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    Root-mean-square errors (RMSE) of the (a) relative humidity (%), (b) temperature (K), and the (c) u and (d) υ components of the wind (m s−1) calculated at 0000 UTC from 1-, 2-, and 3-h 13-km RUC forecasts. Calculations only made in regions with SCP ≥ 1 over a 70-day period.

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    Idealized sounding used as the control sounding. The black line shows the temperature and the gray line shows the dewpoint temperature.

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    Vertical correlations between the 1-h forecast errors at heights every 100 hPa for (a) relative humidity, (b) temperature, (c) u-wind component, and (d) υ-wind component.

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    Histograms showing the distributions of the surface-based CAPE (J kg−1) for the soundings perturbed with the (a) 1-, (b) 2-, and (c) 3-h forecast errors.

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    Hodographs showing the wind profiles for the soundings perturbed with the (a) 1-, (b) 2-, and (c) 3-h forecast errors, with the control sounding wind profile overlaid in black.

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    Simulated reflectivity (dBZ) and storm-relative winds (m s−1) at 1 km AGL at (a) 30, (b) 60, (c) 90, and (d) 120 min into the simulation for the control run.

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    Simulated reflectivity (dBZ) and storm-relative winds (m s−1) at 1 km AGL at 120 min from four different simulations.

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    Supercell success rate vs simulation time (min) for 1-, 2-, and 3-h environmental error runs.

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    Spaghetti plots of the 40-dBZ-reflectivity contour from all 100 simulations for the 1-h error runs at (a) 30, (b) 60, (c) 90, and (d) 120 min with the control run 40-dBZ contour overlaid in black.

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    Frequency (scaled 0–100) of at least 40-dBZ reflectivity calculated at each grid point for the 1-h error runs at (a) 30, (b) 60, (c) 90, and (d) 120 min with the control run 40-dBZ-reflectivity contour overlaid in black.

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    Time series of the domain-maximum frequency of at least 40-dBZ reflectivity for all 100 runs perturbed with the 1-, 2-, and 3-h environmental forecast errors.

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    Time series of domain-maximum frequency of 5-min accumulated rainfall at thresholds from 1 to 10 mm for the (a) 1-, (b) 2-, and (c) 3-h error runs.

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    Area of the cold pool as defined by the −1-K perturbation potential temperature contour at 100 m AGL for the (a) 1-, (b) 2-, and (c) 3-h forecast errors. The solid black line shows the values for the control run and the dotted black lines show the 5th and 95th percentiles of the areas from the perturbed runs.

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    Time series of the domain-maximum frequency of UH ≥ 50 m2 s−2 for all 100 runs perturbed with the 1-, 2-, and 3-h environmental forecast errors.

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    UH paths for the right-moving storm from the runs with the (a) 1-, (b) 2-, and (c) 3-h environmental forecast errors, with the path from the control run overlaid in black.

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    The UH paths from Fig. 13 smoothed using kernel density estimation from the runs with (a) 1-, (b), 2-, and (c) 3-h environmental forecast errors. Probability isolines every 0.0004, beginning at 0.0001. The path from the control run is indicated by the dotted line.

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On the Predictability of Supercell Thunderstorm Evolution

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  • 1 Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/National Severe Storms Laboratory, Norman, Oklahoma
  • | 2 NOAA/National Severe Storms Laboratory, Norman, Oklahoma
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Abstract

Supercell thunderstorms produce a disproportionate amount of the severe weather in the United States, and accurate prediction of their movement and evolution is needed to warn the public of their hazards. This study explores the practical predictability of supercell thunderstorm forecasts in the presence of typical errors in the preconvective environmental conditions. The Advanced Research Weather Research and Forecasting model (ARW-WRF) is run at 1-km grid spacing and a control run of a supercell thunderstorm is produced using a horizontally homogeneous environment. Forecast errors from supercell environments derived from the 13-km Rapid Update Cycle (RUC) valid at 0000 UTC for forecast lead times up to 3 h are used to define the environmental errors, and 100 runs initialized with environmental perturbations characteristic of those errors are produced for each lead time. The simulations are analyzed to determine the spread and practical predictability of supercell thunderstorm forecasts from a storm-scale model, with the control used as truth.

Most of the runs perturbed with the environmental forecast errors produce supercell thunderstorms; however, there is much less predictability for storm motion and structure. Results suggest that an upper bound to the practical predictability of storm location with the current environmental uncertainty for a 1-h environmental forecast is about 2 h, with the predictability of the storms decreasing to 1 h as lead time increases. Smaller-scale storm features, such as midlevel mesocyclones and regions of heavy rainfall, display much less predictability than storm location. Mesocyclone location is predictable out to 40 min or less, while heavy 5-min rainfall location is not predictable.

Corresponding author address: Rebecca M. Cintineo, CIMSS, University of Wisconsin—Madison, 1225 W. Dayton St., Madison, WI 53706. E-mail: rebecca.cintineo@ssec.wisc.edu

Abstract

Supercell thunderstorms produce a disproportionate amount of the severe weather in the United States, and accurate prediction of their movement and evolution is needed to warn the public of their hazards. This study explores the practical predictability of supercell thunderstorm forecasts in the presence of typical errors in the preconvective environmental conditions. The Advanced Research Weather Research and Forecasting model (ARW-WRF) is run at 1-km grid spacing and a control run of a supercell thunderstorm is produced using a horizontally homogeneous environment. Forecast errors from supercell environments derived from the 13-km Rapid Update Cycle (RUC) valid at 0000 UTC for forecast lead times up to 3 h are used to define the environmental errors, and 100 runs initialized with environmental perturbations characteristic of those errors are produced for each lead time. The simulations are analyzed to determine the spread and practical predictability of supercell thunderstorm forecasts from a storm-scale model, with the control used as truth.

Most of the runs perturbed with the environmental forecast errors produce supercell thunderstorms; however, there is much less predictability for storm motion and structure. Results suggest that an upper bound to the practical predictability of storm location with the current environmental uncertainty for a 1-h environmental forecast is about 2 h, with the predictability of the storms decreasing to 1 h as lead time increases. Smaller-scale storm features, such as midlevel mesocyclones and regions of heavy rainfall, display much less predictability than storm location. Mesocyclone location is predictable out to 40 min or less, while heavy 5-min rainfall location is not predictable.

Corresponding author address: Rebecca M. Cintineo, CIMSS, University of Wisconsin—Madison, 1225 W. Dayton St., Madison, WI 53706. E-mail: rebecca.cintineo@ssec.wisc.edu

1. Introduction

Although they account for only a small percentage of thunderstorms, supercell thunderstorms have a large societal impact since most of them are severe (Burgess and Lemon 1991) and they produce a disproportionate amount of the hazards associated with thunderstorms (Duda and Gallus 2010). Those hazards include heavy rain, large hail, damaging straight-line winds, and tornadoes, with most strong or violent tornadoes associated with supercell thunderstorms (Moller et al. 1994). These long-lived, organized storms, first termed “supercells” by Browning (1962), have been studied extensively using radar observations and, while many characteristics are associated with supercells, the main feature that differentiates them from other thunderstorm modes is their deep, persistent, rotating updraft (Thompson 1998; Doswell and Burgess 1993).

Since the 1970s, the structure and evolution of supercells have been simulated and examined using convective-scale numerical weather prediction models to learn more about the physical processes that produce the various storm features and the influence of varying the storm environment (e.g., Weisman and Klemp 1982, 1984). The success of the convective models to qualitatively reproduce thunderstorm development and evolution has led to the recent implementation of convective-scale numerical forecast systems that provide explicit forecasts of convection out to 12 h or longer. Increasing computing power and the decreasing grid spacing of numerical models has led to the possibility of utilizing storm-scale models in operational settings to forecast the development of thunderstorms and their associated hazards. With the “Warn-on-Forecast” approach to issuing warnings based upon model ensemble forecasts of storm features being considered (Stensrud et al. 2009), instead of waiting for their detection, an investigation of the predictability of supercell thunderstorms from a practical operational standpoint is warranted and is the focus of this study. The confidence that a forecaster can place in the forecasts of supercell thunderstorms using storm-scale models is investigated, given the typical uncertainty of the environmental forecast 1, 2, and 3 h prior to the initiation of convection.

Many studies have looked at the predictability of large-scale weather features, most frequently examining the error growth of the geopotential height forecasts at a specified pressure level (e.g., Lorenz 1982; Dalcher and Kalnay 1987; Molteni and Palmer 1993; Bengtsson and Hodges 2006). Others have focused on the predictability on the mesoscale (e.g., Warner et al. 1984; Anthes et al. 1985; Zhang et al. 2003, 2006, 2007) and numerous studies have also delved into the predictability of the climate and its features (e.g., Kirtman 2003; Chen and Cane 2008). However, few studies have been performed that have investigated the predictability of the weather on the storm scale, in which more complex, three-dimensional motions and turbulence become important.

Lorenz (1969) used a turbulence-based approach to initially theorize that, while the predictability of larger, synoptic-scale motions is around a few weeks, predictability decreases with decreasing horizontal scale to the point where it is on the order of only a couple hours for storm-scale motions with 20-km wavelengths. However, that theoretical limit could be either increased or decreased in practice because of the inherent nature of storm-scale atmospheric phenomena. Lilly (1986) proposed that the highly helical nature of supercell thunderstorms and their resulting high degree of organization as compared to other storms might likewise act to suppress the turbulent dissipation within storms, and therefore the energy cascade, enhancing their predictability. However, Lilly (1990) found that the actual helicity of supercells is only a fraction of what is theoretically possible, and so its suppression of the energy cascade may be limited. A sensitivity study was performed by Droegemeier and Levit (1993) to see if storms in low- or high-shear environments, which are conducive to multicell or supercell storms, respectively, were more sensitive to identical changes in initial conditions. They found that more confidence could be placed in the forecast of the supercell than the forecast of a multicell storm, which is consistent with the hypothesis of Lilly (1986).

Droegemeier (1997) pointed out that Lorenz’s estimate of the limit of storm-scale predictability may have been too long since the turbulence-based approach he used assumed the turbulent flow to be continuous, which does not take into account the intermittency of storms in both time and space. Knowledge of the forcing of small-scale phenomena could also impact the range of their predictability, with predictability lengthened in the presence of weaker atmospheric instability or greater forcing by surface features (e.g., Anthes 1986). Interactions between storms also influence their evolution, and so errors in the forecast of one storm would result in errors in the prediction of the development of other nearby subsequent storms (Bluestein and Weisman 2000). Storms can also modify their environments, further influencing their predictability (Brooks et al. 1994; Weisman et al. 1998). Therefore, there are many factors and limitations that would need to be taken into account in a comprehensive study of supercell predictability.

The common approaches to exploring predictability, and even the definition of predictability, for large-scale atmospheric features may not necessarily be appropriate for the mesoscale because of the nature of the phenomena and operational application (Warner et al. 1984). The location and development of smaller-scale features is what is important on the mesoscale and thus a more operationally practical perspective must be taken. Warner et al. (1984) suggest that the definition of predictability for the smaller scales should be changed to include the growth in error to where the forecast no longer provides predictive utility to forecasters. The same is true for the storm scale, and the present study seeks to provide a more practical approach to predictability based upon specific storm features. This approach is similar to that of previous studies that investigated the predictability of mesoscale convective systems (MCSs) (Stensrud and Wicker 2004; Wandishin et al. 2008, 2010).

The predictability investigated here is meant to provide an upper limit on the predictability of supercell thunderstorms, since the environment and storm initialization method used are highly idealized. The initial model environment is horizontally homogeneous and therefore not necessarily realistic since it leaves out the effects of boundaries, surface topography, land use, and large-scale forcing, which could serve to either increase or decrease the predictability of the storms, depending on the situation. Spatially varying vertical shear can also influence the evolution of storms, yet is not captured by a horizontally homogeneous environment (Richardson et al. 2007). Holding the environment constant throughout the simulation is not a realistic depiction of what happens in the actual atmosphere, as shown by Ziegler et al. (2010) and Bluestein (2009). The accuracy of the initial conditions on the convective scale, such as when radar data are assimilated into a model, can also affect the predictability of the storm (Snyder and Zhang 2003) but is not considered in this study. Convective initiation, which has been found to be difficult to predict and to be sensitive to small errors in the planetary boundary layer (Crook 1996; Brooks et al. 1993), is guaranteed in our simulations and so only the predictability of the evolution of the storm is investigated. It is assumed that the model used is perfect and that any divergence in the solutions is solely due to the errors in the initial atmospheric state. While it is well known that model physics and parameterizations can affect storm simulations (Gilmore et al. 2004; Cohen and McCaul 2006; Dawson et al. 2010), the parameterizations are kept constant for all the model runs in this study.

Section 2 discusses the methodology used for this predictability study, the computation of the typical environmental forecast errors, the procedure chosen to perturb the control sounding with those errors, and the setup of the numerical model. The results of initializing and running the model with the perturbed soundings are described in section 3, and a discussion of those results is provided in section 4.

2. Methodology

This study seeks to determine the predictability of a supercell thunderstorm with respect to errors in the initial storm environment. Environmental errors at 1-, 2-, and 3-h forecast lead times are computed for environments that are expected to produce supercell thunderstorms from an operational mesoscale model, and those errors are then used to construct 100 environmental perturbations on a control supercell sounding for each of the forecast lead times. The homogeneous environment of a limited-area storm-scale model is defined by the perturbed soundings and a storm is initiated using a warm bubble, similar to past studies (e.g., Crook 1996). The resulting storm simulations are analyzed for both their variability and the divergence from the storm initialized using the control sounding, which is considered to be the “truth.” Specific features of the storms are used to quantify the variability as this gives more insight into the practical predictability of the forecasts.

a. Computation of the environmental errors

Data from the 13-km Rapid Update Cycle (RUC) are used to calculate environmental forecast errors from an operational mesoscale model in regions supportive of supercells. RUC is an operational numerical weather prediction model run by the National Centers for Environmental Prediction (NCEP) that assimilates weather data and produces short-range forecasts out to 12 h with 1-h frequency. By assimilating weather observations to update its analyses, it is able to produce more accurate short-term forecasts (Benjamin et al. 2004). For this study, the analysis time of 0000 UTC, which is a typical time for thunderstorm development in the United States, is used as the best estimate of the atmospheric state. RUC forecasts valid at 0000 UTC with 1-, 2-, and 3-h lead times, which would be issued at 2300, 2200, and 2100 UTC, respectively, are used to compute the forecast errors for the environment over a spatial domain limited to a region encompassing most of the continental United States east of the Rocky Mountains, which is where most supercell thunderstorms in the United States generally occur (Brooks et al. 2003a,b; Doswell et al. 2005). There are uncertainties in the RUC analysis itself, such that the errors computed here are estimates of the actual forecast errors and likely provide a lower bound on these errors.

Within that domain, the supercell composite parameter (SCP) (Thompson et al. 2002) is used to define the area in which to compute the forecast errors to ensure that the errors are computed only within environments that have sufficient buoyancy and wind shear to support supercell thunderstorms. The SCP definition used includes normalized values of most unstable convective available potential energy (MUCAPE), the bulk Richardson number shear (BRN shear), which is one measure of the deep layer shear, and 0–3-km storm-relative helicity (SRH) and is calculated as
eq1
The result is a dimensionless number for which values greater than or equal to 1 have been found to indicate an environment that is expected to be supportive of supercell thunderstorms (Thompson et al. 2002).

The dates for which the forecast errors are computed are the days on which the environment was known to have supported supercell thunderstorms for the period of January–June 2010, selected using the archive of severe thunderstorm events from the Storm Prediction Center (SPC; Storm Prediction Center 2012). This yields a total of 70 days from which to compute the environmental errors. Data for 4 and 5 June 2010 are left out of the analysis as RUC data for those 2 days were incomplete on the National Oceanic and Atmospheric Administration (NOAA) Operational Model Archive and Distribution System (NOMADS) website.

The root-mean-square errors (RMSE) for the temperature, relative humidity, and u and υ winds are computed over all 70 days and all grid points within the regions defined by an SCP of at least 1. This gives a total of 349 546 grid points used in the calculations of the RMSE and from which random errors could be chosen to perturb the control sounding. If the horizontal spatial correlations of the errors were computed, they would likely show that there are fewer unique grid points for computing the errors, and so fewer degrees of freedom. The errors were computed at all 37 vertical levels available from the RUC, which are isobaric levels every 25 hPa from 1000 hPa at the lowest level up to 100 hPa at the highest atmospheric level (Fig. 1). The calculated RMSE profiles demonstrate a similar vertical structure to the errors found by Benjamin et al. (2004) when the 20-km RUC forecasts were verified against rawinsonde observations. The 1-, 2-, and 3-h forecast errors display similar trends, though with the values increasing with increasing lead time, as expected.

Fig. 1.
Fig. 1.

Root-mean-square errors (RMSE) of the (a) relative humidity (%), (b) temperature (K), and the (c) u and (d) υ components of the wind (m s−1) calculated at 0000 UTC from 1-, 2-, and 3-h 13-km RUC forecasts. Calculations only made in regions with SCP ≥ 1 over a 70-day period.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

b. The control sounding and its perturbation

The control sounding used in this study is an idealized supercell sounding, compliments of George Bryan (2010, personal communication; Fig. 2). It has surface-based convective available potential energy (CAPE) of 2315 J kg−1, convective inhibition (CIN) of −44 J kg−1, and a lifted condensation level (LCL) of 880 hPa, which corresponds to a height above ground level of 741 m. The winds veer with height, producing a 0–6-km vector wind difference, referred to hereafter as wind shear, of 22 m s−1 and a clockwise hodograph with 171 m2 s−2 of 0–3-km storm-relative helicity. The large amount of CAPE and the wind shear create a sounding that is typical of environments supportive of supercell thunderstorms, with an SCP value of 2.3. Since the shear is at the lower end of the spectrum for supercell environments, a sounding with a greater amount of shear may lead to differing results given the same environmental errors as used in this study.

Fig. 2.
Fig. 2.

Idealized sounding used as the control sounding. The black line shows the temperature and the gray line shows the dewpoint temperature.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

Perturbations are added to the control sounding based upon the RUC model errors for the three forecast times. Since the errors do not have a Gaussian distribution—so normality cannot be assumed—errors are randomly drawn from the RUC error dataset for specified pressure levels. Errors in between these pressure levels are interpolated. The pressure levels for which errors are drawn are chosen through examination of the vertical error correlations and determining the depths over which the correlations decrease to zero. The Pearson correlation coefficient is computed for temperature, relative humidity, and wind errors every 100 hPa to determine the vertical correlation of the errors (Fig. 3). The vertical pressure difference at which the correlation drops to near zero is approximately 200 hPa but varies somewhat depending on the environmental variable. The spacing deemed appropriate for each variable, shown in Table 1, is used to apply a new random variable to the control sounding.

Fig. 3.
Fig. 3.

Vertical correlations between the 1-h forecast errors at heights every 100 hPa for (a) relative humidity, (b) temperature, (c) u-wind component, and (d) υ-wind component.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

Table 1.

Pressure levels (hPa) at which new random errors were applied to the sounding.

Table 1.

A random draw from the RUC errors at the pressure levels given in Table 1 for each variable is used to construct the perturbations to the control sounding. A polynomial spline is used to interpolate the perturbations to model levels between the assigned levels and generate a complete perturbation profile to add to the control sounding. To keep the soundings physical, supersaturation is avoided by limiting the relative humidity throughout the sounding to 100%. Initial testing indicated that a sounding with a saturated layer or a lapse rate that is dry adiabatic or greater than dry adiabatic above the lifting condensation level would cause the model to generate convection over the entire domain, which is unphysical, so soundings with these characteristics are discarded and replaced by other randomly perturbed soundings. In this way, 100 different perturbed soundings to initialize the storm-scale weather prediction model are created for each of the three forecast lead times. The vertical correlations that were computed for the perturbations applied to the soundings resemble those of the RUC errors (not shown), giving confidence in the method used.

The vertical profiles of the RMSE of the relative humidity, temperature, and u- and υ-wind perturbations that were applied to the sounding have general shapes and magnitudes similar to the profiles of the RMSE calculated from the entire RUC dataset. When the mean perturbed soundings are plotted, they match up quite well with the control sounding (not shown). Since we applied perturbations to both temperature and relative humidity, the resulting error distributions for mixing ratio are slightly larger in the sounding perturbations than suggested by the RUC dataset with the differences decreasing with height. The soundings that resulted from the perturbation of the control sounding display quite a range of variability, especially with regard to CAPE (Fig. 4). For the 1-h forecast errors, the soundings have surface-based CAPE (SBCAPE) that varies from 780 up to 5907 J kg−1. The mean is 2408 J kg−1, which is fairly close to the value of 2315 J kg−1 for the control run, and the interquartile range (IQR) is 954 J kg−1. Thompson et al. (2003) found a similar IQR of about 900 J kg−1 for the 1-h SBCAPE errors from the 40-km RUC-2. The SBCAPE from the 1-h-lead-time RUC data used in this study had a larger IQR at 1625 J kg−1, while the mean was a lower at 1409 J kg−1. When considering only RUC SBCAPE values greater than 250 J kg−1, the IQR decreased to 1396 J kg−1 and the mean increased to 1737 J kg−1. The mean SBCAPE for the perturbed soundings decreases to 2190 and 2253 J kg−1 for the 2- and 3-h errors, respectively, but the spread increases as the lead time increases such that the IQRs are 1116 and 1154 J kg−1, respectively.

Fig. 4.
Fig. 4.

Histograms showing the distributions of the surface-based CAPE (J kg−1) for the soundings perturbed with the (a) 1-, (b) 2-, and (c) 3-h forecast errors.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

The mean 0–6-km wind-shear values for all 100 perturbed soundings are close to the value from the control sounding, though they increase slightly with increasing forecast lead time to 22.6, 22.9, and 23.3 m s−1 for the 1-, 2-, and 3-h errors, respectively. There is a greater amount of spread with time as the standard deviations also increase with increasing lead time to 2.0, 2.4, and 3.1 m s−1. The wind profiles of the perturbed runs are shown in Fig. 5. The SCP values are greater than 1, indicating environments favorable for supercells, for 92%, 93%, and 89% of the 1-, 2-, and 3-h environmental errors, respectively.

Fig. 5.
Fig. 5.

Hodographs showing the wind profiles for the soundings perturbed with the (a) 1-, (b) 2-, and (c) 3-h forecast errors, with the control sounding wind profile overlaid in black.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

c. Numerical model

The control and perturbed soundings are used to initialize idealized runs of the Advanced Research Weather Research and Forecasting model (ARW-WRF), version 3.2.1 (Skamarock et al. 2008), used as a three-dimensional, nonhydrostatic storm-scale model with 1-km horizontal grid spacing. Bryan et al. (2003) discuss the potential need for higher resolution for simulating deep moist convection, but for the present purpose, 1-km horizontal grid spacing should be sufficient while remaining computationally affordable. The horizontal domain is 150 km × 150 km, chosen to be large enough to keep the 2-h storm simulation within the domain. We use 55 stretched vertical levels, allowing for a higher density of layers in the boundary layer, with about 30-m vertical spacing between the lowest levels increasing to about 570-m spacing at the top of the atmosphere, located at 20 km AGL. The microphysics option used is the Lin–Farley–Orville (LFO) microphysics scheme (Lin et al. 1983). Since the simulation is idealized and cloud-resolving, the radiation, surface, and boundary layer physics are turned off and there is no cumulus parameterization. A 1.5-order three-dimensional turbulent kinetic energy closure scheme is used for subgrid-scale mixing and there is no upper-level damping applied. A sixth-order horizontal advection scheme and a third-order vertical advection scheme are used with open boundary conditions on the domain edges.

A single input sounding is used to create a horizontally homogeneous atmosphere with which to start the model simulation. The convection within the model is initiated by introducing an artificial 4-K thermal bubble with a horizontal radius of 10 km into the initial atmosphere just above the surface, which ensures convective initiation. The simulation run using the control sounding to initialize the model is integrated out to 2 h of simulation time, with the model output available every 5 min of simulation time, and is the “truth” against which the model runs initialized with the perturbed soundings are compared. All simulations have the same model setup, yielding ensembles of 100 different 2-h simulations for each of the three lead times.

d. Supercell definition

The one characteristic that has been used to unambiguously differentiate supercells from other thunderstorms is a quasi-steady rotating updraft that persists for tens of minutes (Thompson 1998; Doswell and Burgess 1993). Therefore, having a storm with a large, persistent, rotating updraft is the basic dynamical definition of a supercell. It has been suggested that the convective time scale, over which a parcel travels through a storm’s updraft, is 20–30 min (Doswell and Burgess 1993; Doswell 2001; Markowski and Richardson 2010), and so that length of time is used as a minimum lifetime for a supercell mesocyclone.

Updraft helicity (UH) is a useful parameter for the detection of mesocyclones and is described by Kain et al. (2008) as the product of vertical velocity and vertical vorticity integrated over a depth of the atmosphere. It is given by the equation
eq2
where w is the vertical velocity (m s−1) and ζ is the vertical vorticity (s−1). For looking at midlevel rotation in a storm, the integral is taken over the layer from z0 = 2000 m to zt = 5000 m AGL. Kain et al. (2008) find a UH value of at least 50 m2 s−2 to be a good indicator of rotating updrafts, so that threshold is used to define a mesocyclone in this study.

The definition employed in this study is that a supercell exists in the model when there is a rotating updraft, defined by UH values of at least 50 m2 s−2, that lasts for at least 25 min. Similar to Hocker and Basara (2008), the storm cell is said to have initiated with the first occurrence of a 40-dBZ echo and ended when there is no longer a mesocyclone.

3. Results

The model run initiated with the control sounding produces deep convection that splits into a persistent right-moving supercell and less-organized convection that moves off to the left (Fig. 6). The first 40-dBZ radar signature is produced at 1 km AGL at 20 min into the simulation, the same time at which the precipitation downdraft reaches the ground and the updraft at 4 km begins to split. By 30 min, there are two completely distinct updrafts at 4 km (not shown). At the time of the storm split, the rainfall accumulation drops off and the updraft speed decreases, consistent with previous studies (e.g., Klemp et al. 1981; Rotunno and Klemp 1985). The rainfall and updraft increase again after the storm splits. The left-moving storm develops into a region of less-organized, multicellular convection and additional convection develops on the edge of the cold pool. The right-moving storm, which is the focus of this study, maintains its supercell characteristics for the remainder of the 2-h simulation, giving it a lifetime of 100 min by the end of the simulation, which would have been longer had the simulation been allowed to run further.

Fig. 6.
Fig. 6.

Simulated reflectivity (dBZ) and storm-relative winds (m s−1) at 1 km AGL at (a) 30, (b) 60, (c) 90, and (d) 120 min into the simulation for the control run.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

The variation among the simulations in the ensemble gives an idea of the confidence that can be placed in a forecast. An example of some of that variation is seen when looking at the simulated reflectivity at the end of several of the perturbed simulations (Fig. 7). In some runs, the right-moving supercell dissipates by 120 min, whereas in other runs the convection is much more widespread. Predictability is investigated by looking at how quickly the features of the storms in the ensembles of perturbed runs diverge from one another and from the features in the control simulation. The time length of the practical predictability for various storm features refers to the time since model initialization, even though supercell characteristics may not appear during the first 20 min of simulation.

Fig. 7.
Fig. 7.

Simulated reflectivity (dBZ) and storm-relative winds (m s−1) at 1 km AGL at 120 min from four different simulations.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

a. Supercell success rate

According to the criteria for a supercell described previously, 97% of the 1-h forecast error–perturbed runs, 98% of the 2-h forecast error runs, and 92% of the 3-h forecast error runs produce a supercell with a mesocyclone that lasts for at least 25 min (Fig. 8). With fewer storms becoming supercells in the 3-h error runs, there are also fewer that remain supercells over the remainder of the simulation time. By the end of the 2-h simulation, 81% of the 1-h error runs, 82% of the 2-h error runs, and 74% of the 3-h error runs still have a right-moving supercell storm. The mean lifetime of a supercell is roughly constant in the 1- and 2-h error runs at 92 min but is several minutes shorter at 86 min as the forecast lead time increases to 3 h. Thus, the convective mode forecasts for supercells are very predictable in the presence of typical 1–3-h environmental forecast errors.

Fig. 8.
Fig. 8.

Supercell success rate vs simulation time (min) for 1-, 2-, and 3-h environmental error runs.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

b. Storm evolution and movement

1) Frequency of 40-dBZ simulated reflectivity

The evolution and movement of the storm during the simulation can give insight into how far out the forecast of a storm’s position is useful to a forecaster and how rapid storm location errors grow. One measure of the predictability of storm placement is the amount of overlap between the storms in the perturbed runs (Fig. 9). At 30 min, there appears to be good agreement in the placement of the storms, as judged by the 40-dBZ contours. By 60 min, the placement is still reasonable, but by 90 min and later there is a lot of spread between the runs. At 120 min, the main, right-moving storm in the control run appears to lag behind a majority of storms in the perturbed runs and the locations of the storms in the perturbed runs often do not overlap the control run. Similar results are found for the 2- and 3-h error runs.

Fig. 9.
Fig. 9.

Spaghetti plots of the 40-dBZ-reflectivity contour from all 100 simulations for the 1-h error runs at (a) 30, (b) 60, (c) 90, and (d) 120 min with the control run 40-dBZ contour overlaid in black.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

The picture of what is happening becomes clearer when the frequency of simulated 40-dBZ or greater reflectivity for the perturbed runs is plotted (Fig. 10), with the 40-dBZ contour of the control run overlaid. Once again, the 1-h error runs are shown, but the 2- and 3-h error runs depict a similar spatial pattern, though with lower frequencies overall. At 30 min, there is overlap between about 90% of the runs. By 60 min, the number of runs that have overlapping reflectivity of at least 40 dBZ is still around 85% to 90% and the 50% density contour matches up fairly well with the control contour. The control supercell starts to lag behind the area of higher frequency around 80 min into the simulation, and there is a maximum overlap of only about 55% of the runs for the right-moving storms by the end of the 2 h. The convection to the north, which was a result of the left-moving supercell that split off and additional convection on the edge of the cold pool, displays a higher frequency since the convection in that area was more persistent and widespread and thus more likely to have overlap. The right-moving storms cover a smaller area and are more isolated, so the overlap of their 40-dBZ reflectivity falls off faster over time.

Fig. 10.
Fig. 10.

Frequency (scaled 0–100) of at least 40-dBZ reflectivity calculated at each grid point for the 1-h error runs at (a) 30, (b) 60, (c) 90, and (d) 120 min with the control run 40-dBZ-reflectivity contour overlaid in black.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

Analyses of the domain-maximum frequency of at least 40-dBZ simulated reflectivity for all three forecast lead times show that at no time do all the simulations overlap, even for the 1-h forecast lead time errors (Fig. 11). Not all of the storms that initialize with their first 40-dBZ contour at the same time overlap at that time, which seems to be due to the area of the storms at 1 km not becoming large enough for a majority of them to overlap until about 30 min into the simulations. The greatest frequency of at least 40 dBZ is around 40 min, which is not long after most of the storms split, and it decreases after that. For a 1-h lead time, which shows the greatest amount of predictability, there is 80% or greater overlap between 30 min to just a little over 1 h. The overlap then drops off steadily, reaching just over 60% by the end of the 2-h simulation. The other two forecast lead times show similar trends, but the domain-maximum frequencies decrease as the lead time increases.

Fig. 11.
Fig. 11.

Time series of the domain-maximum frequency of at least 40-dBZ reflectivity for all 100 runs perturbed with the 1-, 2-, and 3-h environmental forecast errors.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

While individual users may have greater or lesser tolerance for position error, an accurate storm location prediction is critical to issuing hazardous weather warnings. A subjective comparison of the spaghetti (Fig. 9) and the domain-maximum frequency plots (Fig. 11) allows us to estimate a frequency value for which the usefulness of the forecasts is lost. Storm locations from the 100 simulations show reasonably good overlap through 60 min and arguably out to 90 min (Figs. 9a–c). The number of perturbation runs that have overlap with the right-moving control storm based on the 40-dBZ threshold is found and, for the 1-h error runs, an increasing number of runs have distinct separation from the control beginning at 70 min (not shown). However, a large fraction of the storms at 120 min are spatially far enough apart that it becomes difficult to conclude that they are the same storm from 90 min earlier without additional information. Out of the 100 runs, 40% have no overlap with the control storm and so have completely lost their association with it. Thus, we relate the 60% domain-maximum frequency value with the loss of useful storm location information for warning operations and that value is chosen as a reasonable threshold for the loss of practical predictability for storm feature location. Depending on the user, other frequency threshold values can be chosen, such as 85% if overlap between all of the storms is required or 70% if having no overlap between 20 of the 100 runs can be tolerated.

If the 60% domain-maximum frequency value is chosen as an indicator for when practical predictability is lost, then the 1-h error runs provide useful information on storm location out to 2 h. However, practical predictability is lost for the 2-h error runs at 85 min and is lost for the 3-h error runs at roughly 60 min. This suggests that with characteristic short-term environmental errors, useful storm location forecasts can extend out to between 1 and 2 h. Since the maximum frequencies decrease roughly linearly with time, decreasing the threshold value increases the predictability by roughly 20 min for every 10% drop. This 2-h predictability time is longer than the range of values suggested in real data cases by Stensrud and Gao (2010), Aksoy et al. (2010), and Dawson et al. (2012), as would be expected from a perfect model experiment. The differences in predictability limits derived from perfect model and real data cases can provide an estimate of the role of model error.

2) 5-min rainfall accumulations up to 2 mm

The domain-maximum frequency is likewise found for the rainfall accumulations for each 5-min interval over the simulation time for rainfall accumulation thresholds from 1 to 10 mm (Fig. 12). The areal extents of the 1- and 2-mm rainfall accumulations tend to match or slightly fall inside the region of 40-dBZ reflectivity (not shown). Thus, it is not surprising that the domain-maximum frequencies for these thresholds mimic that found for 40-dBZ reflectivity, with the frequencies increasing to a maximum around 40 min before decreasing with the storm split. These results suggest a predictability length for the 1-mm rainfall region of 120 min for the 1-h error runs, decreasing to 85 min for the 3-h error runs. The frequencies for the higher accumulation thresholds will be discussed further when looking at the smaller-scale features within the storms.

Fig. 12.
Fig. 12.

Time series of domain-maximum frequency of 5-min accumulated rainfall at thresholds from 1 to 10 mm for the (a) 1-, (b) 2-, and (c) 3-h error runs.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

3) Cold pool area

Precipitation falling from the storm enhances the storm’s downdraft through evaporative cooling as the precipitation falls through subsaturated air and evaporates. When the downdraft reaches the ground, the air, which is cooler than the surrounding air at the surface, spreads beneath the storm to form a cold pool, which is a broad-scale feature of the storm. The edge of the cold pool, also termed the gust front, is defined by the −1°C perturbation potential temperature isotherm at 100 m AGL. The total area of the cold pool is calculated and compared (Fig. 13). By the end of the 2-h simulation, the mean maximum cold-pool size for the runs perturbed with the 1-h errors is 2689 km2, for the 2-h errors is 2475 km2, and for the 3-h errors is 2293 km2, which are all much larger than the control run’s cold-pool size of 1164 m2. This decrease in mean cold-pool area with increasing forecast lead time is likely due to fewer supercells being maintained within the ensemble of runs for the longer lead times. These results indicate that predictions of cold-pool area are very sensitive to the initial environmental errors.

Fig. 13.
Fig. 13.

Area of the cold pool as defined by the −1-K perturbation potential temperature contour at 100 m AGL for the (a) 1-, (b) 2-, and (c) 3-h forecast errors. The solid black line shows the values for the control run and the dotted black lines show the 5th and 95th percentiles of the areas from the perturbed runs.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

c. Storm structure

1) Mesocyclone path

Smaller-scale features within supercell thunderstorms are likely more difficult to predict accurately than the location of the storm as a whole. However, knowing the location of those features is important to forecasting the path of severe weather, such as knowing the path of a mesocyclone to predict the possible track of a tornado. A time series of the domain-maximum frequency for UH of at least 50 m2 s−2 indicates that for most of the simulation time there is much less overlap between the runs, and so less predictability, for the location of the mesocyclone than for the storm as a whole (Fig. 14). The frequency peaks around 20 min and then falls off dramatically. By the end of the simulation, there is less than 20% overlap between the storm mesocyclones for all three lead times. If we again use the 60% domain-maximum frequency threshold to define the limit of practical predictability, then mesocyclone location is predictable out to roughly 35 min for the 1-h error runs decreasing to 25 min for the 3-h error runs. This 35-min predictability limit is roughly consistent with the results from Dawson et al. (2012), who examined simulations of the Greensburg, Kansas, tornadic supercell thunderstorm.

Fig. 14.
Fig. 14.

Time series of the domain-maximum frequency of UH ≥ 50 m2 s−2 for all 100 runs perturbed with the 1-, 2-, and 3-h environmental forecast errors.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

To investigate the variability and predictability of the direction and length of the right-moving storm’s track, the path of the maximum positive UH within the right-moving storm is examined. The length of the control simulation’s UH path from the starting point to the ending point is 61.8 km in a direction of 29° with respect to the x axis (Fig. 15). The mean UH pathlengths for the perturbed runs are somewhat longer than that of the control run for all three forecast lead times, with lengths of 64.5, 64.9, and 62.3 km, respectively. As may be expected, the variability of the pathlengths increases with increasing lead time, with a standard deviation of 14.01 km at a 1-h lead time increasing to 23.3 km at a 3-h lead time. The control storm moves at a mean speed of about 10.9 m s−1 over its lifetime, while the mean speeds for the perturbed runs are faster at 12.2 m s−1 for the 1-h errors, 12.8 m s−1 for the 2-h errors, and 12.5 m s−1 for the 3-h errors, with standard deviations of 1.4, 1.8, and 2.6 m s−1, respectively. The longer mesocyclone pathlengths and faster speeds of the perturbed storms are consistent with the lag in the location of the control run when overlaid on the frequency of 40 dBZ or greater simulated reflectivity seen previously.

Fig. 15.
Fig. 15.

UH paths for the right-moving storm from the runs with the (a) 1-, (b) 2-, and (c) 3-h environmental forecast errors, with the path from the control run overlaid in black.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

The control run and many perturbed runs show a clear transition to a more rightward-moving storm during the first hour of the simulation. The different environments not only change the mean wind in the cloud layer, but also influence the amount of turning once the storm becomes supercellular. The directions of the UH paths with respect to the positive x axis have a range of 70° for the 1-h error runs, 65° for the 2-h error runs, and 86° for the 3-h error runs. The wider range in the 3-h error run directions is primarily due to one rogue model run that has the main storm taking a much sharper right turn than the rest of the storms among all of the simulations. While the path of that storm is atypical, it still should be kept in mind that the track of that particular simulation is a possibility given the environmental errors.

When the paths are smoothed using kernel density estimation (KDE) (Wilks 2006), a clearer picture of storm behavior emerges (Fig. 16). KDE is a method for smoothing data by combining probability density functions for individual data points. A larger fraction of the storms in the 2- and 3-h error runs than the 1-h error runs take a sharper right turn, yielding mean path directions that are displaced to the right of the control run by 0.88° and 1.31°, respectively. The supercell mode with small rightward turns are still present in the 2- and 3-h error runs but are not as prevalent as seen in the 1-h error runs. The combination of the differences in the lengths and directions of the UH paths leads to large differences in UH location among the runs for all three lead times and explains the rapid decrease in practical predictability of the mesocyclone location.

Fig. 16.
Fig. 16.

The UH paths from Fig. 13 smoothed using kernel density estimation from the runs with (a) 1-, (b), 2-, and (c) 3-h environmental forecast errors. Probability isolines every 0.0004, beginning at 0.0001. The path from the control run is indicated by the dotted line.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0166.1

2) 5-min rainfall accumulations above 2 mm

The lower predictability of the smaller-scale features within the storm is also seen when looking at the frequency values for the 5-min rainfall accumulation thresholds above 2 mm, at which point the finer-scale features of the storm’s rainfall become more apparent (Fig. 12). The frequency values decrease as the rainfall rate threshold is increased, which makes sense as the lighter rain rates cover broader areas and are therefore more likely to have overlap among the perturbed simulations. Most of the rainfall thresholds have an initial frequency peak around 40 min followed by a second peak 20–30 min later. At higher rainfall thresholds, the secondary peak is actually higher than the initial one. Using a 60% domain-maximum frequency to determine when practical predictability is lost suggests that all 5-min accumulated rainfall totals above 5 mm are unpredictable in terms of location. For the 3-h error runs, all accumulated rainfall totals above 2 mm are unpredictable. Thus, the locations with the highest 5-min rainfall are less predictable than the mesocyclone location.

3) Domain-maximum updraft velocity

In addition to the spatial variability of the storm features given the environmental forecast errors, the variability in the strength of the storm is investigated by looking at the updraft speed. Similar to the storm in the control run, many of the storms reach their peak updraft speeds within the first half hour of the perturbed simulations. As the storm splits, the updraft speed decreases and does not increase again to its original value for most of the model runs. The mean peak updraft velocity for the 1-h error runs is 62 m s−1, the same as the control run, with a standard deviation of 12 m s−1. The 2-h error runs are similar, having a mean maximum updraft speed of 61 m s−1 and a standard deviation of 13 m s−1. The mean maximum updraft speed decreases to 57 m s−1 for the 3-h error runs, while the standard deviation increases to 17 m s−1. Those differences among the runs at the three lead times are consistent with what is seen visually when the updraft velocities of all the runs for each lead time are plotted as a time series (not shown). The variation of the evolution of the domain-maximum updraft speeds over the simulation time between the model runs does not appear to change much between the 1- and 2-h lead time ensembles, but several of the 3-h error runs have the updraft velocity fall off dramatically because of storm dissipation. While maximum updraft speeds are highly irregular over the course of each individual run, the predictability of updraft speed exceeding 20 m s−1 is very high. Predictability decreases as updraft speed increases. The irregularity of the updraft speeds causes the updraft helicity values to also be highly irregular over each run (not shown).

4. Discussion and conclusions

Almost all of the of the 1- and 2-h forecast error model runs produce storms that fit the criteria for a supercell, while 92% of the 3-h-lead-time error runs produce supercells. That means that there can be a high level of confidence placed in the forecast of a supercell given the uncertainty in the forecast environment with up to 3 h of lead time. This result underlies current severe weather forecast practices that outline regions where supercells are likely days in advance based upon environmental forecasts (Grams et al. 2012). However, not all of the runs produced convection that lasted long enough to be classified as a supercell, highlighting limits to storm predictability. For all three forecast lead times, about 80% of the runs that produce a supercell maintain the storm for the remainder of the simulation.

The practical predictability of the storm features decreases with the size of the feature, assuming the definition of predictability used herein. Storm location and the region of lightest rainfall are the most predictable, with domain-maximum frequencies suggesting useful location forecasts are possible out to about 2 h. Given the 1-h-lead-time environmental errors, 90% of the storm locations defined by reflectivity above 40 dBZ overlap with the control run at 70 min into the simulation. By 15 min later, however, only 60% of the locations overlap with the control storm. By the end of the full 2 h, only 55% of the perturbed run locations have overlap of the right-moving storms. The location of the midlevel mesocyclone is much less predictable than the storm location, with useful forecasts out to no more than 40 min for 1-h environmental errors decreasing to 25 min for 3-h errors. The predictability decreases even further when examining the locations of heaviest 5-min accumulated rainfall totals, with the locations unpredictable for accumulations above 5 mm. The predictions of cold-pool areal extent clearly show the difficulties in predicting that field accurately in the presence of environmental errors.

One limitation of this study and its applicability to the real-world environment is that the initial environment is initialized with a single point sounding and is therefore horizontally homogeneous. The real atmosphere contains inhomogeneities, such as airmass boundaries and influences from topographic features, and other storms may already be within the environment at the storm’s initialization time that could affect the storm’s subsequent evolution through their outflow boundaries or interaction between the storms themselves. A storm may either strengthen or deteriorate as it rides along or crosses over a boundary (Maddox et al. 1980; Atkins and Weisman 1999; Wilson and Megenhardt 1997; Rasmussen et al. 2000; Bunkers et al. 2006). Ziegler et al. (2010) found that when a storm moved into a more stable environment, it was able to persist longer, suggesting that the exact effects of crossing boundaries are not completely known.

Another limitation is the use of a thermal bubble inserted into the initially homogeneous atmosphere to artificially initiate a storm since simulations may be sensitive to the magnitude and size of the initial thermal bubble (Lilly 1990; McPherson and Droegemeier 1991; McPherson 1991; Brooks 1992). In operational use, the initial fields of the storm could be obtained with radar and inserted into the cloud-scale model to initiate the storm, which can also introduce additional error into a simulation (Snyder and Zhang 2003). A similar approach was tested in the initial phase of this study by taking the winds and thermal profile of the control storm once it had formed in the simulation and inserting them into the model at the initial time, but the results were largely unchanged. The idealized environment and the assumption of convective initiation suggest that this study likely provides an upper bound to the actual predictability of supercell thunderstorms. Using smaller horizontal grid spacing than the 1-km resolution used here may also result in predictability being lost even faster.

Results from this study confirm that using an ensemble to produce a probabilistic storm-scale forecast may work well, in contrast to individual deterministic forecasts. The ensemble mean is especially useful in this case for the forecast of the direction of the storm’s path, as seen when analyzing the UH paths. The mean path is close to the control for all three forecast lead times, despite the fact that there were fewer storms that were maintained, creating greater variability, for the 3-h error runs. Overall, however, it appears that forecasts of supercell thunderstorm location, regions of heaviest rainfall, and mesocyclone location beyond 1–2 h are not yet possible given the current errors in the forecast of the storm environment.

Acknowledgments

This study was funded by the NOAA Warn-on-Forecast project. We gratefully acknowledge the helpful suggestions provided by Drs. Michael Richman and Xuguang Wang of the School of Meteorology at the University of Oklahoma, Dr. Chris Snyder at NCAR, as well as the very constructive and helpful comments from two anonymous reviewers. We further thank Kent Knopfmeier for his help in learning how to run the WRF model. Funding was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA-University of Oklahoma Cooperative Agreement #NA11OAR4320072, U.S. Department of Commerce.

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