1. Introduction
Atmospheric blocks are persistent, quasi-stationary anticyclones (Rex 1950) that can impact midlatitude weather hazards (Sillmann 2011; Pfahl and Wernli 2012; Booth et al. 2021), cyclonic weather systems (Mattingly et al. 2015; Yamazaki et al. 2015; Booth et al. 2017), and climate [reviewed in Lupo (2020)]. As such, it is important to understand how blocking will respond to anthropogenic climate change (e.g., Woollings et al. 2018). However, we first need to understand and quantify the skill of the most recent generation of general circulation models (GCMs) in capturing blocking in current climates and determine how the representation of blocking depends on model general circulation features. Therefore, the work herein analyzes the climatological and dynamical features of blocking in integrations of GFDL’s atmosphere-only and coupled atmosphere–ocean comprehensive models for the recent past (i.e., historical integrations from the model intercomparison projects).
Past assessments of GCMs show that the models have issues in capturing blocking. For instance, D’Andrea et al. (1998) analyzed how well the climatological features of blocking were captured in the first Atmospheric Model Intercomparison Project (AMIP). They found that all 15 models underestimated blocking in both the Pacific and Atlantic regions. Since then, various studies have assessed the climatology of blocking across different generations of coupled models that participated in Coupled Model Intercomparison Project (CMIP) experiments (Scaife et al. 2011; Barnes et al. 2012; Masato et al. 2013; Anstey et al. 2013; Davini and D’Andrea 2020). In all cases modeled blocking climatology did not quantitatively match reanalysis. Furthermore, biases in blocking have been found to vary greatly across models, with the Pacific and Atlantic sometimes showing opposite signs in biases (Matsueda et al. 2009; Masato et al. 2013; Jiang et al. 2019).
In the multimodel mean of the CMIP6 models, blocking across the Northern Hemisphere is biased low in terms of blocking frequency (Davini and D’Andrea 2020; Schiemann et al. 2020). These biases have been attributed to mean-state biases (Scaife et al. 2011; Davini and D’Andrea 2016; Kleiner et al. 2021). Other more targeted studies, however, suggest that subgrid-scale processes that would likely be more accurately represented by increasing horizontal resolution could be causing biases in a model’s representation of blocking (Jung et al. 2012; Anstey et al. 2013; Davini et al. 2017; Jiang et al. 2019; Steinfeld et al. 2020). Thus, the current state of the literature suggests that both the large-scale and small-scale dynamical features of GCMs might explain model blocking biases.
Theoretical work on blocking offers additional motivation as one considers potential mechanisms for model biases. The recent idealized modeling work of Paradise et al. (2019) suggests that the dynamical details of the models could have important impacts on the blocking climatology. The authors systematically analyze the stationary wave, jet, and high-frequency eddy feedback using the “traffic jam” theory introduced by Nakamura and Huang (2018). Paradise et al. (2019) found that the stationary wave and high-frequency eddy forcing exhibited a direct relationship with blocking, whereas stronger jets led to less blocking.
Other authors have found the position of the jet, and thus waveguide, to be key to blocking. In work with early models and observations, Yeh (1949) found blocking to be more persistent for higher jet latitudes. Recently, Wang and Kuang (2019) expanded upon the idealized modeling work of Shutts (1983) to show that the orientation of high-frequency eddies, not their presence alone, plays a pivotal role in maintaining blocks, yielding results in agreement with Yeh (1949) in terms of jet latitude, eddy orientation, and blocking. Using comprehensive models, however, Barnes and Hartmann (2010) found a decrease in blocking for higher jet latitudes. Clearly, a full theory of blocking frequency and its relationship to the mean state is not yet settled. These studies provide context and motivation for more detailed analysis of the links between large-scale features of GCM atmospheric dynamics and modeled blocking.
With this in mind, the study herein investigates the climatology and dynamics of blocking in version 4 of GFDL’s atmosphere-only and coupled atmosphere–ocean models (AM4 and CM4). The remainder of the paper is organized as follows: section 2 covers the data and methods. In section 3a, we analyze model simulation of the stationary wave and upper-level jet. In section 3b, we evaluate the blocking climatology. In section 3c, block area and duration in the GFDL models is compared to reanalysis. The background flow and transient eddy forcing during block onset is investigated in sections 3d and 3e, respectively; for this, block-centered compositing analyses of geopotential height, low-frequency zonal wind, and high-frequency eddy forcing are separately carried out for Pacific and Atlantic blocking. Section 4 provides a discussion of consistencies and inconsistencies in general circulation and blocking biases in the models. Section 5 presents conclusions.
2. Data and methods
a. General circulation models
This work analyzes general circulation and blocking in Geophysical Fluid Dynamics Laboratory’s (GFDL) atmosphere-only model AM4 (Zhao et al. 2018) and coupled atmosphere–ocean model CM4 (Held et al. 2019). Previous studies have shown strong agreement between GFDL blocking simulations and corresponding CMIP ensemble means (Masato et al. 2013; Davini and D’Andrea 2016). AM4 is computed at roughly 100-km resolution with 33 vertical levels. AM4 is forced with prescribed time-evolving sea surface temperatures (SSTs) and sea ice distributions. AM4 serves as the atmospheric component for the coupled model CM4, which is part of the ensemble from phase 6 of the Coupled Model Intercomparison Project (CMIP6). CM4 consists of AM4 coupled to the ocean model, OM4 (Adcroft et al. 2019), and sea ice model SIS2.0 (Adcroft et al. 2019). The CM4 simulation is not retuned relative to the AM4 simulation with prescribed forcing.
The primary difference between AM4 and CM4 is ocean forcing. AM4 is forced by prescribed SSTs while CM4 is coupled to an ocean model. Generally, the mean SSTs in CM4 are colder than AM4 during winter (December–February; Fig. 1). These biases have been documented in Held et al. (2019; see their Fig. 13); for the most part, they are smaller than biases in previous GFDL models. CM4 is also coupled to a dynamic sea ice model, whereas the sea ice in AM4 is a time-evolving parameterization based on observations. CM4 also uses a different land model, LM4.0.01, compared to AM4, which uses LM4.0. The version LM4.0.01 contains different settings controlling albedos of snow masking involving vegetation and glaciers. More information on this can be found in Held et al. (2019).
Sea surface temperature (SST) in AM4 (contours) and difference in SST between CM4 and AM4 (shading). The most equatorward contour is 30°C, and the contour interval is 5°C.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
Sea surface temperature (SST) in AM4 (contours) and difference in SST between CM4 and AM4 (shading). The most equatorward contour is 30°C, and the contour interval is 5°C.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
Sea surface temperature (SST) in AM4 (contours) and difference in SST between CM4 and AM4 (shading). The most equatorward contour is 30°C, and the contour interval is 5°C.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
The jet at 250 hPa, stationary wave at 500 hPa, and blocking produced by the GFDL models are compared with ECMWF ERA5 reanalysis (Hersbach et al. 2020). ERA5 is produced at roughly 30-km horizontal resolution with 137 vertical levels. For all models in this paper, daily mean data are interpolated into 2.0° latitude × 2.5° longitude grids. We focus only on winter defined as December–February (DJF) from 1980 to 2014.
b. Block tracking, climatology, and regional sorting
To identify and track blocks, this work implements the 500-hPa geopotential height (Z500) metric described by Dunn-Sigouin and Son (2013, herein DS13). This hybrid metric searches for strong positive anomalies in Z500 (
Positive anomaly amplitude of at least 1.5 standard deviations
Area of at least 2.5 × 106 km2
Meridional gradient reversal of Z500 as described in DS13
Quasi-stationary condition: 50% area overlap between successive time steps
Satisfaction of the above criteria for at least 5 days
We choose this metric due to its straightforward implementation, as well as its ability to capture high-amplitude wave breaking events (DS13). Barnes et al. (2012) found that similar Z500 metrics yield similar blocking properties and climatological features compared to potential temperature or vorticity-based metrics. For specific details of the tracking algorithm, the reader is referred to DS13.
For each time step at each grid point, the block tracker yields a block identification flag of 1 or 0 corresponding to the presence and absence, respectively, of blocking. Climatological spatial distributions of blocking frequency, hereinafter referred to as the blocking climatology, are computed by averaging 2D latitude–longitude grids of block identification flags over all DJF days. Note that, in this work, blocking frequency indicates the percentage of DJF time steps that a grid point was identified as blocked, not the number of individual events. The blocking climatology for DJF in ERA5 from 1980–2014 is shown in Fig. 2a.
(a) Blocking climatology C (shading) for ERA5 averaged over December–February (DJF). Red boxes show the boundaries used to define the Pacific and Atlantic regions. (b) Area-weighted meridional mean of the midlatitude DJF blocking climatology
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(a) Blocking climatology C (shading) for ERA5 averaged over December–February (DJF). Red boxes show the boundaries used to define the Pacific and Atlantic regions. (b) Area-weighted meridional mean of the midlatitude DJF blocking climatology
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(a) Blocking climatology C (shading) for ERA5 averaged over December–February (DJF). Red boxes show the boundaries used to define the Pacific and Atlantic regions. (b) Area-weighted meridional mean of the midlatitude DJF blocking climatology
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
Previous studies have found distinct differences between Pacific and Atlantic blocking in the Northern Hemisphere (Hartmann and Ghan 1980; Nakamura et al. 1997). Furthermore, within general circulation models, blocking simulation biases in the Pacific and Atlantic are often in disagreement in terms of sign and magnitude (Matsueda et al. 2009; Masato et al. 2013). Thus, for this study, blocking is sorted into two major regions of study: the Pacific region, and the Atlantic region. These regions are indicated by the red boxes in Fig. 2a.
The spatial extent of these regions is determined as follows. The DJF blocking climatology C for ERA5, AM4, and CM4 is separately calculated. Next, the area-weighted meridional-mean of C,
Figure 2b shows two distinct peaks in
In our analysis of block duration, we have to account for the fact that some blocks move out of the study region during their individual life cycles. To avoid miscounting, we classify the blocks based on their origin, and we keep track of their life cycles based on their time within the study regions as follows. A block is classified as originating in the Pacific or Atlantic if the location of its
c. Stationary wave and mean zonal wind
Two blocking-relevant general circulation features are examined within this paper: the stationary wave and zonal wind. Results presented in this paper for the stationary wave and the zonal wind were not strongly impacted by the inclusion or removal of blocked grid points in each respective calculation.
The stationary wave is calculated on the Z500 field. The stationary wave at each grid point
d. Transient eddy forcing: Wave activity flux
The wave activity flux W (Takaya and Nakamura 2001, herein TN01) can be described as the “ageostrophic flux of geopotential” and represents the pseudomomentum of Rossby waves. Convergent W indicates the halted propagation and absorption of Rossby waves (TN01). The W convergence is associated with decreased zonal flow, the amplification of Rossby waves, and accompanies wavebreaking (Nakamura et al. 1997; TN01; Wolf and Wirth 2017), reinforcing blocked flows (TN01).
We note that the phase propagation term in the TN01 formulation is omitted in our analysis. This is due to difficulties in accurately calculating phase speed on all pressure levels for each model. However, in a comparison with the results of Wolf and Wirth (2017), the stationary term was found to dominate (not shown). As discussed in section 3e, block-centered compositing of W as calculated above yields blocking onset that is physically consistent with previous dynamical descriptions of blocking (e.g., Nakamura et al. 1997; TN01; Paradise et al. 2019). In addition, it is generally true that phase speed tends to zero near the upstream flank of blocked flows (Nakamura and Huang 2018), which would act to suppress the phase propagation term in the complete TN01 formulation. Thus, we take W, as defined above, to suffice for the analyses within this paper.
e. Block-centered compositing
To assess any biases in background flow and high-frequency forcing during blocking onset, block-centered compositing is implemented following the methods of Narinesingh et al. (2020). In this work, Z500,
To construct the composites, a given field around the
f. Statistical significance testing
To discern statistically significant differences between the GFDL models (AM4 and CM4) and reanalysis (ERA5), the Mann–Whitney U test is employed. One advantage of the U test over other methods such as the t test is that the U test is nonparametric. For each year in each model, the blocking climatology is calculated. Then, for each grid point, U tests are performed between the distributions of the annual blocking frequency in ERA5 and the distributions of annual blocking frequency in AM4 or CM4 at that grid point. The comparison of the distributions gives a robust, nonparametric approach for quantifying the differences in the blocking climatologies. A 95% confidence interval is imposed throughout this paper. The same procedure is followed for the stationary wave and jet analyses.
The block-centered compositing analysis also utilizes the U test. For ERA5, a given field around the centroid of each block in the region of interest is collected and put into a three-dimensional matrix with dimensions longitude by latitude by block number. The same is done for the GFDL models. Then at each corresponding grid point relative to the block centroid, U tests are performed between ERA5 and the GFDL models.
3. Results
a. General circulation features
Tung and Lindzen (1979) suggested that blocking is the product of resonant amplification of stationary waves by transient eddies. Also, stronger stationary waves in idealized models lead to a nonlinear increase in blocking (Paradise et al. 2019; Narinesingh et al. 2020). The zonal wind too plays a key role in blocking: on one hand a stronger instantaneous jet carries greater momentum and is thus more difficult to halt, but on the other hand blocking frequency is greater in winter than summer (e.g., Pfahl and Wernli 2012), when the time-mean jet (and baroclinicity) is stronger as compared to summer [explored in idealized models in Hassanzadeh et al. (2014)]. Due to the importance of the stationary wave and upper-tropospheric zonal wind to blocking, we begin by analyzing their representation in the models.
1) Stationary wave
The stationary wave pattern (Fig. 3) over the northern Pacific basin is generated by the orography and land–sea forcing of Asia and North America, as well as forcing from the tropical Pacific (Held et al. 2002; White et al. 2017; Park and Lee 2021). It features a low pressure, baroclinically rich region in the basin entrance (Chang et al. 2002) that is flanked on its equatorward side by the Pacific upper-level jet maximum (Figs. 3 and 5). On the downstream side of the ocean basin, there is an anticyclonic stationary wave anomaly forced primarily by the Rocky Mountains and the overall North American topography (Broccoli and Manabe 1992). In the Atlantic basin, an east–west, high–low stationary wave dipole is observed (Fig. 3), similar to the Pacific. This is primarily due to land–sea contrast and topography of both North America and Europe (Seager et al. 2002) and, to a lesser extent, the Gulf Stream (Brayshaw et al. 2009).
(top) DJF stationary wave at 500 hPa (
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(top) DJF stationary wave at 500 hPa (
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(top) DJF stationary wave at 500 hPa (
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
AM4 and CM4 produce qualitatively similar stationary wave patterns compared to reanalysis (Figs. 3a,b), although some biases exist (Figs. 3c,d). Near the Atlantic and Pacific blocking maxima (Fig. 2a), both models share similar biases (Figs. 3c,d). In the Pacific, the positive stationary anomaly over the eastern Pacific Ocean is significantly enhanced and biased toward the southwest in both models but decreases over land toward the pole (Figs. 3c,d). For the Atlantic dipole pattern in
Overall, AM4 has less stationary wave biases than CM4 (Figs. 3c,d), which is likely to be partially driven by differences in SSTs (Fig. 1; Ting and Held 1990; Ting 1991). Both models, however, share similar biases in regions where blocking occurs the most (Figs. 2 and 3). In the Pacific region, AM4 contains root-mean-square (rms) error of 24.8 m whereas CM4 contains an error of 23.4 m. Little significant difference is found between the models in this region (Fig. 4). In the Atlantic region, CM4 contains a higher regional rms error value (20.2 m) compared to AM4 (15.8 m); however, this disagreement is not significant over the whole region. It is driven locally by a more positive stationary wave around northern Africa (Figs. 3 and 4), where blocking occurs only 0%–3% of winter days (Fig. 2).
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
2) Zonal background flow
Figure 5 shows the time mean zonal wind at 250 hPa (
(top) DJF mean zonal wind at 250 hPa,
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(top) DJF mean zonal wind at 250 hPa,
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(top) DJF mean zonal wind at 250 hPa,
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
Overall, the jet in CM4 has a much larger bias than AM4 (Figs. 5c,d). In the Pacific, the jet maximum is equatorward of that in reanalysis (Fig. 5d), whereas the jet in AM4 has no such bias (Fig. 5c). In the Atlantic, the equatorward bias of the jet maxima in CM4 is greater than AM4 (Fig. 6a). Consistent with this, differences in the zonal mean zonal wind in AM4 are minimal (Fig. 6b), whereas the biases in CM4 indicates a notable equatorward shift in the jet (Fig. 6c).
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Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
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Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
In a previous version of the GFDL GCM, Delworth et al. (2006) also found an equatorward shift in zonal circulation when comparing a coupled model with an atmosphere-only model. This shift was associated with an equatorward contraction of the subtropical gyre and Hadley cell, and it contributed to cold biases in SST in the coupled model (Delworth et al. 2006). Clearly, CM4 exhibits a similar contraction of midlatitude circulation compared to AM4, and this has been documented previously (Held et al. 2019). Consistent with this atmospheric circulation change, there is a cold bias in the coupled model SST in both the Atlantic and Pacific (Fig. 1). Held et al. (2019) suggest that the contraction of CM4’s midlatitude circulation is a result of tropical cold biases in the upper troposphere, with lesser contribution from extratropical SST biases. The causes of the equatorward shift in CM4’s zonal winds pose interesting research questions; however, it is beyond the scope of this work. With relevance to blocking, the main message of this section is that CM4’s zonal background flow is equatorward shifted and has a much larger bias compared to AM4.
The forcing of the midlatitude atmosphere by the ocean in the winter is strongly related to meridional SST gradients, especially at the western boundary currents (e.g., Hoskins and Valdes 1990). Therefore, we also analyzed SST gradients for the models (Fig. 7). Over the west Pacific and Atlantic Oceans CM4 has weaker gradients in the midlatitudes compared to AM4. These differences in SST gradients likely contribute to the biases in the zonal wind. But it is interesting to note that the Atlantic SST biases are as large as those in the Pacific, whereas the zonal wind biases are much larger in the Pacific. This supports the suggestions of Held et al. (2019) discussed above, which states that the zonal wind biases are more dependent on tropical forcing biases than midlatitude SST biases. For the purposes of this paper, a key takeaway is this: due to biases in the coupled model, the SST gradients in CM4 are weaker than those in AM4.
(a),(b) Negative of the meridional gradient of SST (shading) in (a) AM4 and (b) CM4. (c) Negative meridional gradient of SST in AM4 (contours) and difference between CM4 and AM4 (shading). The outer contour is 0°C km−1 and the contour interval is 0.01°C km−1.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(a),(b) Negative of the meridional gradient of SST (shading) in (a) AM4 and (b) CM4. (c) Negative meridional gradient of SST in AM4 (contours) and difference between CM4 and AM4 (shading). The outer contour is 0°C km−1 and the contour interval is 0.01°C km−1.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(a),(b) Negative of the meridional gradient of SST (shading) in (a) AM4 and (b) CM4. (c) Negative meridional gradient of SST in AM4 (contours) and difference between CM4 and AM4 (shading). The outer contour is 0°C km−1 and the contour interval is 0.01°C km−1.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
b. Blocking climatology
Figure 8 shows the winter blocking climatology for ERA5, AM4, and CM4. Both GFDL models produce a pattern in the blocking climatology that is qualitatively similar to reanalysis (Figs. 8a,b) and consistent with previous findings (Tyrlis and Hoskins 2008; DS13). The blocking climatology features a bimodal pattern with a Pacific maximum just equatorward of the Aleutian Peninsula, and an Atlantic maximum near Greenland that extends into Europe.
(top) DJF blocking climatology for ERA5 (contours) and in the GFDL models (shading): (a) AM4 and (b) CM4. (bottom) Blocking climatology for ERA5 (contours) and GFDL models minus ERA5 (shading): (c) AM4 and (d) CM4. White stippling in (c) and (d) denotes regions where the blocking climatology in the GFDL models differs significantly from ERA5. For the ERA5 blocking climatology in all panels, the outer contour and contour interval are 2%.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(top) DJF blocking climatology for ERA5 (contours) and in the GFDL models (shading): (a) AM4 and (b) CM4. (bottom) Blocking climatology for ERA5 (contours) and GFDL models minus ERA5 (shading): (c) AM4 and (d) CM4. White stippling in (c) and (d) denotes regions where the blocking climatology in the GFDL models differs significantly from ERA5. For the ERA5 blocking climatology in all panels, the outer contour and contour interval are 2%.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(top) DJF blocking climatology for ERA5 (contours) and in the GFDL models (shading): (a) AM4 and (b) CM4. (bottom) Blocking climatology for ERA5 (contours) and GFDL models minus ERA5 (shading): (c) AM4 and (d) CM4. White stippling in (c) and (d) denotes regions where the blocking climatology in the GFDL models differs significantly from ERA5. For the ERA5 blocking climatology in all panels, the outer contour and contour interval are 2%.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
Overall, the blocking climatologies of AM4 and CM4 are similar and share various common biases. In both models too much blocking is generated along the northeastern Pacific coastline (Figs. 8c,d), with significant excess found near the Rocky Mountains. In the Atlantic region, both GFDL models simulate a significant lack of blocking in the Icelandic Basin extending into northern Europe, and an excess of blocking near the Azores high. In line with those biases, the Atlantic blocking maximum is shifted roughly 7.5° south in both GFDL models (Figs. 8c,d).
Figure 9a shows the differences in the blocking climatology between CM4 and AM4. In the Pacific region CM4 produces less blocking than AM4; however, this is not significant and occurs within a region of large interannual blocking variability (Fig. 9b; Tyrlis and Hoskins 2008). In fact, no significant differences are found between the blocking climatologies of AM4 and CM4 in the Pacific and Atlantic regions. In addition, compared to ERA5 both models also exhibit similar biases in interannual variability (not shown).
(a) Blocking climatology for AM4 (contours) and CM4 minus AM4 (shading). Magenta stippling indicates regions where the blocking climatology in CM4 differs significantly from AM4. (b) Standard deviation of the blocking climatology in AM4 (contours) and CM4 (shading). The outer contours and contour interval are both 2% in (a) and (b).
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(a) Blocking climatology for AM4 (contours) and CM4 minus AM4 (shading). Magenta stippling indicates regions where the blocking climatology in CM4 differs significantly from AM4. (b) Standard deviation of the blocking climatology in AM4 (contours) and CM4 (shading). The outer contours and contour interval are both 2% in (a) and (b).
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(a) Blocking climatology for AM4 (contours) and CM4 minus AM4 (shading). Magenta stippling indicates regions where the blocking climatology in CM4 differs significantly from AM4. (b) Standard deviation of the blocking climatology in AM4 (contours) and CM4 (shading). The outer contours and contour interval are both 2% in (a) and (b).
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
Both models show similar amounts of error (Table 1) except in the Pacific region, where CM4 has roughly 25% less error than AM4. This is significant using a U test across all years. Still, the errors found here are similar in terms of relative magnitude, and within a region of high variability (Fig. 9b). The Atlantic and entire midlatitude regions also contain less error in CM4 than AM4, but these differences are not significant. These results were found to be robust to changes ±10° in the eastern and western limits, ±5° to the northern limit, and +5° to the southern limit of each region. Note that the block tracking algorithm only searches for blocks poleward of 30°.
Normalized RMS error F [Eq. (2)] for regional blocking in AM4 and CM4 compared against ERA5. All regions cover only the midlatitudes (30°–75°N). The Pacific, Atlantic, and all midlatitude regions extend longitudinally over 153.75°E–118.75°W, 71.25°W–16.25°E, and 0°–360°, respectively. The asterisk (*) indicates significant differences between the models.
The relative agreement in error over the entire midlatitudes further emphasizes the similarities in climatological blocking biases between the models, albeit with some compensating errors. This is despite there being major disagreement between the zonal circulation (Figs. 5 and 6) and SST (Fig. 7) in both models. This will be commented on further in the discussion section (section 4).
c. Block count, duration, and area
To gain better insight into the drivers of the blocking frequency biases, we next analyze block event statistics. Table 2 shows the duration and mean number of blocking events per year for the reanalysis and GFDL models by region. In the Pacific region, the GFDL models are in close agreement with ERA5 in terms of number of events per year but simulate an almost 1-day-longer average duration. This difference is not statistically significant, however, due to a large standard deviation in block duration, but the difference is consistent with the enhanced amount of blocking in the Pacific. AM4 and CM4 also produce Pacific blocks whose individual sizes are roughly 0.5 and 0.4 million km2 larger than those in reanalysis, respectively (Table 3). This difference is not statistically significant because of the large spread in block sizes.
For ERA5 and both GFDL models (AM4 and CM4), block duration (days), standard deviation of block duration (days), and mean number of events per DJF in each region.
For ERA5 and both GFDL models (AM4 and CM4), mean block area and standard deviation of block area in each region. Both values are in units of 106 km2.
In the Atlantic region, less blocking is simulated in the GFDL models compared to reanalysis (Table 2). A similar number of events per year is found, but the GFDL models have a lower, albeit not significant, average duration of 0.6–0.7 days (Table 2). This decrease in duration agrees with the decrease in blocking frequency (Figs. 8c,d). In terms of area, Atlantic blocks tend to be similar in size across all models and have a smaller average area than Pacific blocks (Table 3).
To summarize, Pacific blocks in the GFDL models are, on average, slightly more persistent and larger than those in reanalysis. Atlantic blocks in the GFDL models are similar in size to reanalysis, but there is a suggestion of shorter average durations. However, we cannot discount the possibility that these differences for the both the Pacific and Atlantic are due to natural variability rather than being a systematic bias. Still, the fact that AM4 and CM4 both exhibit such similar biases in terms of sign and magnitude of the biases in each region adds to the robustness of likeness in blocking biases between the models.
These results for block size and duration are consistent with biases in the blocking climatology (which are statistically significant), showing too much blocking in the Pacific, and too little in the Atlantic. We also note that the block area and duration biases in AM4 and CM4 are another example of common blocking biases between the models, in addition to biases in the climatology.
d. Zonal background flow during block onset
To assess background flow properties during the onset phase of blocking, compositing analysis of 30-day low-pass filtered zonal wind at 250 hPa (U250) is performed. Figures 10a and 10b show these composites for the Pacific and Atlantic regions, respectively, using ERA5.
(top) For the block onset phase, block-centered composites of unfiltered 500-hPa geopotential height (m; contours) and 30-day low-pass-filtered 250 hPa zonal wind U250 (shading) for (a) Pacific and (b) Atlantic blocks in ERA5. (middle),(bottom) For the block onset phase, block-centered composites of unfiltered 500-hPa geopotential height (contours) and difference between block-center composited U250 in the GFDL models and ERA5 (shading): (middle) computed using AM4 for (c) Pacific and (d) Atlantic blocks and (e),(f) computed using CM4 for (e) Pacific and (f) Atlantic blocks. Magenta stippling in (c)–(f) indicate significant differences between the corresponding GFDL model and ERA5.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(top) For the block onset phase, block-centered composites of unfiltered 500-hPa geopotential height (m; contours) and 30-day low-pass-filtered 250 hPa zonal wind U250 (shading) for (a) Pacific and (b) Atlantic blocks in ERA5. (middle),(bottom) For the block onset phase, block-centered composites of unfiltered 500-hPa geopotential height (contours) and difference between block-center composited U250 in the GFDL models and ERA5 (shading): (middle) computed using AM4 for (c) Pacific and (d) Atlantic blocks and (e),(f) computed using CM4 for (e) Pacific and (f) Atlantic blocks. Magenta stippling in (c)–(f) indicate significant differences between the corresponding GFDL model and ERA5.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(top) For the block onset phase, block-centered composites of unfiltered 500-hPa geopotential height (m; contours) and 30-day low-pass-filtered 250 hPa zonal wind U250 (shading) for (a) Pacific and (b) Atlantic blocks in ERA5. (middle),(bottom) For the block onset phase, block-centered composites of unfiltered 500-hPa geopotential height (contours) and difference between block-center composited U250 in the GFDL models and ERA5 (shading): (middle) computed using AM4 for (c) Pacific and (d) Atlantic blocks and (e),(f) computed using CM4 for (e) Pacific and (f) Atlantic blocks. Magenta stippling in (c)–(f) indicate significant differences between the corresponding GFDL model and ERA5.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
Both the Pacific and Atlantic regions feature U250 composite maxima upstream and poleward from the blocking center (Figs. 10a,b). There are also minima in composite U250, downstream-equatorward of the block center for both regions. Similar patterns are found when raw 250-hPa zonal wind is composited for 30 days prior to blocking onset (not shown).
In terms of differences between regions, the Pacific Z500 composite during the onset phase has a distinct ridge (in fact, it has an omega shape, but to our knowledge there is no automated metric for classifying omega blocks), and U250 is stronger (Fig. 10a). In the Atlantic, the diffluent flow pattern is more pronounced (Fig. 10b) and the Z500 composite contours exhibit more of an overturning pattern, which is consistent with anticyclonic wavebreaking (e.g., Davini et al. 2012).
AM4 (Figs. 10c,d) and CM4 (Figs. 10e,f) both capture an anticyclonic wavebreaking signature in the Atlantic and ridge behavior in the Pacific. In the Pacific, AM4 exhibits no significant biases, but CM4 has an equatorward shift in composite U250 (Fig. 10e) mirroring what was found for the climatological location of the jet (Figs. 5b,d).
The Atlantic blocks feature no significant biases in the upstream and central blocking region for both AM4 and CM4. Downstream-equatorward of the composite block center, however, both models have enhanced zonal flow compared to reanalysis. In addition, AM4 has suppressed zonal flow downstream-poleward of the block center.
e. Transient eddy forcing
Convergence of transient eddy pseudomomentum acts to reinforce blocking by slowing down the westerly flow (Hoskins et al. 1983; Trenberth 1986; Takaya and Nakamura 2001) and replenishing anomalous PV (Shutts 1983; Nakamura and Wallace 1993; Yamazaki and Itoh 2013a). Here, we assess the high-frequency (6-day high-pass-filtered) eddy forcing of blocking in the models using the wave activity flux pseudomomentum, W.
Figure 11 shows block-centered composites of
(a),(c),(e) For the onset phase of Pacific blocking events, block-centered composites of positive 500-hPa geopotential height anomalies (solid contours), negative 500-hPa geopotential height anomalies (dashed contours), column-integrated wave activity flux W (arrows), and ∇ ⋅ W (shading) for (a) ERA5, (c) AM4, and (e) CM4. (b),(d),(f) As in (a), (c), and (e), but for Atlantic blocks. Positive (negative) geopotential height contours have an outer contour of 50 (−20) m and a contour interval of 50 (−20) m. W is calculated using 6-day high-pass-filtered fields. Vectors with magnitudes less than 5 × 104 kg m−2 s−2 are masked. Magenta stippling indicates significant differences in ∇ ⋅ W between (b) ERA5’s Pacific and Atlantic blocks, and (c)–(f) the corresponding GFDL model and ERA5.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(a),(c),(e) For the onset phase of Pacific blocking events, block-centered composites of positive 500-hPa geopotential height anomalies (solid contours), negative 500-hPa geopotential height anomalies (dashed contours), column-integrated wave activity flux W (arrows), and ∇ ⋅ W (shading) for (a) ERA5, (c) AM4, and (e) CM4. (b),(d),(f) As in (a), (c), and (e), but for Atlantic blocks. Positive (negative) geopotential height contours have an outer contour of 50 (−20) m and a contour interval of 50 (−20) m. W is calculated using 6-day high-pass-filtered fields. Vectors with magnitudes less than 5 × 104 kg m−2 s−2 are masked. Magenta stippling indicates significant differences in ∇ ⋅ W between (b) ERA5’s Pacific and Atlantic blocks, and (c)–(f) the corresponding GFDL model and ERA5.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(a),(c),(e) For the onset phase of Pacific blocking events, block-centered composites of positive 500-hPa geopotential height anomalies (solid contours), negative 500-hPa geopotential height anomalies (dashed contours), column-integrated wave activity flux W (arrows), and ∇ ⋅ W (shading) for (a) ERA5, (c) AM4, and (e) CM4. (b),(d),(f) As in (a), (c), and (e), but for Atlantic blocks. Positive (negative) geopotential height contours have an outer contour of 50 (−20) m and a contour interval of 50 (−20) m. W is calculated using 6-day high-pass-filtered fields. Vectors with magnitudes less than 5 × 104 kg m−2 s−2 are masked. Magenta stippling indicates significant differences in ∇ ⋅ W between (b) ERA5’s Pacific and Atlantic blocks, and (c)–(f) the corresponding GFDL model and ERA5.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
Both the Pacific (Fig. 11a) and Atlantic (Fig. 11b) high pressure centers are flanked by low pressure minima on their equatorward sides. In the Atlantic, however, the north–south dipole axis is tilted compared to the Pacific region, perhaps related to the southwest-to-northeast orientation in the North Atlantic’s climatological circulation. The Atlantic blocks in ERA5 (Fig. 11b) demonstrate stronger W convergence compared to those in the Pacific (Fig. 11a). This difference is statistically significant.
The GFDL models (Figs. 11c–f) capture the same patterns of W convergence as reanalysis (Figs. 11a,b). There is some suggestion, however, that the Atlantic blocks in AM4 (Fig. 11d) and CM4 (Fig. 11f) demonstrate less forcing, although these differences are not significant throughout the upstream-equatorward convergence area. Both models also reproduce the differences in Atlantic (Figs. 11d,f) and Pacific (Figs. 11c,e) blocking in terms of high–low dipole orientation.
One aspect the models fail to reproduce is the differences in magnitude of W convergence between the Atlantic and Pacific regions. Aside from this, however, the results of this subsection suggest that the GFDL models properly represent the onset phases of both Pacific and Atlantic blocking in terms of transient eddy forcing and geopotential height evolution.
4. Discussion
Using an idealized traffic-jam model, Paradise et al. (2019) and others found blocking occurrence responds to changes in the stationary wave (Tung and Lindzen 1979; Luo 2005), jet (Barnes and Hartmann 2010; de Vries et al. 2013), and eddy forcing (Shutts 1983; Yamazaki and Itoh 2013b). As such, here we discuss consistencies and inconsistencies in the GFDL models regarding blocking and the aforementioned circulation features. As a reminder, we note that the jet and stationary wave analysis discussed throughout this paper were found to be insensitive to the removal or inclusion of the time steps with blocks.
The models generate too much blocking in the Pacific region and too little blocking in the Atlantic (Fig. 8). In both models, this result is consistent with the enhanced positive stationary wave anomaly found in the Pacific and weakened stationary wave in the Atlantic (Fig. 3). This also agrees with Paradise et al. (2019), who found a positive relationship between blocking and stationary wave amplitude.
The Pacific and Atlantic blocking biases shared by AM4 and CM4 are also in agreement with theory and other previous results regarding stationary waves. In the wave activity traffic jam theory of blocking developed by Nakamura and Huang (2018), an enhanced stationary wave results in a region’s decreased capacity for wave activity fluxes, thus leading to blocking. Furthermore, Narinesingh et al. (2020) also found increases in blocking when an idealized moist GCM was configured into a strong stationary wave regime compared to zonally symmetric and weaker stationary wave integrations.
The relationship between the blocking climatology and the zonal wind in AM4 and CM4 is not so clear, however. Despite CM4 containing an equatorward shifted zonal flow compared to AM4 (Fig. 6), the models exhibit similar biases in terms of their blocking climatologies (Fig. 8). Barnes and Hartmann (2010) found that higher blocking frequencies corresponded to equatorward jets in CMIP models. Their result agrees with the Pacific overgeneration of blocks in CM4 but disagrees with CM4 and AM4’s Atlantic blocking deficiencies.
CM4’s Pacific blocks also contain enhanced zonal background flow on the upstream-equatorward flank of the blocking high (Fig. 10e), near the meridional high–low dipole (Fig. 11e). This is inconsistent with the findings of Paradise et al. (2019), who found decreased blocking in stronger zonal flows. In the Atlantic, the decrease in blocking near Iceland is also not expected given the weakened background flow (Fig. 5). In terms of transient eddy forcing during the onset phase of blocking, the GFDL models show little difference from reanalysis (Fig. 11). This is despite various jet biases between the models. Yamazaki and Itoh (2013b) also found results consistent to ours, where transient eddy forcing of blocks was found to be insensitive to jet strength and placement. Taken together, these results regarding the zonal winds suggest the model biases in blocking may come from any of the following:
mean-state biases in the stationary wave or physics that is not fully captured by the models,
blocks in the Pacific and Atlantic having substantial differences in their interaction with the background flow, or
aspects of blocking onset and maintenance that have not yet been considered.
Maintenance of blocking is also critical to blocking longevity (Shutts 1983; Pfahl et al. 2015). Figure 12 shows block centered composites of ∇ ⋅ W during the strongest days of blocks as defined by the maximum
(a),(c),(e) For the strongest days of Pacific blocking events, block-centered composites of positive 500-hPa geopotential height anomalies (solid contours), negative 500-hPa geopotential height anomalies (dashed contours), column-integrated wave activity flux W (arrows), and ∇ ⋅ W (shading) for (a) ERA5, (c) AM4, and (e) CM4. (b),(d),(f) As in (a), (c), and (e), but for Atlantic blocks. Positive (negative) geopotential height contours have an outer contour of 50 (−20) m and a contour interval of 50 (−20) m. W is calculated using 6-day high-pass-filtered fields. Vectors with magnitudes less than 5 × 104 kg m−2 s−2 are masked. Magenta stippling in (c)–(f) indicates significant differences in ∇ ⋅ W between the corresponding GFDL model and ERA5.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(a),(c),(e) For the strongest days of Pacific blocking events, block-centered composites of positive 500-hPa geopotential height anomalies (solid contours), negative 500-hPa geopotential height anomalies (dashed contours), column-integrated wave activity flux W (arrows), and ∇ ⋅ W (shading) for (a) ERA5, (c) AM4, and (e) CM4. (b),(d),(f) As in (a), (c), and (e), but for Atlantic blocks. Positive (negative) geopotential height contours have an outer contour of 50 (−20) m and a contour interval of 50 (−20) m. W is calculated using 6-day high-pass-filtered fields. Vectors with magnitudes less than 5 × 104 kg m−2 s−2 are masked. Magenta stippling in (c)–(f) indicates significant differences in ∇ ⋅ W between the corresponding GFDL model and ERA5.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
(a),(c),(e) For the strongest days of Pacific blocking events, block-centered composites of positive 500-hPa geopotential height anomalies (solid contours), negative 500-hPa geopotential height anomalies (dashed contours), column-integrated wave activity flux W (arrows), and ∇ ⋅ W (shading) for (a) ERA5, (c) AM4, and (e) CM4. (b),(d),(f) As in (a), (c), and (e), but for Atlantic blocks. Positive (negative) geopotential height contours have an outer contour of 50 (−20) m and a contour interval of 50 (−20) m. W is calculated using 6-day high-pass-filtered fields. Vectors with magnitudes less than 5 × 104 kg m−2 s−2 are masked. Magenta stippling in (c)–(f) indicates significant differences in ∇ ⋅ W between the corresponding GFDL model and ERA5.
Citation: Journal of Climate 35, 12; 10.1175/JCLI-D-21-0486.1
Little difference is found between the GFDL models and ERA5 during the strongest days, except there is some suggestion that AM4’s Pacific W convergence is greater (Fig. 12c). This could indicate enhanced transient eddy forcing, consistent with the overgeneration of blocking in the region. However, a similar difference is not found in CM4.
Herein we focus on the transient eddy maintenance of blocking through wave-activity fluxes, but other studies have found latent heating (Pfahl et al. 2015) to play a prominent role as well. Thus, a more comprehensive look at the dynamic and thermodynamic maintenance of blocking throughout their life cycle is warranted in future study.
Overall, stationary wave biases remain the most consistent with blocking biases for the GFDL models, but the work here cannot attribute causality without more rigorous testing of the models. In future work, we plan on investigating the response of blocking to changes in the stationary wave and jet as well as dynamic and thermodynamic maintenance mechanisms. We note that such a study would need to consider the coupling between the general circulation features themselves, as well as block maintenance mechanisms.
5. Summary and conclusions
GFDL’s atmosphere only (AM4) and coupled atmosphere–ocean (CM4) general circulation models reproduce the overall spatial pattern of the blocking climatology (Fig. 8) with a similar number of events per DJF season (Table 2). In the Pacific, however, the modeled blocking frequency is biased high compared to reanalysis. This could be due to each model’s tendency to generate blocks that are spatially too large and last too long, although the large variability in block duration and area makes it difficult to conclusively say so.
In the Atlantic region, AM4 and CM4 both have less blocking than reanalysis. Here, the distribution of spatial size of individual blocks is similar to reanalysis, but there is a suggestion that they are slightly less persistent, albeit with high uncertainty.
Blocking onset dynamics is also assessed within the models. In terms of the 500-hPa geopotential height field, both models produce differences between Pacific and Atlantic blocking that match with observations (Fig. 10). In the Pacific, the Z500 field features an amplified ridge during blocking onset, whereas in the Atlantic a signature of anticyclonic wavebreaking is found.
The background zonal flow during block onset is generally captured within the models (Fig. 10), except CM4 features an equatorward shift for Pacific blocks. In terms of high-frequency eddy forcing during blocking onset, both models produce similar patterns in wave activity flux convergence compared to reanalysis (Fig. 11). The models do not, however, produce the stronger convergence found for Atlantic blocking compared to Pacific.
Our analysis of general circulation features previously shown to influence blocking revealed a mixture of results. First, both models capture the overall spatial pattern of the stationary wave (
For the zonal wind, there were differences between the models that did not align with differences in blocking. CM4 features an equatorward bias in the Pacific jet location (
Despite large differences in the jet and SSTs between AM4 and CM4, the two models produce similar blocking climatologies (Fig. 8). Overall, the commonalities in blocking climatology, duration, and area biases in AM4 and CM4 suggest a weak sensitivity to the difference in zonal flow (Fig. 6) and ocean forcing (Fig. 7) between the models—or some compensating biases. At the same time, both models exhibit similar stationary wave and blocking climatology biases, and few transient eddy forcing biases (Figs. 11 and 12). This could suggest that the stationary wave could play the more prevalent role in driving the models’ biases in blocking. Further study is planned to test this hypothesis.
Acknowledgments.
This publication was supported through NOAA Educational Partnership Program/Minority-Serving Institutions award number NA16SEC4810008 to the Center for Earth System Sciences and Remote Sensing Technologies at The City College of New York. The authors thank The City College of New York, NOAA Center for Earth System Sciences and Remote Sensing Technologies, and the NOAA Office of Education, Educational Partnership Program for fellowship support for Veeshan Narinesingh. Contents are solely the responsibility of the award recipient and may not represent official views of NOAA or the U.S. Department of Commerce. The authors thank Wenhao Dong and Spencer Clark for facilitating the process of obtaining the model data directly. We thank the reviewers and editor, whose feedback helped improve the manuscript.
Data availability statement.
ERA5 data utilized for this work can be accessed from the European Center for Medium-Range Weather Forecasts (ECMWF; https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5). GFDL AM4 and CM4 data can be accessed from the World Climate Research Programme (WRCP) Coupled Model Intercomparison Project 6 (CMIP6; https://esgf-node.llnl.gov/search/cmip6/).
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