1. Introduction
Atmospheric blocking is a class of quasi-stationary and persistent weather systems in the middle and high latitudes. A blocking pattern is characterized by a high pressure component as a ridge or closed high with southerly flow prevailing on the western side and northerly flow on the eastern side in the Northern Hemisphere. From onset to decay, the blocking flow deforms slowly, substantially reducing and generally reversing midlatitude westerly winds to easterly winds. The deforming patterns travel at a speed of 1°–5° longitude per day (approximately 1–5 m s−1; Liu 2020), much slower than the usual synoptic ridges and troughs of Rossby waves. Such quasi-stationarity and persistence create obstruction and disruption of normal westerly winds and storm tracks for a prolonged period of time, causing extreme weather events in situ, upstream, and downstream in midlatitudes during all seasons (Mendes et al. 2008; Sillmann et al. 2011; Pfahl and Wernli 2012; Bieli et al. 2015; Brunner et al. 2017; Woollings et al. 2018).
The blocking frequency at 500-hPa geopotential height (Z500) in the Northern Hemisphere during December–February (DJF) and June–August (JJA) seasons was commonly diagnosed in observations, validated in GCM simulations, and verified in weather forecasts (Lupo 2020). Northern Hemisphere blocks persist mostly in the Atlantic–Europe (ATL-EU) and Pacific–North America (PNA) sectors, indicating a geographical preference. More blocking days ensue in DJF than in JJA in these regions by a factor of 3–5, exhibiting a seasonal preference. Similar occurrences are distributed in the upper, middle, and lower troposphere, forming a quasi-barotropic structure (Liu 2020). In addition, the occurrences have a log-linear distribution with duration (or “lifetime”; Pelly and Hoskins 2003), and the lifetime is positively correlated with the intensity. The geographical preference, seasonality, and quasi-barotropic structure of blocking were also observed in the Southern Hemisphere (Liu 2020).
It is a challenge to simulate the blocking frequency satisfactorily by GCMs participating in all CMIP phases (Davini and D’Andrea 2016). In a set of CMIP5 (Taylor et al. 2012) GCMs without GFDL models, the blocking frequency was underestimated in the ATL-EU sector and slightly overestimated in the PNA, although the geographical and seasonal preferences were reproduced reasonably well (Dunn-Sigouin and Son 2013). Two recent comparisons—one (Davini and D’Andrea 2020) including all available GCMs for CMIP3 (Meehl et al. 2007), CMIP5, and CMIP6 (Eyring et al. 2016) and the other (Schiemann et al. 2020) covering 30 European GCMs for CMIP5 and CMIP6—indicated that the multimodel ensemble of each CMIP phase tended to underestimate the blocking occurrences in both the ATL-EU and PNA sectors. Corresponding to the biased simulations were low-confidence projections of blocking in GCMs (Davini and D’Andrea 2020) with impacts either to strengthen (Cassou and Cattiaux 2016; Brunner et al. 2018) or to weaken (Barnes et al. 2013) under climate change, and less skillful onset and persistence predictions by early operational weather forecast systems (Tibaldi and Molteni 1990; Watson and Colucci 2002; Mauritsen and Källén 2004; Hamill and Kiladis 2014; He et al. 2019).
Diagnosing the causes of model biases to improve blocking simulations remains elusive. Higher model horizontal resolutions help to reduce the biases by better resolving subgrid-scale processes, such as the mechanical uplift of mountains, as well as diabatic processes in surface flux exchange and moist convection (Pithan et al. 2016; Schiemann et al. 2017; Steinfeld and Pfahl 2019). These processes were demonstrated to be essential for blocking formation and maintenance by forcing quasi-stationary planetary waves and fueling low potential vorticity (Riboldi et al. 2019). However, nonlinear interactions among these processes make it difficult to fine-tune individual parameterization schemes before determining the most biased blocking aspects.
Large differences in the detection of blocking have impeded investigations. In general, the blocking flow in the Northern Hemisphere manifests as five patterns on daily Z500 charts: an omega-shaped ridge, a solitary high, a north–south dipole of highs, an anticyclonic wave breaking with the high folding with an extension from southwest to northeast, or a cyclonic wave breaking (Woollings et al. 2018; Liu 2020). These complex structures are difficult to detect objectively and consistently, and different blocking indices were proposed to measure disparate features. All indices separately determined the blocking on a given day [instantaneous blocking (IB)] and a blocking event or persistent block (PB) from IBs that persist for consecutive days, whereas the criteria for IBs and/or PBs were different, resulting in diverse blocking frequencies. Several types of widely used indices are summarized next, focusing on their distinctions [see reviews in Barriopedro et al. (2010) and Woollings et al. (2018)].
Blocking detection began with Rex (1950). The Rex index requires a reversal of the westerly flow to easterly at Z500, equivalent of meridional pressure gradients through the geostrophic relation, in reference to the central blocking latitude fixed at 60°N. Once the reversal occurs at a longitude, an IB is defined from 40° to 80°N and extends in longitude by ∼20°. Some later studies (e.g., Colucci 2001) required the reversal also occurring on those longitudes. A PB develops from at least four consecutive and overlapping IBs. In the 1990s, the Rex index was revised slightly and automated for diagnosing gridded GCM simulations and predictions (Lejenäs and Økland 1983; Tibaldi and Molteni 1990, hereafter TM1990), and the TM1990 version has been widely used because of its simplicity. However, the reversal requirement excludes high-impact persistent ridges and weak omega-shaped blocks. In addition, the one-dimensional formulation limits TM1990 in regional applications with newer high-resolution model outputs.
Three paths have been followed to improve blocking detection. The first identified and tracked PBs as persistent positive anomalies of Z500 above certain thresholds after removing the climatology as long-term means (Dole and Gordon 1983; Pinheiro et al. 2019) or 31-day running means (Schiemann et al. 2020). Resulting large positive anomalies consequently included persistent ridges. However, the positive anomalies sometimes originated from a weakened climatological trough, such as that over the northern Pacific in winter, causing large distances between anomalous centers and actual ridges and misidentifications of weakened troughs as blocking (Liu 2020). Similarly based on persistent anomalies, the potential vorticity at the tropopause (Schwierz et al. 2004) or in the vertical average (Croci-Maspoli et al. 2007) was adopted, exploiting its correspondence to Z500 and the wave-breaking dynamics of blocking (Pelly and Hoskins 2003). The second path extended the TM1990 version from one to two dimensions by varying the central blocking latitude between 25°N (Masato et al. 2013) or 35°N (Scherrer et al. 2006) and 75°N, as well as requiring additional spatial persistence (Davini and D’Andrea 2016, 2020). The extensions also detected nonblocking patterns (Liu 2020), although the resultant blocking frequency remained more common in the ATL-EU than in the PNA by a factor of 3 (Pelly and Hoskins 2003). The third used a hybrid approach combining the reversal of zonal winds in TM1990 and the large persistent positive anomalies in Dole and Gordon (1983), Barriopedro et al. (2010), and Dunn-Sigouin et al. (2013). However, the combination preserved the mismatch between positive anomalies and actual highs, also resulting in misidentifications (Liu 2020).
The mismatch was effectively eliminated by using the zonal eddy anomalies of geopotential heights after removing the zonal means that do not contribute to meridional winds, a key component of blocking highs. Combining zonal eddies with the reversal of absolute geopotential heights (ABS) formed a unified eddy–ABS index (Liu 2020; see summary in section 2) capable of distinguishing traditional PBs and nonblocking persistent ridges characterized by a set of parameters for their onset, duration, intensity, moving speed, etc. This index is adopted to address several questions concerning the lasting biases of the blocking simulations in GCMs.
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What types of PBs in lifetime contribute most to the biases in the ATL-EU and PNA?
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How are the biases related to PB onset, intensity, persistence, and quasi-stationarity?
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How are persistent ridges simulated in comparison with blocking biases?
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Do these biases occur and differ in the lower and upper troposphere as well as in the Southern Hemisphere?
These issues were investigated in 10 GFDL GCMs for CMIP5 and CMIP6. Because the blocking biases are different in GCMs with diverging configurations, diagnostics targeting succeeding models from one institution may highlight more persistent and notable biases than an ensemble of GCMs from multiple institutions (e.g., Davini and D’Andrea 2020). Section 2 introduces the data, models, and methodologies used. Section 3 validates the simulations in terms of blocking frequency and several rates. Section 4 describes how the duration, onset, persistence, and quasi-stationarity contribute to the biases. Diagnostic sensitivity tests demonstrate that the climatology, particularly its zonal eddy component, contributes significantly to these biases. A summary and discussion of the study are presented in section 5.
2. Data, models, and methodology
a. Observations
Observational daily Z500 and Z250 were derived from the NCEP–NCAR Reanalysis (NNR; Kalnay et al. 1996) and the ECMWF Reanalysis v5 (ERA5; Hersbach et al. 2020). The two isobaric levels and time periods, 1975–2005 and 1979–2008, were selected to correspond to the model integrations described below. The results are not sensitive to the small difference in the time coverage (not shown). The NNR products have a horizontal resolution of 2.5° × 2.5° longitude by latitude, which is the default grid spacing for the Eddy-ABS settings. The ERA5 at 0.25° × 0.25° was interpolated to the NNR resolution using the Climate Data Operator toolkit (Schulzweida 2019).
b. GFDL models
Table 1 summarizes the fundamentals of the 10 models for analysis. These models, five for CMIP6 with the number four in the names, include atmosphere-only models (two HIRAMs and AM4), fully coupled climate models (CM3, CM4, and variants), and comprehensive Earth system models (ESM2M, ESM2G, ESM4, and variants). The models are configured with different horizontal and vertical resolutions and succeeding physical parameterizations in the atmospheric components. For example, ESM2 and CM3 adopt AM2 and AM3 physical packages at a 200-km horizontal resolution, while CM4 and ESM4 employ AM4 physical packages at a 100-km horizontal resolution. Differences in physical processes among AM2, AM3, HIRAM, and AM4 were documented by Zhao et al. (2018a,b). In addition, the ocean components differ among the models. For instance, ESM2M uses the Modular Ocean Model version 5, ESM2G includes the Generalized Ocean Layered Model, and CM4 and ESM4 adopt the Modular Ocean Model version 6, combining the advantages of both preceding ocean models. These different components may impact the blocking simulations through sea surface temperature and sea ice concentrations. For details of each model, the reader is referred to the corresponding publication provided in Table 1. In addition, both CMIP5 and CMIP6 historical integrations use radiative forcing associated with observed greenhouse gas concentrations, which makes it statistically meaningful to compare the results with observations. We selected time-overlapped 30-yr integrations for the comparison, that is, 1975–2005 for the historical experiments and 1979–2008 for the Atmospheric Model Intercomparison Project (AMIP; Phillips et al. 2004) type runs forced with observed sea surface temperature and sea ice concentrations. Extending the data coverage to 2014 in the CMIP6 integrations yielded similar results (not shown). All model outputs were downloaded on longitude–latitude grids and bilinearly interpolated to 2.5° × 2.5° resolution. Modeled geopotential heights were provided at multiple isobaric levels. Because of missing data at 850 hPa, our analysis focused on Z500 and Z250.
Configurations of 10 GFDL GCMs for analysis.
c. Decomposing geopotential heights
Here the overbar and square brackets represent the time and zonal mean, respectively, and the prime (′) and asterisk (*) are their deviations. The climatology
d. The eddy–ABS approach
The unified eddy–ABS index (Liu 2020) distinguishes four types of objects, including highs, IBs, PBs, and persistent highs as the persistent maxima of geopotential heights (PMZs). It targets zonal eddies Z* [in geopotential meters (gpm)] above certain thresholds in percentiles defined below and subject to widely used criteria for the reversals in the meridional gradients of geopotential heights, persistence, and quasi-stationarity. The approach identifies those objects separately at Z500 and Z250 in the Northern and Southern Hemisphere.
In essence, a high is defined as enclosed contiguous grid points with zonal eddies Z* above the 75th percentile in the corresponding month. The percentile (Liu 2020) is derived from the Z* values on grid points between 40° and 80° latitudes separately in the Northern and Southern Hemispheres and in the 90-day windows centered in the month during 1975–2005. This percentile effectively removes weak highs. For consistency, we adopted the 75th percentile of the observations as the reference for comparison, as using the values of each simulation caused very slight differences in blocking statistics (discussed in section 4). A few practical steps from Liu (2020) are summarized below, including several relevant definitions (see Fig. 1 for a schematic).
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Each high consists of a core and expansions. On daily charts, the global maximum of zonal eddies Z* is located for a core that is surrounded by grid points with Z* values decreasing away but within 95% of the maximum. The expansions include all points contiguous to the core, and the Z* values decrease to the 75th percentile. The core and expanded grid points are labeled 1 as the first high on a global mask map initialized with zeros.
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The second high is similarly detected from the remaining grid points and is labeled 2.
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The first two steps are repeated until no more cores can be identified. The succeeding highs, if any, are enumerated from three and labeled correspondingly on the mask map.
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Steps 1–3 are applied to all daily charts, and the highs are enumerated each time. Several parameters of a high are defined as follows. Based on the core points, the intensity (in gpm) is the averaged zonal eddies, and the central location is represented by the mass-weighted longitude and latitude. Based on all the points, the width is the difference in longitudes between the west and east boundaries, and the area (in km2) is the total coverage. These parameters are recorded only for the member highs of a PB or PMZ tracked below.
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After the highs on all maps have been identified, IBs are determined. Starting from the first high on a day, an IB forms with a reversal of the meridional gradients of geopotential heights in reference to any latitude within the high, equivalent to varying the central blocking latitude (Davini and D’Andrea 2016). In the Northern Hemisphere, the reversal corresponds to a gradient of less than −10 gpm per degree latitude in the north and greater than 0 gpm in the south of the central blocking latitude, as in TM1990. The IBs on each day are enumerated, and the enclosed grid points are labeled with the corresponding number on an IB mask map.
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A PB is tracked from IBs using the criteria for persistence and quasi-stationarity that require at least four consecutive IBs (only one for each day) with a maximum overlap between the adjacent two and no more than 10° between their central longitudes. Once an IB becomes a member of a PB, its grid points are labeled 1 on a PB mask map. The computed and recorded parameters of each IB high are defined above, and a few parameters of the PB are specified as follows: the onset date corresponds to the first IB on the track, the duration is the total number of member IBs (equivalent in days), the moving speed in longitudes per day is the averaged zonal distance of the adjacent IB pairs, the maximum intensity (in gpm) is the maximum of member IBs, and the average intensity is the mean of those IBs.
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PMZs are separately tracked from highs using the same criteria of PBs for persistence and quasi-stationarity. The grid points of a member high are labeled 1 on the PMZ mask map. Clearly, a PMZ can be a PB when all highs on the track are IBs, and it can also be persistent ridges with fewer than four consecutive IBs. Each PMZ has the same set of parameters as the PB defined in the previous step.
Schematic diagram for the eddy–ABS approach. See text for the definitions of the Z*, 75th percentile, core, high, PMZ, IB, and PB.
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
Finally, the grid points of the highs and IBs with a label greater than 1 are changed to 1, meaning one occurrence per day, to diagnose the frequency of each type.
e. Three blocking-relevant rates
The objects detected by the eddy–ABS approach represent different stages of persistent ridges or PBs evolving from highs or IBs. Their separation makes it possible to diagnose the percentage contribution of each stage using three rates on a grid point during a season. The instantaneous blocking rate (IB-r) represents the percentage of IBs formed out of all highs, or IB-r = IBs/highs × 100%. Here, the number of IBs is required to be no smaller than four to exclude small occurrences. This rate validates successful IB onsets using the reversal criterion.
The persistent blocking rate (PB-r) is defined as the formation of PBs out of IBs, or PB-r = PBs/IBs × 100%, where the number of PBs is at least four to mask out small occurrences. This rate describes the successful formation of PBs owing to their persistence and quasi-stationarity.
The persistent-stationary ridge rate (PSR-r) represents the percentage of non-PBs among PMZs, or PSR-r = (1 − PBs/PMZs) × 100%, where the number of PBs is at least four days for comparison with PB-r. This rate separates nonblocking ridges from PMZs, as they account for as much as 50% of occurrences (discussed in section 3a), and they have not been detected by blocking indices requiring the reversal of zonal winds (e.g., TM1990 and its variants).
f. Spatial correlation and root-mean-square error
The spatial correlation and root-mean-square error are defined conventionally between two series of data to assess the overall similarities in climatological blocking frequencies between models and observations. We paired the data on selected grid points where at least four blocking days in a season occur in observations, which confines the grid points at latitudes of 20°–80° and eliminates rare blocking occurrences as true negatives.
3. Blocking statistics in observations and GCMs
a. Blocking statistics in observations
The blocking frequency (in days per season) and the three blocking-related rates defined in section 2e in the observations are displayed as references for validating the GFDL GCM simulations. Several centers in blocking days (markers) are shared approximately at Z500 and Z250 over the ATL-EU, PNA, and southwest Pacific (SWP) during all seasons, and those for DJF and JJA are shown in Fig. 2 for NNR. The first is located near 7.5°W and 55°N at both Z500 and Z250 in DJF (Figs. 2a and 2b), near 35°E and 57.5°N at Z500 and spread to the central Atlantic at Z250 in JJA (Figs. 2c and 2d). The second is close to 130°W and 55°N in DJF; it splits into two smaller ones around 50°N in JJA. The third is in the vicinity of 150°W–180° and 60°S in both DJF and JJA. These common centers symbolize the geographical preferences and quasi-barotropic nature of blocking occurrences (Pelly and Hoskins 2003).
Blocking days at (a),(c) Z500 and (b),(d) Z250 in (top) DJF and (bottom) JJA averaged during 1975–2005 in the NCEP–NCAR reanalysis. Contours start at 4 with an interval of 4 days. The × markers in each panel represent the locations of maximum blocking frequency in the PNA, ATL-EU, and SWP regions.
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
During each season, the frequency centers across the three areas are different. In particular, the ATL-EU center is stronger than the PNA center by a factor of 2, for example, about 32 versus 16 days at Z500 in DJF (Fig. 2a). The factor of 2 here is smaller than the factor of 3 disclosed by TM1990 and variants (e.g., Pelly and Hoskins 2003), mainly because the eddy–ABS approach can detect more blocking grid points using zonal eddies (Liu 2020). The SWP center is the weakest among the three, except for at Z500 in JJA nearly reaching the magnitude in the PNA during DJF. A close inspection indicates that the barotropicity is more evident in the PNA with similar values at Z500 and Z250 than in the ATL-EU and SWP where the frequency decreases with height. Blocking occurs more frequently in cool seasons than in warm seasons, demonstrating a seasonal preference. During March–May and September–November (Fig. S1 in the online supplemental material), the blocking frequency elucidates transitional features. The differences in blocking frequency, barotropicity, and seasonality were attributed to distinct mechanisms in physical and dynamical processes, including topography, land–sea contrast, and diabatic heating [see reviews in Woollings et al. (2018) and Lupo (2020)]. How the differences manifest in the processes of highs evolving into IBs, in persistence and quasi-stationarity are displayed next.
The formation of an IB is characterized by a reversal of prominent westerly flow to easterly in reference to a latitude within the high. This can be statistically represented by IB-r during each season (Fig. 3). The IB-r distributions agree well with the blocking frequency in terms of geographical and seasonal preferences, and the barotropic structure. It is larger in the ATL-EU than in the PNA and SWP regions at the corresponding centers of blocking frequencies (contours and markers in Fig. 3), reaching 85% at Z500 and Z250 over northern Europe in DJF (Figs. 3a and 3b). The rates in the three areas are smaller in the warm seasons (Figs. 3c and 3d) than in the cold seasons. They are smaller in the Southern Hemisphere, suggesting different processes for IB formation. It is noteworthy that IB-r is larger at Z500 than at Z250 in both hemispheres, indicating that more IBs form in the middle troposphere than in the upper troposphere. The mechanisms of such differences merit further investigation.
IB-r in percentage (shading) at (a),(c) Z500 and (b),(d) Z250 during (top) DJF and (bottom) JJA in the NCEP–NCAR Reanalysis. Shaded are grid points with at least 4 days of IBs. The three contours in each panel are 8, 16, and 32 blocking days, and the × markers are the same as in Fig. 2.
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
The PB-r in each season represents the statistical contributions of persistence and quasi-stationarity to the blocking frequency, as shown in Fig. 4. Over the three key areas, PB-r agrees with the distributions of the blocking frequency and IB-r. Around the centers of blocking days, it is largest at Z500 in the ATL-EU, greater than 80% in northern Europe during DJF (Fig. 4a), and in eastern Europe and western Asia during JJA (Fig. 4c). It is smaller in the PNA and much smaller in the SWP, with values of approximately 60%. The PB-r at Z250 is smallest over the SWP, at only 40% (Fig. 4d).
As in Fig. 3, but for the PB-r where the number of PB days is at least 4.
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
Persistent and stationary ridges or nonblocking PMZs can cause extreme weather as PBs do (Liu et al. 2018). Although these ridges are not separately tracked by the Eddy-ABS approach, their occurrence rate (PSR-r in percentage; cf. section 2f) can be derived by subtracting the frequency of PBs from that of PMZs. In general, the PSR-r varies with the blocking frequency during different seasons (Fig. 5). Specifically, around the blocking frequency centers (markers), the PSR-r at Z500 in DJF (Fig. 5a) is ∼25% at 7.5°W over northeastern Europe, ∼50% along the northwestern coast of North America, and ∼60% in the southwest Pacific. At Z250 (Fig. 5b), it is larger by 10%–20% in the three areas. During JJA at Z500 (Fig. 5c), the PSR-r shifts with the blocking frequency. It is ∼30% in eastern Europe, ∼60% in the North Pacific, and ∼25% in the SWP. At Z250 (Fig. 5d), it becomes slightly smaller in the first two areas and larger in the third. The largely varying PSR-r near the blocking frequency centers suggests that both PBs and persistent ridges should be validated in model simulations. The features in Figs. 2–5 are very similar in ERA5 (e.g., Fig. 2 vs Fig. S2) and during 1979–2008 (not shown).
As in Fig. 3, but for the PSR-r where the number of days of PBs is at least 4.
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
b. Blocking statistics in GFDL GCMs
In this section, the blocking frequencies at Z500 and Z250 during DJF and JJA simulated by the 10 GFDL GCMs are validated with reference to the observational results discussed above. As an initial measure of success, all simulations have reproduced the geographical and seasonal preferences and the barotropic structure of blocking frequencies during all seasons, despite the difference in the maximum blocking frequency between the ATL-EU and PNA being smaller in the models. Displayed below are biases as the differences from observations on two-dimensional maps, as well as spatial correlations and root-mean-square errors over the globe.
The blocking frequency at Z500 during DJF is first validated in geographical distributions. In the ATL-EU, the locations of the maximum frequency in CM3, CM4C192, CM4, ESM4, ESM4AMIP, and CM4AMIP (red markers in Fig. 6) match well with those in the observations (black markers), whereas they deviate more by 5° longitude in ESM2G, ESM2M, and HIRAMC180 and by 50° longitude in HIRAMC360. The CMIP6 group shows clear improvements in the locations of the maximum blocking frequency.
Differences of DJF blocking days at Z500 in GFDL models from observations (shading of at least 8 days) with a contour interval of 2 days (the zero contour is omitted). The × markers represent the centers of blocking days in observations (black) and each model (red). CMIP6 models have the number 4 in the names.
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
A common bias over the ATL-EU is a substantial underestimation of the blocking frequency with a center around 0°W and 60°N near that of the observations (Fig. 6). The maximum biases diverge among the GCMs. Starting from the most negative in days, the center is −18 in ESM2M, −14 in ESM2G, −10 in ESM4AMIP and HIRAMC360, −8 in CM3, CM4C192, ESM4, CM4, and CM4AMIP, and −6 in HIRAMC180. Because the maximum frequency in observations is approximately 32 days (cf. Fig. 2a), these negative values correspond to underestimates between 20% and 50%, which is like other models for CMIP3-6 (Davini and D’Andrea 2020). The central differences are smaller in the five integrations for CMIP6 than for CM3, ESM2G, and ESM2M, demonstrating improvements in the more recent versions of the GCMs. It is noteworthy that CM4C192 for CMIP6 and HIRAMC180 for CMIP5 have the smallest underestimation, probably because of their relatively high horizontal resolutions (∼50 km), as reported in other studies (e.g., Anstey et al.2013; Schiemann et al. 2017). Nevertheless, an even higher resolution in HIRAMC360 (∼25 km) does not further improve the simulation in this region.
In the PNA sector, the locations of the maximum blocking frequency in most models (red markers in Fig. 6) match those in observations (black markers), except for ∼20° longitude more westward in ESM2G, HIRAM180, and HIRAM360 and more eastward in ESM2M. The common bias is a significant overestimation of the blocking frequency with a center near the western coast of North America. Starting from the largest, the overestimated frequency in days is 10 in HIRAMC360 and HIRAMC180, 8 in CM4, and 6 in the rest of the GCMs, except for 4 in ESM4. A close inspection indicates that the maximum overestimates are farther westward in ESM2G, eastward in CM3 and ESM2G than in other models. The overestimation is up to 60% of observations, much larger than the biases of either underestimation (Davini and D’Andrea 2020) or slight overestimation (Dunn-Sigouin and Son 2013), including or without GFDL models. The contributions of several blocking aspects to these biases are discussed in the next section. Because the five models for CMIP6 share a center of overestimation with similar magnitudes and locations, they have been grouped for the composite analysis shown below.
Over the SWP during DJF, the centers of blocking frequencies in the GCMs mostly deviate eastward by 5°–30° longitude from those in observations (red vs black markers), with the smallest distance in CM4C192, CM4, and ESM4. In addition, all models have underestimated blocking occurrences. The maximum difference in days is −8 in CM3 and ESM2M, −6 in ESM2G, −4 in ESM4AMIP and HIRAMC360, and −2 in the rest. These values, in combination with the distance between the blocking frequency centers, account for 25%–70% of the observations. The biases of the blocking frequency at Z250 during DJF are comparable to those at Z500 (see Fig. S3).
Simulated biases of the blocking frequency during JJA also demonstrate geographical and seasonal preferences and barotropicity. At Z500 (Fig. 7), biases in the Northern Hemisphere are characterized by negative and positive centers around 55°–60°N, mostly on top of the observational centers (shading and black markers). The modeled maximum blocking frequency (red markers) agrees well with observations over the ATL-EU, whereas it deviates more eastward over the PNA and westward over the SWP. In the ATL-EU, an underestimation of 6 days occurs over the Atlantic, and an overestimation of 8 days occurs in eastern Europe. These values are smaller than those in DJF, although they still account for approximately 40% of the observations. The five CMIP6 models show disparate biases, with the smallest being CM4C192. In the PNA, overestimates occur in all GCMs, while they are substantially smaller in the CMIP6 models. It is noteworthy that ESM4AMIP is an outlier with a 6-day overestimation in western Canada. In the SWP, all GCMs overestimate the blocking frequency with a center near 180° and 60°S. The overestimation is substantially smaller in the four AMIP runs forced by the observed sea surface temperature, suggesting that model biases in sea surface temperature (Zhao et al. 2018a,b) may contribute to the blocking bias in this area. The biases of the blocking frequency at Z250 during JJA are much smaller than those at Z500 (Fig. S4). Figure S5 compares the modeled maximum blocking frequencies over the three key areas with those in observations.
The modeled blocking frequency is further validated in terms of spatial correlations and root-mean-square errors over the globe during DJF and JJA in reference to the observations. The comparisons are summarized in Fig. 8, where darker colors represent results closer to the observations. For example, the ERA5 has the darkest colors for both parameters, closest to the NNR. The correlations are large and mostly above 0.8 at Z500 (second column) and Z250 (fourth column) during DJF and at Z500 during JJA (sixth column), whereas it is smaller and drops to 0.77 at Z250 during JJA (eighth column). In contrast, the root-mean-square error is larger at Z500 and Z250 during DJF (third and fifth columns) and at Z500 during JJA (seventh column), and it is smallest at Z250 during JJA (ninth column). Similar biases in blocking frequencies occur during the March–May and September–November seasons (not shown), and the CMIP6 GCMs perform better than the earlier versions. In the next section we show how blocking biases manifest in the eddy intensity, blocking types in lifetime, IB conversion, persistence, quasi-stationarity, and biased mean state.
Spatial correlations (COR) and root-mean-square errors (RMSE) of blocking days between models and observations. Grid points with at least 4 blocking days in observations are counted.
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
4. Ingredients of blocking biases
a. Eddy intensity
Because zonal eddies are used to represent highs, IBs, PBs, and PMZs, their modeled intensity can indicate potential systematic biases. For consistency, the intensity is represented by the 75th percentile and compared with observations using histograms. In the Northern Hemisphere, most models simulate zonal eddies at Z500 only slightly weaker than observations in DJF and JJA, as indicated by the blue and red bars starting from three slightly lower than the first two (Fig. 9a). The bars for the models at Z250 are lower than the observations, particularly during DJF (blue in Fig. 9b), indicating somewhat larger underestimates.
The 75th percentile of zonal eddies of geopotential heights in the Northern Hemisphere (40°–80°N) at (a) 500 and (b) 250 hPa during DJF (blue) and JJA (red) in 1975–2005.
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
In the Southern Hemisphere, the modeled eddies are stronger than those in the observations at Z500 and Z250 in JJA and less strong in DJF (not shown). HIRAMC360 has the highest, approximately 93 gpm, or 15% stronger than the 80 gpm in the observations. However, such a large difference contributes only ∼5% (∼1 day) more blocking frequency (not shown), which is marginal. In addition, the lack of observations in the Southern Ocean may include uncertainties in the validations. Overall, the modeled eddy intensity plays a small role in the biases, which is also supported by the fact that only slightly different blocking frequencies are diagnosed when using the 75th percentile of the zonal eddies in geopotential heights from each model (not shown).
b. Blocking types in lifetime
Next, we focus on how the blocking aspects contribute to the substantial biases in the CMIP6 model group. The blocking frequency at Z500 has a log-linear distribution with lifetime in probability distribution histograms (Pelly and Hoskins 2003; Liu 2020). This distribution can be similarly shown by the reversed cumulative distribution functions of the total blocking days with lifetime, where the days are accumulated in the reverse order of the conventional cumulative distribution function. In addition, the reversed cumulative distribution functions more clearly display how different types of blocking in lifetime contribute to the biased frequencies over the three key regions. Figure 10 shows all persistent blocks with an onset (the first IB on a blocking track) located in 5°W–15°E over the ATL-EU (top) and in 145°–125°W for the PNA during DJF (middle), and in 180°–160°E for the SWP during JJA (bottom). In general, modeled total blocking days agree with observations (thick black for the NNR and gray for the ERA5) with a log-linear distribution in which blocking occurs most at the shortest lifetime and decreases at an e-folding rate thereafter (Liu 2020).
Reversed cumulative distribution functions (RCDFs) of total blocking days in lifetime at Z500 over (a) ATL-EU with onset longitudes in 5°W–15°E during DJF, (b) PNA with onset longitudes in 145°–125°W during DJF, and (c) SWP with onset longitudes in 180°–160°W during JJA. The period is 1975–2005 for observations and non-AMIP integrations, and 1979–2008 for the AMIP runs by the five CMIP6 models. The various distributions correspond to different observations, models, and diagnostic tests.
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
However, the simulated blocking types in the lifetime show different biases in the three areas. In the ATL-EU at Z500 during DJF (Fig. 10a), all thin-solid-colored lines for the models are in the range of 450–780 at the 4-day lifetime, far below the 850 in observations, indicating an underestimation of 10%–45%. Most models underestimate 5–6-day blocking by 10%–30%. The smaller number of short-lived blocks contributes primarily to the underestimated frequency in the ATL-EU (cf. Fig. 6). It is noteworthy that some modeled blocks tend to last longer. For example, a few blocks with a lifetime of 18–22 days occur in CM4C192 (thin blue), 29 days in ESM4 (green), and 31 days in CM4 (red), whereas the longest lifetime is only 23 days in the observations.
In the PNA at Z500 during DJF (Fig. 10b), all thin colored lines are in the range of 600–780 at the 4-day lifetime, well above the observational total of 560–600 (thick black and gray lines). These lines are nearly parallel for the 4–12-day events, indicating a close agreement among the models. It is noteworthy that each of the two persistent blocks of 14 and 15 days in ERA5 (gray) corresponds to two events of ∼7 days in the NNR (not shown). Modeled long-life events last more than 13 days with a maximum of 27 (red for CM4), contrasting the longest events of only 12 days in observations, and these events account for the substantial overestimates of blocking frequencies (cf. Fig. 6).
In the SWP at Z500 during JJA (Fig. 10c), a dramatic overestimation occurs in blocking with a lifetime of 4–6 and 10–12 days, as indicated by steeper reversed cumulative distribution functions. For 4-day blocks in the probability distribution function histogram (not shown), the total number of blocking days is approximately 50 in the observations, but between 60 and 120 and approximately 20%–100% more in the models. Similarly, for 5–6-day events, the total number of blocking days is approximately 75 in the observations and 70–140 in the models, indicating a dramatic overestimation as well. After compensating for the small underestimates, the overestimates at those lifetimes eventually contribute to the substantial overestimation of the blocking frequency in this area.
c. Intensity and moving speed of blocking in PNA
The dramatically overestimated blocking frequency in the PNA during DJF is disclosed for the first time. It is intriguing to further examine how the intensity and moving speed of PBs with a lifetime of up to 12 days are related. These two aspects are compared in histograms with lifetimes in terms of average intensity and moving speed (see the definitions in section 2e). Blocking intensity has been known to positively correlate with the lifetime at Z500 (Liu 2020). This correlation is evident in both observations and model simulations. More importantly, the simulated intensity tends to be larger than that in observations, especially for blocks of 5, 6, and 12 days, which is indicated by the color bars generally higher than the black (Fig. 11a). The stronger blocks contrast that zonal eddies are slightly weaker in the simulations (cf. Fig. 9a). In addition, the simulated persistent blocks tend to move slower than those in the observations, particularly with lifetimes of 4 and 12 days, as shown by the lower bars in Fig. 11b. Understanding why modeled persistent blocks in the PNA with a lifetime of up to 12 days tend to be stronger and move slower merits future investigation.
Averaged (a) central intensity and (b) absolute moving speed of persistent blocks for each type in lifetime within 12 days in the PNA sector during DJF in 1975–2005 for the NCEP–NCAR reanalysis and non-AMIP runs and in 1979–2008 otherwise.
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
d. Biases in the three rates
The biased blocking frequency over the three areas is positively correlated with IB-r, PB-r, and PSR-r (Fig. 12). In the Northern Hemisphere during DJF (left column), the underestimation in the ATL-EU corresponds to a lower IB-r and PB-r by approximately −10% and a higher PSR-r by 15%, suggesting less formation of IBs caused by the reversal of zonal winds and in PBs contributed by persistence and quasi-stationarity. In contrast, dramatic overestimates occur in the PNA during DJF and in the SWP during JJA (right column in Fig. 12), corresponding to a higher IB-r (Fig. 12b) and PB-r (Fig. 12d) by 15%, but a lower PSR-r by −15% (Fig. 12f).
Differences of (a),(b) IB-r, (c),(d) PB-r, and (e),(f) PSR-r at Z500 in the CMIP6 composites from the NCEP–NCAR reanalysis in (left) the Northern Hemisphere (NH) during DJF and (right) the Southern Hemisphere (SH) during JJA.
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
e. Contributions by biased climatology
Biases in climatological geopotential heights can contribute to the biased blocking frequency by impacting highs, IBs, and their persistence and quasi-stationarity separately defined in the Eddy-ABS approach, although biased blocking simulations can in turn impact the climatology (Scaife et al. 2010; Davini and D’Andrea 2016). For example, climatological zonal eddies are dynamically associated with quasi-stationary planetary waves in the middle-high latitudes, which is an essential factor for blocking formation through Rossby wave resonance (Altenhoff et al. 2008). We thus investigated how the simulated mean state contributes to the blocking biases by diagnostic sensitivity tests on all the models. Because the results are similar and CM4C192 has the smallest biases in blocking frequency, this GCM is selected for demonstration.
In the CM4C192 simulations, climatological geopotential heights at 500 and 250 hPa are smaller than in the observations, particularly over the three key areas (shading in Fig. 13). In the ATL-EU during DJF, the climatology is approximately 40 gpm smaller at 500 hPa and 60 gpm smaller at 250 hPa, and the zonal eddies are approximately 20 and 40 gpm smaller, respectively (Figs. 13a and 13b). In the PNA during DJF, the climatology is approximately 40 gpm smaller at 500 and 250 hPa, and the zonal eddies are approximately 20 gpm smaller. In the SWP during JJA, a quasi-stationary wave train is evident in both the climatology and zonal eddies with +100 gpm in the west, −60 gpm in the middle, and +60 gpm in the east of the shading, and the negative center coincides with that of the blocking frequency (cf. Fig. 2). These nonuniform differences contribute differently to the biased blocking frequencies.
Differences of (left) climatology
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
We designed two diagnostic sensitivity tests. The first replaces modeled climatological geopotential heights with those in observations, and the second replaces only the zonal eddies (CM4C192NNRm and CM4C192NNRme in Table 1). In both cases and compared to observations, the 75th percentile of the zonal eddies is slightly increased at Z500 and Z250 during DJF and JJA (Fig. 9), which negligibly changes the simulated blocking frequency. However, the distribution of blocking with lifetime is dramatically improved over the three areas. In the ATL-EU during DJF (Fig. 10a), the total number of days accumulated down to 4-day blocking increases to 830 in CM4C192NNRm, close to the observations. In CM4C192NNRme, the overall increment is more dramatic, such that the total number of days exceeds those in the observations. In the PNA during DJF (Fig. 10b), the longest blocking becomes 19 days in CM4C192NNRme, shorter than the 24 days in CM4C192 and the 25 in CM4C192NNRm, indicating that climatological zonal eddies notably impact the blocking persistence. A close inspection indicates that CM4C192NNRme produces more blocking with a lifetime of 12–15 days than CM4C192NNRm and CM4C192. For blocking with a lifetime of up to 12 days, the two tests make it slightly stronger (Fig. 11a) and move faster to be closer to the speed in observations (Fig. 11b). Overall, CM4C192NNRme impacts the overestimation more than CM4C192NNRm, suggesting that climatological eddies contribute more to blocking frequency in the PNA during DJF.
The most dramatic changes occur in the SWP during JJA (Fig. 10c). The numbers of days for blocking with lifetimes of 4, 6, 7, and 10 become very close to those in observations, those for 5 and 8 days are smaller, and only those at 12 days are larger in the probability distribution function histograms (not shown). These changes substantially reduce the biased blocking frequency. However, a shift of dramatic overestimates of frequency occurs on the western and eastern sides of the SWP (shown below), and thus changes the total number of days for blocking.
The blocking frequency also shows significant changes (Fig. 14). In the ATL-EU during DJF, it is increased by 6 days in CM4C192NNRm and 7 in CM4C192NNRme at Z500, 6 in CMC192NNRm, and 8 in CM4C192NNRme at Z250. These values reduce the biased underestimation by 50% (cf. Figs. 6 and 7), and the reduction is primarily contributed by climatological zonal eddies. In the PNA during DJF, an increase of 1 day in CMC192NNRm and 3 in CM4C192NNRme occurs on the northeastern side of the shading at both Z500 and Z250, while a decrease of about 1–2 days occurs on the southwestern side (Figs. 14a–d). The decrease reduces the overestimation biases by 10%–20% (cf. Fig. 6d), despite even larger biases occur in northwestern Canada and Alaska. In the SWP during JJA, a reduction of 12 blocking days occurs in both CM4C192NNRm and CM4C192NNRme near the center of the blocking frequency in observations (cf. Fig. 6). This reduction nearly removes the large overestimation (cf. Fig. 7d). It is noteworthy that an increase in blocking at 4–5 days occurs on the eastern and western sides of the South Pacific (not shown), which tends to widen the biases. In addition, climatological zonal eddies primarily contribute to these changes in the SWP.
Blocking frequency differences in (a)–(d) DJF and (e),(f) JJA with an interval of 1 day (the zero contour is omitted). The differences are derived by subtracting blocking days in original CM4C192 from those in revised CM4C192 with (left) climatology
Citation: Journal of Climate 35, 15; 10.1175/JCLI-D-21-0456.1
5. Summary and discussion
The validation of the blocking frequency in GCMs is a persistent challenge owing, in part, to the large differences among the detection methods. This study employs the Eddy-ABS approach, which targets blocking highs as positive zonal eddies with established reversals of zonal winds. Because the maximum zonal eddies match the locations of high pressure systems, this index reduces the methodological uncertainties to a minimum. In addition, the method separately identifies highs, IBs, PBs, and persistent highs, which makes it possible to diagnose the onset, persistence, and quasi-stationarity of blocking and makes process-oriented diagnostics of blocking simulations more practical. Because CMIP GCMs tend to commonly underestimate the blocking frequency (Davini and D’Andrea 2020), we selected 10 GFDL GCMs for recent CMIP5 and CMIP6 to diagnose their general skills and investigate how blocking frequency biases manifest in other blocking features. NNR was used as the reference for validations, partly because of its consistency with ERA5.
These models, despite different settings in resolution, physical processes, and air–sea coupling, have successfully reproduced several salient features of the blocking frequency in observations. The first is a strong geographical preference by which blocking occurs mainly in the ATL-EU, PNA, and SWP areas. The second is an established seasonal preference, in which blocking occurs more frequently in cool seasons. The third is a quasi-barotropic structure in the vertical direction with similar distributions at Z500 and Z250. The last is a log-linear distribution of the blocking frequency with lifetime and a positive correlation between intensity and lifetime. The first two features generally agree with those in GCMs for CMIP3-6 reported in recent studies (Davini and D’Andrea 2020). In addition, different blocking frequencies over the three key areas are reproduced compared to observations. The frequency in the ATL-EU is twice as large as that in the PNA and is the smallest over the SWP. The frequency decreases slightly upward in the Northern Hemisphere but more dramatically in the Southern Hemisphere.
However, notable biases are simulated, particularly for the three blocking active regions. Compared with observations at Z500 and Z250, a substantial underestimation of up to 50% occurs in the ATL-EU during DJF, while a significant overestimation of up to 70% occurs in the SWP during JJA and by 60% in the PNA during DJF. The ATL-EU underestimate was recently diagnosed in other GCMs (Davini and D’Andrea 2020), while the large overestimates in the PNA and SWP are disclosed for the first time. In general, the five GCMs for CMIP6 share biases in magnitude and location, and they show substantial improvements over the three low-resolution versions of CMIP5. The two HIRAMs at very high resolutions during the CMIP5 era also improve the blocking simulations, although the magnitudes and locations are different.
These biased blocking frequencies are associated with slightly weaker zonal eddies in the Northern Hemisphere, whereas the contributions from the weaker eddies appear to be marginal. Short-lived persistent blocks with a lifetime of up to 6 days significantly contribute to the underestimation in the ATL-EU and the overestimation in the SWP, while blocking longer than 12 days in the GCMs, but not in observations, primarily contributes to the overestimation in the PNA. Modeled blocks with a lifetime shorter than 13 days in the PNA tend to be stronger and move more slowly than their counterparts in observations, indicating that intensity, persistence, and quasi-stationarity all play a role. In addition, the substantial underestimates in the ATL-EU correspond to lower instantaneous blocking rates and persistent blocking rates but higher persistent-stationary ridge rates, and the substantial overestimates in the PNA and SWP correspond to higher instantaneous blocking rates and persistent blocking rates but lower persistent-stationary ridge rates.
Biased climatological geopotential heights contribute significantly to the biased blocking frequencies. Two diagnostic tests were performed in all GCMs by separately replacing modeled climatological geopotential heights and zonal eddies with those in the observations. The results represented by CM4C192 demonstrate slight changes in eddy intensity and dramatic changes in the number of short-lived blocks, the magnitude (strengthened), and the moving speed (accelerated) of blocking up to 12 days in the PNA. The changes correspond to dramatic improvements in the central blocking frequency over the ATL-EU, PNA, and SWP, except for large overestimates occur as new biases on the western and eastern sides of the SWP as well as northwestern Canada and Alaska. These locations correspond to the exit regions of the jet streams and quasi-stationary planetary waves with a large amplitude. The tests suggest that the biased climatology contributes linearly to blocking formations, such that full blocking is not always necessary for reasonable statistics of onset and dissipation of extreme events, as also suggested by Liu et al. (2018). Of course, the dynamics of blocking cannot be fully linear and improving the mean state remains a desirable goal for this reason. Whether the blocking frequency may in turn contribute to the biased climatology in these models, including the interaction between blocking and jet streams and the resonance of transient and quasi-stationary planetary waves, merits further investigation following Scaife et al. (2010) and Davini and D’Andrea (2016).
The validations disclose moderate sensitivity of the blocking frequency to model resolution, as the simulations are modestly improved in CM4C192 and HIRAMC180. The sensitivity of the blocking frequency is moderate to air–sea coupling or the observed sea surface temperature in AMIP-type runs in the Northern Hemisphere, but more in the SWP. Whether the observed sea surface temperature at higher frequencies plays a role will be investigated by numerical experiments in future studies. The above diagnostics will be applied to other GCMs participating in CMIP5 and CMIP6 for their systematic success and biases, and the comparison will disclose whether the results found here represent an outlier. The new results will help more robustly project the blocking frequency under climate change and shed light on future model development.
Acknowledgments.
NCEP–NCAR Reanalysis data were provided by the NOAA/OAR/ESRL PSL, Boulder, Colorado, USA, from their website at https://psl.noaa.gov/. Reed is supported in part by the Department of Energy Office of Science award number DE-SC0019459 and the National Science Foundation (Grant AGS-1648629). The authors thank Dr. Isaac Held for providing helpful feedback on the draft version of this manuscript. We also thank the four reviewers for their constructive comments to help substantially improve the manuscript.
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