Evaluation of WRF Simulation of Deep Convection in the U.S. Southern Great Plains

S. C. Pryor aDepartment of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York

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F. Letson aDepartment of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York

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T. Shepherd aDepartment of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York

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R. J. Barthelmie bSibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York

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Abstract

The Southern Great Plains (SGP) region exhibits a relatively high frequency of periods with extremely high rainfall rates (RR) and hail. Seven months of 2017 are simulated using the Weather Research and Forecasting (WRF) Model applied at convection-permitting resolution with the Milbrandt–Yau microphysics scheme. Simulation fidelity is evaluated, particularly during intense convective events, using data from ASOS stations, dual-polarization radar, and gridded datasets and observations at the DOE Atmospheric Radiation Measurement site. The spatial gradients and temporal variability of precipitation and the cumulative density functions for both RR and wind speeds exhibit fidelity. Odds ratios > 1 indicate that WRF is also skillful in simulating high composite reflectivity (cREF, used as a measure of widespread convection) and RR > 5 mm h−1 over the domain. Detailed analyses of the 10 days with highest spatial coverage of cREF > 30 dBZ show spatially similar reflectivity fields and high RR in both radar data and WRF simulations. However, during periods of high reflectivity, WRF exhibits a positive bias in terms of very high RR (>25 mm h−1) and hail occurrence, and during the summer and transition months, maximum hail size is underestimated. For some renewable energy applications, fidelity is required with respect to the joint probabilities of wind speed and RR and/or hail. While partial fidelity is achieved for the marginal probabilities, performance during events of critical importance to these energy applications is currently not sufficient. Further research into optimal WRF configurations in support of potential damage quantification for these applications is warranted.

Significance Statement

Heavy rainfall and hail during convective events are challenging for numerical models to simulate in both space and time. For some applications, such as to estimate damage to wind turbine blades and solar panels, fidelity is also required with respect to hail size and joint probabilities of wind speed and hydrometeor type and rainfall rates (RR). This demands fidelity that is seldom evaluated. We show that, although this simulation exhibits fidelity for the marginal probabilities of wind speed, RR, and hail occurrence, the joint probabilities of these properties and the simulation of maximum size of hail are, as yet, not sufficient to characterize potential damage to these renewable energy industries.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: S. C. Pryor, sp2279@cornell.edu

Abstract

The Southern Great Plains (SGP) region exhibits a relatively high frequency of periods with extremely high rainfall rates (RR) and hail. Seven months of 2017 are simulated using the Weather Research and Forecasting (WRF) Model applied at convection-permitting resolution with the Milbrandt–Yau microphysics scheme. Simulation fidelity is evaluated, particularly during intense convective events, using data from ASOS stations, dual-polarization radar, and gridded datasets and observations at the DOE Atmospheric Radiation Measurement site. The spatial gradients and temporal variability of precipitation and the cumulative density functions for both RR and wind speeds exhibit fidelity. Odds ratios > 1 indicate that WRF is also skillful in simulating high composite reflectivity (cREF, used as a measure of widespread convection) and RR > 5 mm h−1 over the domain. Detailed analyses of the 10 days with highest spatial coverage of cREF > 30 dBZ show spatially similar reflectivity fields and high RR in both radar data and WRF simulations. However, during periods of high reflectivity, WRF exhibits a positive bias in terms of very high RR (>25 mm h−1) and hail occurrence, and during the summer and transition months, maximum hail size is underestimated. For some renewable energy applications, fidelity is required with respect to the joint probabilities of wind speed and RR and/or hail. While partial fidelity is achieved for the marginal probabilities, performance during events of critical importance to these energy applications is currently not sufficient. Further research into optimal WRF configurations in support of potential damage quantification for these applications is warranted.

Significance Statement

Heavy rainfall and hail during convective events are challenging for numerical models to simulate in both space and time. For some applications, such as to estimate damage to wind turbine blades and solar panels, fidelity is also required with respect to hail size and joint probabilities of wind speed and hydrometeor type and rainfall rates (RR). This demands fidelity that is seldom evaluated. We show that, although this simulation exhibits fidelity for the marginal probabilities of wind speed, RR, and hail occurrence, the joint probabilities of these properties and the simulation of maximum size of hail are, as yet, not sufficient to characterize potential damage to these renewable energy industries.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: S. C. Pryor, sp2279@cornell.edu

1. Introduction

Organized convection is a major contributor to annual total precipitation and a source of very high rainfall rates (RR), hail, and high wind gusts over the Southern Great Plains (SGP) of the United States (Fig. 1). Indeed, mesoscale convective systems (MCSs) contribute 30%–70% of precipitation received during the warm season (defined as April to September) over a region extending from the Rocky Mountains east to the Mississippi River (Feng et al. 2019; Fritsch et al. 1986). The total accumulated precipitation from mesoscale organized convection during the 1982 warm season exceeded 30 cm over a vast swath of northeastern Texas and eastern Oklahoma and thus contributed nearly 50% of total annual precipitation (Fritsch et al. 1986). A more recent analysis has shown MCSs generate 30%–70% of warm-season precipitation and up to one-half of annual total precipitation over most of Texas and Oklahoma (Feng et al. 2021). Within the SGP, MCSs are most frequent in spring and are closely connected to the large-scale circulation (Yang et al. 2017). MCSs during the spring and autumn “commonly initiate under strong baroclinic forcing and favorable thermodynamic environments” and “feature both large and deep convection, with a large stratiform rain area and high volume of rainfall” (Feng et al. 2019). Conversely, summer (June–August) “MCSs often initiate under weak baroclinic forcing, featuring a high-pressure ridge with weak low-level convergence acting on the warm, humid air associated with the low-level jet” (Feng et al. 2019).

Fig. 1.
Fig. 1.

(a) Mean annual frequency of lightning strikes (2002–14) from the NLDN (Rudlosky and Fuelberg 2010) mapped to 12-km resolution. Also shown is the annual frequency of hail days derived from GPM data from 2014 to 2022 (contours). Note that these data have a spatial resolution of 2°. (b) Mean annual frequency (2005–21) of hailstorms and thunderstorms by state from the NOAA Storm Reports (red shading). Also shown are the state-by-state IC of wind energy (cyan) and solar (black; top 10 states only) as of the end of 2020 (American Clean Power 2021). The area of each dot is proportional to IC. Wind and solar installed capacities in Texas at the end of 2020 were 5.3 (solar) and 33 (wind) GW. The light-gray boxes indicate the Southern Great Plains and three domains used in the simulations with the WRF Model presented herein (see details in Fig. 2).

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

Over the continental United States, hail damage produces approximately 60% of total annual property loss caused by severe weather (Murillo and Homeyer 2019). Both observations (e.g., estimates from the Global Precipitation Mission; Bang and Cecil 2019; Fig. 1a) and simulations indicate that severe hail occurs in the SGP on approximately 5% of all days (Prein and Holland 2018; Trapp et al. 2019). According to one prior study, parts of Oklahoma and Texas experience an average of one severe hail day per year, which is defined as a day with maximum estimated size of hail (MESH) above 29 mm (Cintineo et al. 2012). The U.S. National Oceanic and Atmospheric Administration (NOAA) documents “the occurrence of storms and other significant weather phenomena having sufficient intensity to cause loss of life, injuries, significant property damage, and/or disruption to commerce” at the county level in the NOAA Storm Events Database (https://www.ncdc.noaa.gov/stormevents/). According to data from the associated NOAA Storm Reports for 2005–21, an average of over 2000 events described as “thunderstorms” or “hailstorms” occur in Texas per year (Fig. 1b).

The fidelity with which numerical models reproduce organized convection and associated hydrometeors remains comparatively poor even when regional models are applied at convection-permitting spatial scales (Scaff et al. 2020). Model fidelity is challenged by factors such as the complexity of cloud microphysics processes (Morrison et al. 2020; Tao et al. 2016) and strong, nonlinear atmosphere–surface coupling (Dai et al. 2021; Feng et al. 2018). Hail occurrence, number concentration, and diameter are particularly challenging to simulate (Adams-Selin et al. 2019; Gagne et al. 2017; Snook et al. 2016). This is in part because hail production and indeed the environmental conditions responsible for hail generation and hail fall are still incompletely understood (Davenport 2021; Kumjian and Lombardo 2020). For example, even the 1D WRF-HAILCAST model, in which hail diameter is projected from modeled cloud liquid- and solid-phase water and vertical velocities, only achieved forecasts of hail sizes within 12 mm of measurements two-thirds of the time (Adams-Selin and Ziegler 2016).

Observational evidence suggests that the generation of cold pools caused in part by downdrafts’ transport of cold, dry air from the middle troposphere toward the surface tends to be associated with precipitation rates > 2 mm h−1 and is key to the organization of multicell convection (Schlemmer and Hohenegger 2014). Numerical simulations indicate a strong positive association between the updraft and downdraft area and cold-pool vertical extent and intensity (Marion and Trapp 2019), and that the ability of cold pools to initiate development of further convective cells and organize convection is critically dependent on the cold-pool depth and advection speed (Haerter et al. 2019). Previous research focused on the SGP has found that the areal extent of stratiform precipitation associated with midlatitude deep convection tends to be underestimated in convection-permitting model simulations (i.e., with a grid spacing Δx = 1 km) performed with a wide array of microphysics schemes (Han et al. 2019). Conversely, simulations tend to produce excessively intense updraft velocities and too wide an area of high composite reflectivity (cREF > 45 dBZ; Fan et al. 2017). Numerical simulation of precipitation, advection speeds, cold-pool characteristics, and cloud properties associated with convective systems are substantially improved by use of so-called convection-permitting grid spacing and thus a decrease of Δx from 12 to 4 km (Prein et al. 2021). MCS updraft and downdraft widths were smaller, the updraft depth was shallower, and the median updraft and downdraft velocities were slightly lower in simulations with Δx = 1 km, relative to those with Δx = 4 km (Prein et al. 2021). Decreasing Δx from 4 km in simulations of MCSs led to improved representation of the updraft and downdraft properties relative to radar wind profiler observations in the SGP (Wang et al. 2020). Idealized simulations of individual thunderstorms also indicate that grid spacing of 1 km led to improved representation of deep convective structures relative to simulations at 2 km (Verrelle et al. 2015). Additional previous research found MCS simulation fidelity is enhanced by use of Δx = 1 km rather than 3 km due largely to better representation of the cold pool (Squitieri and Gallus 2020). Based on this research, a grid spacing of 1.3 km is used here in the innermost simulation domain.

There are clear societal needs with regard to high-fidelity short-term forecasts and climate-scale simulations of deep convection and the associated hazards. Specific to the SGP, Dallas–Fort Worth, Texas, suffered $800 million in hail damage in a single event in 2011 (Brown et al. 2015), and another event in May 1995 caused $2 billion of damage and 109 injuries (Edwards and Thompson 1998). The SGP is also characterized by large wind and solar resources and deployments (Figs. 1 and 2). Both exhibit vulnerability to damage from extremely heavy rainfall and hailstones associated with deep convection (Letson et al. 2020a,b; Makarskas et al. 2021). With respect to solar panels and both residential and commercial properties, the primary source of damage derives from kinetic energy transfer during hailstone impacts. Hence, the hydroclimatic parameters of interest are the hailstone diameter, mass, terminal fall velocity υt, and number (Brown et al. 2015; Makarskas et al. 2021). For wind turbines, the damage is manifest as roughening of the wind turbine blade leading edge. This leading-edge erosion (LEE) is also, to the first order, the result of material stresses caused by kinetic energy transfer from falling hydrometeors. In this case, however, the closing velocity is dictated by both the hydrometeor υt and the blade rotational speed. The linear speed of the blade tip is zero at wind speeds below cut-in (when the wind turbine begins to generate electrical power), rises rapidly as wind speed increases, and then is constant at wind speeds above those where power output is equal to the rated capacity of the wind turbine (Fig. 3). Hydrometeor υt is lower than the wind turbine tip speed and thus plays a secondary, but important, role and is dictated by the diameter, phase, and density (Fig. 3). The number of hydrometeors, mass, and phase are complex functions of cloud microphysics and environmental thermodynamics. The number density of larger, more massive droplets with higher υt increases rapidly with RR (Fig. 3).

Fig. 2.
Fig. 2.

(a) Topography in the simulation domains and location of wind turbines based on the USGS wind turbine database (Hoen et al. 2018), updated as of April 2022. (b) Locations of NWS ASOS and dual-polarization Doppler radar in domain d03 and the DOE ARM site at Lamont. Also shown are the four subregions—NW, NE, SW, and SE—that are used to examine the spatial variability in atmospheric conditions.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

Fig. 3.
Fig. 3.

(a) Wind turbine rotational speed [revolutions per minute (label RPM)], tip speed (label Tip; m s−1), and electrical power production (label P; MW) as a function of wind speed for the International Energy Agency (IEA) 15-MW reference wind turbine (Gaertner et al. 2020). This reference turbine represents typical characteristics of a wind turbine that would generate 15 MW of electrical power under optimal wind conditions. Power production begins at ∼4 m s−1 and ceases at hub-height wind speeds > 25 m s−1. Thus, no RPM or tip-speed data are plotted outside this range. (b) Illustrative terminal fall velocities for rain droplets and hail computed using Vt,rain=k[(ρo/ρair)R]1/2 and Vt,hail=[(8/3)(|g|/CD)(ρi/ρair)R]1/2, where R = droplet or hailstone radius (m), k = 220 m1/2 s−1, ρo = air density at sea level (1.225 kg m−3), ρair = air density at the droplet altitude (0.999ρo), ρi = density of ice (917 kg m−3; Kumjian and Lombardo 2020; Shpund et al. 2019), and CD = drag coefficient with a value of 0.55 (Stull 2017) or 0.5 (Kumjian and Lombardo 2020). (c) Mean droplet number density as a function of RR (see legend) derived from the optical disdrometer deployed at the DOE ARM site at Lamont (Fig. 2) based on 1-min observations from 2017 to 2021.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

Evidence that blade LEE may reduce annual electricity production from wind turbines by an average of 1%–5% (Froese 2018) has spurred development of advanced methods for detection (Du et al. 2020) and prevention/reduction by application of protective tapes (Major et al. 2021) and/or use of erosion-safe mode in wind farm control where the wind turbine rotational speed is reduced during extreme hydroclimatic events (Hasager et al. 2021; Tilg et al. 2020). To accurately project the relative cost–benefit of these actions requires both accurate forecasts 1) of the total accumulated kinetic energy that is likely to be transferred into the blades during their lifetime (20–30 yr) and 2) short-term forecasts of individual events that are likely to be highly erosive. Making an assessment of the former relies on correct representation of the marginal and joint probabilities of hub–height wind speeds, rainfall rates, and also hail occurrence and diameter (Letson et al. 2020a). For the latter, there is a need for fidelity at the event level to permit costing of decisions to slow the wind turbine blade rotation to reduce blade material stresses from hydrometeor impacts that also cause lost electricity production and revenue.

Previous research that estimated kinetic energy transfer to operating wind turbines in different regions within the contiguous United States using data from dual-polarization Doppler radar found particularly high values and hence LEE potential in the SGP due to the prevalence of high wind speeds, heavy rainfall, and hail (Letson et al. 2020a; Fig. 1a). Other atmospheric phenomena are also associated with wind turbine damage. These include lightning strikes that, like hail and high RR, are also associated with deep convection and have a relatively high frequency of occurrence in the SGP (Fig. 1a). Specific to the SGP, previous analyses have suggested that, in a location with an annual rate of 5–6 lightning strikes per kilometer squared, about 5% of 1.5-MW wind turbines in a wind farm experienced some level of lightning damage to their blades (Katsaprakakis et al. 2021). While a range of lightning protective measures are available (International Electrotechnical Commission 2019), lightning attachment to the tips of wind turbine blades can result in delamination (70% of cases in the SGP), debonding, and shell and/or tip detachment (Candela Garolera et al. 2016). Degradation of aerodynamic performance and uneven loading of the wind turbine is also associated with ice accumulation during periods of freezing rain. A range of mitigation measures can be deployed to reduce ice buildup (Madi et al. 2019), but in environments with high freezing-rain frequency and up to 3% of hours in a year exhibiting meteorological icing, annual electricity production can be reduced by up to 5% (Pedersen et al. 2022). A substantial fraction of U.S. National Weather Service (NWS) Automated Surface Observing System (ASOS) stations include an icing sensor that permits detection of freezing rain (Jones et al. 2004). Data from ASOS stations within the primary study region considered here (domain d03; Fig. 2a) indicate that, during 2017, freezing rain was detected in an average of 0.08% of all 5-min periods. This suggests icing is likely not a dominant source of lost electricity production or increased wind turbine maintenance costs in the SGP. Here, we focus on the meteorological drivers of LEE.

Here, we present a WRF simulation comprising seven months during 2017. Our research objectives are to quantify the degree to which the simulation performs the following:

  1. The simulation generates a realistic representation of the hydroclimate in terms of the frequency and intensity of precipitation and the occurrence of hail and maximum estimated size of hail as derived from in situ and remote sensing observations. Specifically, we test that our a priori postulates that

    • the positive bias in hail frequency and spatial extent found in a previous WRF simulation of June–July 2014 for this model configuration and study domain (Letson et al. 2020b), and also in a simulation also performed with the Milbrandt–Yau microphysics scheme of a severe hail event in Colorado (Labriola et al. 2019b), is manifest in all seasons,

    • model fidelity for these hydroclimate properties exhibits marked seasonality due to variations in the spatial extent of convection and degree of coupling to the larger-scale atmospheric environment (Feng et al. 2019), and

    • while model-derived cREF accurately reproduces the time evolution of radar-derived measurements, there is positive bias in the spatial extent of cREF > 30 dBZ (Fan et al. 2017).

  2. The simulation exhibits skill for conditions during intense convective events. For the 10 dates with greatest spatial occurrence of composite reflectivity above 30 dBZ (Nisi et al. 2018), we provide detailed assessments of model skill, including hydrometeor type, and diagnose that skill in the context of convective duration and dynamics. Specifically, we test our a priori postulate that the WRF simulation reproduces the domainwide precipitation accumulation as reported in a range of observational datasets during these dates despite excessively intense updraft velocities and too wide an area of high composite reflectivity (cREF > 45 dBZ; Fan et al. 2017).

  3. The simulation reproduces the joint probability distribution of hydroclimate parameters and wind speeds of particular importance to the wind energy industry. Our a priori postulate is that this simulation will, consistent with past evaluations of WRF applied at convection-permitting resolution over the SGP, exhibit substantial skill for the marginal probabilities of key hydroclimate parameters and wind speeds. However, we further postulate that the simulation of the joint probability distributions represents a substantially more stringent test of the model and will be less good especially in aspects critical to dictating wind turbine LEE. We further evaluate whether this WRF simulation represents key spatial gradients in the occurrence of highly erosive meteorological events (i.e., co-occurrence of high wind speeds and heavy rainfall/hail).

2. Data and methods

a. WRF simulation

The simulation presented herein is performed using WRF (v3.8.1) with cold restarts every 14 days and a 6-h spinup period. Triple-nested simulation domains are used (Fig. 2 and Table 1). These domains are centered on a region with very high wind energy penetration. The entire outermost domain covers an area of 4.4 million km2 and is centered on northern Texas. As of April 2022, this area contained almost 40 000 wind turbines with a cumulative installed capacity (IC) of >75 GW (Hoen et al. 2018). This is over 60% of the current total U.S. installed capacity (American Clean Power 2021). Over 42 GW from a total of >22 000 wind turbines is located within the innermost simulation domain (domain d03) that is the focus of analyses presented herein.

Table 1

WRF simulation settings.

Table 1

Simulation fidelity for deep convection and related hazards is generally improved by data assimilation (Segele et al. 2013; Snook et al. 2016). Here, we do not perform data assimilation since the goal of this work is to quantify inherent model skill. We note that previous simulations performed without data assimilation with the WRF Model at a grid spacing of 4 km indicate realistic representation of structure and frequency of precipitation associated with MCSs over the central United States (Yang et al. 2017).

The simulation settings are selected to provide consistency with a prior 25-day test simulation of summer conditions (8 June–2 July 2014) over the SGP. That simulation exhibited some degree of fidelity for key meteorological properties (Letson et al. 2020b). Specifically, precipitation accumulation and RR exhibit similar magnitudes and spatial patterns to those inferred from radar and tipping-bucket rain gauges. The spatial variability of near-surface wind speeds also exhibits relatively close agreement with in situ measurements. The mean odds ratio for hail prediction across 11 radar stations is 4.6, with a range of 0.89–10.46. However, a positive bias in terms of hail frequency and spatial extent is evident. The short duration of the simulation precluded evaluation of the joint probabilities of hail or RR and wind speeds. As in that work, and other recent regional simulations (Qiu et al. 2020; Zscheischler et al. 2021), initial and lateral boundary conditions (LBCs) for the simulation presented herein are provided from the ERA-Interim reanalysis (Dee et al. 2011) and are updated every 6 hours. Daily sea surface temperature data are provided by the Real-Time Global SST dataset (Reynolds and Chelton 2010). No nudging or data assimilation is applied. One-way nesting is used. Output for parameters analyzed herein is stored every 10 min.

The calendar year 2017 is selected based on analyses that indicate that it is representative of typical radar hail climate in the study region in terms of the seasonality and absolute number of hail reports in each calendar month (Fig. 4a). The original intent had been to simulate the entire period from January to September 2017 to sample months with varying amounts of deep convection, RR, and hail frequency. However, even using 45 vertical layers and short time steps Δt led to violations of the Courant–Friedrichs–Lewy (CFL) condition [CFL = ctz) ≤ 1], where Δz = vertical grid spacing when high vertical velocities c are simulated (De Moura and Kubrusly 2013). Tests showed a much smaller time step (Δt ∼1 s in the innermost domain) might allow simulation of April and May, but limitations on computational resources precluded doing so.

Fig. 4.
Fig. 4.

(a) Monthly total radar-derived hail reports within domain d03 for 2014–21. (b) Frequency of radar hail reports in domain d03 and WMO hail codes from the optical disdrometer at the DOE ARM site (number of ARM hail codes) during January–September 2017. Colored lines denote the number of radar-derived hail reports with MESH > 0, 10, 20, 30, 40, and 50 mm. Months not simulated (April and May) are shown with a gray background.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

The five falling hydrometeors treated in the Milbrandt–Yau double-moment microphysics scheme are rain, ice, snow, graupel, and hail (Milbrandt and Yau 2005). This scheme performed relatively well in our prior evaluation (Letson et al. 2020b) and in terms of precipitation generation from a squall line in the SGP but underestimated the highest RR (Fan et al. 2017). An ensemble of simulations with data assimilation and this microphysics scheme also exhibited fidelity in terms of hail occurrence and size for the supercell storms in the SGP on 20 May 2013 (Snook et al. 2016). The microphysics parameters are used to derive estimated radar reflectivity (at 10-cm wavelength) as a diagnostic output variable using the WRF “do_radar_ref=1” namelist setting (Koch et al. 2005; Min et al. 2015).

b. Datasets used in the model evaluation

Two datasets from the NWS ASOS network (Fig. 2) are presented here. Sustained wind speeds at 10 m above ground level (AGL) U10 (m s−1) as measured using Vaisala, Inc., 2D sonic anemometers and RR as sampled using a Frise Engineering Co. heated tipping-bucket rain gauge. These data are reported every 5 min and sampled at 10-min intervals for use in the WRF evaluation.

Inferred radar reflectivity, precipitation type, and RR from the WRF simulation are evaluated using nine NWS S-band dual-polarization Doppler radars (WSR-88D; Fig. 2b). The following data products from within 200 km of each radar station are regridded onto the WRF grid within domain d03 and sampled at a 10-min resolution:

  1. reflectivity (dBZ) at six elevation angles (0.5°–3.1°),

  2. cREF [dBZ; based on previous radar-based analyses that have employed a cREF threshold of 30 dBZ as an index of storm initiation (Nisi et al. 2018), we use this threshold as an indicator of convective activity],

  3. RR (mm h−1) and total monthly precipitation accumulation [the minimum RR identified by the WSR-88D rainfall algorithm is 0.2544 mm h−1 (0.01 in. h−1; Fulton et al. 1998); RR are reported in 16 classes (defined in inches per hour) at 0, 2.54, 6.36, 12.7, 19.1, 25.4, 31.8 38.2, 44.5, 50.9, 63.6, 76.3, 102, 153, and 204 mm h−1],

  4. hail reports issued based on reflectivity, hydrometeor aspect ratio, vertically integrated liquid water content, and altitude of the melting layer (Crum et al. 1998; NOAA 2017; Seo et al. 2015; Wallace et al. 2019; Witt et al. 1998) [these reports include only the geographic centroid of the cell in which hail is inferred and the maximum expected hail size, which is the diameter that 75% of observed hail diameters should fall below (Ortega 2018; Wendt and Jirak 2021)], and

  5. Hybrid hydrometeor classification (HHC; Park et al. 2009) [here, we present data on four of the HHC classes: hail, graupel, snow, and rain; graupel is differentiated from hail using a diameter threshold of 5 mm (American Meteorological Society 2015)].

The radar hail reports do not include the geographic extent of hail, and multiple studies have found spatial mismatches between hail swaths inferred from radar and surface hail reports due to melting between the radar detection height and the ground, the complexity and possible errors in the hail detection algorithm, and horizontal advection of hail stones as they fall (Adams-Selin et al. 2019; Brook et al. 2021). Nevertheless, dual-polarization radar is widely considered to be the best dataset for characterization of hail climates and to provide evaluation of numerical models (Murillo and Homeyer 2019). When comparing the spatial extent of hail from WRF and radar, each radar hail report is assumed to cover an area equal to 45 domain d03 grid cells or 76 km2. This scaling factor is based on 1) the median size of contiguous grid cells in the WRF simulation with cREF > 40 dBZ, which has been used as threshold for radar hail detection (Witt et al. 1998), and 2) climatologies of hail production from southern France that found a typical storm produces hail over a 6-km-wide swath, has an average advection speed of 15 m s−1, has a duration of 14 min (yielding a distance of 13 km), and also gives an areal extent of 76 km2 (Dessens 1986). This estimate is naturally a first-order approximation, and we do not imply that such an area would be simultaneously subject to hailfall at the ground.

Many of the fidelity assessments for precipitation presented here use radar observations because it is available with high temporal resolution (<10 min) and is available over almost all of the domain. It also provides consistency with other analyses that employ radar estimates of cREF, reflectivity, and/or hail occurrence. Nevertheless, radar-derived RR have a number of uncertainties associated with them. Thus, we also use two gridded precipitation datasets: Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement (GPM) mission (IMERG; Huffman et al. 2020b). We use the multisatellite precipitation estimate with gauge calibration—precipitationCal (Huffman et al. 2020a). The data are archived at a 0.1° by 0.1° spatial resolution and a 30-min temporal resolution and have units of millimeters per hour. The IMERG data also have a quality assurance index (0–1) associated with each record, with higher values indicating higher data quality (Huffman 2019; Huffman et al. 2019a). The mean value of the data-quality flag in grid cells where nonzero precipitation occurs during the 10 days analyzed herein ranges from 0.41 (24 June) to 0.67 (29 March). Thus, based on preliminary guidance, these data are treated as being of moderate quality. We also analyze the Stage IV NCEP/Environmental Modeling Center (EMC) product that merges observations from 140 radars and ∼5500 rain gauges over the continental United States (Lin and Mitchell 2005). It has a 4 km × 4 km spatial resolution and hourly temporal resolution and has been used as a reference against which other datasets are evaluated (Beck et al. 2019).

The U.S. Department of Energy operates an Atmospheric Radiation Measurement (ARM) hub within the SGP near Lamont, Oklahoma (36.6072°N, −97.4875°E; Fig. 2b). At this site an optical (Parsivel2) disdrometer (Bartholomew 2020; Tokay et al. 2014) measures droplet counts in 32 classes and also encodes the presence of hail using the WMO synoptic present weather code 89. Wind speeds close to the mean wind turbine hub height (90 m AGL) are measured using a Halo Photonics Doppler lidar (Newsom and Krishnamurthy 2020).

c. Analysis methods and skill metrics

The seven simulated months are divided into three seasons. Winter is defined as January and February and has a low hail prevalence. Summer is defined as June, July, and August, has the highest hail frequency (Fig. 4b), and lies within what is frequently referenced as the “warm” season where convection is frequent across the contiguous United States (Goines and Kennedy 2018). A transition season is defined as March and September. Both months have a moderate frequency of hail reports. These definitions are also largely consistent with the seasonality of environmental contexts/spatial extents of MCS that is described above (Feng et al. 2019).

Four subregions within domain d03 (Fig. 2b) are used to examine the degree to which the WRF simulation captures spatial gradients in the wind and hydroclimate. These subregions are each 260 km by 260 km square and are located in the center of the four quadrants of domain d03. Observational data from these subregions illustrate marked west–east gradients of precipitation (Sun et al. 2016). For example, the mean annual total precipitation at the four ASOS stations closest to the center of the subregions computed for 2005–21 is 480, 764, 379, and 932 mm for northwest (NW), northeast (NE), southwest (SW), and southeast (SE), respectively. The wind resource and mean wind speed exhibit a northwest-to-southeast gradient across domain d03, with localized enhancement along the coast (Pryor et al. 2020). For example, the mean annual frequencies of wind speeds at 10 m AGL greater than 10 m s−1 at those same ASOS stations are 7.8%, 5.1%, 3.4%, and 1.4%, respectively. The number of wind turbines and total installed capacity (April 2022) of wind turbines in these subregions of domain d03 are >2600 and >5 GW for NW, >2100 and >3.9 GW for NE, 5809 and >10 GW for SW, and 680 and >1.2 GW for SE.

Simulation fidelity assessment focuses on four core aspects:

  1. The first aspect is climatology and marginal probability distributions of key parameters. Spatial maps of seasonal total precipitation and cumulative density functions (CDFs) of RR and MESH from WRF are compared with estimates from radar while CDF of wind speeds are compared with those from ASOS. These assessments are performed domainwide and in the four subregions. Rank (Spearman) correlation coefficients are used in the evaluation because these variables are not Gaussian distributed (Wilks 2020).

  2. Another aspect is forecast accuracy. Time series of domainwide occurrence of high cREF and RR are used to assess temporal fidelity and to identify 10 days with widespread deep convection. Some analyses employ metrics based on contingency tables of categorical events in each 10-min period: i) occurrence of hail, i.e., any hail accumulation in WRF or one or more hail reports from radar; ii) deep convection where cREF > 30 dBZ covers 5% or more of d03 in either the radar mapped to the WRF grid or in the WRF simulation output; and iii) RR > 5 mm h−1 over 5% or more of domain d03. In these cases, model skill is summarized using hit rate
    H=aa+c
    ,
    • false alarm rate
      F=bb+d
      ,
    • and odds ratio (Stephenson 2000)
      θ=H1H/F1F
      ,
    • where a is the number of correct forecasts, b is the number of event forecasts when none occurred, c is the events that occurred but are not forecast, and d is correct negatives, respectively. The odds ratio is the “odds of making a good forecast (a hit) to the odds of making a bad forecast (a false alarm)” (Stephenson 2000). The term θ = 1 indicates independence of forecasts and observations, whereas θ values > 1 reflect increased association and increasing forecast skill. Confidence intervals are derived for the natural logarithm of θ because it more closely approximates a Gaussian distribution (Agresti 2018) as
      ln(θ)±zα/2×SE
      ,
    • where zα/2 is the value drawn from a z distribution at a confidence level specified by α (1.96 for 95% confidence level and 1.64 for 90% confidence level) and SE is the standard error that is computed from the contingency table values (a, b, c, and d) as
      SE=1a+1b+1c+1d
      .
  3. Another aspect is intense events. The 10 dates with highest coverage of radar-derived cREF > 30 dBZ (Fig. 5h) are (listed in descending order of the spatial coverage) 29 March, 14 February, 20 February, 15 January, 24 June, 16 January, 4 July, 6 August, 26 September, and 7 August. For these 10 days we analyze the relative spatial coverage of high RR and reflectivity, examine hydrometeor type, and provide cross-sectional transects through regions with high reflectivity.

  4. The final aspect is the joint probabilities of wind speed, RR, and hail occurrence.

Fig. 5.
Fig. 5.

Mean monthly number of 10-min periods with cREF > 30 dBZ in each season from (a)–(c) WRF and (d)–(f) radar in each domain d03 grid cell, and time series of the number of d03 cells with cREF > 30 dBZ from (g) WRF and (h) radar. The ten 24-h periods with highest total number of cells with cREF > 30 dBZ are denoted by the gray background in (h). (i)–(t) Spatiotemporal CDFs of cREF from WRF and radar for each subdomain (see Fig. 2) in each season (wint = January and February, trans = March and September, sum = June, July, and August). These CDFs include all 10-min periods in all grid cells with cREF > 0. Data reported from radar are categorical, whereas those from WRF are continuous.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

Analyses presented here use different RR thresholds. RR > 0 mm h−1 is the natural definition, but even when models are applied at convection-permitting scales the excess drizzle problem is not entirely removed (Meredith et al. 2020). The 1 mm h−1 threshold is the American Meteorological Society definition of the highest RR associated with drizzle, which is defined as comprising precipitation with droplet diameters of <0.5 mm (Huschke 1959). A threshold of 5 mm h−1 is defined as heavy rainfall by the U.S. Geological Survey. A RR of 5 mm h−1 is also approximately the midpoint of the World Meteorological Organization definition of moderate rainfall, which is defined as RR of 2.5–10 mm h−1 sustained for 3 min.

Joint probability distributions are computed for the ARM site using the disdrometer and wind speeds at 90 m AGL and WRF output for the grid cell containing Lamont as well as output for all of domain d03 and subregions therein. These latter analyses use wind speeds at 10 m AGL from ASOS and RR from radar versus WRF output. In these analyses RR classes are chosen to emphasize the heaviest rainfall events. Thus, the RR classes are >0–5 mm h−1, and in 10 mm h−1 the classes are centered on 10, 20, 30, 40, and 50 mm h−1. These are defined based, in part, on analyses of disdrometer data from the ARM site (2017–21). Of the 2 436 497 one-minute data records, 102 899 (∼4%) indicate the presence of precipitation. For RR of 0–5, 5–15, 15–25, 25–35, 35–45, and 45–55 mm h−1, the mean number density of rain droplets in a diameter D class centered at 3.75 mm is 0.172, 1.53, 3.99, 7.46, 11.0, and 12.6 m−3 mm−1, respectively (Fig. 3c). There are 457 occurrences of hail, and consistent with past research, for hydrometeor D > 4 mm, the number density of hailstones (when they occur) actually exceeds that of rain droplets. For a RR of 25–35 mm h−1 and D centered at 5.5 mm, the mean number density of hail is 2.26 m−3 mm−1 whereas for rain droplets it is 0.633 m−3 mm−1. The wind speeds at 10 m AGL are discretized into five classes: 0–2, 2–5, 5–7, 7–15, and >15 m s−1. Assuming a power-law relationship for wind speed dependence on height and a power-law exponent of 1/7, these classes correspond to the following conditions at the hub height. Class 1 (0–2 m s−1) indicates wind speeds below cut in, when the wind turbine rotor is unlikely to be turning. Class 2 indicates wind turbine blade rotation at a low and fairly constant speed. Class 3 covers the transition to the rated power and attainment of the highest (and constant) rotational speed (class 4). Class 5 defines wind speeds closest to or above cutout wind speeds. The joint probability distributions are built using a 30-km radius around each ASOS station in which the empirical estimates use the ASOS wind speed during each 10-min period and the spatial radar-derived RR within that same radius. The WRF output is sampled in these same areas.

3. Results

a. Spatiotemporal variability of cREF, precipitation, hail, and wind speeds metrics

There are many sources of error in the WRF-derived equivalent radar reflectivity, and direct comparability to radar reflectivity is not expected (Koch et al. 2005). Nevertheless, the Spearman rank correlation between the time series of the spatial extent of modeled and radar-derived cREF > 30 dBZ is 0.79 (Figs. 5g,h). It is noteworthy that the spatial extent of grid cells with a high frequency of cREF > 30 dBZ in each season and the frequency with which large areas of domain d03 are simultaneously covered by cREF > 30 dBZ are substantially higher from WRF than in radar observations (Fig. 5). This overestimation is most marked in the summer months (cf. Figs. 5c,f) but is consistent through the entire simulation (Figs. 5g,h). The positive bias in the frequency with which high cREF is simulated is also manifest in all subregions of domain d03 (cf. Figs. 5a–f,m–t). The positive bias in the occurrence of cREF > 30 dBZ is consistent with previous research that has shown for a relatively wide array of model configurations WRF, when applied at convection-permitting scales and without data assimilation, tends to generate too wide of a region of moderate-to-high inferred cREF (Fan et al. 2017; Han et al. 2019; Tao et al. 2016). Despite the positive bias in the frequency of cREF > 30 dBZ, closer agreement is found for the spatial patterns of monthly mean total precipitation in each season and the time series of domainwide mean RR (Figs. 6a–h). The CDF plots for the subregions of domain d03 also exhibit a high degree for results from WRF and radar (Figs. 6i–t). The region of very high precipitation in the WRF output for the southeast of domain d03 during summer (cf. Figs. 6c,e) is due almost entirely to the northern displacement of Hurricane Harvey. Hurricane Harvey made landfall 25 August 2017 and between 25 and 30 August yielded rainfall totals along the coast of southern Texas in excess of 1000 mm and of over 750 mm in Houston, Texas (van Oldenborgh et al. 2017). The enhanced northern penetration of Hurricane Harvey in this simulation led to substantial (excess) precipitation in the southeast corner of domain d03.

Fig. 6.
Fig. 6.

Mean monthly total accumulated precipitation in each season from (a)–(c) WRF and (d)–(f) radar in each domain d03 grid cell, and time series of 10-min RRs from (g) WRF and (h) radar. (i)–(t) Spatiotemporal CDFs of RR from WRF and radar for each subregion (see Fig. 2) in each season (wint = January and February, trans = March and September, sum = June, July, and August). These CDFs include all 10-min periods in all grid cells with RR > 0. Data reported from radar are categorical, whereas those from WRF are continuous.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

The Spearman rank correlation coefficient r between the time series of 10-min domain d03 mean RR from WRF and radar is 0.67 (Figs. 6g,h). However, the simulation generates nonzero RR too frequently. Nonzero RR are reported in over 13% of the total sample of all grid cells and all 10-min time periods in WRF, but only 1.2% of radar estimates. If the sample of RR > 5 mm h−1 is collected in space (i.e., each grid cell) and time (each 10-min period) from WRF for domain d03 and each of the four subregions of domain d03, much better agreement is found. The probability of occurrence of RR > 5 mm h−1 in domain d03 is 0.42% in radar and 0.38% in WRF output. The ratio of the marginal probability of occurrence of RR > 5 mm h−1 from WRF to that from radar in grid cells within the four subregions of domain d03 ranges from 0.8 to 1.5. Consistent with some past research (Kendon et al. 2021), there is also evidence that very heavy rainfall is simulated too frequently relative to radar (Fig. 6), particularly in the subregions NE and SE. This leads to a positive bias in mean monthly precipitation totals and higher domainwide mean RR during the 10 days with highest spatial coverage of cREF > 30 dBZ (Fig. 6), which is discussed in more detail below.

Hail is considerably less frequent in the winter than summer in both radar and WRF. For example, one or more hail cells are identified from radar data in 24 10-min periods in the NW subregion and 66 in the SE subregion during January and February. During the three summer months, radar-derived hail cells are identified in these subregions in 544 and 402 10-min periods. The overall probability of hail occurrence (i.e., nonzero hail accumulation) sampled in space and time in WRF simulations is 3–5 times that from radar even after scaling the radar observations by a factor of 45. This positive bias is largest in the NW subregion, where the WRF simulations exhibit nonzero hailfall in 1% of the spatiotemporal sample (i.e., all 10-min periods sampled in all grid cells), while the scaled radar data indicate a frequency ∼0.2%. The bias in hail frequency is smallest in the SE subregion, where the probability from WRF is 0.33% and that from scaled radar is 0.11%.

Radar-derived hail properties including MESH have been previously evaluated (Cintineo et al. 2012; Murillo and Homeyer 2019; Ortega 2018). Specific to the current study region, one analysis of radar-derived hail occurrence and MESH found higher implied frequency of hail from radar in west Texas than is manifest in observer reports, which was largely ascribed to deficiencies in the observer-based analysis (Cintineo et al. 2012). A further study over the contiguous United States found a statistically significant, positive relationship between the daily number of severe hail observer-based reports and the area with radar-based nonzero MESH (Schlie et al. 2019). The synthesis of comparisons of the current WRF simulation with radar in terms of the overall probability of occurrence and MESH (Fig. 7) is that hail is present in the simulation too frequently but that during the transition and summer seasons the relative frequency of large hail (MESH > 25 mm) is higher in the radar observations (Figs. 7i–l). This is consistent with previous research that has indicated the Milbrandt–Yau microphysics scheme generated MESH estimates on the lower end of those from WRF microphysics schemes for a severe hail event in Colorado (Labriola et al. 2019a). Analyses of the joint probability of MESH from radar and WRF (Fig. 8) also indicate that in time periods and grid cells where both indicate the presence of hail, WRF simulations overestimate the probability of occurrence of large MESH during January and February and underestimate the probability of occurrence of large MESH in the transition and summer months.

Fig. 7.
Fig. 7.

(a)–(l) Spatiotemporal CDFs of MESH from WRF and radar. CDFs of MESH are for all 10-min periods when hail is present. MESH from radar is categorical. (m)–(x) Wind speeds at 10 m AGL U10 from WRF and ASOS for each subregion in each season. Gray lines in (m)–(x) show individual ASOS stations (ASOS ind), and blue lines show the mean for all ASOS stations (ASOS all) in each subregion (Fig. 2). Red dotted lines show U10 from WRF output in all ASOS-containing cells.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

Fig. 8.
Fig. 8.

Joint distributions of MESH from WRF and radar during all 10-min periods and locations (grid cells) when hail is present in both datasets. The white dotted line y = x is included to facilitate comparison. Note that the frequency of occurrence of the joint classes of MESH from WRF and radar is shown on a logarithmic scale, and the scale is truncated at 100 to aid legibility. The discretization used for the radar and WRF MESH estimates reflects the unique values found in each dataset.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

Odds ratios for categorical forecasts of hail occurrence, and cREF > 30 dBZ or RR > 5 mm h−1 over at least 5% of domain d03 indicate that the WRF simulation is highly skillful (Fig. 9). Ratio θ is greater than 1 for all seasons and all subregions of domain d03 and none of the 95% confidence intervals on ln(θ) intersect zero. Forecast skill, measured by both the absolute magnitude of θ and the ratio of the width of the confidence interval on θ () computed from Eq. (4) to the value of θ (i.e., /θ) is consistently lowest (smallest value of θ and /θ) in summer, although the number of 10-min periods that meet the criteria of an event is higher in summer. For example, in subregion NW the total number of radar-detected hail events is 544 [a (hits) = 428 + c (misses) = 116] as compared with 24 in winter and 153 in the transition months. Both hail frequency and model skill in forecasting hail occurrence also exhibit spatial variability. In the NW subregion the radar observations indicate evidence for hail in radar data on 746 of all 10-min periods, while WRF indicates nonzero hail accumulation on 1709 10-min periods. In the SE, 536 and 956 10-min periods fulfill these conditions. Accordingly, θ is higher for the SE than NW for the transition and summer months.

Fig. 9.
Fig. 9.

Odds ratios θ for categorical forecasts from WRF vs radar for the presence of hail and cREF > 30 dBZ and RR > 5 mm h−1 over more than 5% of the area of each subregion (see Fig. 2b) for each season. The color scale is capped at 100 to make gradations between lower θ more visible.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

WRF-derived near-surface wind speeds exhibit a strong dependence on model configuration (particularly PBL and surface schemes; Hahmann et al. 2020) but generally exhibit fidelity in areas of flat terrain (Hahmann et al. 2020; Hawbecker et al. 2017; Letson et al. 2020b; Pryor and Hahmann 2019). Comparisons of wind speeds from WRF and ASOS are subject to a number of important caveats. Sustained 2-min mean wind speeds as reported by ASOS sonic anemometers are rounded up to the nearest knot and values below 3 kt (1.543 m s−1) are recorded as “calm” or 0 m s−1. Conversely, the WRF values are for the model time step and are spatial averages. With these caveats, the current simulations reproduce the wind climate seasonality. Consistent with ASOS wind speed observations and the observed seasonal pattern of wind turbine power production (Pryor et al. 2020), wind speeds from WRF are lowest in the summer months. Spearman r of 10-m wind speeds from ASOS and WRF (sampled at ASOS stations) are highest in the winter and transition season months (r > 0.5 in all seasons) and the ratios of the temporal standard deviations are close to 1. The simulations also reproduce key aspects of the U10 probability distribution from ASOS stations in the different subregions of domain d03 (Figs. 7m–x).

b. Days with large spatial coverage of high cREF

The 10 days with highest spatial coverage of cREF > 30 dBZ (Figs. 5g,h) exhibit high precipitation accumulation from both WRF and radar (Figs. 6g,h). Evaluation relative to point observations is plagued by a double penalty (for displacement in time and/or space; Prein et al. 2013). Thus, here we focus principally on domainwide precipitation over the entire day. Consistent with the other analyses presented above, the 24-h precipitation accumulation from WRF exceeds those from radar on 8 of the 10 days (Fig. 10). The ratios of mean d03 precipitation accumulation from radar to WRF range from 0.26 (4 July) and 0.41 (24 June) to 2.35 (14 February) and 2.76 (16 January).

Fig. 10.
Fig. 10.

(a) Scatterplot of 24-h total WRF and ASOS precipitation (mean total across all ASOS station-containing cells of snow, rain, hail, and graupel) on the 10 dates with highest spatial extent of cREF > 30 dBZ (Fig. 5; see legend). The whiskers show the interquartile range (IQR) among all ASOS stations and ASOS station–containing WRF cells. (b) Mean 24-h total precipitation over all of domain d03 from IMERG, Stage IV, and radar vs WRF precipitation on those same dates.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

WRF underestimates both the mean 24-h total precipitation as sampled for grid cells containing ASOS stations and spatial variability (Fig. 10a). These observations also emphasize that these 10 days are associated with very high localized precipitation of up to 100 mm in a 24-h period at some ASOS stations. WRF output exhibits reasonable accord with the total domain-d03 mean 24-h precipitation from radar, IMERG, and Stage IV for these dates. Applying a threshold of 0.25 mm as “measurable” daily accumulated precipitation (Arguez et al. 2012), data from radar indicate the spatial coverage of domain d03 with nonzero precipitation on these 10 dates (listed as in Fig. 10b) is 77%, 60%, 50%, 59% (15 January), 40%, 60%, 53% (4 July), 38%, 46%, and 43%. Comparable values from the WRF output are 84%, 95%, 70%, 90% (15 January), 38%, 78%, 23% (4 July), 73%, 70%, and 61% of domain d03. The Spearman r between WRF and radar of domainwide precipitation received on these dates is 0.53. Substantial precipitation is also indicated on these dates by the other observational datasets (Fig. 10). For example, the spatial coverage of daily accumulated precipitation above 0.25 mm within domain d03 from IMERG ranges from 91% (29 March) to 51% (24 June), and the domainwide mean 24-h total precipitation again from IMERG ranges from 7.6 (26 September) to 22.8 mm (29 March).

The WRF output exhibits closer accord with IMERG in terms of total precipitation accumulation than with Stage IV. The slopes and intercept values of linear fits (y = mx + c, where x is the observation and y is WRF) to the daily mean total precipitation accumulation shown in Fig. 10b yield values of m = 1.17 and c = −3.2 (IMERG), m = 1.74 and c = −1.22 (radar), and m = 1.68 and c = −11.66 (Stage IV).

Analyses of model output for 3 of the 10 dates (29 March, 24 June, and 16 January) with highest spatial coverage of cREF > 30 dBZ illustrate the following: first, in both radar and WRF more spatially extensive areas of high reflectivity and precipitation are present in events during the transition season and winter (Fig. 11). Second, consistent with past research, these case studies indicate WRF simulates a wider swath of high cREF (>40 dBZ or >30 dBZ) and a narrower stratiform area (Fan et al. 2017; Fig. 11). Nevertheless, the spatial extent of nonzero precipitation at the time of maximum spatial extent of cREF > 30 dBZ is relatively well reproduced. Third, transects through a line of organized convection as indicated by radar and simulated with WRF exhibit important similarities in terms of the vertical extent of high reflectivity for 29 March and 24 June, but the transect for 16 January exhibits a greater depth of high reflectivity than is evident in the radar data, and the simulated vertical velocities from WRF within this region are much higher than in the other two cases (Fig. 11). These transects also illustrate the presence in the WRF Model output of horizontally limited intense updraft cores associated with high inferred reflectivity in the upper model levels. Last, hail production in WRF is frequently associated with information in the radar HHC that indicates either the presence of hail or either graupel and/or snow (Fig. 12). Thus, while hailfall at the ground appears to be oversimulated, radar data are consistent with the presence of solid hydrometeors in the clouds.

Fig. 11.
Fig. 11.

The cREF from (a)–(c) radar and (d)–(f) WRF during example 10-min periods on 29 Mar, 24 Jun, and 16 Jan. Also shown by the white outlines and shading are areas where precipitation is occurring. Vertical profiles of reflectivity from (g)–(i) radar (from the elevation scans at 0.5°, 0.9°, 1.3°, 1.8°, 2.4°, and 3.1°) and (j)–(l) WRF, along with (m)–(o) vertical wind speed w and height of the melting layer from WRF, along the transects shown by the black lines in (a)–(f).

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

Fig. 12.
Fig. 12.

Hydrometeor classes during 29 Mar, 24 Jun, and 16 Jan: time series of the number of domain d03 cells with each precipitation type from (a)–(c) radar and (d)–(f) WRF, and maps for the time of most widespread precipitation from radar, showing output from (g)–(i) radar and (j)–(l) WRF. Radar hydrometeor classes are consolidated from 10 to 4 to match the WRF hydrometeor classes. “Trace” precipitation from WRF is shown for any cell with RR < 0.15 mm h−1.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

The excess presence of solid hydrometeors (hail and graupel; Figs. 12c,f,i,l) and the excess duration of deep convective (and nonzero precipitation; cf. Figs. 12c,f) in the current simulation of 16 January may also be linked to the very high modeled vertical velocities (Fig. 11o), excess vertical cloud development (as manifest in the vertical extent of high radar reflectivity; cf. Figs. 11i,l), and possible feedbacks from the resulting cold pool (see discussion in section 1). Simulations of a squall line that occurred on 20 May 2011 during the MC3E experiment found evidence for excess vertical extent of REF > 30 dBZ and positive bias in vertical velocities in simulations with all of the eight microphysics schemes tested (Fan et al. 2017). Of particular relevance to the current work, the bias in updraft velocities was particularly marked in simulations of the Milbrandt–Yau microphysics scheme, although the vertical extent of REF > 30 dBZ was not particularly marked in the simulation with the Milbrandt–Yau microphysics scheme (Fan et al. 2017).

c. Joint probabilities of wind speeds, rainfall rates, and hail occurrence

The fidelity assessment summarized above implies the WRF simulation exhibits skill in reproducing the marginal probabilities and spatial variability of wind speeds, RR and hail, and aspects of individual convective events. For applications to wind turbine blade LEE, these are necessary prerequisites for damage assessment but insufficient to ensure accuracy of such assessments. The demand for fidelity in both wind speed and precipitation type (hydrometeor)/RR and specifically the co-occurrence of high RR and wind speed provides an extremely stringent challenge for atmospheric models. Performance in this context is described below.

Datasets collected at the DOE ARM facility allow a pointwise evaluation of WRF, but for some of the simulation period the disdrometer and/or wind profiler were not operational (e.g., January and February). This low data volume and bias toward sampling the warm-season months, plus the challenges in comparing point observations of wind speed and RR, limit detailed interpretation. Nevertheless, the WRF simulation appears to underestimate the relative frequency of very high RR at this site. At this location, as in most of domain d03, WRF rains too often but at relatively low RR; RR > 45 mm h−1 are observed by the disdrometers on ∼0.5% of all periods with RR > 0 mm h−1 but only 0.04% of WRF output from that grid cell when precipitation is simulated (Fig. 13). The compensating bias in precipitation frequency means the absolute frequency of RR > 45 mm h−1 is within a factor of 2 of the observations. There is a positive bias in simulated wind speeds at/near wind turbine hub heights during periods of precipitation (Fig. 13). Wind speeds at hub height exceed 10 m s−1 in lidar observations in <6% of periods with RR > 0, while this threshold is exceeded in >13% of WRF output during periods with precipitation. Such biases will offset each other in terms of inferred total kinetic energy transferred to rotating wind turbine blades. The negative bias in high RR will lead to a negative bias in the number, size, and υt from the most erosive hydrometeors, but the positive bias in wind speed at wind turbine hub height means there will be a positive bias in blade rotational speed and thus the closing velocity.

Fig. 13.
Fig. 13.

Joint probabilities of wind speed at hub height (label WS) and RR for all periods when both WRF output and observations are available, and RR > 0 mm h−1 from (a) DOE ARM observations (Obs) and (b) WRF. The color bar is truncated to highlight variations in color for lower frequency but high-impact events. Note that the classes of rainfall rate are not equal. The class denoted by <5 shows RR above 0 and less than 5 mm h−1. All other classes have a bin width of 10 mm h−1 and are centered on the value shown.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

For the domainwide and subregional analyses, the relative frequency of occurrence of hail in each U10 class is well represented in the WRF simulation, while the relative frequency of liquid precipitation (of any intensity) for U10 > 7 m s−1 exhibits a positive bias relative to radar-based observations within 30 km of each ASOS station (Fig. 14). This subsampling yields the finding that 2.8% of periods when precipitation is observed are associated with RR > 25 mm h−1 and wind speeds at which the wind turbine blades would be rotating, while the comparable value from WRF is 3.8%. Considering wind speeds where the wind turbine blades would likely be at their maximum rotational speed U10 (7–15 m s−1), RR > 25 mm h−1 are almost 2 times as frequent in the WRF output. This comparison, in contrast to pointwise analyses at the ARM facility, implies kinetic energy transfer to the blades from liquid hydrometeor impacts is likely to be overestimated if calculated from the WRF simulation output. Both the WRF simulation and the radar estimate of hail occurrence also indicates that a substantial fraction of the time when hail is indicated also occurs during periods when the wind turbine would be rotating (Fig. 14), and further, nearly 30% of all hail events are associated with wind speeds at which the wind turbine blades are rotating at, or close to, their maximum speed (i.e., U10 > 7 m s−1). Hail impacts are thought to be associated with higher kinetic energy transfer and material stresses due to the hardness and relatively large diameter of the hydrometeors (Keegan et al. 2013).

Fig. 14.
Fig. 14.

Joint probabilities of 10-m wind speed U10 and RR from (a) observations and (b) WRF in domain d03 for all periods with RR > 0 mm h−1. The color bar is limited to frequencies of 0%–10% to help to highlight variations in color for events with lower frequency but high impact. Note that the classes of rainfall rate are not equal. The class denoted by <5 shows RR above 0 and less than 5 mm h−1. All other classes have a bin width of 10 mm h−1 and are centered on the value shown. The marginal probabilities of RR are shown in each left-hand subpanel (these probabilities include events with RR = 0 mm h−1). The lower panels show the marginal probability distributions of U10 in each class (black) along with the fraction of total rain and hail events associated with each U10 class, shown in blue and red, respectively.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

When the four subregions of domain d03 are considered, the joint probabilities of U10 and RR and the occurrence of hail in different wind speed classes are relatively well reproduced. However, the WRF simulation output fails to reproduce the clear west–east gradient in the co-occurrence of high U10 and high RR evident in observations from the four subdomains (Fig. 15). Closer accord is found for NW and SW subdomains, but in the two eastern subregions, the occurrence of all RR in the U10 class 7–15 m s−1 is substantially overestimated.

Fig. 15.
Fig. 15.

As in Fig. 14, but from (a),(c),(e),(g) observations and (b),(d),(f),(h) WRF for each of the subregions of domain d03.

Citation: Journal of Applied Meteorology and Climatology 62, 1; 10.1175/JAMC-D-22-0090.1

4. Summary and concluding remarks

Accurate simulation of hydroclimate conditions even in convection-permitting regional climate simulations is extremely challenging. Further, objective assessment of such simulations, particularly for hail occurrence and size, is not aided by the relative paucity of direct observations and the assumptions implicit in deriving hail estimates from radar. Nevertheless, the WRF simulation presented herein is shown to exhibit fidelity in important aspects of the hydroclimate. Returning to our original objectives, we show that the marginal probabilities and spatial patterns of RR and wind speeds exhibit close accord with radar and gridded datasets and in situ observations. Further, the odds ratios of hail occurrence and high RR are indicative of simulation skill at the event level, even in the absence of data assimilation or nudging. Consistent with our a priori expectations, there is clear positive bias in the spatial extent of high composite reflectivity and model fidelity for hail occurrence, and size is lowest in the summer months. Case study analyses of high spatial extent of cREF and precipitation equally indicate credibility with respect to the vertical structure of deep convection and the presence of solid-phase hydrometeors in clouds. They also provide preliminary evidence that the excess production of hail in the simulation is due to a combination of deep convection that is too intense during the cold season and possible misallocation of hydrometeors between the six classes treated by the microphysics scheme.

Application of WRF to generate a priori estimates of wind turbine blade LEE or to enable an erosion-safe operational mode represents both a critical research need as society makes a transition to a lower-carbon energy supply and an opportunity to consider more holistically model skill. Despite the positive aspects of the simulation fidelity assessment described above, these are not sufficient to ensure skill in the joint probabilities of hail occurrence or high RR with wind speed, particularly in comparisons for specific subregions of the simulation domain and in pointwise comparison at the DOE SGP ARM site. For example, while this 7-month WRF simulation captures some of the spatial variability in these joint probabilities, this simulation underestimates the west–east gradient in the co-occurrence of high wind speeds, when wind turbine tip speeds are maximized and RR > 25 mm h−1.

Because of the high computational burden of simulations such as those presented herein, only selected months from a representative year in terms of the radar-derived hail climate are considered. Quantification of the degree to which model fidelity assessments presented herein are generalizable requires simulation of multiple complete years to allow sampling of a wide range of meteorological conditions and environmental contexts for deep convection. Future work should also evaluate whether different model formulations and advanced/improved microphysics schemes can achieve higher skill in terms of the joint probabilities of intense precipitation and high wind speeds. Development of such a large model ensemble should also include alternative sources of the LBC (e.g., ERA5; Hersbach et al. 2020). Improved assessment of modeling capability and relative performance of different ensemble members is key to the development of recommended best practice, prioritizing areas for model improvement, and would greatly benefit the growing renewable energy community in the Southern Great Plains and beyond.

Acknowledgments.

This research is supported by the U.S. Department of Energy (DOE) Office of Science (DE-SC0016438), the DOE Office of Energy Efficiency and Renewable Energy via Sandia National Laboratory, and NASA (80NSSC21K1489). Computational resources are provided by the NSF Extreme Science and Engineering Discovery Environment (XSEDE) (award TG-ATM170024) and the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported under Contract DE-AC02-05CH11231. The authors express gratitude to the three anonymous reviewers for their helpful comments and suggestions and to Brian Naess for providing access to the NLDN data.

Data availability statement.

The Stage IV precipitation dataset is available from https://data.eol.ucar.edu/dataset/21.093. The IMERG dataset is available from https://disc.gsfc.nasa.gov (Huffman et al. 2019b). Data were obtained from the Atmospheric Radiation Measurement (ARM) User Facility, a DOE Office of Science User Facility managed by the Biological and Environmental Research Program [for laser disdrometer data and wind speed data see Wang et al. (2016) and Shippert et al. (2010), respectively]. NEXRAD radar data are available from https://www.ncei.noaa.gov/products/radar/next-generation-weather-radar. NWS ASOS data are available from ftp://ftp.ncdc.noaa.gov/pub/data/asos-fivemin/. The NOAA Storm Events Database is available at https://www.ncdc.noaa.gov/stormevents/. Data from the NASA Passive Microwave Hail Climatology Data Products V1 dataset are available for download from https://search.earthdata.nasa.gov/. The U.S. NDLN dataset regridded to the CMAQ CONUS grid are available from https://www.cmascenter.org/download/data/nldn.cfm. All model output used in the analyses presented here, including a sample namelist, is available online (http://portal.nersc.gov/archive/home/projects/m2645/www/public_data_2017_SGP_hail).

REFERENCES

  • Adams-Selin, R. D., and C. L. Ziegler, 2016: Forecasting hail using a one-dimensional hail growth model within WRF. Mon. Wea. Rev., 144, 49194939, https://doi.org/10.1175/MWR-D-16-0027.1.

    • Search Google Scholar
    • Export Citation
  • Adams-Selin, R. D., A. J. Clark, C. J. Melick, S. R. Dembek, I. L. Jirak, and C. L. Ziegler, 2019: Evolution of WRF-HAILCAST during the 2014–16 NOAA/hazardous weather testbed spring forecasting experiments. Wea. Forecasting, 34, 6179, https://doi.org/10.1175/WAF-D-18-0024.1.

    • Search Google Scholar
    • Export Citation
  • Agresti, A., 2018: An Introduction to Categorical Data Analysis. 3rd ed. John Wiley and Sons, 400 pp.

  • American Clean Power, 2021: Clean Power Quarterly 2020 Q4. ACP Rep., 27 pp., https://cleanpower.org/resources/american-clean-power-market-report-q4-2020/.

  • American Meteorological Society, 2015: “Graupel.” Glossary of Meteorology, https://glossary.ametsoc.org/wiki/Graupel.

  • Arguez, A., I. Durre, S. Applequist, R. S. Vose, M. F. Squires, X. Yin, R. R. Heim Jr., and T. W. Owen, 2012: NOAA’s 1981–2010 U.S. climate normals: An overview. Bull. Amer. Meteor. Soc., 93, 16871697, https://doi.org/10.1175/BAMS-D-11-00197.1.

    • Search Google Scholar
    • Export Citation
  • Bang, S. D., and D. J. Cecil, 2019: Constructing a multifrequency passive microwave hail retrieval and climatology in the GPM domain. J. Appl. Meteor. Climatol., 58, 18891904, https://doi.org/10.1175/JAMC-D-19-0042.1.

    • Search Google Scholar
    • Export Citation
  • Bartholomew, M. J., 2020: Laser disdrometer instrument handbook. U.S. Department of Energy Office of Scientific and Technical Information Tech. Rep. DOE/SC-ARM-TR-137, 22 pp., https://doi.org/10.2172/1226796.

  • Beck, H. E., and Coauthors, 2019: Daily evaluation of 26 precipitation datasets using Stage-IV gauge-radar data for the CONUS. Hydrol. Earth Syst. Sci., 23, 207224, https://doi.org/10.5194/hess-23-207-2019.

    • Search Google Scholar
    • Export Citation
  • Brook, J. P., A. Protat, J. Soderholm, J. T. Carlin, H. McGowan, and R. A. Warren, 2021: HailTrack—Improving radar-based hailfall estimates by modeling hail trajectories. J. Appl. Meteor. Climatol., 60, 237254, https://doi.org/10.1175/JAMC-D-20-0087.1.

    • Search Google Scholar
    • Export Citation
  • Brown, T. M., W. H. Pogorzelski, and I. M. Giammanco, 2015: Evaluating hail damage using property insurance claims data. Wea. Climate Soc., 7, 197210, https://doi.org/10.1175/WCAS-D-15-0011.1.

    • Search Google Scholar
    • Export Citation
  • Candela Garolera, A., S. F. Madsen, M. Nissim, J. D. Myers, and J. Holboell, 2016: Lightning damage to wind turbine blades from wind farms in the US. IEEE Trans. Power Delivery, 31, 10431049, https://doi.org/10.1109/TPWRD.2014.2370682.

    • Search Google Scholar
    • Export Citation
  • Cintineo, J. L., T. M. Smith, V. Lakshmanan, H. E. Brooks, and K. L. Ortega, 2012: An objective high-resolution hail climatology of the contiguous United States. Wea. Forecasting, 27, 12351248, https://doi.org/10.1175/WAF-D-11-00151.1.

    • Search Google Scholar
    • Export Citation
  • Crum, T. D., R. E. Saffle, and J. W. Wilson, 1998: An update on the NEXRAD program and future WSR-88D support to operations. Wea. Forecasting, 13, 253262, https://doi.org/10.1175/1520-0434(1998)013<0253:AUOTNP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dai, Y., I. N. Williams, and S. Qiu, 2021: Simulating the effects of surface energy partitioning on convective organization: Case study and observations in the US Southern Great Plains. J. Geophys. Res. Atmos., 126, e2020JD033821, https://doi.org/10.1029/2020JD033821.

    • Search Google Scholar
    • Export Citation
  • Davenport, C. E., 2021: Environmental evolution of long-lived supercell thunderstorms in the Great Plains. Wea. Forecasting, 36, 21872209, https://doi.org/10.1175/WAF-D-21-0042.1.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, https://doi.org/10.1002/qj.828.

    • Search Google Scholar
    • Export Citation
  • De Moura, C. A., and C. S. Kubrusly, Eds., 2013: The Courant–Friedrichs–Lewy (CFL) Condition: 80 Years after Its Discovery. Springer, 237 pp., https://doi.org/10.1007/978-0-8176-8394-8.

  • Dessens, J., 1986: Hail in southwestern France. I: Hailfall characteristics and hailstorm environment. J. Appl. Meteor. Climatol., 25, 3547, https://doi.org/10.1175/1520-0450(1986)025<0035:HISFIH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Du, Y., S. Zhou, X. Jing, Y. Peng, H. Wu, and N. Kwok, 2020: Damage detection techniques for wind turbine blades: A review. Mech. Syst. Signal Process., 141, 106445, https://doi.org/10.1016/j.ymssp.2019.106445.

    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 30773107, https://doi.org/10.1175/1520-0469(1989)046<3077:NSOCOD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Edwards, R., and R. L. Thompson, 1998: Nationwide comparisons of hail size with WSR-88D vertically integrated liquid water and derived thermodynamic sounding data. Wea. Forecasting, 13, 277285, https://doi.org/10.1175/1520-0434(1998)013<0277:NCOHSW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Fan, J., and Coauthors, 2017: Cloud‐resolving model intercomparison of an MC3E squall line case: Part I—Convective updrafts. J. Geophys. Res. Atmos., 122, 93519378, https://doi.org/10.1002/2017JD026622.

    • Search Google Scholar
    • Export Citation
  • Feng, Z., L. R. Leung, R. A. Houze Jr., S. Hagos, J. Hardin, Q. Yang, B. Han, and J. Fan, 2018: Structure and evolution of mesoscale convective systems: Sensitivity to cloud microphysics in convection‐permitting simulations over the United States. J. Adv. Model. Earth Syst., 10, 14701494, https://doi.org/10.1029/2018MS001305.

    • Search Google Scholar
    • Export Citation
  • Feng, Z., R. A. Houze Jr., L. R. Leung, F. Song, J. C. Hardin, J. Wang, W. I. Gustafson Jr., and C. R. Homeyer, 2019: Spatiotemporal characteristics and large-scale environments of mesoscale convective systems east of the Rocky Mountains. J. Climate, 32, 73037328, https://doi.org/10.1175/JCLI-D-19-0137.1.

    • Search Google Scholar
    • Export Citation
  • Feng, Z., and Coauthors, 2021: A global high-resolution mesoscale convective system database using satellite-derived cloud tops, surface precipitation, and tracking. J. Geophys. Res. Atmos., 126, e2020JD034202, https://doi.org/10.1029/2020JD034202.

    • Search Google Scholar
    • Export Citation
  • Fritsch, J. M., R. J. Kane, and C. R. Chelius, 1986: The contribution of mesoscale convective weather systems to the warm-season precipitation in the United States. J. Climate Appl. Meteor., 25, 13331345, https://doi.org/10.1175/1520-0450(1986)025<1333:TCOMCW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Froese, M., 2018: Wind-farm owners can now detect leading-edge erosion from data alone. Windpower Engineering and Development, accessed 14 August 2018, https://www.windpowerengineering.com/wind-farm-owners-can-now-detect-leading-edge-erosion-from-data-alone/.

  • Fulton, R. A., J. P. Breidenbach, D.-J. Seo, D. A. Miller, and T. O’Bannon, 1998: The WSR-88D rainfall algorithm. Wea. Forecasting, 13, 377395, https://doi.org/10.1175/1520-0434(1998)013<0377:TWRA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gaertner, E., and Coauthors, 2020: IEA Wind TCP Task 37: Definition of the IEA 15-megawatt offshore reference wind turbine. NREL Tech. Rep. NREL/TP-5000-75698, 54 pp., https://www.osti.gov/biblio/1603478.

  • Gagne, D. J., II, A. McGovern, S. E. Haupt, R. A. Sobash, J. K. Williams, and M. Xue, 2017: Storm-based probabilistic hail forecasting with machine learning applied to convection-allowing ensembles. Wea. Forecasting, 32, 18191840, https://doi.org/10.1175/WAF-D-17-0010.1.

    • Search Google Scholar
    • Export Citation
  • Goines, D. C., and A. D. Kennedy, 2018: Precipitation from a multiyear database of convection‐allowing WRF simulations. J. Geophys. Res. Atmos., 123, 24242453, https://doi.org/10.1002/2016JD026068.

    • Search Google Scholar
    • Export Citation
  • Haerter, J. O., S. J. Böing, O. Henneberg, and S. B. Nissen, 2019: Circling in on convective organization. Geophys. Res. Lett., 46, 70247034, https://doi.org/10.1029/2019GL082092.

    • Search Google Scholar
    • Export Citation
  • Hahmann, A. N., and Coauthors, 2020: The making of the New European Wind Atlas—Part 1: Model sensitivity. Geosci. Model Dev., 13, 50535078, https://doi.org/10.5194/gmd-13-5053-2020.

    • Search Google Scholar
    • Export Citation
  • Han, B., and Coauthors, 2019: Cloud-resolving model intercomparison of an MC3E squall line case: Part II. Stratiform precipitation properties. J. Geophys. Res. Atmos., 124, 10901117, https://doi.org/10.1029/2018JD029596.

    • Search Google Scholar
    • Export Citation
  • Hasager, C. B., F. Vejen, W. R. Skrzypiński, and A.-M. Tilg, 2021: Rain erosion load and its effect on leading-edge lifetime and potential of erosion-safe mode at wind turbines in the North Sea and Baltic Sea. Energies, 14, 1959, https://doi.org/10.3390/en14071959.

    • Search Google Scholar
    • Export Citation
  • Hawbecker, P., S. Basu, and L. Manuel, 2017: Realistic simulations of the July 1, 2011 severe wind event over the Buffalo Ridge Wind Farm. Wind Energy, 20, 18031822, https://doi.org/10.1002/we.2122.

    • Search Google Scholar
    • Export Citation
  • Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 19992049, https://doi.org/10.1002/qj.3803.

    • Search Google Scholar
    • Export Citation
  • Hoen, B. D., J. E. Diffendorfer, J. T. Rand, L. A. Kramer, C. P. Garrity, and H. E. Hunt, 2018: United States wind turbine database v4.3. U.S. Geological Survey, American Clean Power Association, and Lawrence Berkeley National Laboratory, accessed 14 January 2022, https://doi.org/10.5066/F7TX3DN0.

  • Huffman, G. J., 2019: IMERG v06 quality index. NASA, 5 pp., https://gpm.nasa.gov/sites/default/files/2020-02/IMERGV06_QI_0.pdf.

  • Huffman, G. J., D. T. Bolvin, E. J. Nelkin, E. F. Stocker, and J. Tan, 2019a: V06 IMERG release notes. NASA GSFC Doc., 15 pp., https://gpm.nasa.gov/resources/documents/imerg-v06-release-notes.

  • Huffman, G. J., E. F. Stocker, D. T. Bolvin, E. J. Nelkin, and J. Tan, 2019b: GPM IMERG Final Precipitation L3 Half Hourly 0.1° × 0.1° V06, Goddard Earth Sciences Data and Information Services Center (GES DISC), accessed 2 May 2022, https://doi.org/10.5067/GPM/IMERG/3B-HH/06.

  • Huffman, G. J., D. T. Bolvin, E. J. Nelkin, and J. Tan, 2020a: Integrated Multi-satellitE Retrievals for GPM (IMERG). NASA GSFC Tech. Doc. 612, 83 pp., https://docserver.gesdisc.eosdis.nasa.gov.

  • Huffman, G. J., and Coauthors, 2020b: Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement (GPM) mission (IMERG). Satellite Precipitation Measurement, V. Levizzani et al., Eds., Advances in Global Change Research, Vol. 67, Springer, 343–353.

  • Huschke, R. E., Ed., 1959: Glossary of Meteorology. Amer. Meteor. Soc., 638 pp.

  • International Electrotechnical Commission, 2019: Wind energy generation systems—Part 24: Lightning protection. International Standard IEC61400, International Electrotechnical Commission, 191 pp., https://standards.iteh.ai/catalog/standards/iec/6aae4b87-f0f6-474c-a3ce-da2b91697249/iec-61400-24-2019.

  • Jiménez, P. A., J. Dudhia, J. F. González-Rouco, J. Navarro, J. P. Montávez, and E. García-Bustamante, 2012: A revised scheme for the WRF surface layer formulation. Mon. Wea. Rev., 140, 898918, https://doi.org/10.1175/MWR-D-11-00056.1.

    • Search Google Scholar
    • Export Citation
  • Jones, K. F., A. C. Ramsay, and J. N. Lott, 2004: Icing severity in the December 2002 freezing-rain storm from ASOS data. Mon. Wea. Rev., 132, 16301644, https://doi.org/10.1175/1520-0493(2004)132<1630:ISITDF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kain, J. S., 2004: The Kain–Fritsch convective parameterization: An update. J. Appl. Meteor., 43, 170181, https://doi.org/10.1175/1520-0450(2004)043<0170:TKCPAU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • 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, https://doi.org/10.1007/978-1-935704-13-3_16.

  • Katsaprakakis, D. A., N. Papadakis, and I. Ntintakis, 2021: A comprehensive analysis of wind turbine blade damage. Energies, 14, 5974, https://doi.org/10.3390/en14185974.

    • Search Google Scholar
    • Export Citation
  • Keegan, M. H., D. Nash, and M. Stack, 2013: Numerical modelling of hailstone impact on the leading edge of a wind turbine blade. Proc. EWEA Annual Wind Energy Event 2013, Vienna, Austria, European Wind Energy Association, 1–11, https://strathprints.strath.ac.uk/id/eprint/42830.

  • Kendon, E. J., A. F. Prein, C. A. Senior, and A. Stirling, 2021: Challenges and outlook for convection-permitting climate modelling. Philos. Trans. Roy. Soc., A379, 20190547, https://doi.org/10.1098/rsta.2019.0547.

    • Search Google Scholar
    • Export Citation
  • Koch, S. E., B. Ferrier, M. T. Stoelinga, E. Szoke, S. J. Weiss, and J. S. Kain, 2005: The use of simulated radar reflectivity fields in the diagnosis of mesoscale phenomena from high-resolution WRF model forecasts. Preprints, 11th Conf. on Mesoscale Processes, Albuquerque, NM, Amer. Meteor. Soc., J4J.7, https://ams.confex.com/ams/32Rad11Meso/webprogram/Paper97032.html.

  • Kumjian, M. R., and K. Lombardo, 2020: A hail growth trajectory model for exploring the environmental controls on hail size: Model physics and idealized tests. J. Atmos. Sci., 77, 27652791, https://doi.org/10.1175/JAS-D-20-0016.1.

    • Search Google Scholar
    • Export Citation
  • Labriola, J., N. Snook, Y. Jung, and M. Xue, 2019a: Explicit ensemble prediction of hail in 19 May 2013 Oklahoma City thunderstorms and analysis of hail growth processes with several multimoment microphysics schemes. Mon. Wea. Rev., 147, 11931213, https://doi.org/10.1175/MWR-D-18-0266.1.

    • Search Google Scholar
    • Export Citation
  • Labriola, J., N. Snook, M. Xue, and K. W. Thomas, 2019b: Forecasting the 8 May 2017 severe hail storm in Denver, Colorado, at a convection-allowing resolution: Understanding rimed ice treatments in multimoment microphysics schemes and their effects on hail size forecasts. Mon. Wea. Rev., 147, 30453068, https://doi.org/10.1175/MWR-D-18-0319.1.

    • Search Google Scholar
    • Export Citation
  • Letson, F., R. J. Barthelmie, and S. C. Pryor, 2020a: RADAR-derived precipitation climatology for wind turbine blade leading edge erosion. Wind Energy Sci., 5, 331347, https://doi.org/10.5194/wes-5-331-2020.

    • Search Google Scholar
    • Export Citation
  • Letson, F., T. J. Shepherd, R. J. Barthelmie, and S. C. Pryor, 2020b: WRF modelling of deep convection and hail for wind power applications. J. Appl. Meteor. Climatol., 59, 17171733, https://doi.org/10.1175/JAMC-D-20-0033.1.