1. Introduction
Tropical cyclones (TCs) are synoptic-scale systems that contain mesoscale and convective-scale features such as eyewalls and rainbands. To produce accurate forecasts of TC impacts, including storm surges, flooding, and wind damage, reliable numerical weather prediction (NWP) of these features is essential. It is recognized that numerical predictions of TC intensity and structure require horizontal grids of ≤4-km spacing to simulate these features, including sharp gradients of momentum and moisture (e.g., Alaka et al. 2022). It is also expected that nonhydrostatic, cloud-permitting simulations yield superior representations of TCs. However, operational global model grids are still too coarse (≥9-km spacing) to resolve the necessary features, and they are still primarily used by forecasters for track prediction.
To accelerate progress in intensity prediction, initiatives such as NOAA’s Hurricane Forecast Improvement Project (HFIP; Gall et al. 2013; Gopalakrishnan et al. 2020) and the U.S. Navy’s directed research initiatives (Doyle et al. 2017) have invested in the development of limited-area, TC-following nests of grid spacing ≤4 km to resolve small-scale features in TCs and efficiently deliver 3–6-hourly predictions. The HFIP High-Resolution Hurricane Forecast Test (NOAA 2009), which represented a community effort to examine the benefits of higher resolution for a variety of models, did not substantially improve TC prediction, although results from some individual models (e.g., Davis et al. 2010) and more recent nested models (e.g., Hazelton et al. 2022) have been more encouraging.
In current nested models, the vortex initialization and physics are often built and tuned for TC performance. These models have recently contributed to improvements to National Hurricane Center (NHC) predictions of intensity (Cangialosi et al. 2020). Their predictions of TCs in complex environments are a result of superior representations of smaller-scale processes, such as the influence of vertical wind shear on vortex tilt and humidification and their interactions [e.g., Hazelton et al. (2020) and references therein]. While the results have been encouraging, nested modeling possesses limitations, including inconsistencies in physics and initialization, compared with those of their parent domains. For example, the innermost nests are usually cloud permitting, whereas their parent domains parameterize convection. Nesting is a tool that can provide high-resolution TC forecasts until operational computer resources can support convection permitting or resolving in global models (e.g., Alaka et al. 2022).
In parallel, global NWP has been advancing, with computational resources allowing for enhanced resolution and representation of physical processes. Given that global NWP systems are evaluated for many applications, one needs to ensure that the altered representation of a TC in a model does not yield unexpected effects downstream. Different centers have different methods for initializing TCs, ranging from assimilation of central pressure data provided by forecasters (e.g., Kleist 2011; Heming 2016) to no special modifications for TCs [e.g., ECMWF Integrated Forecasting System (IFS); Magnusson et al. 2019]. Another difference between global and nested models is their physical parameterizations. In global models, we generally expect that interactions across multiple scales are represented more accurately. However, the question remains about whether they produce TCs that are too weak, with unrealistically large eyewalls. Judt et al. (2021) compared nine global models of 2.5–7.8-km grid spacings over a 40-day period. These models yielded a variety of TC structures, several of them sufficiently realistic to suggest that with improved computational power, initialization, and physics, future global models of comparable resolution will contribute to advances in TC prediction.
At ECMWF, operational evaluations and research experiments related to TC forecasting are continuously ongoing (Magnusson et al. 2019). Recent experiments include model resolution changes; dynamical core developments, including a nonhydrostatic core; reduction of the model time step; new formulations for interactions between dynamics and physics; explicit deep convection; and coupling to the ocean model. The success of the ocean coupling experiments led to its operational implementation in 2017–18, resulting in reduced spurious deepening of TCs thanks to cooling via the interactive ocean (Mogensen et al. 2017; Magnusson et al. 2019). A modification to the surface roughness parameterization in the coupled system, which led to a reduction in drag coefficients for strong winds, was implemented in cycle 47r1 in 2020 (Bidlot et al. 2020; Li et al. 2021). Driven in part by the anticipated future grid resolution upgrade in the IFS, another recent modification has been a major upgrade to the moist physics (Bechtold et al. 2020), which was implemented in cycle 47r3 in 2021.
In 2021, several experiments were conducted at ECMWF during the active 2020 Atlantic hurricane season to understand the key sensitivities and potential for improvement to TC forecasts. A synthesis of all the experiments, together with a detailed account of TC activities at ECMWF, is provided in Magnusson et al. (2021). In this paper, we present a synthesis and evaluation of a few experiments relative to a 9-km ECMWF model with upgraded moist physics (referred to as EC9). A parallel experiment with a 4-km ECMWF model (EC4) yielded the most significant improvements to the predictions of TC intensity and structure, and the influence of this resolution change is a central focus of this paper. The effect of the modification to the drag coefficient [at 9 km (EC9-NoDragCap)] and the influence of turning off the parameterization of deep convection [at 4 km (EC4-Explicit)] are also reported here.
The other key objective of this paper is to benchmark EC4 against a high-performing regional operational model of comparable grid spacing [4 km (CO4)] that is designed for TCs [Coupled Ocean–Atmosphere Mesoscale Prediction System–Tropical Cyclone (COAMPS-TC); Doyle et al. 2014]. COAMPS-TC is selected here to address the Office of Naval Research Tropical Cyclone Rapid Intensification (TCRI) directed research initiative, although other regional models are equally suitable for comparison. The main sensitivities and differences are documented here to inform the TC prediction community of the capabilities of current (and experimental) global and regional NWP systems in predicting TC structure and intensity. The results are stratified based on different initial intensities, given that different modeling challenges arise for weak, disorganized tropical storms versus compact, symmetric hurricanes.
In section 2, we describe the modeling frameworks and experiments. In section 3, the analysis and forecast errors, as well as structural characteristics of the forecasts, are illustrated for Hurricane Laura (2020). The statistical evaluations of position, minimum pressure, maximum wind speed, and radius of maximum winds, together with the pressure–wind relationship, are presented in section 4, followed by concluding remarks in section 5.
2. Modeling frameworks and experiments
a. ECMWF
The ECMWF experiments use IFS, version 47r1 (ECMWF 2020), which was operational between June 2020 and May 2021. The model is global, with a hydrostatic, spectral dynamical core. The deterministic forecast is of ∼9-km horizontal grid spacing, with 137 vertical levels up to 0.01 hPa. The parameterization of deep convection is based on the mass flux approach with a modified CAPE closure, leading to an improved diurnal cycle of convection (Bechtold et al. 2008, 2014). The cloud and large-scale precipitation scheme is based on Tiedtke (1993), with substantial upgrades, including separate prognostic variables for cloud water, ice, rain, snow, and cloud fraction and improved parameterization of microphysical processes (Forbes and Ahlgrimm 2014). The atmospheric model is coupled to the ECMWF Ocean Wave Model (ECWAM) dynamical wave model and the 0.25° three-dimensional NEMO ocean model (Mogensen et al. 2017). The wave model exchanges information with the ocean model (Breivik et al. 2015). For example, if the drag is reduced by the wave model, both the atmosphere and ocean will use that information.
The experiments include the moist physics upgrade that became operational in IFS, version 47r3, in October 2021 (Bechtold et al. 2020). The interactions between turbulence in the lowest part of the troposphere, convective motions, and cloud physics are parameterized in an efficient and scale-independent manner. A key component of this upgrade is a revision to the convective closure that accounts for, beyond the convective instability, the total moisture advection, producing more realistic mesoscale convective systems (Becker et al. 2021). However, initial evaluations of the physics upgrade revealed a sensitivity to the convective closure. TCs and especially the eyewall constitute extreme cases of total moisture advection, and an excessive increase in convective stabilization led to TCs that were too shallow. A correction in cycle 47r3 excluded the moisture advection term in regions where the vertically integrated saturation fraction exceeds 0.94, marking the transition to resolved moist overturning.
All of the ECMWF experiments are initialized from the operational analyses, which are produced by a four-dimensional variational data assimilation scheme (4D-Var; Rabier et al. 2000). Analyses from each 8-h early delivery data assimilation window are provided as first guesses for the 12-h window, which is a time extension of the data assimilation analysis (Sleigh et al. 2020). To provide background error statistics, a 50-member ensemble of 4D-Var assimilations is run with a lower horizontal resolution (Bonavita et al. 2012). The first main ECMWF experiment (EC9) is run with the operational ∼9-km grid spacing and the upgraded moist physics described above. The second main ECMWF experiment (EC4) is an ∼4-km version of the model, with all other aspects being identical.1 The primary purpose of EC9 versus EC4 is to investigate and evaluate the impact of increasing the resolution.
The first additional experiment (EC9-NoDragCap) is identical to EC9, but with an earlier formulation of the ocean surface drag coefficient for momentum Cd in which no reduction was applied for high winds. The purpose is to understand the sensitivity of the TC forecasts to the recent operational specification of Cd that reduces the drag at high winds. The momentum exchange with the sea surface depends on the roughness length, which for high winds is expressed as a function of surface stress, air density, gravitational acceleration, and a sea-state-dependent Charnock parameter produced by the wave model. The Charnock parameter has been prescribed considerably smaller for winds of >30 m s−1 (>60 kt). With this formulation, the EC4 simulation of Hurricane Laura (2020) produces substantially smaller values of Cd for winds of >30 m s−1 (Fig. 1). Further details of ECMWF’s previous and ongoing work to reduce the surface drag are provided by Magnusson et al. (2021) and Li et al. (2021) and in the appendix.
Drag coefficient Cd as a function of the 10-m wind speed for EC4 with the old Cd formulation, EC4, and CO4. The ECMWF values are derived from the Hurricane Laura case, collecting Cd values for all open ocean points and plotting the bin average and 1 standard deviation in each bin. The COAMPS-TC values of Cd for winds > 35 m s−1 are computed iteratively using the COARE algorithm (Fairall et al. 2003).
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
The second additional experiment (EC4-Explicit) investigates the use of explicit convection at 4 km. It is identical to EC4, but with the deep convection parameterization turned off. We note that the shallow convection in the parameterization scheme for clouds and large-scale precipitation remains turned on in EC4-Explicit and EC4.
TCs for these experiments are tracked using the operational tracker (Magnusson et al. 2021), which estimates the TC position, minimum surface pressure (Pmin), maximum 10-m wind speed (Vmax), and radius of maximum winds (RMW) at the full model resolution.
b. COAMPS-TC
The operational COAMPS-TC system used in this paper features an atmospheric model with a nonhydrostatic dynamical core, a fixed 36-km grid outer mesh, and storm-following 12- and 4-km inner meshes (Doyle et al. 2014). This model uses 40 vertical levels, with the top near 10 hPa, and is coupled to the Navy Coastal Ocean Model (NCOM). The NOAA Global Forecast System (GFS) is used for initial and boundary conditions here, with no cycling of COAMPS-TC. For TCs with initial Vmax <55 kt (1 kt = 0.51 m s−1), the vortex is downscaled from the parent GFS analysis. For TCs with initial Vmax ≥55 kt, a synthetic, balanced vortex is inserted in the moving mesh, replacing the GFS analysis. The synthetic vortex is based on a modified Rankine radial profile of tangential winds that is fit to the analyzed RMW and the radius of 34-kt winds from the operational NHC analysis. Hence, the analyzed intensity in COAMPS-TC is identical to the NHC value. Further details of the initialization, including the vortex height, are provided in Komaromi et al. (2021).
In contrast to ECMWF, the COAMPS-TC physics includes explicit deep convection in the 4-km mesh. In the outer meshes, the subgridscale deep convection is parameterized based on the mass flux closure of Kain and Fritsch (1993). Shallow convection is parameterized on all three meshes, using Tiedtke (1989). The planetary boundary layer (PBL) scheme is a 1.5-order turbulent kinetic energy scheme based on Mellor and Yamada (1982), and the microphysics scheme is based on Lin et al. (1983). The drag coefficient Cd uses relationships from Powell et al. (2003), Donelan et al. (2004), and Donelan (2018), leveling off at surface winds of 26 m s−1 (50 kt) and decreasing above 42.5 m s−1 (83 kt). It is very similar to the current ECMWF formulation (Fig. 1). Further details of the physical parameterizations are provided in Doyle et al. (2012, 2014) and Komaromi et al. (2021).
c. Experiment period
The EC9 and EC4 experiments are conducted between 15 August and 18 November 2020 and compared against the corresponding CO4 predictions initialized every 12 h, at 0000 and 1200 UTC. There was unusually high TC activity in the Atlantic Ocean basin during this period, with 19 named TCs, 12 of which reached hurricane intensity (Fig. 2). Of note were three large hurricanes in the central North Atlantic (Paulette, Teddy, Epsilon) and, remarkably, nine hurricanes in the Gulf of Mexico and western Caribbean Sea, including five in October and November (Laura, Marco, Nana, Sally, Gamma, Delta, Zeta, Eta, Iota). Eight of these hurricanes had undergone rapid intensification (RI; ≥30 kt in 24 h) during their lifetime. In this paper, only those times when the TC was a tropical depression, tropical storm, or hurricane are included. The homogeneous sample across all experiments is 177 initialization times.
All Atlantic basin TCs during the evaluation period of 15 Aug–18 Nov 2020. The TCs that developed into hurricanes are labeled.
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
3. Case illustration: Hurricane Laura (2020)
Laura made landfall near Cameron, Louisiana, around 0600 UTC 27 August 2020 as a category-4 hurricane. At 1200 UTC 24 August, the model initialization time in this section, Laura was a tropical storm located just south of Cuba, with an intensity of 50 kt/1002 hPa. Laura then underwent six consecutive RI episodes from 0600 UTC 25 August. This TC is selected for its importance to society, the challenges in predicting RI, the availability of observations, and its representativeness of some capabilities and deficiencies.
The position predictions of Laura up to its landfall are accurate, although EC9-NoDragCap deviates to the left (Fig. 3a). In the remainder of this section, we focus on intensity and structure. The 9-km ECMWF predictions do not capture RI, peaking no stronger than 960 hPa and 75 kt (Figs. 3b,c). In contrast, EC4 captures RI, albeit 12 h after Laura’s actual RI, with Pmin = 927 hPa and Vmax = 130 kt at 60 h (best-track Pmin = 937 hPa and Vmax = 130 kt). CO4 accurately predicts the intensification of Vmax, although Pmin at peak intensity is too shallow by 18 hPa. EC4-Explicit produces an unrealistic RI, with Pmin = 901 hPa and Vmax = 155 kt.
The 0–84-h ECMWF and COAMPS-TC predictions of Hurricane Laura initialized on 1200 UTC 24 Aug 2020: (a) position, (b) Pmin, (c) Vmax, and (d) RMW. The legend for the predictions is provided in (d). The NHC best track is in black. Landfall is at +66 h.
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
The RMW provides a verifiable quantity related to the inner-core structure. The initial RMW in the ECMWF analysis (126 km) is larger than the verification (46 km). An eyewall in each ECMWF simulation then develops from the first day (Fig. 3d). In contrast, by design of the initial TC in COAMPS-TC, the CO4 RMW is closer to the verification. The RMW predictions demonstrate that even the 9-km ECMWF model can create a compact eyewall, and a question arises about whether the winds in the eyewall can be accurately represented.
We next illustrate the near-surface (10 m) wind fields for 60-h predictions valid 6 h prior to Laura making landfall, compared with a synthetic aperture radar (SAR) pass at the same time (Fig. 4). The methodology, strengths, and limitations of the SAR in estimating surface winds in intense hurricanes are described in Mouche et al. (2019) and Combot et al. (2020). Laura was located on the western edge of the satellite swath, and only its eastern half was sampled. The SAR winds exceed 120 kt on the eastern side of the eyewall, with hurricane-force winds extending 85 km to the east of the center (Fig. 4a). EC9-NoDragCap develops a ragged eyewall, with limited hurricane-force winds (Fig. 4b). EC9, with the updated Cd, possesses a tighter, partially closed eyewall (Fig. 4c) with a radius close to the verification (Fig. 3d). However, the winds are too weak. EC4 produces a closed eyewall, and the distribution and magnitude of the most intense winds are largely consistent with the SAR (Fig. 4d). In EC4-Explicit, a tight eyewall with a high wind maximum is evident, demonstrating deepening that is too explosive when parameterized deep convection is turned off (Fig. 4e). This result is in contrast to COAMPS-TC, where the inclusion of convective parameterization in the inner mesh produced TCs that were too intense (not shown). CO4 produces a closed eyewall with a radius and Vmax close to verification and a wind structure that resembles the available SAR data (Fig. 4f).
Observations and 60-h ECMWF and COAMPS-TC predictions of 10-m surface wind speed (kt; shaded) and wind barbs (kt) initialized on 1200 UTC 24 Aug 2020: (a) SAR pass valid at 0010 UTC 27 Aug 2020 (m s−1), (b) EC9-NoDragCap, (c) EC9, (d) EC4, (e) EC4-Explicit, and (f) CO4.
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
The radial profile of the surface wind in EC9 (Fig. 5a) confirms that the wind is too weak, with the peak at <80 kt. However, as indicated from Figs. 3d and 4c, the radius of this peak wind is close to the best-track value. The azimuthally averaged radial wind, representing the surface inflow, approaches 30 kt just outside the eyewall. The azimuthally averaged total wind decreases slowly with radius out to (and beyond) 200 km. The vertical wind structure reveals a height of maximum wind at 925 hPa, and 90-kt winds extend up to ∼730 hPa (Fig. 5b). Above this level, the eyewall does not slope outward with height. An inflow exceeding 5 kt is evident only below 900 hPa, and the outflow extends from a radius of ∼30 km and is vertically centered on 150 hPa (Fig. 5c). The azimuthally averaged outflow is weak, with the radial component mostly not exceeding 10 kt. The warm core,2 with a maximum temperature excess of ∼8 K, possesses two peaks, between 200 and 300 hPa and at ∼600 hPa.
Sixty-hour ECMWF and COAMPS-TC predictions initialized on 1200 UTC 24 Aug 2020: (a),(d),(g) surface wind speeds (kt), showing NHC best-track maximum wind speed (black line) and its radius, 64-, and 50-kt wind radii (black dots); maximum wind speed at each radius (red); azimuthally averaged wind speed (orange); azimuthally averaged azimuthal wind (green); and azimuthally averaged radial wind (blue); (b),(e),(h) vertical cross section of azimuthally averaged horizontal wind speed; and (c),(f),(i) vertical cross sections of azimuthally averaged radial wind (shaded) and azimuthally averaged temperature anomaly (contours; K).
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
The EC4 maximum wind speed and eyewall radius compare well to those of the best track (Fig. 5d), and a sharp wind decay outside the eyewall is evident, consistent with observations of major hurricanes (Willoughby et al. 2006). The radial wind exceeds 40 kt at the surface, indicating a strong inflow that is advecting angular momentum into the eyewall. In marked contrast to EC9, the vertical wind structure reveals that the peak wind exceeds 130 kt, and 90-kt winds extend up to 300 hPa (Fig. 5e). The eyewall slopes slightly farther outward with height than EC9. There is a stronger, deeper inflow layer with a radial wind of 10 kt at 900 hPa (Fig. 5f). The upper-tropospheric outflow in EC4 is stronger and higher than in EC9, vertically centered around 100 hPa. A lower, stronger warm core of 14 K is evident. Interestingly, EC4 has a lower-tropospheric outflow between 750 and 900 hPa and within 35 km of the center.
CO4, whose Vmax forecast was of similar high quality to that of EC4, shows a similar radial profile of maximum wind (Fig. 5g). Given the greater asymmetry of CO4 relative to EC4, the azimuthally averaged wind is substantially lower than the maximum wind. The surface inflow is not as strong, peaking at 30 kt. The vertical wind structure in CO4 exhibits a maximum that is comparable in altitude to EC4, with a peak value near 110 kt (Fig. 5h). The 90-kt winds extend up to ∼450 hPa, shallower than EC4. The eyewall slopes farther outward with height than EC4. Combined with this vertical wind structure is a more uniform inflow layer and an outflow that begins at a radius of ∼50 km, farther outward than the ECMWF counterparts due to the greater eyewall slope (Fig. 5i). The CO4 outflow height is centered around 150 hPa, lower than in EC4. A distinct warm core maximum of ∼10 K is evident between 400 and 500 hPa.
The rain rate provides further insights into the TC structure. Laura had a classical radar reflectivity signature as it approached Louisiana, with banding in all quadrants and an eyewall that was open to the south (Fig. 6a). In the ECMWF system, the total rainfall (Fig. 6d) is given by the sum of the rain rates provided by the deep convection scheme at spatial scales smaller than the grid box (Fig. 6b) and by the cloud scheme, which represents larger-scale rainfall (Fig. 6c). For EC4, the rainfall in the rainbands is dominated by the deep convection scheme, whereas the rainfall in the eyewall is dominated by the larger-scale cloud scheme. The reflectivity in the eyewall and rainbands to the east (Fig. 6d) bears similarities to the radar observations, albeit with a smaller eye. On the other hand, when the deep convection scheme is turned off (EC4-Explicit), the simulated reflectivity is less consistent with the radar, with a more asymmetric eyewall and no rainbands (Fig. 6e). This suggests that the parameterization of deep convection is necessary to simulate rainbands in the ECMWF system. In contrast, CO4, which uses explicit convection, simulates an eye, a robust eyewall, and the rainbands east of Laura’s center (Fig. 6f). Finally, the reflectivity structure in EC9 is similar to that in EC4, with the main difference being less intense rainfall on the northern side of the eyewall (not shown).
Observations and 60-h ECMWF and COAMPS-TC predictions of rain rate initialized on 1200 UTC 24 Aug 2020: (a) NEXRAD radar reflectivity (dBZ) from Lake Charles, LA, at 0000 UTC 27 Aug 2020, (b) convective rain rate from EC4, (c) large-scale rain rate from EC4, (d) simulated reflectivity from EC4, (e) simulated reflectivity from EC4-Explicit, and (f) simulated reflectivity from CO4.
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
Figures 3–6 illustrate the structural characteristics of EC4 and CO4, for a forecast in which both models performed well. On the other hand, this and other examples indicated deficiencies in EC9-NoDragCap and EC4-Explicit, which we describe now.
EC9-NoDragCap is consistently weaker than EC9 for hurricanes, with the Laura case being representative of the full sample. At 30 h, once the simulated Laura reaches hurricane force, the wind speed increases in the boundary layer in EC9 when compared with EC9-NoDragCap (not shown). This results in a moderately stronger TC after 36 h in comparison with EC9-NoDragCap (Fig. 3), where we hypothesize that the larger Cd in the old formulation yields an unrealistically strong coupling between the low-level winds and the surface, resulting in too much momentum being extracted from the wind. The differences in inflow structure and vertical motion at 30 h are less noticeable; these only become distinct from 42 h onward. In other words, the first signature of the difference between EC9 and EC9-NoDragCap is from the wind speed in the boundary layer. We also note that there are mechanisms that might counter the higher wind speeds in EC9, such as the possibility of less thermal energy extracted from the ocean, since the heat and moisture exchange coefficients are proportional to the square root of Cd.
EC4-Explicit produces stronger and deeper TCs than EC4, as illustrated in the Laura simulation. In contrast to the drag coefficient experiment, the discrepancy due to the explicit deep convection is evident immediately after initialization. In the ECMWF analysis, Laura was an asymmetric TC with a local wind maximum of 70 kt at 850 hPa (not shown). We now contrast the two 6-h predictions (Fig. 7). First, the heating tendency is maximized in the mid–upper troposphere in EC4-Explicit (Fig. 7b) and is stronger than EC4 (Fig. 7a). This condensational heating in EC4-Explicit is associated with more intense reflectivity patterns (Fig. 7d) and moisture tendencies. The vertical motion is excessive, with unrealistic positive feedback between the heating and upward motion (exceeding −40 Pa s−1), given insufficient lateral mixing, and compensating regions of downdrafts (Fig. 7f). In contrast, EC4 yields more modest updrafts and minimal downdrafts at this time (Fig. 7e). Multiple small and intense vortices develop in the first 6 h around the center in EC4-Explicit, whereas EC4 possesses a clear vorticity maximum at the center (not shown). We hypothesize that due to the downward mixing of momentum in EC4-Explicit, combined with the secondary circulation induced by the mid–upper-tropospheric heating, the lower-tropospheric winds amplify. The sharp horizontal gradient of the heating increases the potential vorticity in the TC and the intensity. In parallel, the top-heavy heating profile, with limited lateral mixing, results in a lower tropopause temperature and a higher intensity via a more efficient Carnot cycle (Emanuel 1986). In EC4, however, the parameterization results in increased lateral mixing via entrainment, and the secondary circulation, vorticity, and Carnot cycle are weaker because of the less-excessive heating. In EC4-Explicit, the induced horizontal wind is maximized around the 850-hPa level and is considerably stronger than in EC4 (Figs. 7g,h). These lower-tropospheric winds influence the boundary layer, which is controlled by the same PBL scheme in EC4 and EC4-Explicit. The induced inflow at 6 h is confined below 900 hPa and is stronger in EC4-Explicit (not shown).
Six-hour ECMWF forecasts for (left) EC4 and (right) EC4-Explicit: (a),(b) vertical distribution of azimuthally averaged temperature tendency (K accumulated over 6 h); (c),(d) simulated reflectivity (dBZ); (e),(f) 400-hPa omega (Pa s−1, green indicates upward motion) and geopotential height (m); and (g),(h) total wind (shaded; kt), wind barbs, and geopotential height (m) at 850 hPa.
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
By 12 h, the temperature anomaly in EC4-Explicit is already deeper and stronger (>4 K between 350 and 800 hPa) than that in EC4 (local maximum of 4 K only around 300 hPa). At later times, the cumulative effect of anomalously high mid–upper-tropospheric heating in EC4-Explicit leads to further intensification and convective bursts by the same arguments, resulting in substantially different intensities and reflectivity patterns. As the TC matures and becomes more consistent with thermal wind balance, the intensification can be inferred from the negative radial gradients of equivalent potential temperature. The reduced instabilities in the parameterized deep convection in EC4 result in a less intense hurricane, with a more coherent eyewall and rainband structure. We finally note that the shallow convection, microphysics, and boundary layer schemes, which are the same in EC4 and EC4-Explicit, are not the triggering differences between the simulations, although they immediately interact and influence the TC evolution.
In the next section, our evaluations will focus on the effects of increasing the resolution in one model (EC4 vs EC9) and a comparison between different NWP systems of comparable resolution (CO4 vs EC4).
4. Evaluation
a. Evaluation methodology
We next present evaluations of 0–120-h predictions (in 12-h increments) of position, Pmin, Vmax, and RMW for EC9, EC4, and CO4 over the full experiment period. The NHC best track is used for verification. The results are also stratified into subsamples based on the best-track initial intensity: weak tropical storms with Vmax <50 kt (TS1), strong tropical storms with 50 ≤ Vmax < 64 kt (TS2), and hurricanes ≥64 kt (TH).3
We compute the mean absolute error (MAE) for each sample. To test the null hypothesis that the position MAE is independent of the initial intensity, we use the two-tailed Welch’s t test that accounts for unequal sample sizes and variances. For Pmin, Vmax, and RMW, we use a two-tailed normal distribution to test the null hypothesis that the sample bias is zero. Finally, we use the two-tailed t test to test the null hypothesis that the absolute error of EC4 (CO4) is indistinguishable from that of EC9 (EC4). One-tailed tests yielded nearly identical results.
At the end of this section, we summarize the corresponding key findings from EC9-NoDragCap and EC4-Explicit, although for brevity, the statistics are not shown.
b. Position forecast errors
For EC9, EC4, and CO4, the average position errors increase monotonically with forecast time, as expected (red lines in Figs. 8a–c). The errors of TCs that are initially weak (TS1; magenta lines) are consistently larger than those that are initially hurricanes (TH; brown lines). For EC9 and EC4, these differences are significant at the 99% level at 12–48 h and at the 95% level at 60–72 and 120 h. For CO4, these differences are also significant at the 99% level at 12–48 h but are not as distinct at later times. We suggest that the larger forecast errors for weaker TCs are due to larger initial condition errors and lower predictability of environmental interactions.
MAE of TC position for (a) EC9, (b) EC4, and (c) CO4 forecasts for the full sample (thick red line and filled circles) and TS1 (magenta line and triangles), TS2 (orange line and inverted triangles), and TH (brown line and diamonds) subsamples. Black squares indicate statistically significant differences in MAE between the TH and TS1 subsamples at the 99% (filled) and 95% (open) levels, respectively. Also shown are mean differences between the position MAEs (km) of (d) EC4 − EC9 and (e) CO4 − EC4 for the same full sample and subsamples. The sample size for each forecast time in the full sample and subsamples is provided in the legend.
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
Next, we compare EC9 versus EC4 (Fig. 8d), in which the only difference is the resolution of the forward integration. For forecasts beyond 24 h, the EC4 errors are smaller than in EC9; however, these reductions do not exceed 10% and are not statistically significant. This is still an encouraging result. The initial position errors in CO4 are smaller than those in EC4 (Fig. 8e). The initial advantage for CO4 disappears after 12 h, and they have similar errors out to 48 h. Beyond 48 h, CO4 possesses lower errors for TS1. Over the full sample, the CO4 error is lower beyond 36 h. However, none of these distinctions are significant, with the average difference between the two models ranging between 5% and 15% beyond 12 h and the large standard deviation of the differences rendering the t statistic lower than the critical values.
We also investigated whether position forecast errors were correlated with intensity forecast errors. No significant correlations were identified (results not shown).
c. Intensity forecast errors (Pmin)
We first investigate the mean nonabsolute error, commonly referred to as the “bias.” For EC9 (Fig. 9a) and EC4 (Fig. 9b), in which the initial conditions are identical, the initial bias of Pmin is high and depends on the TC strength. For TS1, this bias is nearly zero, which is not surprising given that weak tropical storms are shallow with Pmin near 1000 hPa. The initial bias is ∼4 hPa for TS2 and ∼8 hPa for TH, indicating difficulties in the ECMWF data assimilation system initializing a deep TC. Turning our attention to the predictions, a high (weak) bias in EC9 is evident at all times, with 99% significance (Fig. 9a). This bias is pronounced for TS1, indicating that the forecast model regularly struggled to deepen initially weak TCs. For TS2 and TH, the EC9 forecast bias progressively diminishes.
Mean error or bias of Pmin for (a) EC9, (b) EC4, and (c) CO4 forecasts for the full sample (thick red line and filled circles) and TS1 (magenta line and triangles), TS2 (orange line and inverted triangles), and TH (brown line and diamonds) subsamples. (d)–(f) The corresponding MAEs. Also shown are mean differences between the Pmin MAEs (hPa) of EC4 − EC9 and CO4 − EC4 for the same full sample and subsamples. In (a)–(c), (g), and (h), filled squares, open squares, and plus signs indicate statistical significance at the 99%, 95%, and 90% levels, respectively, for the full sample and each subsample. The sample size for each forecast time in the full sample and subsamples is provided in the legend.
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
Encouragingly, the EC4 Pmin forecasts exhibit lower biases (Fig. 9b) due to the higher resolution producing more intense TCs on average. While the weak biases remain mostly significant at the 99% level for TS1, their average magnitudes are lower in EC4 (e.g., ∼5 hPa in EC4 vs ∼10 hPa in EC9 for 72-h forecasts). For TS2, the EC4 forecast bias is near zero. For TH, EC4 is biased too deeply, with 99% significance for 48–72-h forecasts, indicating difficulty in sufficiently weakening an initially powerful TC.
The Pmin biases for CO4 differ markedly from those for EC9 and EC4 (Fig. 9c). While the initial bias for weaker TCs is modest in CO4, the bias for hurricanes is 7 hPa too strong. For nearly all forecast times, the CO4 biases are small and slightly too weak (+0–3 hPa). Some of these biases are statistically significant between the 90% and 99% levels, especially between 12 and 36 h. However, the Pmin biases are consistently much closer to zero in CO4 than in EC4.
The MAE patterns appear qualitatively similar for EC9, EC4, and CO4 (Figs. 9d–f). For tropical storms, the initial MAE is 2–4 hPa. For hurricanes (TH), it is 8–10 hPa, remembering that EC4/EC9 and CO4 have substantial initial biases, albeit in opposite directions. For the full sample, the MAE grows steadily to ∼13 hPa in EC4/EC9 (Figs. 9d,e) and ∼10 hPa in CO4 (Fig. 9f) beyond 96 h. Stratifying the MAE computations by initial intensity, the nature of the MAEs switches after 36 h. For the weakest TCs (TS1), the MAEs switch from initially lowest to highest out to ≥84 h, demonstrating the difficulty in predicting intensity in the medium range when the TC is initially weak. In contrast, for the strongest TCs (TH), the MAEs in Pmin switch from initially highest to lowest, generally decreasing from the large initial MAE.
There are almost no statistically significant differences between the Pmin MAEs in EC9 and those in EC4 (Fig. 9g), despite the differences between their respective biases. Generally, the MAE for TS1 is reduced by up to 3 hPa in the EC4 forecasts, whereas the MAE for TH is increased by up to 3 hPa. These results corroborate the finding that the increased resolution deepens TCs, slightly improving the forecasts for initially weak TCs (which strengthen too slowly) but slightly degrading the forecasts for initially strong TCs (which remain too strong). For CO4 versus EC4, there are a few more statistically significant differences in their respective MAEs of Pmin for stronger TCs (TS2 and TH in Fig. 9h), especially in the 36–72-h forecasts of initial hurricanes (TH), in which CO4 has significantly lower Pmin errors than EC4.
d. Intensity forecast errors (Vmax)
For EC9 (Fig. 10a) and EC4 (Fig. 10b), the initial Vmax bias is too weak, averaging ∼15 kt. The bias depends on the initial TC intensity; for weak TCs (TS1), it is about 5 kt, whereas for hurricanes (TH), it is nearly 30 kt. Given that Vmax is largely driven by small-scale processes, we expect that it will not be captured in a global data assimilation scheme. EC9 forecasts are negatively biased, with 99% significance in the full sample (Fig. 10a), indicating difficulties in spinning up the TC or resolving the verified maximum wind. The negative Vmax bias for EC4, while still 99% significant, is 6–8 kt (>30%) lower than that for EC9 after 48 h (Fig. 10b). This suggests that the increased resolution improves the winds in the eyewall, consistent with the Hurricane Laura illustrations in Figs. 4 and 5.
As in Fig. 9, but for Vmax (kt).
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
As for Pmin, the results for Vmax in CO4 differ substantially from those in EC9 or EC4 (Fig. 10c). By design, the initial Vmax bias in CO4 is expected to be zero for TCs ≥55 kt. Even for weaker TCs, the initial bias is only <5 kt too low. For the forecasts, the Vmax bias remains slightly low, remarkably not exceeding 5 kt. These biases are statistically significant out to 36 h, even though the values are much smaller than those in EC4 and EC9. The primary contribution to this negative bias comes from the subsample of initial hurricanes, in which the bias is 7–10 kt and significant at the 99% level for 12–72-h forecasts.
The Vmax forecast MAE is greater than 15 kt for EC9 (Fig. 10d), with different evolutions in the subsamples. For TS1, it grows from 7 to 24 kt in the first 48 h, whereas for TH, it shrinks from 28 to 16 kt. Similar patterns occur with lower values for EC4 (Fig. 10e). The overall Vmax MAE is reduced by 3–6 kt in EC4, with a distinct improvement to Vmax forecasts in TH at 24–48 h (Fig. 10g). This reduction is consistent with the corresponding Vmax bias reduction in EC4 and is statistically significant at 90%–95% between 12 and 96 h.
Although one might expect, based on their respective biases, that the Vmax MAE is significantly lower for CO4 versus EC4, this is not evident after 24 h (Fig. 10h). While CO4 starts by design with a lower MAE, only small differences are found at ≥36 h. The differences fluctuate depending on the subsamples. In summary, EC4 compares well to CO4 in the overall MAE, but EC4 has more distinct biases. These biases in EC4 are reduced relative to those in EC9.
We now investigate the forecast cases that are responsible for the Vmax errors in CO4. Given that the CO4 errors become statistically indistinguishable from the EC4 errors by 36 h, we choose the homogeneous sample of 36-h forecasts. Of these 139 forecasts, 20 yield CO4 errors that are too weak by ≥20 kt. The Vmax verification in 19 of these cases is at least 75 kt. The list of cases comprises the RI of Sally, Delta, Epsilon, Eta, and Iota; the intensification (non-RI) of Sally, Teddy, and Epsilon; and the landfalls of Laura, Delta, Eta, and Iota. For some of these TCs, there are multiple instances. For the intensifying cases, the predicted intensity change is substantially too low in CO4. For the landfall cases, the predicted intensity is also too low, suggesting that the modeled TCs may be making landfall slightly prematurely. In 13 of these 20 cases, the initial intensity is sufficiently high for the CO4 vortex initialization to be employed. The corresponding EC4 forecasts in these cases also have very large Vmax errors, except for the three Teddy cases. Overall, the primary contributors to the rapid error growth (and negative bias) of Vmax in CO4 are RI cases, with secondary contributions from landfall cases.
Of the same 139 cases of 36-h CO4 Vmax forecasts, 10 are at least 20 kt too strong compared with the verifying value. These correspond to overly high predictions of the intensification of Laura, Paulette, Rene, and Teddy and one forecast of Delta in the Gulf of Mexico, where the actual Delta weakened more than the CO4 prediction. In contrast, only one of these 10 cases has an EC4 Vmax error of +20 kt, with all of the other errors being less than +10 kt, and several of these are in fact too weak. In general, these TCs were relatively large in size, and CO4 has greater difficulty in slowing down their intensification than EC4 does.
e. Pressure–wind relationship
A scatterplot and best-fit line of the pressure–wind (Pmin − Vmax) relationship is used to evaluate the performance of operational models (Bao et al. 2012 and references therein). It is viewed as an indicator of whether the model is capturing the inner-core pressure gradients and whether the relationships compare well against independent observations in the best track.
For 12–72-h forecasts, the pressure–wind relationships are similar, and the results for 24-h forecasts are illustrated in Fig. 11. The CO4 best-fit line is situated closest to the best track (Fig. 11a). EC4 is closer to the verification than EC9 for Vmax >50 kt. This suggests an improved gradient wind balance, the dominant balance in intense TCs (Willoughby 1990). For TC forecasts > 60 kt, EC9 is closer to the best track than EC9-NoDragCap, suggesting that the reduced surface drag for hurricanes in EC9 is allowing the surface winds to strengthen, thereby reducing the low wind bias. This improved relationship is consistent with Bidlot et al. (2020). In Fig. 11b, the computations are repeated for a reduced period (up to 21 September) to accommodate EC4-Explicit. Despite producing far too intense TCs in Pmin and Vmax (Magnusson et al. 2021 and our Fig. 4), EC4-Explicit yields a pressure–wind relationship that seems closer to the observed relationship. This relationship, together with the counterparts of the top rows of Figs. 9 and 10 for EC4-Explicit (not shown), suggests that there are compensating biases for Pmin and Vmax. This is especially true for the subsample of forecasts that were verified as hurricanes, in which the EC4-Explicit bias in Pmin is too deep (less than −15 hPa for 24–60-h forecasts) and the corresponding bias in Vmax is too strong (>13 kt for 24–60-h forecasts).
(a) Pressure–wind relationship for the full homogeneous sample of 24-h forecasts, with quantile best-fit lines for each simulation and the NHC best-track verification. (b) As in (a), but for a reduced homogeneous sample up to 21 Sep 2020, to include EC4-Explicit.
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
If the pressure–wind relationship is based on gradient wind balance arguments, one might suggest that Pmin is sufficient for obtaining Vmax. However, there are several reasons why this may not hold. First, the difference between the axisymmetric component of the wind and Vmax can be between 5 and 15 m s−1 [10–30 kt; Fig. 2 of Vukicevic et al. (2014)]. Gradient wind balance is also compromised at the surface due to frictional processes, and it is not applicable to weaker TCs (Willoughby 1990). Furthermore, the wind field possesses more small-scale features than the pressure field, peaking on a smaller scale. For example, the wind structure in Hurricane Laura’s eyewall is asymmetric, with a small-scale feature containing Vmax (Fig. 4). The axisymmetric component of CO4 (orange line in Fig. 5g) is ∼30 kt smaller than the peak wind (red line in Fig. 5g). Another contributor to the departure from gradient wind balance is the corresponding azimuthally averaged peak radial inflow, which exceeds 20 kt in CO4.
f. RMW
Operational centers and users are placing more attention on TC size, including the RMW. We first illustrate the distributions of all 72-h forecast values in EC9, EC4, and CO4 versus the verifying best-track values (Fig. 12). The best-track distribution peaks between 20 and 40 km (32% of all cases), with the next largest bin between 40 and 60 km (20%) (Fig. 12a). Only five cases have an RMW above 120 km. The distribution for EC9 shows a less pronounced peak between 20 and 40 km and a tail of 22 cases with RMW >120 km (Fig. 12b). For EC4, the distribution has similarities to EC9, again with a long tail (Fig. 12c). In 23 of the 26 cases for which EC4 RMW is greater than 120 km, the corresponding Vmax forecast is less than 50 kt. In other words, the large radii mostly correspond to weak TCs. The remaining three cases correspond to large hurricanes Epsilon and Teddy, when they were north of 34°N and gaining latitude. The results for EC9 are similar. We expect that the change in resolution does not have a significant effect on the RMW for weak simulated TCs or large TCs in the midlatitudes.
Distributions of RMW for (a) the NHC best track, used as verification, and the corresponding 72-h (b) EC9, (c) EC4, and (d) CO4 forecasts. The homogeneous sample size is 86. Outlier cases with RMW >400 km are not shown.
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
Although the 20–40-km peak in EC4 is lower than that in EC9, there are more cases (eight vs zero) in which RMW of less than 20 km is predicted. For CO4, the RMW distribution is more similar to the verification, although the peak lies in the 40–60-km bin (Fig. 12d). Overall, ECMWF provides a wider range of RMW values because of challenges in some cases of building and contracting an eyewall. However, especially at 4 km, it can produce compact eyewalls, as can COAMPS-TC.
The full sample and TS1 subsample of EC9 forecasts of RMW out to 96 h are biased to be ≥30 km too large, with 99% significance (Fig. 13a). EC4 shows a slightly smaller bias (Fig. 13b). CO4 impressively shows minimal bias, except for the small TH sample beyond 84 h (Fig. 13c).
As in Fig. 9, but for RMW (km).
Citation: Monthly Weather Review 151, 8; 10.1175/MWR-D-22-0236.1
For EC9 and EC4, the initial MAE is revealing (Figs. 13d,e). TS1 possesses an initial MAE of greater than 80 km, signifying difficulties in initializing the wind structure while recognizing that the RMW is volatile for weak TCs. For TH, the initial MAE is ∼30 km, suggesting that hurricane eyewalls in ECMWF analyses are larger than those in nature. By 48 h, the MAE values converge to ∼60 km. In comparing EC4 versus EC9, it is seen that there is no clear improvement in the RMW forecasts (Fig. 13g). Although the 96–120-h bias and MAE for TH are larger in EC4, the sample is tiny (from four to six) and dominated by Hurricane Teddy, in which the resolution is not expected to influence the RMW.
For CO4, the MAE is much smaller (Fig. 13f). The initial MAE for TS1 is ∼50 km, whereas that for TH is less than 10 km, as expected given the RMW initialization. After 48 h, the overall MAE converges to ∼40 km, in contrast to 60 km in EC4. These differences between CO4 and EC4 are 95%–99% significant for 12–108-h forecasts, with most of the superiority in CO4 coming from TS1. These results suggest that EC4 does not contract the eyewall in intensifying TCs to the extent that CO4 does. The COAMPS-TC RMW usually decreases in a realistic fashion, although there is a tendency for the COAMPS-TC eyewall to stay a little larger at high intensity (not shown). Other regional models, such as NOAA’s Hurricane Analysis and Forecast System (HAFS), are also demonstrating the capability to contract eyewalls (Hazelton et al. 2022).
The results of Figs. 13 and 10 can be used to suggest why the EC4 Vmax forecasts for TS1 are biased weaker than their CO4 counterparts, even though CO4 does not use the special vortex initialization for these weak storms. The initial RMW bias in EC4 exceeds 30 km (too large) in Fig. 13b, whereas the initial RMW bias in CO4 exceeds −20 km (too small) in Fig. 13c. We suggest that these initially larger wind structures in EC4 are one reason why the EC4 forecasts are less intense and have broader eyewalls. We also suggest that EC4 has difficulty in contracting eyewalls. There are several potential physical reasons why one model may contract the eyewall faster than the other; however, it is difficult to isolate model components that may be responsible. The interactions across the models’ respective parameterizations, and how they are configured, are expected to be partially responsible (Magnusson et al. 2022).
g. EC9-NoDragCap and EC4-Explicit
EC9 with the operational surface roughness provides no significant changes to the TC position forecasts compared with EC9-NoDragCap (not shown), with the improvement to the Hurricane Laura forecast not being representative (Fig. 3a). EC9 consistently produces Pmin 3–6 hPa deeper for stronger TCs, although this does not result in clear reductions in MAE. Most significantly, for initial hurricanes (TH), EC9 yields a 6–7-kt improvement in 12–60-h forecasts of Vmax. EC9 produces 10–20-km reductions of RMW for 24–60-h forecasts of TH, with slight reductions to the MAE. Overall, the reduced drag coefficient at high winds leads to more times in which the simulated 10-m winds reach hurricane force (25 in EC9 vs 16 in EC9-NoDragCap), although this number is smaller than the actual number of hurricane instances (43) in our sample. In EC9-NoDragCap, there is only one instance of a simulated hurricane with an RMW <40 km, whereas in EC9, there are 12 such instances, indicating that EC9 can also produce tighter eyewalls given the reduced drag at hurricane-force wind speeds.
EC4-Explicit degrades the ≥48-h TC position forecasts by ∼30 km when compared with EC4 (not shown). The Pmin is biased up to 9 hPa deeper, resulting in 99% significant degradations to 24–72-h Pmin forecasts. The Vmax forecasts are biased too strong in EC4-Explicit, resulting in ≥48-h average errors ∼6 kt larger than in EC4. The results for RMW are inconclusive.
5. Concluding remarks
We have compared tropical cyclone (TC) predictions using two NWP systems, emphasizing intensity (Pmin and Vmax) and structure (RMW) for 19 Atlantic basin TCs between 15 August and 18 November 2020. ECMWF aims to predict the global atmosphere in the medium range, whereas the limited-area COAMPS-TC framework is tailored for predicting TCs. A new experimental version of ECMWF with a 4-km grid provided a first opportunity to evaluate the impact of model resolution on ECMWF forecasts of intensity and structure (EC9 vs EC4) and compare a global model with a 4-km grid (EC4) with a specialized regional TC system (CO4) to investigate the differences between systems with similar resolutions.
The illustration of one case (Hurricane Laura), in which EC4 and CO4 performed well, demonstrated their capabilities to predict intensity and produce compact eyewalls. EC4 and CO4 produced simulated rain rates that generally resembled the observed radar reflectivity. In EC4, the eyewall rain rate was dominated by the large-scale cloud scheme, while the rainband rain rate was dominated by the parameterized deep convection.
The average position errors of initially weak TCs were consistently higher than those of initial hurricanes. The EC4 (CO4) position forecast errors were smaller than those in EC9 (EC4), but not statistically significantly so.
For Pmin, EC4 yielded deeper TCs than EC9. There was often difficulty in predicting deepening from the tropical storm stage, although the Laura case provided a counterexample. For initial hurricanes, in which the EC9 and EC4 values were initially too high (weak), their forecast biases then became too low (strong), indicating difficulties in predicting the weakening of a hurricane. Overall, the Pmin MAEs in EC4 were smaller, but not significantly, than those in EC9. The CO4 biases for Pmin were smaller than the EC4 biases. The Pmin MAE for initial hurricanes was also smaller in CO4, although this did not hold for the full sample.
For Vmax, the results were more distinct. The initial ECMWF Vmax was biased weak by ∼15 kt. The forecast bias for EC4, while still weak, was 6–8 kt (>30%) lower than that for EC9 after 48 h. Unlike for Pmin, their respective Vmax MAEs were substantially different, with a 3–6-kt reduction in EC4, suggesting that model resolution plays a larger role in predicting Vmax compared with Pmin. For CO4, in which the initial Vmax bias was small by design (for TCs ≥ 55 kt), the forecasts maintained a remarkably small bias of ≤5 kt. However, only minimal statistical differences between the CO4 and EC4 MAEs were found for ≥36-h forecasts. Most of the large negative Vmax errors in CO4 were for TCs undergoing RI, with secondary contributions from landfalling cases. Several factors may contribute to the limited intensification of the TC, including the lack of a secondary circulation in the initialization, and these issues are under investigation. For the cases with large positive Vmax errors, the TCs were relatively large in size, and CO4 had greater difficulty in weakening them than EC4.
The CO4 pressure–wind relationship was closest to that of the best-track verification. EC4 was distinctly closer to the verification than EC9 for Vmax of >50 kt.
For RMW, the initial EC9 and EC4 values were biased too large by ∼30 km. Their respective forecasts yielded similar distributions, with tails of large RMWs corresponding to weaker tropical storms or large TCs gaining latitude. The higher resolution resulted in a slightly lower RMW bias, although this did not translate to statistical improvements. The ECMWF forecasts, especially at 4 km, produced compact eyewalls in several cases, but did not sufficiently contract the eyewall in many others. ECMWF is currently investigating eyewall contractions on experimental global grids of <4-km spacing. Most CO4 predictions of RMW were less than 60 km, consistent with the verifying values, with minimal biases. The MAE in CO4 was significantly smaller than in EC4 in most cases, likely as a result of more realistic initial TCs combined with better modeling of eyewall processes.
One additional experiment demonstrated that EC9 with a reduced drag coefficient Cd at high wind speeds produced lower biases than EC9-NoDragCap for stronger TCs. The larger Cd in the old formulation resulted in an unrealistically strong coupling between the low-level winds and the surface, thereby extracting too much momentum from the wind. The new Cd as a function of surface wind speed at ECMWF is very similar to the independently developed COAMPS-TC counterpart for wind speeds of >30 m s−1.
A second additional experiment, EC4-Explicit, yielded TCs that were unrealistically intense. The lack of the parameterization created an abnormally strong mid–upper-tropospheric condensational heating, resulting in very intense updrafts and downdrafts, and stronger wind and vorticity structures. This result suggests that the parameterization of deep convection is necessary in the current ECMWF model framework to cap the convection and its associated inner-core warming, even if its grid spacing is reduced to 4 km. The seemingly robust EC4-Explicit pressure–wind relationship is a result of compensating biases. In contrast to ECMWF, the COAMPS-TC system performs well with explicit deep convection (not shown here). We note that it is difficult to conclude from studies such as this one whether explicit convection is beneficial in a certain NWP framework by comparing it with another NWP framework.
Our results reinforce the message from NOAA’s High-Resolution Hurricane Forecast Test (NOAA 2009) that increasing the resolution will not by itself improve TC forecasts. In addition to the physics package, the forecasts also depend on the initialization of the TC structure, with ECMWF and COAMPS-TC using opposite philosophies. For strong TCs (≥55 kt), COAMPS-TC constructs a vortex based on Vmax and RMW values supplied by forecasters, resulting in lower biases that carry through to 5 days. ECMWF does not use this information, instead relying on its 4D-Var assimilation to make incremental changes to the TC structure (Bonavita et al. 2017).
The package of physics schemes in regional TC models such as COAMPS-TC has been advanced with the specific goal of improving TC intensity forecasts. We emphasize the need to model and analyze the interplay between physical processes across multiple schemes, where the modification of one element (e.g., parameterized vs explicit deep convection) depends on the relationships prescribed between the other schemes. Given ECMWF’s need to be accountable across a range of global metrics, its physics (and initialization) packages are not tuned specifically for TCs. It remains debatable whether the inclusion of TC-specific packages will improve global TC predictions without degrading atmospheric predictions outside the TC. Nevertheless, the lessons learned from the TC-specific physics schemes and their interplay are expected to help improve global model performance as the resolution increases. One example is the PBL scheme, which is expected to be suboptimal in global models since the PBL structure is very different in TCs (e.g., Zhang et al. 2012, 2015, 2018). The mixing lengths may not be valid for TCs, and errors in vertical diffusion may occur. A recent study by Chen et al. (2022) has demonstrated the importance of tuning the PBL scheme to better capture the intensity evolution, in their case by modifying a turbulent kinetic energy–based eddy diffusivity mass flux scheme. We also note that the ECMWF model remains hydrostatic. Given that vertical accelerations and deep convection are intricately related, nonhydrostatic effects are expected to become important in high-resolution simulations of convective systems. When large heating rates occur, a nonhydrostatic model is expected to yield lower vertical velocities. Accordingly, regional TC models such as COAMPS-TC and HWRF are nonhydrostatic, and global predictions of TCs in nonhydrostatic models have been evaluated (Judt et al. 2021). At ECMWF, although nonhydrostatic model testing and evaluation are underway, nonhydrostatic effects have been found so far to be negligible, even on a 3-km grid (Zeman et al. 2021).
The COAMPS-TC system has served as a useful benchmark for the ECMWF simulations of comparable resolution, with its lower forecast biases likely due to the initialization and physics packages both being tuned specifically for TCs. As for all regional models, there remains room for improvement, including the need for higher consistency between consecutive model integrations and the accurate capture of intensification processes from initially very weak TCs. Other models can be added for future intercomparison in our framework, such as NOAA’s new Hurricane Analysis and Forecasting System (HAFS; Hazelton et al. 2021, 2022).
Our results suggest the potential for future gains in TC forecasting, once the capability exists for 4-km global models to be run operationally. The data assimilation, a computationally intensive part of NWP, will need to resolve finer scales and exploit observations to correct and sharpen eyewall structures. Improvements to the PBL, surface layer, and atmosphere–ocean wave coupling will benefit TC forecasts; for example, increasing the ocean model resolution is expected to better capture narrow ocean wakes and air–sea interaction processes underneath the eyewall. Nonhydrostatic modeling and the transition to explicit convection with parallel reformulations of the interconnected physics schemes are expected to yield long-term benefits.
Conclusions from evaluation studies are sensitive to the evaluation methods. They vary and can even oppose each other, depending on how the subsamples are stratified by intensity. Reductions in biases also do not guarantee a reduction in MAE. While we have performed quantitative evaluations against surface variables in the NHC best track, our comparisons of the TC structure have only been qualitative. A future goal is to introduce advanced evaluation methods over multiple TCs, including surface wind radii by quadrant, precipitation structures, and comparisons against satellite data. Quantitative evaluations of the vertical structure against aircraft data, including in-flight observations, Doppler radar, and dropsondes, are feasible for composites of TCs (e.g., Hazelton et al. 2022). Examples of structural metrics that have been evaluated include the azimuthal-mean RMW at 2-km altitude, horizontal decay of tangential winds, and sharpness of the azimuthal-mean wind peak (Hazelton et al. 2018); vortex depth, vortex tilt, and eyewall slope (Stern et al. 2014 and previous papers); boundary layer structure and inflow (Zhang et al. 2011, 2012, 2015; Chen et al. 2022); and the warm core (Stern and Zhang 2016). Structural evaluations of the warm core are limited by the small number of dropsonde measurements in the eye due to aircraft altitudes being typically ∼700 hPa or below. Further process-based diagnostics can also be developed, especially if high-frequency online outputs are available beyond the standard operational outputs used in our paper. Diagnostics, such as surface fluxes, temperature and water vapor tendencies, PBL inflow depth, mixing above the boundary layer and in clouds, and inward advection of equivalent potential temperature, will continue to advance developments in global and regional models.
We note that explicit scale awareness is only built in the parameterization of deep convection, which depends largely on the convective available potential energy and moisture convergence. The full, scale-dependent, mass flux equations [e.g., Eq. (3) of Malardel and Bechtold (2019)] are linearized to depend on the horizontal resolution. The empirical fit applies a factor of 0.6 (40% reduction) at 4.5 km with respect to the nominal mass flux at 9 km. No explicit scale awareness is built in the cloud microphysics and the shallow convection, both scaling with the input dynamical and/or turbulent tendencies, while the turbulent tendencies depend on the local surface heat and momentum fluxes as well as on the local Richardson number.
We define the temperature anomaly as the difference between the air temperature and a reference value that is computed as the average temperature within an annulus of 300–700-km radius from the TC center, following Munsell et al. (2017) and Stern and Zhang (2016), and that thermal wind is dependent on the horizontal temperature gradient between the TC center and its environment. Since the COAMPS-TC inner grid does not expand out to 700 km, the reference temperature for EC4 is used for CO4. The difference between these reference temperatures is not expected to exceed 1°C, which is less than 10% of the temperature anomaly values.
We also performed the same evaluations stratified by the verifying-time intensity. While these can be insightful and are occasionally referred to below, the sampling technique is intrinsically biased at longer forecast times. For example, even with an unbiased model, the category that only includes verifying hurricanes will consistently overpredict Pmin and underpredict Vmax on average, purely due to the stratification choice.
Acknowledgments.
Sharanya J. Majumdar gratefully acknowledges support from ONR Grant N00014-20-1-2075 and the University of Miami and ECMWF for jointly supporting a sabbatical year at ECMWF. James D. Doyle gratefully acknowledges support from ONR Grant Program Element 0601153N, TCRI Departmental Research Initiative. We thank Jon Moskaitis for providing the COAMPS-TC fields; Brian McNoldy for providing the graphical wind speed scale and the NEXRAD graphic; and David Richardson, David Nolan, and Andrew Hazelton for their perspectives. The SAR data were obtained online (https://cyclobs.ifremer.fr/app/tropical). Last, we thank three anonymous reviewers, whose comments and suggestions substantially improved the paper.
Data availability statement.
The ECMWF model fields are available from the ECMWF MARS. COAMPS-TC data are available upon request. The evaluation software is available from the first author by request.
APPENDIX
Reduction of the ECMWF Surface Drag for High Winds
This section describes past and ongoing work at ECMWF aimed at providing more realistic outputs of the surface drag in high wind regimes.
The ECMWF forecast system has been coupled to a wave model since 1998. In this framework, the surface roughness over the ocean is specified using a sea-state-dependent Charnock parameter that is updated by the wave model (Janssen 1991). The Charnock relation links the surface aerodynamic roughness length to the surface stress, and because of the quasi-linear nature of the Janssen approach, more momentum was extracted from the wind when the sea state was growing. Therefore, the drag coefficient Cd over the ocean tended to increase with wind speed, in line with findings from earlier observation campaigns (Edson et al. 2013). However, it later became accepted that Cd should generally attain maximum values for winds exceeding ∼20 m s−1 but should level off or even decrease for very strong winds >30 m s−1 in TCs or intense midlatitude windstorms (Holthuijsen et al. 2012). The physical processes that might be responsible remain a matter of active research, but ultimately, there is a decoupling between the low-level winds and the surface for strong wind situations (flow separation, spray generation, and wave dissipative effects absent at lower wind conditions, impact of heavy rain), all of which would reduce the ability of the wave fields to gain momentum.
In addressing the need to reduce Cd for high winds, the wave spectrum in the ECMWF wave model was found to contain unphysically steep waves under hurricane conditions. A maximum steepness limit was introduced, resulting in reduced drag for high winds (Magnusson et al. 2019). This work was followed by a revised parameterization for wind input and whitecap dissipation based on Ardhuin et al. (2010). In this approach, the wind input was still modeled using Janssen’s work, except that an ad hoc parameterization of the sheltering by long waves of shorter waves that limited their ability to extract momentum was introduced and controlled with a tunable sheltering coefficient. This version was introduced into ECMWF operations. Under normal wind conditions, the average Cd was ensured to still be in agreement with Edson et al. (2013). For high winds, the drag was reduced but was still found to be too large.
As a next step, based on the work of Donelan (2018), it was suggested that Cd should be sharply reduced for winds above 33 m s−1. Noting that other operational systems were already imposing a Cd in line with Donelan’s work, ECMWF modified Janssen’s formulation to impose a sharp reduction of the parameterized contribution of the short gravity–capillary waves to the overall Charnock parameter for winds above 33 m s−1, resulting in the Cd illustrated in Fig. 1. The idea is that a strong decoupling between the winds and the short waves is occurring for those conditions. The new model yielded a better pressure–wind relation (Bidlot et al. 2020).
Ongoing work at ECMWF seeks to extend the current model with a simplified model for the impact of the short gravity–capillary waves on the overall stress (Janssen and Bidlot 2023) and allow for an extension of the theory to account for nonlinear feedback on the growth rate of the waves by wind. With this extension, the rapid decrease of Cd for strong winds can be captured, as the short gravity–capillary waves are less able to take in momentum from the wind, as hypothesized with the aforementioned simple reduction scheme. This starts to be the case for storm conditions (wind speed > 20 m s−1) well before the threshold of 33 m s−1 of the simple reduction scheme. At the same time as the sea state grows and larger and longer waves appear, the growth rate of the waves is reduced, essentially sheltering further growth. With this new development, it will no longer be necessary to add this ad hoc sheltering effect that was introduced in Ardhuin et al. (2010).
REFERENCES
Alaka, G. J., Jr., X. Zhang, and S. G. Gopalakrishnan, 2022: High-definition hurricanes: Improving forecasts with storm-following nests. Bull. Amer. Meteor. Soc., 103, E680–E703, https://doi.org/10.1175/BAMS-D-20-0134.1.
Ardhuin, F., and Coauthors, 2010: Semiempirical dissipation source functions for ocean waves. Part I: Definition, calibration, and validation. J. Phys. Oceanogr., 40, 1917–1941, https://doi.org/10.1175/2010JPO4324.1.
Bao, J.-W., S. G. Gopalakrishnan, S. A. Michelson, F. D. Marks, and M. T. Montgomery, 2012: Impact of physics representations in the HWRFX on simulated hurricane structure and pressure–wind relationships. Mon. Wea. Rev., 140, 3278–3299, https://doi.org/10.1175/MWR-D-11-00332.1.
Bechtold, P., M. Köhler, T. Jung, F. Doblas-Reyes, M. Leutbecher, M. J. Rodwell, F. Vitart, and G. Balsamo, 2008: Advances in simulating atmospheric variability with the ECMWF model: From synoptic to decadal time-scales. Quart. J. Roy. Meteor. Soc., 134, 1337–1351, https://doi.org/10.1002/qj.289.
Bechtold, P., N. Semane, P. Lopez, J.-P. Chaboureau, A. Beljaars, and N. Bormann, 2014: Representing equilibrium and non-equilibrium convection in large-scale models. J. Atmos. Sci., 71, 734–753, https://doi.org/10.1175/JAS-D-13-0163.1.
Bechtold, P., R. Forbes, I. Sandu, S. Lang, and M. Ahlgrimm, 2020: A major moist physics upgrade for the IFS. ECMWF Newsletter, No. 164, ECMWF, Reading, United Kingdom, 24–32, https://www.ecmwf.int/en/elibrary/19720-major-moist-physics-upgrade-ifs.
Becker, T., P. Bechtold, and I. Sandu, 2021: Characteristics of convective precipitation over tropical Africa in storm-resolving global simulations. Quart. J. Roy. Meteor. Soc., 147, 4388–4407, https://doi.org/10.1002/qj.4185.
Bidlot, J.-R., F. Prates, R. Ribas, A. Mueller-Quintino, M. Crepulja, and F. Vitart, 2020: Enhancing tropical cyclone wind forecasts. ECMWF Newsletter, No. 164, ECMWF, Reading, United Kingdom, 33–37, https://www.ecmwf.int/en/elibrary/81182-enhancing-tropical-cyclone-wind-forecasts.
Bonavita, M., L. Isaksen, and E. Hólm, 2012: On the use of EDA background error variances in the ECMWF 4D-Var. Quart. J. Roy. Meteor. Soc., 138, 1540–1559, https://doi.org/10.1002/qj.1899.
Bonavita, M., and Coauthors, 2017: On the initialization of tropical cyclones. ECMWF Tech. Memo. 810, 39 pp., https://www.ecmwf.int/en/elibrary/17677-initialization-tropical-cyclones.
Breivik, Ø., K. Mogensen, J.-R. Bidlot, M. A. Balmaseda, and P. A. E. M. Janssen, 2015: Surface wave effects in the NEMO ocean model: Forced and coupled experiments. J. Geophys. Res. Oceans, 120, 2973–2992, https://doi.org/10.1002/2014JC010565.
Cangialosi, J. P., E. Blake, M. DeMaria, A. Penny, A. Latto, E. N. Rappaport, and V. Tallapragada, 2020: Recent progress in tropical cyclone intensity forecasting at the National Hurricane Center. Wea. Forecasting, 35, 1913–1922, https://doi.org/10.1175/WAF-D-20-0059.1.
Chen, X., G. H. Bryan, A. Hazelton, F. D. Marks, and P. Fitzpatrick, 2022: Evaluation and improvement of a TKE-based eddy-diffusivity mass-flux (EDMF) planetary boundary layer scheme in hurricane conditions. Wea. Forecasting, 37, 935–951, https://doi.org/10.1175/WAF-D-21-0168.1.
Combot, C., A. Mouche, J. Knaff, Y. Zhao, Y. Zhao, L. Vinour, Y. Quilfen, and B. Chapron, 2020: Extensive high-resolution synthetic aperture radar (SAR) data analysis of tropical cyclones: Comparisons with SFMR flights and best track. Mon. Wea. Rev., 148, 4545–4563, https://doi.org/10.1175/MWR-D-20-0005.1.
Davis, C., W. Wang, J. Dudhia, and R. Torn, 2010: Does increased horizontal resolution improve hurricane wind forecasts? Wea. Forecasting, 25, 1826–1841, https://doi.org/10.1175/2010WAF2222423.1.
Donelan, M. A., 2018: On the decrease of the oceanic drag coefficient in high winds. J. Geophys. Res. Oceans, 123, 1485–1501, https://doi.org/10.1002/2017JC013394.
Donelan, M. A., B. K. Haus, N. Reul, W. J. Plant, M. Stiassnie, H. C. Graber, O. B. Brown, and E. S. Saltzman, 2004: On the limiting aerodynamic roughness of the ocean in very strong winds. Geophys. Res. Lett., 31, L18306, https://doi.org/10.1029/2004GL019460.
Doyle, J. D., and Coauthors, 2012: Real-time tropical cyclone prediction using COAMPS-TC. Advances in Geosciences, Vol. 28, C.-C. Wu and J. Gan, Eds., World Scientific, 15–28, https://doi.org/10.1142/9789814405683_0002.
Doyle, J. D., and Coauthors, 2014: Tropical cyclone prediction using COAMPS-TC. Oceanography, 27, 104–115, https://doi.org/10.5670/oceanog.2014.72.
Doyle, J. D., and Coauthors, 2017: A view of tropical cyclones from above: The Tropical Cyclone Intensity (TCI) experiment. Bull. Amer. Meteor. Soc., 98, 2113–2134, https://doi.org/10.1175/BAMS-D-16-0055.1.
ECMWF, 2020: Summary of cycle 47r1. European Centre for Medium-Range Weather Forecasts, https://www.ecmwf.int/en/forecasts/about-our-forecasts/evolution-ifs/cycles/summary-cycle-47r1.
Edson, J. B., and Coauthors, 2013: On the exchange of momentum over the open ocean. J. Phys. Oceanogr., 43, 1589–1610, https://doi.org/10.1175/JPO-D-12-0173.1.
Emanuel, K. A., 1986: An air–sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585–605, https://doi.org/10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.
Fairall, C. W., E. F. Bradley, J. E. Hare, A. A. Grachev, and J. B. Edson, 2003: Bulk parameterization of air–sea fluxes: Updates and verification for the COARE algorithm. J. Climate, 16, 571–591, https://doi.org/10.1175/1520-0442(2003)016<0571:BPOASF>2.0.CO;2.
Forbes, R. M., and M. Ahlgrimm, 2014: On the representation of high-latitude boundary layer mixed-phase cloud in the ECMWF global model. Mon. Wea. Rev., 142, 3425–3445, https://doi.org/10.1175/MWR-D-13-00325.1.
Gall, R., J. Franklin, F. Marks, E. N. Rappaport, and F. Toepfer, 2013: The Hurricane Forecast Improvement Project. Bull. Amer. Meteor. Soc., 94, 329–343, https://doi.org/10.1175/BAMS-D-12-00071.1.
Gopalakrishnan, S., and Coauthors, 2020: 2019 HFIP R&D activities summary: Recent results and operational implementation. NOAA HFIP Tech. Rep. HFIP2020-1, 42 pp., https://repository.library.noaa.gov/view/noaa/26468.
Hazelton, A., L. Harris, and S.-J. Lin, 2018: Evaluation of tropical cyclone structure forecasts in a high-resolution version of the multiscale GFDL fvGFS model. Wea. Forecasting, 33, 419–442, https://doi.org/10.1175/WAF-D-17-0140.1.
Hazelton, A., X. Zhang, S. Gopalakrishnan, W. Ramstrom, F. Marks, and J. A. Zhang, 2020: High-resolution ensemble HFV3 forecasts of Hurricane Michael (2018): Rapid intensification in shear. Mon. Wea. Rev., 148, 2009–2032, https://doi.org/10.1175/MWR-D-19-0275.1.
Hazelton, A., and Coauthors, 2021: 2019 Atlantic hurricane forecasts from the global-nested Hurricane Analysis and Forecast System: Composite statistics and key events. Wea. Forecasting, 36, 519–538, https://doi.org/10.1175/WAF-D-20-0044.1.
Hazelton, A., J. A. Zhang, and S. Gopalakrishnan, 2022: Comparison of the performance of the observation-based hybrid EDMF and EDMF-TKE PBL schemes in 2020 tropical cyclone forecasts from the global-nested Hurricane Analysis and Forecast System. Wea. Forecasting, 37, 457–476, https://doi.org/10.1175/WAF-D-21-0124.1.
Heming, J. T., 2016: Met office unified model tropical cyclone performance following major changes to the initialization scheme and a model upgrade. Wea. Forecasting, 31, 1433–1449, https://doi.org/10.1175/WAF-D-16-0040.1.
Holthuijsen, L. H., M. D. Powell, and J. D. Pietrzak, 2012: Wind and waves in extreme hurricanes. J. Geophys. Res., 117, C09003, https://doi.org/10.1029/2012JC007983.
Janssen, P. A. E. M., 1991: Quasi-linear theory of wind-wave generation applied to wave forecasting. J. Phys. Oceanogr., 21, 1631–1642, https://doi.org/10.1175/1520-0485(1991)021<1631:QLTOWW>2.0.CO;2.
Janssen, P. A. E. M., and J.-R. Bidlot, 2023: Wind-wave interaction for strong winds. J. Phys. Oceanogr., 53, 779–804, https://doi.org/10.1175/JPO-D-21-0293.1.
Judt, F., and Coauthors, 2021: Tropical cyclones in global storm-resolving models. J. Meteor. Soc. Japan, 99, 579–602, https://doi.org/10.2151/jmsj.2021-029.
Kain, J. S., and J. M. Fritsch, 1993: Convective parameterization for mesoscale models: The Kain–Fritsch scheme. The Representation of Cumulus Convection in Numerical Models, Meteor. Monogr., No. 46, Amer. Meteor. Soc., 165–170.
Kleist, D. T., 2011: Assimilation of tropical cyclone advisory minimum sea level pressure in the NCEP Global Data Assimilation System. Wea. Forecasting, 26, 1085–1091, https://doi.org/10.1175/WAF-D-11-00045.1.
Komaromi, W. A., P. A. Reinecke, J. D. Doyle, and J. R. Moskaitis, 2021: The Naval Research Laboratory’s Coupled Ocean–Atmosphere Mesoscale Prediction System–Tropical Cyclone Ensemble (COAMPS-TC Ensemble). Wea. Forecasting, 36, 499–517, https://doi.org/10.1175/WAF-D-20-0038.1.
Li, D., J. Staneva, J.-R. Bidlot, S. Grayek, Y. Zhu, and B. Yin, 2021: Improving regional model skills during typhoon events: A case study for Super Typhoon Lingling over the northwest Pacific Ocean. Front. Mar. Sci., 8, 613913, https://doi.org/10.3389/fmars.2021.613913.
Lin, Y.-L., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 1065–1092, https://doi.org/10.1175/1520-0450(1983)022<1065:BPOTSF>2.0.CO;2.
Magnusson, L., and Coauthors, 2019: ECMWF activities for improved hurricane forecasts. Bull. Amer. Meteor. Soc., 100, 445–458, https://doi.org/10.1175/BAMS-D-18-0044.1.
Magnusson, L., and Coauthors, 2021: Tropical cyclone activities at ECMWF. ECMWF Tech. Memo. 888, 138 pp., https://www.ecmwf.int/en/elibrary/20228-tropical-cyclone-activities-ecmwf.
Magnusson, L., and Coauthors, 2022: Skill of medium-range forecast models using the same initial conditions. Bull. Amer. Meteor. Soc., 103, E2050–E2068, https://doi.org/10.1175/BAMS-D-21-0234.1.
Malardel, S., and P. Bechtold, 2019: The coupling of deep convection with the resolved flow via the divergence of mass flux in the IFS. Quart. J. Roy. Meteor. Soc., 145, 1832–1845, https://doi.org/10.1002/qj.3528.
Mellor, G. L., and T. Yamada, 1982: Development of a turbulent closure model for geophysical fluid problems. Rev. Geophys., 20, 851–875, https://doi.org/10.1029/RG020i004p00851.
Mogensen, K. S., L. Magnusson, and J.-R. Bidlot, 2017: Tropical cyclone sensitivity to ocean coupling in the ECMWF coupled model. J. Geophys. Res. Oceans, 122, 4392–4412, https://doi.org/10.1002/2017JC012753.
Mouche, A., B. Chapron, J. Knaff, Y. Zhao, B. Zhang, and C. Combot, 2019: Copolarized and cross-polarized SAR measurements for high-resolution description of major hurricane wind structures: Application to Irma category 5 hurricane. J. Geophys. Res. Oceans, 124, 3905–3922, https://doi.org/10.1029/2019JC015056.
Munsell, E. B., F. Zhang, J. A. Sippel, S. A. Braun, and Y. Weng, 2017: Dynamics and predictability of the intensification of Hurricane Edouard (2014). J. Atmos. Sci., 74, 573–595, https://doi.org/10.1175/JAS-D-16-0018.1.
NOAA, 2009: High-resolution hurricane forecast test. NOAA Hurricane Forecast Improvement Project Final Rep., 95 pp., https://dtcenter.ucar.edu/plots/hrh_test/HRH_Report_30Sept.pdf.
Powell, M. D., P. J. Vickery, and T. A. Reinhold, 2003: Reduced drag coefficient for high wind speeds in tropical cyclones. Nature, 422, 279–283, https://doi.org/10.1038/nature01481.
Rabier, F., H. Jarvinen, E. Klinker, J.-F. Mafhouf, and A. Simmons, 2000: The ECMWF operational implementation of four-dimensional variational assimilation. I: Experimental results with simplified physics. Quart. J. Roy. Meteor. Soc., 126, 1143–1170, https://doi.org/10.1002/qj.49712656415.
Sleigh, M., P. Browne, C. Burrows, M. Leutbecher, T. Haiden, and D. Richardson, 2020: IFS upgrade greatly improves forecasts in the stratosphere. ECMWF Newsletter, No. 164, ECMWF, Reading, United Kingdom, 18–23, https://www.ecmwf.int/en/elibrary/81185-ifs-upgrade-greatly-improves-forecasts-stratosphere.
Stern, D. P., and F. Zhang, 2016: The warm-core structure of Hurricane Earl (2010). J. Atmos. Sci., 73, 3305–3328, https://doi.org/10.1175/JAS-D-15-0328.1.
Stern, D. P., J. R. Brisbois, and D. S. Nolan, 2014: An expanded dataset of hurricane eyewall sizes and slopes. J. Atmos. Sci., 71, 2747–2762, https://doi.org/10.1175/JAS-D-13-0302.1.
Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Mon. Wea. Rev., 117, 1779–1800, https://doi.org/10.1175/1520-0493(1989)117<1779:ACMFSF>2.0.CO;2.
Tiedtke, M., 1993: Representation of clouds in large-scale models. Mon. Wea. Rev., 121, 3040–3061, https://doi.org/10.1175/1520-0493(1993)121<3040:ROCILS>2.0.CO;2.
Vukicevic, T., E. Uhlhorn, P. Reasor, and B. Klotz, 2014: A novel multiscale intensity metric for evaluation of tropical cyclone intensity forecasts. J. Atmos. Sci., 71, 1292–1304, https://doi.org/10.1175/JAS-D-13-0153.1.
Willoughby, H. E., 1990: Gradient balance in tropical cyclones. J. Atmos. Sci., 47, 265–274, https://doi.org/10.1175/1520-0469(1990)047<0265:GBITC>2.0.CO;2.
Willoughby, H. E., R. W. R. Darling, and M. E. Rahn, 2006: Parametric representation of the primary hurricane vortex. Part II: A new family of sectionally continuous profiles. Mon. Wea. Rev., 134, 1102–1120, https://doi.org/10.1175/MWR3106.1.
Zeman, C., N. P. Wedi, P. D. Deuben, N. Ban, and C. Schär, 2021: Model intercomparison of COSMO 5.0 and IFS 45r1 at kilometer-scale grid spacing. Geosci. Model Dev., 14, 4617–4639, https://doi.org/10.5194/gmd-14-4617-2021.
Zhang, J. A., F. D. Marks, M. T. Montgomery, and S. Lorsolo, 2011: An estimation of turbulent characteristics in the low-level region of intense Hurricanes Allen (1980) and Hugo (1989). Mon. Wea. Rev., 139, 1447–1462, https://doi.org/10.1175/2010MWR3435.1.
Zhang, J. A., S. Gopalakrishnan, F. D. Marks, R. F. Rogers, and V. Tallapragada, 2012: A developmental framework for improving hurricane model physical parameterizations using aircraft observations. Trop. Cyclone Res. Rev., 1, 419–429, https://doi.org/10.6057/2012TCRR04.01.
Zhang, J. A., D. S. Nolan, R. F. Rogers, and V. Tallapragada, 2015: Evaluating the impact of improvements in the boundary layer parameterization on hurricane intensity and structure forecasts in HWRF. Mon. Wea. Rev., 143, 3136–3155, https://doi.org/10.1175/MWR-D-14-00339.1.
Zhang, J. A., F. D. Marks, J. A. Sippel, R. F. Rogers, X. Zhang, S. G. Gopalakrishnan, Z. Zhang, and V. Tallapragada, 2018: Evaluating the impact of improvement in the horizontal diffusion parameterization on hurricane prediction in the operational Hurricane Weather Research and Forecast (HWRF) model. Wea. Forecasting, 33, 317–329, https://doi.org/10.1175/WAF-D-17-0097.1.