Jeevanjee, Nadir, and Linjiong Zhou, March 2022: On the resolution-dependence of anvil cloud fraction and precipitation efficiency in radiative-convective equilibrium. Journal of Advances in Modeling Earth Systems, 14(3), DOI:10.1029/2021MS002759. Abstract
Tropical anvil clouds are an important player in Earth's climate and climate sensitivity, but simulations of anvil clouds are uncertain. Here we identify and investigate one source of uncertainty by demonstrating a marked increase of anvil cloud fraction with resolution in cloud-resolving simulations of radiative-convective equilibrium. This increase in cloud fraction can be traced back to the resolution dependence of horizontal mixing between clear and cloudy air. A mixing timescale is diagnosed for each simulation using the cloud fraction theory of Seeley, Jeevanjee, Langhans, and Romps (2019) (https://doi.org/10.1029/2018GL080747) and is found to scale linearly with grid spacing, as expected from a simple scaling law. Thus mixing becomes more efficient with increasing resolution, generating more evaporation in middle and lower tropospheric updrafts. This decreases their precipitation efficiency (PE), thereby increasing their overall mass flux, leading to greater detrainment at the anvil level and hence higher anvil cloud fraction. The decrease in PE also yields a marked increase in relative humidity with resolution.
We describe the third version of the Geophysical Fluid Dynamics Laboratory cloud microphysics scheme (GFDL MP v3) implemented in the System for High-resolution prediction on Earth-to-Local Domains (SHiELD). Compared to the GFDL MP v2, the GFDL MP v3 is entirely reorganized, optimized, and modularized into functions. The particle size distribution (PSD) of all hydrometeor categories is redefined to better mimic observations, and the cloud droplet number concentration (CDNC) is calculated from the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA2) aerosol data. In addition, the GFDL MP has been redesigned so all processes use the redefined PSD to ensure overall consistency and easily permit the introduction of new PSDs and microphysical processes. A year's worth of global 13-km, 10-day weather forecasts were performed with the new GFDL MP. Compared to the GFDL MP v2, the GFDL MP v3 significantly improves SHiELD's predictions of geopotential height, air temperature, and specific humidity in the Troposphere, as well as the high, middle and total cloud fractions and the liquid water path. The predictions are improved even further by the use of reanalysis aerosol data to calculate CDNC, and also by using the more realistic PSD available in GFDL MP v3. However, the upgrade of the GFDL MP shows little impact on the precipitation prediction. Degradations caused by the new scheme are discussed and provide a guide for future GFDL MP development.
Gallo, Burkely T., Jamie K Wolff, Adam J Clark, Israel Jirak, Lindsay R Blank, Brett Roberts, Yunheng Wang, Chunxi Zhang, Ming Xue, Timothy A Supinie, Lucas Harris, Linjiong Zhou, and Curtis Alexander, February 2021: Exploring convection-allowing model evaluation strategies for severe local storms using the Finite-Volume Cubed-Sphere (FV3) Model Core. Weather and Forecasting, 36(1), DOI:10.1175/WAF-D-20-0090.13-19. Abstract
Verification methods for convection-allowing models (CAMs) should consider the finescale spatial and temporal detail provided by CAMs, and including both neighborhood and object-based methods can account for displaced features that may still provide useful information. This work explores both contingency table–based verification techniques and object-based verification techniques as they relate to forecasts of severe convection. Two key fields in severe weather forecasting are investigated: updraft helicity (UH) and simulated composite reflectivity. UH is used to generate severe weather probabilities called surrogate severe fields, which have two tunable parameters: the UH threshold and the smoothing level. Probabilities computed using the UH threshold and smoothing level that give the best area under the receiver operating curve result in very high probabilities, while optimizing the parameters based on the Brier score reliability component results in much lower probabilities. Subjective ratings from participants in the 2018 NOAA Hazardous Weather Testbed Spring Forecasting Experiment (SFE) provide a complementary evaluation source. This work compares the verification methodologies in the context of three CAMs using the Finite-Volume Cubed-Sphere Dynamical Core (FV3), which will be the foundation of the U.S. Unified Forecast System (UFS). Three agencies ran FV3-based CAMs during the five-week 2018 SFE. These FV3-based CAMs are verified alongside a current operational CAM, the High-Resolution Rapid Refresh version 3 (HRRRv3). The HRRR is planned to eventually use the FV3 dynamical core as part of the UFS; as such evaluations relative to current HRRR configurations are imperative to maintaining high forecast quality and informing future implementation decisions.
We investigate the sensitivity of hurricane intensity and structure to the horizontal tracer advection in the Geophysical Fluid Dynamics Laboratory (GFDL) Finite-Volume Cubed-Sphere Dynamical Core (FV3). We compare two schemes, a monotonic scheme and a less diffusive positive-definite scheme. The positive-definite scheme leads to significant improvement in the intensity prediction relative to the monotonic scheme in a suite of 5-day forecasts that mostly consist of rapidly intensifying hurricanes. Notable storm structural differences are present: the radius of maximum wind (RMW) is smaller and eyewall convection occurs farther inside the RMW when the positive-definite scheme is used. Moreover, we find that the horizontal tracer advection scheme affects the eyewall convection location by affecting the moisture distribution in the inner-core region. This study highlights the importance of dynamical core algorithms in hurricane intensity prediction.
A two-moment Morrison-Gettelman bulk cloud microphysics with prognostic precipitation (MG2), together with a mineral dust and temperature-dependent ice nucleation scheme, have been implemented into the Geophysical Fluid Dynamics Laboratory's Atmosphere Model version 4.0 (AM4.0). We refer to this configuration as AM4-MG2. This paper describes the configuration of AM4-MG2, evaluates its performance, and compares it with AM4.0. It is shown that the global simulations with AM4-MG2 compare favorably with observations and reanalyses. The model skill scores are close to AM4.0. Compared to AM4.0, improvements in AM4-MG2 include (a) better coastal marine stratocumulus and seasonal cycles, (b) more realistic ice fraction, and (c) dominant accretion over autoconversion. Sensitivity tests indicate that nucleation and sedimentation schemes have significant impacts on cloud liquid and ice water fields, but higher horizontal resolution (about 50 km instead of 100 km) does not.
Harris, Lucas, Xi Chen, William M Putman, Linjiong Zhou, and Jan-Huey Chen, June 2021: A Scientific Description of the GFDL Finite-Volume Cubed-Sphere Dynamical Core, Princeton, NJ: NOAA Technical Memorandum OAR GFDL, 2021-001, DOI:10.25923/6nhs-5897 109pp.
Judt, Falko, Daniel Klocke, Rosimar Rios-Berrios, Benoit Vanniere, Florian Ziemen, Ludovic Auger, Joachim Biercamp, Christopher S Bretherton, Xi Chen, Peter Düben, Cathy Hohenegger, Marat Khairoutdinov, Chihiro Kodama, Luis Kornblueh, Shian-Jiann Lin, Masuo Nakano, Philipp Neumann, William M Putman, Niklas Röber, Malcolm J Roberts, Masaki Satoh, Ryosuke Shibuya, Bjorn Stevens, Pier Luigi Vidale, Nils Wedi, and Linjiong Zhou, June 2021: Tropical cyclones in global storm-resolving models. Journal of the Meteorological Society of Japan. Ser. II, 99(3), DOI:10.2151/jmsj.2021-029579-602. Abstract
Recent progress in computing and model development has initiated the era of global storm-resolving modeling, and with it the potential to transform weather and climate prediction. Within the general theme of vetting this new class of models, the present study evaluates nine global-storm resolving models in their ability to simulate tropical cyclones (TCs). Results indicate that, broadly speaking, the models produce realistic TCs and remove longstanding issues known from global models such as the deficiency in accurately simulating TC intensity. However, TCs are strongly affected by model formulation, and all models suffer from unique biases regarding the number of TCs, intensity, size, and structure. Some models simulated TCs better than others, but no single model was superior in every way. The overall results indicate that global storm-resolving models can open a new chapter in TC prediction, but they need to be improved to unleash their full potential.
A subseasonal-to-seasonal (S2S) prediction system was recently developed using the GFDL SPEAR global coupled model. Based on 20-year hindcast results (2000-2019), the boreal wintertime (November-April) Madden-Julian Oscillation (MJO) prediction skill is revealed to reach 30 days measured before the anomaly correlation coefficient of the real-time multivariate (RMM) index drops to 0.5. However, when the MJO is partitioned into four distinct propagation patterns, the prediction range extends to 38, 31, and 31 days for the fast-propagating, slow-propagating, and jumping MJO patterns, respectively, but falls to 23 days for the standing MJO. A further improvement of MJO prediction requires attention to the standing MJO given its large gap with its potential predictability (15 days). The slow-propagating MJO detours southward when traversing the maritime continent (MC), and confronts the MC prediction barrier in the model, while the fast-propagating MJO moves across the central MC without this prediction barrier. The MJO diversity is modulated by stratospheric quasi-biennial oscillation (QBO): the standing (slow-propagating) MJO coincides with significant westerly (easterly) phases of QBO, partially explaining the contrasting MJO prediction skill between these two QBO phases.
The SPEAR model shows its capability, beyond the propagation, in predicting their initiation for different types of MJO along with discrete precursory convection anomalies. The SPEAR model skillfully predicts the observed distinct teleconnections over the North Pacific and North America related to the standing, jumping, and fast-propagating MJO, but not the slow-propagating MJO. These findings highlight the complexities and challenges of incorporating MJO prediction into the operational prediction of meteorological variables.
This technical note explains updates to the GFDL Finite-Volume Cubed-Sphere Dynamical Core, abbreviated FV3 or FV[superscript 3], and the Split GFDL Microphysics. It does not repeat the contents of earlier documentation, especially publications. A list of publications and prior technical notes describing FV3 is available on the GFDL website.
We present the System for High‐resolution prediction on Earth‐to‐Local Domains (SHiELD), an atmosphere model developed by the Geophysical Fluid Dynamics Laboratory (GFDL) coupling the nonhydrostatic FV3 Dynamical Core to a physics suite originally taken from the Global Forecast System. SHiELD is designed to demonstrate new capabilities within its components, explore new model applications, and to answer scientific questions through these new functionalities. A variety of configurations are presented, including short‐to‐medium‐range and subseasonal‐to‐seasonal prediction, global‐to‐regional convective‐scale hurricane and contiguous U.S. precipitation forecasts, and global cloud‐resolving modeling. Advances within SHiELD can be seamlessly transitioned into other Unified Forecast System or FV3‐based models, including operational implementations of the Unified Forecast System. Continued development of SHiELD has shown improvement upon existing models. The flagship 13‐km SHiELD demonstrates steadily improved large‐scale prediction skill and precipitation prediction skill. SHiELD and the coarser‐resolution S‐SHiELD demonstrate a superior diurnal cycle compared to existing climate models; the latter also demonstrates 28 days of useful prediction skill for the Madden‐Julian Oscillation. The global‐to‐regional nested configurations T‐SHiELD (tropical Atlantic) and C‐SHiELD (contiguous United States) show significant improvement in hurricane structure from a new tracer advection scheme and promise for medium‐range prediction of convective storms.
This document describes the nonhydrostatic solver of the GFDL Finite-Volume Cubed-Sphere Dynamical Core, FV3. The nonhydrostatic solver works identically to the hydrostatic solver except for the need to solve for two new prognostic variables, the vertical velocity and geometric layer depth; and to use the full nonhydrostatic pressure in computing the pressure gradient force. In particular the Lagrangian dynamics described within L04 remains valid and all vertical processes (advection, wave propagation) remain implicit while all horizontal processes are explicit. This document assumes working knowledge of the hydrostatic discretization of FV3 described in LR96, LR97, L97, L04, PL07, and HL13. It is strongly recommended that anyone who wishes to understand the nonhydrostatic FV3 solver read and understand these documents first. Additional relevant material may be found in LPH17 and LH18. All of these documents may be found at www. gfdl.noaa.gov/fv3/fv3-documentation-and-references/.
Motivated by the use of the GFDL microphysics scheme in the FV3GFS, the all-sky radiance assimilation framework has been expanded to include precipitating hydrometeors. Adding precipitating hydrometeors allows the assimilation of precipitation-affected radiance in addition to cloudy radiance. In this upgraded all-sky framework, the five hydrometeors, including cloud liquid water, cloud ice, rain, snow and graupel, are the new control variables, replacing the original cloud water control variable. The Community Radiative Transfer Model (CRTM) was interfaced with the newly added precipitating hydrometeors. Sub-grid cloud variability was considered by using the average cloud overlap scheme. Multiple scattering radiative transfer was activated in the upgraded framework. Radiance observations from the Advanced Microwave Sounding Unit-A (AMSU-A) and the Advanced Technology Microwave Sounder (ATMS) over ocean were assimilated in all-sky approach. This new constructed all-sky framework shows neutral to positive impact on overall forecast skill. Improvement was found in 500 hPa geopotential height forecast in both Northern and Southern Hemispheres. Temperature forecast was also improved at 850 hPa in the Southern Hemisphere and the Tropics.
We use the fvGFS model developed at the Geophysical Fluid Dynamics Laboratory (GFDL) to demonstrate the potential of the upcoming United States Next Generation Global Prediction System for hurricane prediction. The fvGFS retrospective forecasts initialized with the European Centre for Medium‐Range Weather Forecasts (ECMWF) data showed much‐improved track forecasts for the 2017 Atlantic hurricane season compared to the best performing ECMWF operational model. The fvGFS greatly improved the ECMWF's poor track forecast for Hurricane Maria (2017). For Hurricane Irma (2017), a well‐predicted case by the ECMWF model, the fvGFS produced even lower 5‐day track forecast errors. The fvGFS also showed better intensity prediction than both the United States and the ECMWF operational models, indicating the robustness of its numerical algorithms.
A new global model using the GFDL nonhydrostatic Finite-Volume Cubed-Sphere Dynamical Core (FV3) coupled to physical parameterizations from the National Centers for Environmental Prediction's Global Forecast System (NCEP/GFS) was built at GFDL, named fvGFS. The modern dynamical core, FV3, has been selected for National Oceanic and Atmospheric Administration’s Next Generation Global Prediction System (NGGPS) due to its accuracy, adaptability, and computational efficiency, which brings a great opportunity for the unification of weather and climate prediction systems.
The performance of tropical cyclone (TC) forecasts in the 13-km fvGFS is evaluated globally based on 363 daily cases of 10-day forecasts in 2015. Track and intensity errors of TCs in fvGFS are compared to those in the operational GFS. The fvGFS outperforms the GFS in TC intensity prediction for all basins. For TC track prediction, the fvGFS forecasts are substantially better over the northern Atlantic basin and the northern Pacific Ocean than the GFS forecasts. An updated version of the fvGFS with the GFDL 6-category cloud microphysics scheme is also investigated based on the same 363 cases. With this upgraded microphysics scheme, fvGFS shows much improvement in TC intensity prediction over the operational GFS. Besides track and intensity forecasts, the performance of TC genesis forecast is also compared between the fvGFS and operational GFS. In addition to evaluating the hit/false alarm ratios, a novel method is developed to investigate the lengths of TC genesis lead times in the forecasts. Both versions of fvGFS show higher hit ratios, lower false alarm ratios and longer genesis lead times than those of the GFS model in most of the TC basins.
We present a new global‐to‐regional model, cfvGFS, able to explicitly (without parameterization) represent convection over part of the earth. This model couples the Geophysical Fluid Dynamics Laboratory Finite‐Volume Cubed‐Sphere Dynamical Core (FV3) to the Global Forecast System (GFS) physics and initial conditions, augmented with a six‐category microphysics and a modified planetary boundary layer scheme. We examine the characteristics of cfvGFS on a 3‐km continental United States domain nested within a 13‐km global model. The nested cfvGFS still has good hemispheric skill comparable to or better than the operational GFS, while supercell thunderstorms, squall lines, and derechos are explicitly‐represented over the refined region. In particular, cfvGFS has excellent representations of fine‐scale updraft helicity fields, an important proxy for severe weather forecasting. Precipitation biases are found to be smaller than in uniform‐resolution global models and competitive with operational regional models; the 3‐km domain also improves upon the global models in 2‐m temperature and humidity skill. We discuss further development of cfvGFS and the prospects for a unified global‐to‐regional prediction system.
He, Bian, Q Bao, X Wang, and Linjiong Zhou, et al., August 2019: CAS FGOALS-f3-L Model Datasets for CMIP6 Historical Atmospheric Model Intercomparison Project Simulation. Advances in Atmospheric Sciences, 36(8), DOI:10.1007/s00376-019-9027-8. Abstract
The outputs of the Chinese Academy of Sciences (CAS) Flexible Global Ocean-Atmosphere-Land System (FGOALS-f3-L) model for the baseline experiment of the Atmospheric Model Intercomparison Project simulation in the Diagnostic, Evaluation and Characterization of Klima common experiments of phase 6 of the Coupled Model Intercomparison Project (CMIP6) are described in this paper. The CAS FGOALS-f3-L model, experiment settings, and outputs are all given. In total, there are three ensemble experiments over the period 1979–2014, which are performed with different initial states. The model outputs contain a total of 37 variables and include the required three-hourly mean, six-hourly transient, daily and monthly mean datasets. The baseline performances of the model are validated at different time scales. The preliminary evaluation suggests that the CAS FGOALS-f3-L model can capture the basic patterns of atmospheric circulation and precipitation well, including the propagation of the Madden-Julian Oscillation, activities of tropical cyclones, and the characterization of extreme precipitation. These datasets contribute to the benchmark of current model behaviors for the desired continuity of CMIP.
Understanding the root causes of forecast errors and occasional very poor forecasts is essential but difficult. In this paper we investigate the relative importance of initial conditions and model formulation for medium‐range errors in 500‐hPa geopotential height. The question is addressed by comparing forecasts produced with ECMWF‐IFS and NCEP‐GFS forecasting systems, and with the GFDL‐fvGFS model initialised with ECMWF and NCEP initial conditions. This gives two pairs of configurations that use the same initial conditions but different models, and one pair with the same model but different initial conditions. The first conclusion is that the initial conditions play the major role for differences between the configurations in terms of the average root‐mean‐square error for both northern and southern hemispheres as well as Europe and the contiguous U.S (CONUS), while the model dominates the systematic errors. A similar conclusion is also found by verifying precipitation over low latitudes and the CONUS. The day‐to‐day variations of 500‐hPa geopotential height scores are exemplified by one case of a forecast bust over Europe, where the error is found to be dominated by initial errors. The results are generalised by calculating correlations between errors integrated over Europe, CONUS and a region in southeastern Pacific respectively from the different configurations. For Europe and southeast Pacific, the correlations in the medium‐range are highest between the pairs that use the same initial conditions, while over CONUS it is for the pair with the same model. This suggests different mechanisms behind the day‐to‐day variability of the score for these regions. Over CONUS the link is made to the propagation of troughs over the Rockies, and the result suggests that the large differences in parameterisations of orographic drag between the models plays a role.
Stevens, Bjorn, Masaki Satoh, Ludovic Auger, Joachim Biercamp, Christopher S Bretherton, Xi Chen, Peter Düben, Falko Judt, Marat Khairoutdinov, Daniel Klocke, Chihiro Kodama, Luis Kornblueh, Shian-Jiann Lin, Philipp Neumann, William M Putman, Niklas Röber, Ryosuke Shibuya, Benoit Vanniere, Pier Luigi Vidale, Nils Wedi, and Linjiong Zhou, September 2019: DYAMOND: the DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains. Progress in Earth and Planetary Science, 6, 61, DOI:10.1186/s40645-019-0304-z. Abstract
A review of the experimental protocol and motivation for DYAMOND, the first intercomparison project of global storm-resolving models, is presented. Nine models submitted simulation output for a 40-day (1 August–10 September 2016) intercomparison period. Eight of these employed a tiling of the sphere that was uniformly less than 5 km. By resolving the transient dynamics of convective storms in the tropics, global storm-resolving models remove the need to parameterize tropical deep convection, providing a fundamentally more sound representation of the climate system and a more natural link to commensurately high-resolution data from satellite-borne sensors. The models and some basic characteristics of their output are described in more detail, as is the availability and planned use of this output for future scientific study. Tropically and zonally averaged energy budgets, precipitable water distributions, and precipitation from the model ensemble are evaluated, as is their representation of tropical cyclones and the predictability of column water vapor, the latter being important for tropical weather.
Wang, Lei, Q Bao, W-C Wang, Y Liu, Guoxiong Wu, and Linjiong Zhou, et al., July 2019: LASG Global AGCM with a Two-moment Cloud Microphysics Scheme: Energy Balance and Cloud Radiative Forcing Characteristics. Advances in Atmospheric Sciences, 36(7), DOI:10.1007/s00376-019-8196-9. Abstract
Cloud dominates influence factors of atmospheric radiation, while aerosol-cloud interactions are of vital importance in its spatiotemporal distribution. In this study, a two-moment (mass and number) cloud microphysics scheme, which significantly improved the treatment of the coupled processes of aerosols and clouds, was incorporated into version 1.1 of the IAP/LASG global Finite-volume Atmospheric Model (FAMIL1.1). For illustrative purposes, the characteristics of the energy balance and cloud radiative forcing (CRF) in an AMIP-type simulation with prescribed aerosols were compared with those in observational/reanalysis data. Even within the constraints of the prescribed aerosol mass, the model simulated global mean energy balance at the top of the atmosphere (TOA) and at the Earth’s surface, as well as their seasonal variation, are in good agreement with the observational data. The maximum deviation terms lie in the surface downwelling longwave radiation and surface latent heat flux, which are 3.5 W m-2 (1%) and 3 W m-2 (3.5%), individually. The spatial correlations of the annual TOA net radiation flux and the net CRF between simulation and observation were around 0.97 and 0.90, respectively. A major weakness is that FAMIL1.1 predicts more liquid water content and less ice water content over most oceans. Detailed comparisons are presented for a number of regions, with a focus on the Asian monsoon region (AMR). The results indicate that FAMIL1.1 well reproduces the summer-winter contrast for both the geographical distribution of the longwave CRF and shortwave CRF over the AMR. Finally, the model bias and possible solutions, as well as further works to develop FAMIL1.1 are discussed.
The variable-resolution version of a Finite-Volume Cubed-Sphere Dynamical Core (FV3)-based global model improves the prediction of convective-scale features while maintaining skillful global forecasts.
The Geophysical Fluid Dynamics Laboratory (GFDL) has developed a new variable-resolution global model with the ability to represent convective-scale features that serves as a prototype of the Next Generation Global Prediction System (NGGPS). The goal of this prediction system is to maintain the skill in large-scale features while simultaneously improving the prediction skill of convectively-driven mesoscale phenomena. This paper demonstrates the new capability of this model in convective-scale prediction relative to the current operational Global Forecast System (GFS). This model uses the stretched-grid functionality of the Finite-Volume Cubed-Sphere Dynamical Core (FV3) to refine the global 13-km uniform-resolution model down to 4-km convection-permitting resolution over the Contiguous United States (CONUS), and implements the GFDL single-moment six-category cloud microphysics to improve the representation of moist processes.
Statistics gathered from two years of simulations by the GFS and select configurations of the FV3-based model are carefully examined. The variable-resolution FV3-based model is shown to possess global forecast skill comparable with that of the operational GFS while quantitatively improving skill and better representing the diurnal cycle within the high-resolution area compared to the uniform mesh simulations. Forecasts of the occurrence of extreme precipitation rates over the Southern Great Plains are also shown to improve with the variable-resolution model. Case studies are provided of a squall line and a hurricane to demonstrate the effectiveness of the variable-resolution model to simulate convective-scale phenomena.
Liu, P, Y Zhu, Q Zhang, J Gottschalck, M Zhang, C Melhauser, Wei Li, Hong Guan, Xiaqiong Zhou, Dingchen Hou, M Peña, Guoxiong Wu, Y Liu, and Linjiong Zhou, et al., July 2018: Climatology of tracked persistent maxima of 500-hPa geopotential height. Climate Dynamics, 51(1-2), DOI:10.1007/s00382-017-3950-0. Abstract
Persistent open ridges and blocking highs (maxima) of 500-hPa geopotential height (Z500; PMZ) adjacent in space and time are identified and tracked as one event with a Lagrangian objective approach to derive their climatological statistics with some dynamical reasoning. A PMZ starts with a core that contains a local eddy maximum of Z500 and its neighboring grid points whose eddy values decrease radially to about 20 geopotential meters (GPMs) smaller than the maximum. It connects two consecutive cores that share at least one grid point and are within 10° of longitude of each other using an intensity-weighted location. The PMZ ends at the core without a successor. On each day, the PMZ impacts an area of grid points contiguous to the core and with eddy values decreasing radially to 100 GPMs. The PMZs identified and tracked consist of persistent ridges, omega blockings and blocked anticyclones either connected or as individual events. For example, the PMZ during 2–13 August 2003 corresponds to persistent open ridges that caused the extreme heatwave in Western Europe. Climatological statistics based on the PMZs longer than 3 days generally agree with those of blockings. In the Northern Hemisphere, more PMZs occur in DJF season than in JJA and their duration both exhibit a log-linear distribution. Because more omega-shape blocking highs and open ridges are counted, the PMZs occur more frequently over Northeast Pacific than over Atlantic-Europe during cool seasons. Similar results are obtained using the 200-hPa geopotential height (in place of Z500), indicating the quasi-barotropic nature of the PMZ.
