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Experimental Tropical Cyclone Forecasts Using a Variable-Resolution Global Model

COLIN M. ZARZYCKI National Center for Atmospheric Research,* Boulder, Colorado

CHRISTIANE JABLONOWSKI Department of Atmospheric, Oceanic, and Space Sciences, University of Michigan, Ann Arbor, Michigan

(Manuscript received 20 April 2015, in ﬁnal form 5 July 2015)

ABSTRACT

Tropical cyclone (TC) forecasts at Dx ; 14-km horizontal resolution (0.1258) are completed using variable- resolution (V-R) grids within the Community Atmosphere Model (CAM). Forecasts are integrated twice daily from 1 August to 31 October for both 2012 and 2013, with a high-resolution nest centered over the North Atlantic and eastern Pacific Ocean basins. Using the CAM version 5 (CAM5) physical parameterization package, regional refinement is shown to significantly increase TC track forecast skill relative to unrefined grids (Dx ; 55 km, 0.58). For typical TC forecast integration periods (approximately 1 week), V-R forecasts are able to nearly identically reproduce the flow field of a globally uniform high-resolution forecast. Simulated intensity is generally too strong for forecasts beyond 72 h. This intensity bias is robust regardless of whether the forecast is forced with observed or climatological sea surface temperatures and is not significantly miti- gated in a suite of sensitivity simulations aimed at investigating the impact of model time step and CAM’s deep convection parameterization. Replacing components of the default physics with Cloud Layers Unified by Binormals (CLUBB) produces a statistically significant improvement in forecast intensity at longer lead times, although significant structural differences in forecasted TCs exist. CAM forecasts the recurvature of Hurricane Sandy into the northeastern United States 60 h earlier than the Global Forecast System (GFS) model using identical initial conditions, demonstrating the sensitivity of TC forecasts to model configuration. Computational costs associated with V-R simulations are dramatically decreased relative to globally uniform high-resolution simulations, demonstrating that variable-resolution techniques are a promising tool for future numerical weather prediction applications.

1. Introduction proper representation of these features (NOAA Science Advisory Board 2006). Increasing horizontal resolution has been shown to To alleviate these issues, the use of limited-area be critically important in the improvement of numeri- models (LAMs, also referred to as regional or nested cal forecasting over the past few decades. While trop- models) in the forecasting community has become ical cyclone (TC) forecasting has correspondingly popular. These models only simulate a small portion of beneﬁted, current operational grid spacings for global the global domain, allowing for available computational products continue to be less than is required for resources to be ‘‘targeted’’ to a speciﬁc region of interest. This provides greatly increased horizontal resolution over the cyclone itself, which has been shown to * The National Center for Atmospheric Research is sponsored provide a more realistic dynamical representation of by the National Science Foundation. storm structure (e.g., Davis et al. 2010; Jin et al. 2014). However, LAMs require lateral boundary conditions to drive the innermost domain. These boundary condi- Corresponding author address: Colin M. Zarzycki, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO tions are typically derived from global forecast model 80307. output, which is computed at a coarser resolution and E-mail: [email protected] almost always utilizes a different dynamical core and set

DOI: 10.1175/MWR-D-15-0159.1

Ó 2015 American Meteorological Society Unauthenticated | Downloaded 10/06/21 09:29 AM UTC OCTOBER 2015 Z A R Z Y C K I A N D J A B L O N O W S K I 4013 of physical parameterizations, potentially introducing 2. Variable resolution in CAM-SE parent model biases and interpolation errors into the a. CAM-SE LAM (Warner et al. 1997; Mesinger and Veljovic 2013). In addition, the application of the boundary conditions The Community Atmosphere Model (CAM), version to the regional domain is sometimes numerically in- 5.3.1, was used for this study. CAM is jointly developed consistent and ill posed (McDonald 2003). For the pur- at the National Center for Atmospheric Research poses of TC forecasting, LAMs have historically (NCAR) and various Department of Energy (DOE) performed worse than global forecast models in terms of laboratories. All simulations are completed within the TC track beyond three days, in part because of these Community Earth System Model (CESM) framework issues (Gall et al. 2013). (version 1.2), which allows for coupling of land, ocean, Variable-resolution general circulation models and ice models to CAM (Hurrell et al. 2013). Simula- (VRGCMs) serve to apply this idea of targeted, re- tions utilize the spectral element (SE) dynamical core in gional use of computing resources, but can do so with- CAM (Taylor et al. 1997; Taylor 2011; Dennis et al. out the need for externally forced boundary conditions. 2012). The SE scheme’s mathematical compatibility al- Locally high resolution is achievable within a global, lows for exact local conservation of mass, energy, and unified modeling framework, allowing the global and 2D potential vorticity (Taylor and Fournier 2010). The regional scales to interact in a more physically consis- model’s horizontal discretization is built upon a cubed- tent manner. In addition, the same formulation of sphere grid (Dennis et al. 2012). Cubed-sphere grids subgrid processes, such as turbulence and surface fluxes, provide for quasi-uniform mesh spacing over the entire can be applied across the global domain. Some exam- surface of the globe. This eliminates issues such as nu- ples of VRGCMs in recently published literature in- merical instabilities that result from the convergence of clude Skamarock et al. (2012), Harris and Lin (2013), meridians in polar regions on standard latitude–longitude and Zarzycki et al. (2014b), who have all demonstrated grids. The default polynomial degree on each cell ele- increased regional model skill when locally refining ment is three (cubic polynomials), which leads to fourth- horizontal resolution. order spatial accuracy (Taylor and Fournier 2010). Since VRGCMs do not require high resolution over the CAM-SE uses a Runge–Kutta time discretization with a global domain, they come at a greatly reduced compu- floating Lagrangian coordinate on hybrid sigma-pressure tational cost relative to traditional globally uniform surfaces in the vertical. Since spectral element tech- models. This may allow simulations to be run at higher niques are highly localized numerical discretizations, horizontal resolutions, for longer durations, or as multi- they require minimal communication between pro- member ensembles given a predetermined computing cessors on massively parallel computer systems. CAM- load. Ensemble forecasting, in particular, has been shown SE has been shown to scale nearly linearly up to one to greatly improve weather and climate forecasts element per processor (Dennis et al. 2012), making it a (Krishnamurti et al. 1999), with tropical cyclones being a potentially attractive choice for high-resolution runs on notable example (Gall et al. 2013). large computing architectures. In section 2, we offer an introduction to the spectral Because CAM-SE is designed for use with unstruc- element version of the Community Atmosphere Model, tured grids and the hydrostatic primitive equations are the variable-resolution configuration used in this study, solved locally on individual elements, it is trivial to per- the procedure for initializing the model in a forecast form model integrations on nonuniform grids. All cell framework, and the techniques utilized to track tropical elements must be quadrilaterals and conforming (every cyclones and assess forecast errors. Section 3 assesses edge is shared by exactly two elements) (Dennis et al. the results of the base set of simulations while section 4 2012). Any variable-resolution grid fulfilling these two provides results from a suite of physical parameteriza- criteria is, therefore, acceptable for use in CAM-SE tion perturbation experiments that investigate the sen- (Zarzycki et al. 2014b). sitivity of forecasted track and intensity to these The variable-resolution (V-R) grid used in this study modifications. Specific forecasts of Hurricane Sandy are is shown in Fig. 1. The grid is generated using the pro- highlighted in section 5, including a discussion of the cedure outlined in Guba et al. (2014). The base resolu- impact of subgrid physics on the correct forecast of the tion is 0.58 (55 km). This resolution is selected to ensure storm’s recurvature toward the northeastern United that synoptic systems and other large-scale atmospheric States. Section 6 provides parallel scaling results com- features are adequately resolved (Holton 2004). The paring the variable-resolution configuration to forecasts refinement over the North Atlantic and eastern Pacific with globally uniform grids. Finally, conclusions and basins is of a factor of 4, making the resolution in the future work are discussed in section 7. target areas approximately 0.1258 (14 km). This resolution

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FIG. 1. The variable-resolution mesh used in this study. The horizontal resolution ranges from 55 to 14 km (0.58–0.1258). Note that each element shown contains additional 3 3 3 collocation cells.

is finer than most operational global numerical weather the number of elements in a mesh (Zarzycki et al. prediction currently in use, although it is coarser than 2014a). This suggests that the V-R simulations should the innermost, moving nests of regional models used require only ;15% of the computational resources of a specifically for forecasting tropical cyclones (Gall globally uniform 14-km grid. et al. 2013). CAM-SE is coupled to both an ocean/ice and land The default CAM, version 5 (CAM5), physical pa- model through the CPL7 trigrid coupler within the rameterizations suite is used (Neale et al. 2012). Subgrid CESM framework (Craig et al. 2012). The coupler uti- physics of particular interest to TC modeling include lizes conservative remapping weights to allow the at- the model’s planetary boundary layer and moist turbu- mosphere to run in conjunction with more standard lence schemes (Bretherton and Park 2009), prognostic ocean and land grids. SSTs and sea ice concentrations double-moment microphysics with ice supersaturation are provided on a gx1v6 tripole grid (approximately 18). (Morrison and Gettelman 2008), and CAM5’s deep The land model is the Community Land Model (CLM), convective (Zhang and McFarlane 1995) and shallow version 4.0, run in satellite phenology (SP) mode on a convective (Park and Bretherton 2009) parameteriza- 0.23 by 0.318 latitude–longitude grid (Oleson et al. 2010). tions. Further details about the CAM5 configuration can b. Model initialization be found in Neale et al. (2012). Table 1 contains information about grid configura- The model is initialized with analysis from the Na- tions used in this study. The V-R grid comprises 52 611 tional Centers for Environmental Prediction’s (NCEP) elements per model level. The standard CAM5 30 ver- Global Data Assimilation System (GDAS), which is the tical levels are used. A globally uniform CAM-SE grid at same product used in initialization of NCEP’s Global the same 14-km resolution as the fine nest contains Forecast System (GFS) model. The GDAS/GFS analy- 345 600 elements in the horizontal direction. CAM-SE sis is regridded from a 0.5830.58 latitude–longitude grid has been shown to scale nearly linearly with both the (the highest-resolution product available) to the V-R number of processors (Dennis et al. 2012) as well as with CAM-SE mesh using high-order remaps generated with

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TABLE 1. CAM-SE resolutions of interest to this study. Grid spacing Dx (in 8 and km) corresponds to the approximate grid spacing at the equator, defined as the approximate distance between collocation points on an element. Dynamics time steps (dtdyn) are globally constrained by the finest grid scale in an individual variable-resolution simulation, while the fourth-order diffusion coefficient K4 (Dx) (hyperdiffusion) is allowed to vary among individual elements. The physics time step (dtphys) is constant across simulations.

4 21 Setup Dx (8) Dx (km) Elements (No.) dtdyn (s) dtphys (s) K4 (m s ) Uniform high resolution 0.1258 14 345 600 45 1800 1.00 3 1012 Uniform low resolution 0.58 55 21 600 180 1800 1.00 3 1014 Variable resolution 0.58–0.1258 55–14 52 611 45 1800 Varies

the Earth System Modeling Framework (ESMF; Collins the forecast length. We defer to Fillion et al. (1995) for a et al. 2005). No additional vortex bogusing, relocation, full derivation and further discussion of the technique. or other TC-specific initialization procedure is done An example of sea level pressure at 13 h (from ini- following this remap. The model is initialized at 0000 tialization) with and without the digital filtering tech- and 1200 UTC every day between 1 August and 31 nique is shown in Fig. 2. Note the large-amplitude October for 2012 and 2013. We were unable to attain gravity waves that have emanated from mountainous atmospheric analyses for five cycles during the forecast regions (e.g., the Andes and Rocky Mountains) in period. Fig. 2a. These waves result from small imbalances in the Initial conditions that are strictly mapped from one surface mass field due to remapping between model grid to another generally suffer from an unbalanced states with differing topographical roughness. These initial state of the atmosphere. This unbalanced state is a waves are filtered out through the DFI procedure, result of vertical and horizontal interpolation, as well providing a much more homogeneous, numerically sta- as errors in the pressure gradient force near sharp to- ble, and realistic surface pressure field in Fig. 2b. pography, which arise from differences in the model Sea surface temperatures (SSTs) and sea ice concen- orography. This is particularly problematic for variable- trations (SICs) are taken from the NOAA High- resolution models, which require different degrees of Resolution Blended Analysis (Reynolds et al. 2007). topographic smoothing at different grid spacings to Daily average SSTs and SICs for the model initialization maintain numerical stability (Zarzycki et al. 2015). To date are used and assumed to persist during the entire minimize these issues, we apply an offline digital filter forecast period. While more accurate simulations could initialization (DFI). have used temporally varying quantities, this would The technique used in this framework is a forward make comparison with forecast models (which do not filter, which is described in Fillion et al. (1995). This is have access to future ocean conditions) less robust. slightly different than the forward-and-back technique In addition, SSTs are fixed and do not interact with the commonly used in numerical weather prediction (NWP) atmosphere in a coupled sense. It is well known that applications (e.g., Lynch and Huang 1992). A drawback strong, slow-moving TCs can generate cold wakes of forward filter techniques is that the solution remains through turbulent upwelling and heat extraction via noisy for the first few hours of the forecast period, an surface fluxes (Price 1981). This effect provides a nega- effect eliminated by the use of forward-and-back tive feedback on intensity. However, the vast majority of methods. However, a forward filter was preferred to global operational NWP models use fixed SSTs (e.g., eliminate the need to adiabatically integrate backward NCEP Environmental Modeling Center 2003; Donlon in time and, therefore, to provide a more consistent et al. 2012). The addition of a slab, mixed-layer, or fully treatment of diabatic processes. dynamic ocean model within global forecasts is a future To filter, each forecast is initially integrated forward research target. for 6 h. Model state variables are output every 450 s The land is initialized by ‘‘nudging’’ an already (7.5 min), providing 49 data points (with 10 and 16h spunup CLM model state toward one in balance with the inclusive). A Heaviside (unit) step function is applied in atmospheric initial conditions. This is done by first it- Fourier space at each state location to remove high- eratively cycling the model in late July (prior to the frequency noise in the model state variables. Using actual forecast period), where the model is integrated short-term test simulations, we found that using a cutoff for a short period of time (24 h) and the corresponding period [Tc in Fillion et al. (1995)] equal to 6 h provided 24-h land forecast is reingested as initial conditions. reasonable results. The model is then reinitialized from After this cycling has been done between 15 and 30 this filtered forecast at 13 h (the central point of the times, full forecasts are started. To ensure a balanced filtering time period) and integrated for the duration of land condition, each successive forecast is initialized

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FIG. 2. The 13-h forecast of sea level pressure (a) before the application of DFI and (b) after. This particular hindcast was initialized at 0000 UTC 28 Aug 2005 (note Hurricane Katrina in the Gulf of Mexico). with the previous cycle’s 12-h land forecast (e.g., the forecast hour and cyclone. A mean fix is determined CLM initial conditions for the 0000 UTC 21 August run from the six parameters, although parameters with po- are the 12-h forecasted CLM state from the 1200 UTC sition fixes not within an allowable distance from the 20 August simulation). initial guess (275 km) are not used in the mean fix calculation. c. Tracking tropical cyclones and measuring forecast The initial location of the cyclone is defined by the error National Hurricane Center’s (NHC’s) Tropical Cyclone The method used to track the tropical cyclones in Vitals (TCVitals) at forecast initialization. The product model forecast output is described in Marchok (2002). includes estimates of cyclone location and intensity at a The tracker utilizes six primary parameters (850-hPa, specific analysis time (Trahan and Sparling 2012). We 700-hPa, and 10-m relative vorticity; 850- and 700-hPa only track storms observed in the North Atlantic and geopotential height; and mean sea level pressure) to eastern Pacific as they are the two basins under the determine a center fix (geographic location) for a storm. NHC’s purview, as well as the regions where the 14-km An iterative Barnes analysis (Barnes 1964) over pro- portion of the V-R nest is situated. gressively finer grids is completed for each of the six We discuss two ways to quantify forecast performance primary parameters to produce an initial fix for a specific in this manuscript. The first, and simplest, is forecast

Unauthenticated | Downloaded 10/06/21 09:29 AM UTC OCTOBER 2015 Z A R Z Y C K I A N D J A B L O N O W S K I 4017 error (ef ). The variable ef is measured as the absolute 3. Forecast performance of variable-resolution difference between a forecast quantity (Cf ) and its global simulations corresponding observation (C ): obs a. Variable-resolution CAM performance 5 jC 2C j ef f obs . (1) Figures 3a and 3b show the average track and 10-m 2 wind skill for all named cyclones (wind speed $ 17.5 m s 1 Note, that we can also calculate forecast bias with the at initialization) normalized by CLIPER5 (CLP5) and same formulation as in Eq. (1), but using the relative SHIFOR5 (SHF5) as a function of forecast hour. Included difference rather than the absolute difference. are the V-R (14 km) CAM forecasts (CAM, solid black), Using e , forecast skill (S ) can also be calculated as f f as well as a selection of other operational model forecasts ! for the months of August, September, and October in 2012 e 2 e S (%) 5 100 f ,b f ,m , (2) and 2013. Storms in both the North Atlantic and eastern f ,m e f ,b Pacific are included. The names and dates of all included storms are listed in Table 2. where Sf ,m is the skill of a particular forecast (f) from a As with CLP5 and SHF5, these model forecasts are particular model (m), ef ,m is the error of the model, and obtained from the NHC’s a-decks. Models included are ef ,b is the error of some baseline predictor, generally a the NCEP GFS (GFS; global model, Dx ; 28 km, red), statistically based method. The variable ef for storm the Canadian Meteorological Center’s (CMC’s) Global track is measured as the great circle distance between a Environmental Model (GEM; global, Dx ; 33 km, pur- forecast storm center and that published in the NHC’s ple), the Hurricane Weather Research and Forecasting 1 best track database, while ef for storm intensity is the (WRF) Model (HWRF; regional model, Dx ; 9-km inner absolute difference between a forecast 10-m wind speed nest, dark red), and the Geophysical Fluid Dynamics and one that was observed, also in the best track data- Laboratory’s (GFDL’s) regional forecast model (re- base. CAM forecast 10-m winds are derived by taking gional, Dx ; 5-km inner nest, orange). Note, that only the wind speed at the lowest model level (approximately track forecasts are reported for the CMC model. Sample 60 m) and correcting it to 10 m using a logarithmic pro- sizes are color coded at each lead time. Note that the file with an open sea roughness coefficient (Garratt sample sizes may not be identical because of factors such 1992; Wieringa 1992). as missed initialization cycles or the tracker not being For the remainder of this paper, we normalize skill able to detect a coherent vortex in the model output. using CLIPER5 (track) (Aberson 1998) and SHIFOR5 Since these missing cycles exist, the fact that the sample (intensity) (Knaff et al. 2003) as baseline (ef ,b) forecasts. size of the data is large, and various models are run with These products are readily available within the NHC’s different integration lengths, we have chosen not to re- a-decks (files containing operational forecasts for a va- strict these results to a homogenous sample. riety of dynamical and statistical models) and are All dynamical models show positive track forecast 2 available out to 120 h for each forecast cycle. Note that skill out to the end of CLP5’s 120-h forecasts (Fig. 3a). we use 10-m wind rather than minimum sea level pres- The evolution of this skill is also similar across all sure (MSLP) as a measure of TC intensity. We do models, with the highest values occurring between 48 so because no forecast of MSLP was available for and 72 h. In terms of track, CAM falls within the enve- SHIFOR5 in the a-deck files used for the skill calcula- lope of performance of the other models shown here, tions (i.e., no ef ,b). Previous work has indicated that and model error at long lead times (beyond the 120-h small differences may exist between surface wind and normalization offered by CLP5) appears reasonable pressure-based metrics, due to the fact that maximum (Fig. 3c) by either assuming natural extrapolation of wind is generally defined by a localized value whereas error or a comparison to the GFS. MSLP is a system-integrated quantity (e.g., Zhu and With respect to wind forecast skill, CAM performs Zhang 2006). However, absolute 10-m wind errors and similar to the global GFS model through approximately MSLP error (not shown) qualitatively demonstrated 48 h (Fig. 3b). Note that the short-term wind errors are highly similar behavior, implying that using MSLP as an quite large for both CAM and GFS relative to the re- intensity metric in this analysis would result in analo- gional HWRF and GFDL models, highlighting the gous conclusions. ‘‘spinup’’ issues when simulating TCs initialized in global models with coarser grid spacings. Beyond 48 h, however, CAM skill begins to decrease. This runs 1 See http://www.nhc.noaa.gov/data/. counter to other models that all show a stabilization of 2 See http://www.ral.ucar.edu/hurricanes/repository/. skill bounded approximately by 20% and 40% (relative

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FIG. 3. Forecast performance metrics as a function of lead time for all storms during the study period that were 2 tropical storm strength or greater ($17.5 m s 1) at model initialization. Normalized forecast skill is plotted for (a) track and (b) 10-m wind for forecasts out to 120 h. (c) Absolute track error out to the full model forecast length is plotted. (d) Wind bias is shown. The numbers of model forecasts are noted as color-coded text aligned with a particular lead time. to SHF5) between days 2 and 5. Since Fig. 3b shows red, crossed dots indicate particular forecasts from the absolute value of the error (counting storms that CAM at the specified lead time. In Fig. 4a both spreads are forecast too strong and storms forecast too weak generally overlay one another, meaning 48-h CAM equally), we show wind bias in Fig. 3d. This is measured forecasts were very similar to observations. This cor- as the average of the difference of the forecast wind roborates the results in Fig. 3b showing the model is speed minus that which was observed. It is clear that the producing skillful forecasts with little overall bias in in- majority of the problems with the forecast skill in CAM tensity at this lead time. Figures 4b and 4c show the same occur because of an overprediction of intensity. At day curves for 120- and 192-h forecasts. Very few storms 2 5, CAM forecasts, on average, storms that are 6 m s 1 during the 2012–13 hurricane seasons in the North At- stronger than those observed, while both regional lantic and east Pacific reached surface pressures below models (HWRF and GFDL) forecast storms that are 930 hPa, whereas CAM forecasted numerous storms 2 approximately 2–3 m s 1 too strong. The global GFS below this threshold at these longer lead times (red model underforecasts 120-h intensity by approximately markers in the upper-left portion of the panels), high- 2 1ms 1. lighting CAM’s tendency to shift the intensity curve This bias can also be seen in forecast pressure–wind toward overly intense storms with the default model curves shown in Fig. 4. For every forecast, both the configuration. model predicted and observed surface pressures and To isolate storms that were well represented at ini- 10-m winds are paired at a specified lead time. Blue, tialization, metrics for all TCs which were initialized at 2 filled dots indicate observed pressure–wind pairs, while hurricane strength ($33 m s 1) or greater are shown in

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TABLE 2. All storms included in sample that were named (tropical storm strength or greater) at time of model initialization. Storms in the ‘‘AL’’ basin originated in North Atlantic while ‘‘EP’’ storms were in the eastern Paciﬁc. The ﬁrst and last date a storm appeared in the NHC a-deck are listed along with the number of forecast cycles (No.) a particular storm was detected in this study.

Basin Name Start date End date No. AL Ernesto 1200 UTC 2 Aug 2012 0000 UTC 10 Aug 2012 13 AL Florence 0000 UTC 4 Aug 2012 0000 UTC 4 Aug 2012 4 AL Helene 0000 UTC 18 Aug 2012 0000 UTC 18 Aug 2012 1 AL Isaac 0000 UTC 22 Aug 2012 0000 UTC 30 Aug 2012 18 AL Gordon 0000 UTC 16 Aug 2012 0000 UTC 21 Aug 2012 11 AL Joyce 1200 UTC 23 Aug 2012 1200 UTC 23 Aug 2012 1 AL Kirk 0000 UTC 29 Aug 2012 0000 UTC 31 Aug 2012 5 AL Leslie 1200 UTC 30 Aug 2012 0000 UTC 11 Sep 2012 21 AL Michael 0000 UTC 5 Sep 2012 0000 UTC 12 Sep 2012 13 AL Nadine 0000 UTC 12 Sep 2012 0000 UTC 4 Oct 2012 44 AL Oscar 0000 UTC 4 Oct 2012 0000 UTC 5 Oct 2012 3 AL Patty 1200 UTC 11 Oct 2012 0000 UTC 13 Oct 2012 4 AL Rafael 0000 UTC 13 Oct 2012 1200 UTC 16 Oct 2012 8 AL Sandy 0000 UTC 23 Oct 2012 1200 UTC 30 Oct 2012 16 AL Tony 0000 UTC 24 Oct 2012 0000 UTC 26 Oct 2012 5 EP Gilma 1200 UTC 8 Aug 2012 0000 UTC 11 Aug 2012 6 EP Hector 0000 UTC 12 Aug 2012 0000 UTC 15 Aug 2012 7 EP Ileana 0000 UTC 28 Aug 2012 0000 UTC 2 Sep 2012 10 EP John 1200 UTC 2 Sep 2012 1200 UTC 3 Sep 2012 3 EP Kristy 1200 UTC 12 Sep 2012 1200 UTC 16 Sep 2012 8 EP Lane 0000 UTC 16 Sep 2012 0000 UTC 19 Sep 2012 7 EP Miriam 1200 UTC 22 Sep 2012 1200 UTC 27 Sep 2012 11 EP Norman 1200 UTC 28 Sep 2012 0000 UTC 29 Sep 2012 2 EP Olivia 0000 UTC 7 Oct 2012 1200 UTC 8 Oct 2012 4 EP Paul 0000 UTC 14 Oct 2012 1200 UTC 17 Oct 2012 8 EP Rosa 1200 UTC 30 Oct 2012 1200 UTC 31 Oct 2012 3 AL Erin 1200 UTC 15 Aug 2013 0000 UTC 18 Aug 2013 5 AL Fernand 0000 UTC 26 Aug 2013 1200 UTC 26 Aug 2013 2 AL Gabrielle 0000 UTC 5 Sep 2013 0000 UTC 13 Sep 2013 6 AL Humberto 1200 UTC 9 Sep 2013 1200 UTC 18 Sep 2013 16 AL Ingrid 1200 UTC 13 Sep 2013 1200 UTC 16 Sep 2013 7 AL Jerry 1200 UTC 30 Sep 2013 0000 UTC 3 Oct 2013 6 AL Karen 0000 UTC 3 Oct 2013 0000 UTC 6 Oct 2013 7 AL Lorenzo 1200 UTC 21 Oct 2013 1200 UTC 23 Oct 2013 5 EP Gil 0000 UTC 1 Aug 2013 1200 UTC 6 Aug 2013 8 EP Henriette 1200 UTC 4 Aug 2013 0000 UTC 11 Aug 2013 14 EP Ivo 0000 UTC 24 Aug 2013 1200 UTC 24 Aug 2013 2 EP Juliette 1200 UTC 28 Aug 2013 1200 UTC 29 Aug 2013 3 EP Kiko 1200 UTC 31 Aug 2013 0000 UTC 2 Sep 2013 4 EP Lorena 0000 UTC 6 Sep 2013 0000 UTC 7 Sep 2013 3 EP Manuel 0000 UTC 14 Sep 2013 1200 UTC 19 Sep 2013 7 EP Narda 0000 UTC 7 Oct 2013 1200 UTC 8 Oct 2013 4 EP Octave 1200 UTC 13 Oct 2013 0000 UTC 15 Oct 2013 4 EP Priscilla 1200 UTC 14 Oct 2013 1200 UTC 15 Oct 2013 3 EP Raymond 1200 UTC 20 Oct 2013 0000 UTC 30 Oct 2013 20

Fig. 5. Figure 5a shows that track forecast skill is better with unrealistic strengthening of weaker storms during at all lead times when simulating hurricanes relative to the forecast period. all cyclones (Fig. 3a), implying that stronger storms are b. Variable-resolution versus unreﬁned grids better represented in models and generally moved more predictably than weaker cyclones during the study pe- A complimentary set of globally uniform low- riod. Figures 5b and 5d also show that the ‘‘runaway’’ resolution 55-km (0.58) simulations without the reﬁned intensity errors associated with CAM in Figs. 3b and 3d patch was completed. All forcings for these forecasts are not as prevalent with stronger storms. This implies were the same (identical SSTs, ice fraction, and land that CAM’s intensity prediction struggles are associated initial conditions). This is the same resolution as the

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FIG. 4. Pressure–wind curves for CAM forecasts at (a) 148, (b) 1120, and (c) 1192 h from initialization time. Forecasted surface pressure–10-m wind pairs are shown in crossed red circles, observed pairs are indicated by filled blue circles. background resolution in the V-R simulations. As All other aspects of the CAM configuration remain shown in Table 1, this setup contains significantly fewer identical. grid cells. While the physical parameterization time step Previous work with CAM has demonstrated that was equal to the control V-R run (dtphys 5 1800 s), the storms that are more similar physically to observed TCs dynamics were run with a longer time step due to a less are generated as horizontal resolution is increased (e.g., restrictive Courant–Friedrichs–Lewy (CFL) condition. Reed and Jablonowski 2011; Reed et al. 2012; Zarzycki

21 FIG.5.AsinFig. 3, but only including storms that were at least hurricane strength ($33 m s ) at initialization.

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FIG. 6. The 1120-h forecasts for Hurricane Leslie, initialized at 0000 UTC 2 Sep 2012. (a)–(d) The uniform 55-km simulation and 2 2 2 (e)–(h) the forecast from the V-R (14 km) simulation. (a),(e) 850-hPa vorticity (10 5 s 1); (b),(f) 850-hPa horizontal wind (m s 1); 2 (c),(g) simulated radar reflectivity (dBZ); and (d),(h) 500-hPa vertical pressure velocity (Pa s 1). and Jablonowski 2014). An example of the structural one band of ascent present around the storm core differences arising from resolution differences in the (Fig. 6d). While the vast majority of work regarding TC forecast configurations is shown in Fig. 6. As resolution structural sensitivity to horizontal resolution has been is increased because of refinement, the vorticity core of done primarily with limited-area models at or below Hurricane Leslie (1120-h forecast, initialized at 0000 UTC 10-km grid spacings, the dynamical response seen here, 2 September 2012) becomes much stronger and pos- while at coarser resolution, qualitatively agrees with sesses more horizontal structure (Fig. 6e) when com- those studies (e.g., Fierro et al. 2009; Gentry and pared to the unrefined 55-km forecast (Fig. 6a). Similar Lackmann 2010; Manganello et al. 2012; Sun et al. 2013; results are seen for both 850-hPa horizontal wind and Jin et al. 2014). precipitation, with the 14-km simulation generating Figure 7 shows the same metrics as Fig. 3. The V-R stronger winds, a much tighter storm core, and simulation (CAM, Dx ; 14 km) is shown in black while both a low-precipitation eye as well as spiral rainbands the unrefined simulation (CAM-UNI55, Dx ; 55 km) is branching off the central dense overcast region at the marked by the dashed green line. Since the initial con- core of the cyclone (Figs. 6f,g). The 55-km grid shows a ditions are identical, we have removed all intensity re- weaker, broader TC that still retains a central region of strictions on storm selection, and prenamed TCs in the intense precipitation, but lacks the aforementioned NHC a-decks, such as tropical depressions, are included. features seen in the V-R simulation (Figs. 6b,c). Last, Additionally, the samples for the remainder of this the higher resolution of the V-R simulation allows for manuscript are homogenous because of the ability to more intense updrafts at the 500-hPa level, complete control which model cycles were completed using CAM. with a corresponding downdraft in the eye region, as Investigation of the track skill indicates that both well as surrounding branches of vertical motion associ- configurations follow roughly the same pattern with ated with the spiral rainbands seen in the radar re- peak skill occurring at day 3. In Figs. 7a and 7c, the skill flectivity panel (Fig. 6h). The unrefined simulations (error) of the V-R track forecast is higher (lower) than show a larger, weaker peak in vertical motion with only the unrefined case at all lead times, indicating that the

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FIG.7.AsinFig. 3, but comparing the 14-km V-R control model (CAM) to the unrefined 55-km model (CAM-UNI55). increased resolution directly leads to a more accurate model had a lower error (superior performance). If the forecast. Since both models are initialized with identical difference in error between the two models was less than states and use identical subgrid physical parameteriza- 10% of the average error of the control V-R simulation tions, this implies that the grid spacing is the key driver for that lead time, neither model was deemed superior in this behavior. for that forecast. Additionally, black triangles indicate In the early portion of the forecast period (0–96 h), the whether the difference in means seen in Fig. 7 were V-R simulation also outperforms the unrefined grid with statistically significant. Statistical significance is assessed respect to forecasted intensity. However, beyond 96 h, using a standard bootstrap technique (Efron and Gong both the skill and bias are better for the unrefined grid. 1983). Random samples (allowing for replacement) are As previously seen, Fig. 7d indicates that this arises generated from an array of the differences in error be- because of the overintensification of storms in the V-R tween two models for all forecasts. Here, we resample forecasts at long lead times. The unrefined simulations 10 000 times and deem a result statistically significant if likely possess more skill in this case because the lack of both the low and high values of the 80% confidence dynamic resolution (coarser grid spacing) helps offset interval lie on either side of zero (zero representing no the high bias seen in the V-R wind speeds. difference in error). For example, for the track forecast Table 3 contains two measures further comparing the at 120-h lead time, the V-R simulation (CAM) per- two simulations. The frequency of superior performance formed best 62% of the time, while the unrefined sim- (FSP) is shown as a fractional value for both track and ulation (CAM-UNI55) only performed best 26% of the intensity forecasts for all lead times during the 8-day time. In 12% of the cases, the differences between forecasts. Forecasts are first paired by initialization time the forecasts at 120-h lead time were within 10% of the and storm. Track and wind errors are compared at each average forecast error for CAM at that lead time and lead time for each storm forecast to determine which were not counted. In addition, the mean track forecast

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TABLE 3. Frequency of superior performance (FSP) for CAM (14-km V-R control) and unrefined CAM (55-km globally uniform grid) forecasts during the 2012–13 Atlantic tropical season. Statistically significant performance as measured by bootstrapping the mean error at 80% confidence is denoted by a triangle that points toward the model with the highest mean skill. The threshold for superior performance is a difference between forecasts of 10% of the average error of the control simulation (CAM) for that metric and lead time. Forecasts where this threshold is not met are not included in FSP calculations and are why the fractional sums may not equal 1 at a given lead time.

Lead times (h) Metric Model 12 24 36 48 72 96 120 144 168 192 ...... Track CAM 0.54 0.57 0.61 0.64 0.61 0.59 0.62 0.67 0.53 0.55 CAM-UNI55 0.20 0.19 0.21 0.23 0.20 0.26 0.26 0.22 0.35 0.34 ..... Wind CAM 0.70 0.72 0.67 0.66 0.62 0.54 0.45 0.42 0.38 0.34 CAM-UNI55 0.21 0.22 0.27 0.30 0.30 0.36 0.46 0.51 0.53 0.60 mmmm

for CAM was better than CAM-UNI55, determined to more structure within the simulations. For example, a be significant by the aforementioned bootstrapping strong band radiating outward from the southern edge technique, as denoted by the black triangle in the CAM of the central vorticity core is evident in both the left and row at 120 h. middle panels. A secondary vorticity band stretches Atallleadtimes,therefinedgrid(CAM)produceda from the south of the vortex, around the western pe- higher percentage of more accurate track forecasts than riphery of the circulation, and then eastward into the the unrefined grid (CAM-UNI55). The mean difference in Atlantic. These structures are nearly identical in the this performance was significant at all lead times except V-R and 14-km simulation, underscoring the matching 12 h (likely due to the models being initialized with iden- dynamical performance in the high-resolution nest. tical conditions) and at both 168 and 192 h (possibly due to Many features seen in the left two panels are not evident the small number of matching forecasts at these longer in the right panel (uniform 55-km grid), and those that lead times; 99 and 76, respectively). In terms of intensity, are lack the structure and definition seen with the finer the same behavior observed in Fig. 7 is seen in Table 3. grid spacing. CAM performs better at short lead times, but beyond Figure 9 shows a similar analysis for a 5-day forecast of 120 h, CAM-UNI55 exhibits more intensity skill both in 500-hPa relative vorticity over a wider geographic area. terms of the mean forecast (black triangles) and FSP. In this case, the primary storm forecasted is Hurricane Isaac, with the model initialized at 0000 UTC 23 August c. Variable-resolution versus equivalent uniform 2012. As in Fig. 8, we see that, even at 120 h, stark sim- high-resolution grids ilarities exist between the two top panels, implying the An obvious motivating factor for the use of multimodel representation of flow within the V-R high- resolution model grids is decreased computational cost resolution nest is well matched by a traditional uni- when compared to globally uniform high-resolution form simulation. Vorticity structures, such as bands simulations. Because a globally uniform 14-km simula- associated with Isaac in the Gulf of Mexico, a frontal tion took approximately 6 times longer to run than the boundary draped across the continental United States, V-R simulation, only a few (12) simulations were com- and other features over the Atlantic Ocean, are well pleted to compare the forecast behavior of the refined matched. This illustrates the striking similarity between simulations to that with globally uniform high resolution. a uniform high-resolution and refined V-R grid at typical Figure 8 shows the day 3 (172 h) forecast of 500-hPa forecast lead times. relative vorticity for Hurricane Sandy, initialized at While the sample of matching forecasts was too small 0000 UTC 25 October 2012. The left panel depicts the V-R for a formal statistical comparison, a cursory comparison simulation. The middle and right panels are the forecasts of mean forecast performance as a function of lead time using the globally uniform 14- and 55-km simulations, for both the uniform high-resolution and refined V-R respectively. It is apparent that the V-R simulation most grids also indicates nearly identical performance be- closely matches the globally uniform 14-km simulation. tween the two configurations, especially at shorter lead The vorticity maximum associated with Hurricane times. Absolute track errors (10-m wind biases) for Sandy is the same order of magnitude and size. In ad- forecasted TCs in matching cycles at 124, 148, 172, dition, the higher-resolution grids provide significantly 1120, and 1168 h were 156, 277, 345, 260, and 393 km

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25 21 FIG. 8. The 172-h (day 3) 500-hPa relative vorticity (10 s ) forecasts using the (a) V-R 14-km grid, (b) uniform 14-km grid, and (c) uniform 55-km grid. The forecasted storm is Hurricane Sandy. All simulations were initialized at 0000 UTC 25 Oct 2012. In (a), the V-R grid transition region is noted by the black contour.

2 (24.3, 24.6, 22.1, 9.6, and 11.1 m s 1)fortheV-R over those with climatological SSTs (CAM-CLIMO) simulations and 155, 282, 341, 300, and 503 km (Figs. 10a,c). Moreover, intensity error is also relatively 2 (24.3, 24.4, 22.7, 8.8, and 11.7 m s 1) for the uniform similar between the two models (Figs. 10b,d). Short- 14-km simulations. Performance at longer lead times term intensity forecasts (less than or equal to 72 h) are (i.e., beyond 5 days) diverges slightly, although this slightly better with observed SSTs, while the climato- may be due to factors such as small sample size or flow logical SSTs outperform at longer lead times (greater initialized outside of the refined area entering the high- than 72 h). resolution domain in the V-R simulations. Interestingly, Fig. 10d shows that the wind bias is ac- tually reduced at longer lead times in the climatological 4. Sensitivity experiments simulations. This is likely due to the fact that the observed tropical North Atlantic index (TNAI; Enfield et al. a. Observed SSTs versus climatological SSTs 1999), a measure of the average SST between 5.58–23.58N To investigate the impact of initializing with observed and 158–57.58W, is higher in the 2012–13 observations SSTs, we ran a suite of CAM forecasts where ocean than the climatological dataset. The TNAI difference temperatures were initialized with climatological means (calculated as the TNAI of the observed SSTs minus the from 1982 to 2001 (CAM-CLIMO). These amount to TNAI of the climatological SSTs) for August, September, forecasts where one has knowledge of the atmospheric and October was 10.278, 10.518,and10.388C (2012) initial state but no knowledge of the ocean state. Results and 10.308, 10.318,and10.408C (2013). Therefore, the are shown in Fig. 10 and Table 4. climatological data forced the simulation with cooler The results show that model track forecasts initialized SSTs and acted as a somewhat artificial ‘‘brake’’ on the with observed SSTs (CAM) show small improvement overintensification of cyclones in the model.

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FIG.9.AsinFig. 8,butfor1120-h (day 5) forecast of Hurricane Isaac. All simulations initialized at 0000 UTC 23 Aug 2012.

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FIG. 10. As in Fig. 3, but comparing the 14-km V-R control model (CAM) to a 14-km V-R model using climatological SSTs (instead of observed SSTs) at initialization (CAM-CLIMO).

Table 4 shows that the observed SSTs produce more the previous section, suggests that any impact of SST skillful track forecasts with a higher frequency, although forcing appears to be much smaller than the impact of the FSP is more mixed when it comes to predicting storm changing model resolution. intensity. These results would imply that the observed b. Sensitivity to parameterized convection SSTs lead to better track forecasts by impacting the large-scale steering flow rather than more accurately To attempt to discern potential mechanisms for the sys- forecasting storm intensity (and, therefore, internal dy- tematic overintensification of TCs in CAM, we conduct a namics), However, it is worth noting that the means suite of physical parameterization sensitivity simulations. In were not statistically different at any lead time for either these simulations, all forecasted TCs were first sorted by of the metrics. This, in conjunction with the results from their 1120-h 10-m wind bias (difference from observations).

TABLE 4. Comparison of the control V-R simulation forced by observed SSTs (CAM) and an alternative V-R simulation forced by climatological mean SSTs (CAM-CLIMO). The metrics are the same as in Table 3.

Lead times (h) Metric Model 12 24 36 48 72 96 120 144 168 192

Track CAM 0.15 0.30 0.43 0.54 0.53 0.51 0.50 0.59 0.60 0.58 CAM-CLIMO 0.08 0.05 0.13 0.17 0.23 0.31 0.30 0.24 0.25 0.30

Wind CAM 0.24 0.39 0.40 0.45 0.46 0.41 0.47 0.47 0.39 0.42 CAM-CLIMO 0.23 0.33 0.39 0.39 0.35 0.45 0.42 0.44 0.52 0.49

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TABLE 5. Model configurations used in the study. ‘‘Grid’’ defines whether the model was run on a variable-resolution (V-R) or uniform (UNI) mesh. The variable Dx is the nominal grid resolution over the Atlantic and the eastern Pacific (finest grid spacing in V-R simulations). ‘‘Physics’’ is the choice of subgrid physics configuration in the model. The deep convective scheme used is specified. The variable dtphys is the physics time step and dtphys/t is the ratio of the physics time step to the convective relaxation time. ‘‘SST’’ is whether the model was initialized with observed or climatological SSTs. ‘‘Runs’’ are the total number of forecast runs completed for that configuration.

Deep convection Runs Name Grid Dx (km) Physics scheme dtphys (s) dtphys/t SST (No.) Control CAM V-R 14 CAM5 ZM 1800 0.5 Observations 359 CAM-UNI55 UNI 55 CAM5 ZM 1800 0.5 Observations 355 CAM-UNI14 UNI 14 CAM5 ZM 1800 0.5 Observations 15 Sensitivity CAM-CLIMO V-R 14 CAM5 ZM 1800 0.5 Climatology 361 CAM-NEWTAU V-R 14 CAM5 ZM 1800 2 Observations 21 CAM-NODEEP V-R 14 CAM5 None 1800 0.5 Observations 34 CAM-DT450 V-R 14 CAM5 ZM 450 0.5 Observations 34 CAM-CLUBB V-R 14 CLUBB ZM 1800 0.5 Observations 327

The 21 worst forecasts where CAM produced a TC signif- four sensitivity configurations. Note that the skill (er- icantly stronger than observed were then rerun with four ror) for the control simulation is smaller (larger) than separate modifications to the model configuration. those shown in Fig. 3 becausewehaveselectedasubset First, we conduct two sets of simulations testing TC of the most poorly performing forecasts for this forecast sensitivity to the Zhang–McFarlane (ZM) deep analysis. convective scheme in CAM. In the first, the scheme is The track skill for all sensitivity runs is generally the turned off, forcing the large-scale microphysics and same. While some configurations produce slightly more shallow convection routines to represent all rainfall pro- skillful forecasts, none were statistically different given cesses within the TC core (CAM-NODEEP). Con- the relatively small sample sizes. It is clear that either versely, we decrease the convective relaxation time scale increasing the frequency with which the physical pa- t from its default value of t 5 3600 to t 5 900 s while rameterization package is called or completely turning holding the physics time step (dtphys) fixed at 1800 s off the deep convection parameterization in CAM does (CAM-NEWTAU). This setup has been shown to in- little to change the behavior of the control simulation. crease the fraction of total precipitation from the ZM All three setups (CAM, CAM-NODEEP, and CAM- scheme (Williamson 2013). Next is a reduction of the DT450) produce storms that rapidly become too intense physics time step (dtphys) from 1800 s (30 min) to 450 s relative to observations, leading to large values of neg- (7.5 min) to more closely resemble timings used in oper- ative skill when normalized by SHF5 (Figs. 11b,d). ational NWP models (e.g., Jung et al. 2012)(CAM- Conversely, tuning the model to force the deep DT450). Note that the default t is also decreased by a convection scheme to become more active (CAM- factor of 4 (t 5 900 s) such that the dtphys/t ratio (deep NEWTAU) appears to somewhat mitigate the high-intensity convective forcing) remains constant. Last, we run CAM bias, although this configuration still does not provide with Cloud Layers Unified by Binormals (CLUBB) as a skillful intensity forecasts (relative to SHF5). Addi- component of the physical parameterization package tionally, this improvement is maximized out through (CAM-CLUBB). CLUBB is a high-order turbulence 72 h, with forecasted cyclones intensifying at approxi- closure scheme that provides a unified treatment of mately the same rate as the control simulation beyond boundary layer turbulence, stratiform cloud macro- day 3 until the end of the forecast period. physics, and shallow convection (Golaz et al. 2002). Reed et al. (2012) showed that the intensity of ideal- Therefore, using CLUBB replaces these three sets of ized tropical cyclones in CAM-SE is sensitive to the parameterizations in the default CAM configuration physics time step. In those simulations, t was held con- (Bogenschutz et al. 2012, 2013). The version of CLUBB stant. Therefore, shorter physics time steps corre- packaged with CAM, version 5.3.1, and released in April spondingly resulted in smaller dtphys/t ratios, thereby 2013 was used here. All configurations and their notations decreasing the fraction of parameterized deep convec- in this manuscript are summarized in Table 5. tive precipitation. This dependence is also shown in Figure 11 shows the forecast track and wind perfor- Williamson (2013). Results from both studies imply that mance for the control simulation in addition to these increasing the strength of the deep convective scheme

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FIG. 11. As in Fig. 3, but comparing the 14-km V-R control model (CAM) to the physical parameterization sensitivity experiments listed in Table 5. Note that only matching events from the subset of experiments performed are included in the control (CAM) statistics.

(larger dtphys/t) allows deep convection to more ade- those seen using the default physics package for this quately remove instabilities and supersaturation in col- subset of poorly forecast cyclones. umn grid boxes. This, in turn, decreases the strength of Given these results, a more rigorous suite of forecasts the adjustment made by the large-scale microphysics. was completed with the CLUBB configuration to com- Williamson (2013) showed that situations where the pare model performance. The vast majority of initiali- microphysics dominates this adjustment yields strong zation times with the control V-R (CAM) forecasts were local condensation, which is not redistributed in the also completed with CAM-CLUBB, producing 494 column. Correspondingly, strong updrafts and moisture matching cyclones at initialization (473 when normal- convergence result. This implies smaller dtphys/t ratios ized by CLP5 and SHF5). Figure 12 and Table 6 show are expected to produce more thermodynamically effi- the results of these forecasts compared to the control cient, and, therefore, intense, TCs, which is in agree- run. At all lead times, the mean track forecast error for ment with the results seen here. CAM-CLUBB is superior to the default CAM simula- The replacement of the planetary boundary layer, tions (Figs. 12a,c). However, although the mean per- macrophysics, and shallow convection schemes in CAM formance of CAM-CLUBB was superior with respect to with CLUBB appears to have an even more significant track, in many cases, Table 6 shows that the FSP was impact on storm errors. In particular, forecasts of TC slightly greater for CAM. This implies that CAM per- intensity within this subset of storms are greatly im- formed slightly better than CAM-CLUBB by frequency, proved. CAM-CLUBB forecasts show a small negative but in some instances where CAM-CLUBB was supe- bias in wind speed for the majority of the forecast pe- rior the difference in error between the two models was riod, with positive biases occurring at 120 h (Fig. 11d). large. This is shown by the fact that the standard de- 2 However, these biases, on average, are 20 m s 1 less than viation of track error at specific lead times was higher for

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FIG. 12. As in Fig. 3, but comparing the 14-km V-R control model (CAM) to a 14-km V-R model using CAM- CLUBB physical parameterizations.

CAM (not shown). The reasons why the control con- lead times (Fig. 12b). These differences in skill are figuration shows larger variability than CAM-CLUBB is quite pronounced, as evidenced by the statistically unknown and is a topic of future research. It is worth significant differences in the mean (triangles in Table noting that these means are not significant at the 80% 6). Figure 12d shows that the main reason for CAM- level using the bootstrapping technique, so differences CLUBB’s short-term poor performance is under- in the means between CAM and CAM-CLUBB track intensification (or overly slow intensification) of storms errors remain much smaller than the differences in the at short lead times. However, this bias improves from means between CAM and CAM-UNI55, for example. 72 h out to the end of the forecasts (192 h), with CAM- CAM-CLUBB intensity forecasts behave less skill- CLUBB producing quite skillful intensity forecasts at fully than CAM out to 72 h, but surpass it for longer these lead times. This stands in contrast to the control

TABLE 6. As in Tables 3 and 4, but comparing the V-R control simulation (CAM) with V-R simulations utilizing CLUBB (CAM-CLUBB).

Lead times (h) Metric Model 12 24 36 48 72 96 120 144 168 192

Track CAM 0.29 0.35 0.37 0.43 0.47 0.42 0.50 0.52 0.53 0.53 CAM-CLUBB 0.26 0.35 0.36 0.56 0.36 0.44 0.40 0.38 0.38 0.32 .... Wind CAM 0.46 0.57 0.59 0.55 0.50 0.47 0.44 0.38 0.30 0.32 CAM-CLUBB 0.26 0.29 0.33 0.35 0.35 0.42 0.50 0.60 0.58 0.62 mmmmm

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FIG. 13. Storm radial cross section of (left) radial winds, (middle) tangential winds, and (right) vertical pressure velocity for 1120-h (5 day) V-R forecasts of Hurricane Leslie. Forecasts were initialized at 0000 UTC 3 Sep 2012. (top) The control CAM5 V-R forecast and (bottom) the CAM-CLUBB V-R forecast are shown.

CAM simulations, which exhibit an increasing bias out near-surface maximum wind), whereas the structure of to 192 h. the CAM-CLUBB TC is less organized, with a radius of Figure 13 shows a snapshot of the tangentially aver- maximum wind approximately 3 times greater than that aged radial cross section of radial (inflow/outflow) wind, of the control CAM5 simulation. The vertical pressure tangential wind, and vertical pressure velocity of Hur- velocity (Figs. 13c,f) also highlights the intensity bi- ricane Leslie for the V-R control (CAM5, top) and V-R furcation between the two simulations, with CAM5 CAM-CLUBB (bottom) forecasts. Shown is the 1120-h showing a deep, penetrating updraft core in the eyewall. forecast initialized at 0000 UTC 3 September 2012. The Alternatively, CAM-CLUBB shows a much weaker, center of the cross section is defined by the storm’s sea more tilted updraft region that does not reach into the level pressure minimum. These provide insight into upper troposphere. some of the structural differences resulting from the use Only one particular case is shown as an example here, of CLUBB versus the default CAM5 physical parame- but analysis of other storms indicates that these general terization suite. Both surface radial inflow (positive structural differences are robust across the majority of values) and upper-level outflow (negative values) are simulations. While CAM-CLUBB provides more skill- significantly stronger in CAM5 (Fig. 13a) when com- ful forecasts at longer lead times, it does not exhibit as pared to CAM-CLUBB (Fig. 13d), indicative of a much many hallmark characteristics of TC structure as the stronger circulation. The CAM-CLUBB forecast CAM5 simulations, making it unclear whether or not the shows a more vertically diffuse inflow core, indicating improved forecast skill is a function of CLUBB better that near-surface momentum may not be as concen- representing atmospheric processes or merely sup- trated in the model’s lowest levels, thereby decreasing pressing facets underlying the high bias in CAM5 sim- the efficiency of sensible and latent heat fluxes from the ulations. These differences are quite striking and further ocean surface. This is also shown in the tangential wind analysis is necessary to understand the mechanisms (Figs. 13b,e), which indicates a higher maximum wind driving this behavior. However, it is clear that replacing location with CAM-CLUBB. In addition, CAM5 ex- only three parameterizations (boundary layer, shallow hibits tangential wind structure that is more similar convection, macrophysics) has led to a dramatic change to traditional, strong, TCs (calm eye, sloped eyewall, in storm behavior within the model, and the dynamical

Unauthenticated | Downloaded 10/06/21 09:29 AM UTC OCTOBER 2015 Z A R Z Y C K I A N D J A B L O N O W S K I 4031 reasons behind this response are a target of ongoing significantly earlier than either the deterministic GFS or research. GEFS mean. The forecast initialized at 0000 UTC 22 October shows a mean landfall location in coastal Maine 8 days prior to landfall, although the sharpness of 5. Hurricane Sandy the left turn of the storm is not well represented until the The most prolific tropical cyclone in either the North following cycle at 1200 UTC 22 October. For all fol- Atlantic or eastern Pacific during the 2012–13 forecast lowing forecast cycles, CAM is consistent with bringing period was Hurricane Sandy. Sandy was a rare storm Hurricane Sandy back toward the coastline as opposed that made landfall along the mid-Atlantic coast of the to predicting eastward movement out to the open At- United States just before 0000 UTC 30 October 2012. lantic. The skill shown by CAM is similar to that seen in One factor behind Sandy’s destructiveness was the ab- the ECMWF ensemble that also predicted a northeast- normal trajectory the cyclone took as it traversed the ern United States landfall beginning on 22 October western North Atlantic basin. While storms in the mid- (Magnusson et al. 2014). The GFS/GEFS do not forecast latitudes generally turn eastward due to westerly forc- this recurvature until 1200 UTC 24 October and do not ing, Sandy turned back toward the west, moving nearly cluster on a landfall location from Long Island south- perpendicular to the New Jersey coast at landfall. This ward until 1200 UTC 25 October. motion was rather unusual, being estimated to occur We note here that the results demonstrate that using once every seven centuries (Hall and Sobel 2013). the same initial conditions as the GFS model, CAM is This unusual motion posed an interesting challenge able to forecast this recurvature more than a week be- for forecasters. In particular, numerical model guidance fore the storm made landfall. This result is robust across at longer lead times (greater than 72 h) was highly an ensemble of simulations utilizing various grids and scattered. Additionally, the lead time required for indi- perturbations to the physics time step and deep con- vidual models to trend toward a realistic landfall case vective scheme, as shown by the multimember mean for were widely varied. Some models forecasted recurvature CAM. The fact that CAM uses the same initial condi- more than a week in advance while others continued to tions as the deterministic GFS forecast (the DFI results show ‘‘out to sea’’ solutions as late as a few days before in a slightly different state at 16 h, with measured landfall, with the two most frequently scrutinized NWP anomaly correlations between GFS and CAM forecasts models being the GFS [and corresponding GFS-based being approximately 3%–5%, not shown) strongly im- ensemble (GEFS)] and the global model from the Eu- plies that model initialization was not the key reason ropean Centre for Medium-Range Weather Forecasts why the GFS was unable to forecast this recurvature (ECMWF; Blake et al. 2013). during the early stages of Sandy’s evolution. Figure 14 shows track forecasts for Hurricane Sandy These results agree with those in Bassill (2014) who used for the daily 0000 and 1200 UTC cycles between 22 WRF ensembles to demonstrate that differences between October (8 days from landfall) and 25 October (5 days the GFS and ECMWF forecast models were dominated from landfall). The black solid curve is Sandy’s observed by cumulus parameterization. In that study, forecasts track. The thin, pink curves are individual GEFS en- initialized with similar initial conditions showed a clear semble members, with the thicker red curve being the track forecast bifurcation that was delineated by the GEFS ensemble mean. The darker red curve is the de- choice of either the simplified Arakawa–Schubert (GFS) terministic GFS forecast. The thin, light blue forecasts or Tiedtke (ECMWF) cumulus parameterizations. Fur- are CAM ensemble members. These include globally ther work indicates that this difference may be con- uniform 55-km and globally uniform 14-km forecasts as strained by the deep convective entrainment rate in the well as multiple V-R forecasts. These V-R forecasts in- simplified Arakawa-Schubert scheme (Bassill 2015). cluded the default control configuration, the configura- Torn et al. (2015) suggest additional atmospheric sam- tion using climatological SSTs, the configuration with pling to the north of Sandy might have improved forecast the 450-s physics time step, and the configuration where skill as well, although their reasoning behind this can also the deep convective scheme is omitted. The CAM- be rooted in model physics. They showed that, within a CLUBB forecast is shown in green as the subgrid pa- multimember GFS ensemble, moist parameterizations rameterizations were sufficiently different such that the produced less vertical moisture flux convergence and forecast was not considered a physics-perturbed mem- weaker upward motion in members that pushed Sandy ber of the default CAM suite. eastward into the Atlantic Ocean. These effects fed back The CAM ensemble mean forecast is shown in blue. It into the large-scale dynamics, eventually producing a less is readily apparent that CAM forecasts Sandy’s re- amplified subtropical ridge over the Atlantic than what curvature into the eastern seaboard of the United States was observed. These results, as well as those contained in

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FIG. 14. Track forecasts for Hurricane Sandy for each 12-h forecast cycle between 0000 UTC 22 Oct and 1200 UTC 25 Oct 2012 for various conﬁgurations of CAM as well as the GFS/GEFS models. Light, thin lines are ensemble members [CAM (light blue), GEFS (pink)], dark, bold lines are ensemble means [CAM (blue), GEFS (red)], or single, deterministic runs [GFS (dark red), CAM-CLUBB (green)]. The black solid line is the observed storm trajectory.

Unauthenticated | Downloaded 10/06/21 09:29 AM UTC OCTOBER 2015 Z A R Z Y C K I A N D J A B L O N O W S K I 4033 this paper, highlight the potential for significant sensi- TABLE 7. Computational run-time statistics for various config- tivity in tropical cyclone track forecasts to arise from urations discussed in the manuscript. For each resolution/ physical parameterization selection. configuration combination, the median number of central processing units (CPUs), model-simulated days per actual wall-clock day (SD/CD), and simulated model days per day normalized to 6. Computational performance 1000 CPUs (SD/CD/1000) are shown. No. of The primary goal of this study was to investigate the Grid Expt CPUs SD/CD SD/CD/1000 performance of V-R CAM-SE from a forecasting stand- point. Therefore, there was no rigorous effort to control Uniform Control 72 47.6 654.1 55 km for aspects of the study that may have influenced the V-R 14 km Controla 432 25.9 60.5 computational performance of the model. Nevertheless, DT450 192 15.2 79.3 some meaningful data can be ascertained from an in- NODEEP 192 17.8 92.8 formal analysis of the timing results. Table 7 shows the MODTAU900 336 29.2 86.8 median timing statistics for individual forecasts using CLUBB 240 20.3 84.4 Uniform Control 384 5.3 13.8 each model grid as well as the various model configura- 14 km tions for the V-R simulations. Note that the control a forecasts utilizing the V-R grid were completed before a Forecast simulations were completed prior to cluster InfiniBand upgrade. significant update to the cluster’s InfiniBand communication links. This resulted in improved performance for all other forecast simulations. Additionally, timing data 7. Conclusions and future work were not collected for the simulations using climatological SSTs. In this paper we have developed a framework that al- We show model forecast days per actual wall-clock day lows the Community Atmosphere Model to be run as a normalized to 1000 central processing units (CPUs) in an short-term forecast model using variable-resolution grids attempt to normalize the simulations since different with a digital filter initialization scheme. We demonstrate numbers of processors were used for different configu- that increased resolution via regional refinement im- rations. The uniform 55-km forecasts easily produced the proves both TC track and intensity forecasts when com- highest model throughput of all simulations. This is to be pared to identically initialized unrefined simulations expected since the grid contains many less elements (e.g., using CAM-SE. This skill increase likely arises from a 16 times fewer than the uniform 14-km grid), but is also combination of improved representation of the large- integrated with a longer dynamical time step due to a less scale flow, more realistic interactions between TCs and restrictive CFL constraint than either the V-R or uni- their environment, and more accurate representations of form 14-km simulations. small-scale features, which may provide upscale effects to Only considering the forecasts that were completed the synoptic environment. These results demonstrate the following the InfiniBand upgrade, the V-R simulations potential viability of variable-resolution models as alter- produced approximately 80–90 simulated days per wall- natives to either globally uniform or high-resolution clock day, assuming 1000 CPUs. These numbers differ limited-area simulations in future NWP applications. because of the different physical parameterizations that Furthermore, simulations show that, for lead times on the were used, run-to-run variability driven by node selec- order of less than a week, a variable-resolution simulation tion, as well as the relative load on the cluster due to can produce nearly identical forecast behavior inside the other users. Note that these simulations produce ap- refined nest as to that produced by a globally uniform proximately 6–6.5 times more throughput than the uni- simulation of the same high resolution. This can be form 14-km simulations. As shown in Table 1, the achieved with a much lower computational cost, poten- uniform 14-km grid has approximately 6.5 more grid tially enabling further horizontal refinement, additional cells than the V-R simulations. Given the fact that the ensemble members, or longer model integrations. V-R simulation is constrained to the same time step as Hurricane track skill in the control V-R runs with the the uniform 14-km simulations, these results corrobo- default CAM5 physics is comparable to operational rate previous work that has shown that CAM-SE scales models. This occurs even though, in practice, CAM is nearly linearly with the number of elements in the mesh primarily used as a multidecadal climate model at sig- (e.g., Dennis et al. 2012; Zarzycki et al. 2014a) and val- nificantly coarser resolutions. There has been very little idates that variable-resolution simulations can produce validation or subsequent tuning of subgrid physical pa- regionally refined forecasts at a cheaper computational rameterizations at or below 0.258 (28 km) grid spacing. cost than models with globally uniform high resolution. These skillful forecasts highlight the importance of the

Unauthenticated | Downloaded 10/06/21 09:29 AM UTC 4034 MONTHLY WEATHER REVIEW VOLUME 143 large-scale flow on TC track, which is likely well repre- intensity somewhat, implying that the partitioning be- sented in CAM. The performance of CAM-SE with re- tween large-scale microphysics and convective param- spect to TC intensity is worse, however. In the model’s eterization in the moist physics may be playing a default configuration, the error of 10-m wind at long lead significant role in controlling TC intensity, a result also times is approximately the same as the statistical SHF5 seen in Reed et al. (2012). Of all of the sensitivity studies model. Examination of the 10-m wind biases show that shown here, the use of CLUBB in lieu of CAM5’s de- this results from the model producing, on average, fault boundary layer, macrophysics, and shallow con- storms that are stronger than observed. This over- vection schemes played the largest role in modulating intensification was strongest among storms that were the V-R control setup’s tendency to produce TCs weaker at initialization, but appears systematic across stronger than those seen in observations. Interestingly, the majority of forecasts. forecasts using CLUBB tend to intensify TCs more We note that while overall activity was at or slightly slowly and only become more skillful than the control above average for the 2012–13 hurricane seasons for the CAM5 simulations at lead times beyond 72 h. It is also Atlantic and eastern Pacific, only one major hurricane worth noting that the CLUBB configuration still utilizes 2 (10-m wind $ 50 m s 1) occurred in 2013 between the two the default ZM deep convective scheme with the default basins (cf. a 1981–2010 average of seven) (Stewart 2014; convective relaxation time scale (t 5 3600 s). Sensitivity Blake 2014; Pasch 2014; Kimberlain 2014). In particular, studies also showed some degree of sensitivity to this this implies that the ratio of weak to strong storms was convective relaxation time scale t when the default slightly higher during the study period when compared to CAM5 physics were left in place. This strongly implies climatology. It is conceivable that the relative skill of V-R nonlinearities in the moist physics are important in CAM-SE, particularly with respect to intensity, might be driving forecasted TC intensity in CAM. Future work different in years with more numerous intense storms. On will attempt to explore these interactions more thor- one hand, stronger storms may highlight deficiencies oughly, although they highlight just how crucial the arising from the inability of the relatively ‘‘coarse’’ grid choices of these parameterizations are in forecasting spacings in this study to resolve processes in the cyclone TCs in any numerical setup. core, such as eyewall asymmetries and replacement cy- Particular focus was paid to forecasts of Hurricane cles. On the other hand, it is possible that V-R CAM-SE Sandy. Using the same initial conditions as the GFS would perform better with additional strong storms given model, CAM-SE robustly forecasts recurvature of the model’s capability to produce very intense TCs with Sandy at lead times of 18 days, similar to the ECMWF the control configuration. Additional work is needed to model (Magnusson et al. 2014). This stands in contrast determine if this sensitivity exists beyond what was dis- to the performance of the operational GFS model. cussed in section 3a. The fact that CAM-SE was initialized with the same Simulations where climatological SSTs are used instead analysis used in initializing the deterministic GFS and of observed SSTs show little impact on model forecast. ensemble GEFS models provides further evidence Track skill is slightly degraded with climatological SSTs, that model physical parameterizations played the implying that accurate SST representation helps control most critical role in forecasted track spread in the cyclone motion through either local dynamics or large- week before the storm’s landfall (e.g., Bassill 2014). scale steering flow. Intensity skill is slightly improved at The fact that many NWP models generally show longer lead times, although this is likely due to the fact similar average skill [e.g., see Figs. 3 and 5 as well as that the climatological SSTs are cooler, which system- Cangialosi and Franklin (2013)] when averaged over atically reduces intensity through decreased latent and multiple seasons, but can produce wildly different sensible heat fluxes into the model’s lowest level. It is forecasts for individual storms (e.g., Fig. 14) highlights possible that global models are pushing to horizontal the sensitivities of the forecast of individual storms to resolutions that can dynamically support TCs intense model configurations. enough that the assumptions allowing for the use of All simulations shown in this paper used the publicly prescribed SSTs as surface forcing break down. Work is available GDAS analysis for model initialization. Work ongoing to test CAM-SE coupled to slab, mixed layer, is ongoing to allow variable-resolution CAM-SE to be and fully dynamic ocean models to investigate whether used in conjunction with the Data Assimilation Re- ocean–atmosphere interactions are playing a major role search Testbed (DART; Anderson et al. 2009) for native at horizontal resolutions O(D10) km. atmospheric and land data assimilation on variable- Parameterization sensitivity studies were completed resolution grids. This will provide a more physically to attempt to discern potential mechanisms for this in- consistent initial state of the atmosphere and eliminate tensity bias. Increasing deep convective activity reduced the need for digitally filtering the initial conditions.

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Future work will explore this framework as well as Anderson, J., T. Hoar, K. Raeder, H. Liu, N. Collins, R. Torn, and compare model performance with the configuration A. Avellano, 2009: The Data Assimilation Research Testbed: used here to configurations that ingest different data as A community facility. Bull. Amer. Meteor. Soc., 90, 1283–1296, doi:10.1175/2009BAMS2618.1. part of the initialization process. Barnes, S. L., 1964: A technique for maximizing details in numer- While the simulations in this study were not ex- ical weather map analysis. J. Appl. Meteor., 3, 396–409, tended below 14-km horizontal grid spacing because doi:10.1175/1520-0450(1964)003,0396:ATFMDI.2.0.CO;2. of available computing resources and the hydrostatic Bassill, N. P., 2014: Accuracy of early GFS and ECMWF Sandy nature of the dynamical core, the only impediment to (2012) track forecasts: Evidence for a dependence on cumulus parameterization. Geophys. Res. Lett., 41, 3274–3281, completing global, variable-resolution simulations at doi:10.1002/2014GL059839. single-kilometer resolution in a nonhydrostatic ——, 2015: An analysis of the operational GFS simplified Arakawa framework is the behavior of physical parameteriza- Schubert parameterization within a WRF framework: A tions that span the various resolutions of the simula- Hurricane Sandy (2012) long-term track forecast perspec- tions. This manuscript highlights a high bias in tive. J. Geophys. Res. Atmos., 120, 378–398, doi:10.1002/ 2014JD022211. forecast intensity with the default CAM5 physical pa- Blake, E. S., 2014: 2013 Atlantic hurricane season. National Hur- rameterization set; however, this package has not been ricane Center Annual Summary, Tech. Rep., National Hur- tuned for NWP-type simulations at high resolutions. In ricane Center, 9 pp. [Available online at http://www.nhc.noaa. addition, future developments of scale-aware pa- gov/data/tcr/summary_atlc_2013.pdf.] rameterizations are likely to lead to significantly im- ——, T. B. Kimberlain, R. J. Berg, J. P. Cangialosi, and J. L. Beven II, 2013: Tropical cyclone report: Hurricane Sandy. Tech. Rep. proved performance of models at multiple grid AL182012, National Hurricane Center, 157 pp. [Available spacings, which should dramatically reduce some of online at http://www.nhc.noaa.gov/data/tcr/AL182012_Sandy. the biases seen in these simulations and make V-R pdf.] models a more feasible tool for next-generation Bogenschutz, P. A., A. Gettelman, H. Morrison, V. E. Larson, weather forecasting. D. P. Schanen, N. R. Meyer, and C. Craig, 2012: Unified parameterization of the planetary boundary layer and shallow convection with a higher-order turbulence closure in the Acknowledgments. The authors thank Mark A. Taylor Community Atmosphere Model: Single-column experi- for assistance in running CAM-SE as well as fruitful ments. Geosci. Model Dev., 5, 1407–1423, doi:10.5194/ discussions regarding model behavior and configura- gmd-5-1407-2012. tions, Paul A. Ullrich for assisting in grid generation ——, ——, ——, ——, C. Craig, and D. P. Schanen, 2013: Higher- and providing computational support, and Timothy order turbulence closure and its impact on climate simulations in the Community Atmosphere Model. J. Climate, 26, 9655– Marchok for providing the operational TC tracker. 9676, doi:10.1175/JCLI-D-13-00075.1. Some of the forecast statistics were computed with the Bretherton, C. S., and S. Park, 2009: A new moist turbulence param- help of the Model Evaluation Tools (MET) package eterization in the Community Atmosphere Model. J. Climate, developed by the Developmental Testbed Center 22, 3422–3448, doi:10.1175/2008JCLI2556.1. (http://www.dtcenter.org/met/users/index.php). Diana Cangialosi, J. 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