CMIP6 historical simulations from 14 model families was evaluated against TropFlux observations. WWEs were identified using equatorially averaged (2.5°S–2.5°N) and 120-day high-pass filtered zonal wind stress using the methods in Puy et al. (2016). For each WWE, several attributes were saved including the WWE’s zonal extent, area-weighted central time and longitude, and intensity measured using integrated wind work (IWW), which is the sum of zonal wind stress over the time–longitude space of the event.
Most simulations underpredict the annual frequency of WWEs with a multimodel mean value of 4.60 WWEs per year compared to the observed rate of 6.06 WWEs per year (Table 1). The simulations tend to have a westward bias in WWE location and underpredict WWE occurrence in the west Pacific between 140°E and 180° where observed WWEs are most common (Figs. 4 and 5).
Not all simulations underestimate WWE frequency in the west Pacific including the MIROC-ES2H, MPI-ESM-1-2-HAM, and MPI-ESM1-2-LR (i.e., Figs. 5v,y,aa), which tend to overpredict the frequency of WWEs in the west Pacific and have strong westward biases.
A few models show bimodal, as opposed to unimodal, distributions with their most prominent peak in the eastern Pacific [i.e., IPSL-CM6A-LR and IPSL-CM6A-LR-INCA (Figs. 4t–u) and NorESM2-MM (Fig. 4cc)]. Simulations mimic the variations in WWE IWW across different zonal extents and durations with varying degrees of success. Like the observations, most simulations show that WWE-mean IWW increases as WWE duration and zonal extent increase. This indicates that at least the simulations have a correct relationship between IWW, zonal extent, and duration. However, the WWEs in several models are bound to smaller zonal extents and durations than the observations (i.e., the CMCC simulations, CNRM-ESM2-1, GFDL CM4, HadGEM3-GC31-MM the INM simulations, IPSL-CM5A2-INCA, MPI-ESM1-2-HR, and UKESM1-0-LL; Fig. 6). The simulations also generally produce weaker WWEs for comparable WWE zonal extents and durations (Fig. 6).
Biases in the simulated WWEs were linked to biases in MJO and CRW variability in the simulations as the two atmospheric wave types are known sources of WWEs (e.g., Fasullo and Webster 2000; Seiki and Takayabu 2007; Puy et al. 2016; Feng and Lian 2018). Most simulations underpredicted the fraction of WWEs that overlapped with MJO or CRW convection. The multimodel mean showed 22.8% and 16.3% of WWEs overlap exclusively with the MJO and CRW, respectively, while 8.0% of WWEs overlap with both MJO and CRW convection. These values are lower than observations that showed 31.1%, 22.6%, and 12.7% of WWEs overlap with convection in MJOs or CRW or both, respectively (Fig. 7). Simulations that greatly underpredicted MJO and CRW variance also severely underpredicted the total WWE forcing (i.e., total IWW) in the west Pacific and the fraction of WWEs associated with MJO or CRW convection (Fig. 8), suggesting that both the MJO and CRW are important for WWE production. Previous works have also suggested that MJO skill is important for replicating WWEs (i.e., Kim et al. 2020, 2022; Li et al. 2022). However, not all WWEs overlapped with MJOs or CRWs indicating that improving simulated MJO and CRW variability is not a cure-all for WWE production in models. Additional analysis of MJO and CRW near-surface zonal wind structure could help illuminate why some simulations that produce reasonable MJO and CRW variance nevertheless underestimate the fraction of WWEs occurring in their MJOs and CRWs and the total IWW in the west Pacific (e.g., CESM2-FV2, GFDL CM4).
WWE occurrence and characteristics were also related to ENSO conditions based on previous works that showed WWEs were strongly modulated by ENSO variability (e.g., Lengaigne et al. 2003; Yu et al. 2003; Eisenman et al. 2005; Gebbie et al. 2007; Tziperman and Yu 2007). As in observations, most simulations had a higher annual frequency of WWEs during El Niño versus La Niña conditions (Fig. 10), though the multimodel mean annual rate during both ENSO conditions was lower than observations. There was no relationship between the fraction of time the simulations spent in El Niño and the overall annual frequency of WWEs.
Further work is needed to understand the westward bias in WWE locations in the simulations. It was not related to biases in the mean position of the eastern edge of the west Pacific warm pool as has been previously hypothesized. Also, a deeper analysis of individual models is warranted to further tease out causes of WWE biases in their model. Our future work will evaluate the ocean response to the WWEs identified in the IPSL, NorESM, and MPI models as their CMIP6 simulations provided sufficient daily ocean output for analysis. We anticipate that the misrepresentation of WWE characteristics in those models will have ramifications for WWE-generated downwelling oceanic Kelvin waves and subsequent SST warming and El Niño development. WWE biases in the simulations may also contribute to uncertainty in the predictions of Pacific SSTs in a warmer climate since biases in WWE characteristics may rectify ENSO biases (Capotondi et al. 2006; Neale et al. 2008; Deser et al. 2012). For now, knowledge of WWE deficiencies in models through the diagnostics developed here can facilitate improvement to their representation in future model versions, as well as motivate the distribution of high temporal (i.e., daily) model output to analyze WWEs in future CMIP versions.
Acknowledgments.
We are grateful for the insightful reviews by Brandon Wolding and two anonymous reviewers. We thank Maria Gehne for her publicly available Python code (Gehne 2021) that we modified to filter OLR for the MJO and CRW detection. This work was sponsored by the NOAA Modeling, Analysis, Predictions, and Projections project NA19OAR4320073. Emily Riley Dellaripa and Eric Maloney were also supported by the NASA CYGNSS, under Grant 80NSSC21K1004. Emily Riley Dellaripa was further supported by DOE Regional and Global Model Analysis DE-SC0020092.
Data availability statement.
Data from CMIP6 simulations are available for download at https://esgf-node.llnl.gov/projects/esgf-llnl/. TropFlux zonal wind stress data (Praveen Kumar et al. 2013) are available at https://incois.gov.in/tropflux/. NOAA interpolated outgoing longwave radiation (OLR; Liebmann and Smith 1996) and Extended Reconstructed SST, version 5 (Huang et al. 2021), data are provided by the NOAA PSL, Boulder, Colorado, USA, from their website at https://psl.noaa.gov/data/gridded/data.olrcdr.interp.html and https://psl.noaa.gov/data/gridded/data.noaa.ersst.v5.html, respectively.
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