Operational Numerical Weather Prediction Models: Outline

Operational Numerical Weather Prediction Models

Waylon Collins DOC/NOAA/National Weather Service Weather Forecast Office Corpus Christi 1 September 2016 Operational Numerical Weather Prediction Models: Outline

 Model Development Summary  Review of select parameterizations, data assimilation, and initialization  Specific Global, Mesoscale, and Cloud-allowing NWP models  Select parameterizations and NWP skill based on limited literature search; implications for operational NWP models  What atmospheric phenomena can be resolved/simulated by a particular NWP model?  Predictability  Summary NWP Model Development: Summary  Determinism: Latter states evolve from earlier ones in accordance with physical laws. (Laplace, 1996; Lorenz 1993)  Primitive equations: Based on Newton’s 2nd law of motion, equation of state, conservation of mass, thermodynamic energy equation (Bjerkness 1904) (model dynamics)  Discretization: Atmospheric fluid  finite grid elements. Continuity of time  finite time increment [finite difference equations]  Parameterizations: Account for the implicit effects of (emulate) unresolved processes (model physics)  Initial value problem: Initial values provided by data assimilation  Data Assimilation: “Using all the available information to determine as accurately as possible the state of the atmospheric or oceanic flow” (Talagrand, 1997) NWP Model Development: Summary  Initialization: Balanced analysis (e.g. Glickman, 2000; Stull, 2015)  Forward integration  Primary (t, u, v, etc.) and Secondary variable/parameter (CAPE, simulated reflectivity, etc.) output Discretization: NWP Model Grid Cell Depiction Example (Stull, 2015) Review of select parameterizations, data assimilation, and initialization Select parameterizations

Kalnay (2003) Select Parameterizations: PBL/Turbulence

Motivation to account for PBL/Turbulence (Randall, et al., 1985; Stensrud, 2007)

 The PBL is the layer adjacent to the earth wherein turbulence is the dominate mechanism responsible for the vertical redistribution of sensible heat, moisture, and momentum  Sensible/latent heat turbulence fluxes most important source for moist static energy for atmospheric circulations  PBL friction the most prevalent atmospheric KE sink  Potential for deep convection (via CAPE) and convective mode (via wind profile) related to PBL structure Select Parameterizations: PBL/Turbulence

Problem: Representation of turbulent flow in the primitive equations requires a grid spacing ≤ 50-m (Stensrud, 2007)

Solution: Reynolds averaging to account for the statistical effects of subgrid scale eddies (Stensrud, 2007)

u = u + u u → spatial average over a grid box u → subgrid scale perturbation Select Parameterizations: PBL/Turbulence

Turbulence Closure Problem (Warner, 2011) Select Parameterizations: PBL/Turbulence

Turbulence Closure Approaches (Warner, 2011)

Local Closure: Relate unknown variables (what must be parameterized) to known variables at nearby vertical grid points

Nonlocal Closure: Relate unknown variables (what must be parameterized) to known variables at any number of vertical grid points Select Parameterizations: PBL/Turbulence

Example of problem with Local PBL scheme:

Local closure approximation of vertical heat flux:

휕휃 휃′푤′ = −Κ − 훾 퐻 휕푧

Local closure approximation of vertical heat flux near zero in center of PBL (unless correction 훾 applied), yet studies reveal that heat transfer exist throughout the PBL

Warner (2011); originally adapted from Stull (1991) Select Parameterizations: Microphysics Motivation to account for cloud mircophysics Microphysical processes govern formation, growth, and dissipation of cloud particles which influences development and evolution of moist convection (Stensrud, 2007) Problem Foregoing processes occur on molecular scales, thus unresolved by NWP models Solution Explicit microphysics parameterization  explicitly represent clouds and associated microphysical processes (Stensrud, 2007) Select Parameterizations: Microphysics (Warner, 2011) Select Parameterizations: Microphysics Parameterize: • Phase changes of water • Various interactions between cloud and precipitation particles Two classes of microphysical parameterizations based on how size distribution represented: Bulk: Use analytical equation (gamma, exponential, log-normal, etc.) to parameterize particle size distribution for each species; size spectra evolution from predictive equations for the following moments (used in operational NWP models) • Single moment  Predict only particle mixing ratio • Double moment  Predict particle mixing ratio and number concentrations (more realistic particle size distribution and size sorting) • Triple moment  Predict mixing ratio, number concentration, and reflectivity Bin: Discretize particle size distribution into finite size/mass categories (“bins”); predictive equations for each size bin and species (computationally expensive; used in research) Morrison (2010); Stensrud (2007); Warner (2011) Select Parameterizations: Microphysics Initialization of microphysical parameters/variables: Problem: Difficult to determine initial values • Existence of select atmospheric species only inferred by satellite imagery or surface observations • Vertical and horizontal distribution of species unknown • Must initialize with corresponding circulations Solutions . Assume zero number concentrations at NWP model initialization and assume that realistic values will spin up within 3-6 h of NWP model start. . Use values from analysis background/first guess (output from short-term NWP prediction) . Use output from Newtonian relaxation/nudging

Warner (2011) Select Parameterizations: Convection Motivation to Account for Convection Deep Moist convection  Important to the prediction of atmospheric circulations (Stensrud, 2007)  Warms environment via compensating subsidence, and dries the atmosphere via removal of water vapor (Warner, 2011) Shallow convection  Modifies the surface radiation budget, and influences the turbulence/structure of the PBL (Randall et al. 1985) Problem NWP grid spacing of ≤ 100-m needed to resolve convective clouds (Bryan et al 2003; Petch 2006)  not feasible for state-of-the-art operational NWP models.

Solution Parameterize the implicit effects of subgrid scale convection (e.g Molinari and Dudeck, 1986; Molinari and Dudeck, 1992) Select Parameterizations: Convection

Convective Parameterization Overall Objective (Arakawa, 1993)  Properly represent convective timing, location, evolution and intensity  Properly define the environmental modification to convection in order to accurately predict subsequent convection Select Parameterizations: Convection Categorizing convective parameterization schemes (Warner, 2011) A. Deep Layer (Equilibrium) Control (convection controlled by CAPE development) and Low Level (Activation) Control (convection controlled by removal of CIN) B. Represent only deep convection, shallow convection, or both C. Classified in terms of atmospheric grid scale variables affected by convection D. Define the final atmospheric state after convection effected the change (static scheme) or simulate the process by which the change takes place (dynamic scheme) Trigger Function: Set of criteria that prescribe time/location of the parameterized convection activation Select Parameterizations: Convection Relationship between parameterized sub-grid scale convection and resolved-scale convection (Warner, 2011) A. Precipitation can be produced as a byproduct of the activation of moist convection by the convective parameterization scheme and by explicit prediction of grid-scale precipitation by microphysical parameterization B. Parameterized precipitation is generated within a sub-saturated grid box (since convection parameterized is of sub-grid scale), while resolved scale precipitation in the microphysics scheme requires grid box saturation C. Convective parameterization generally does not produce cloud water/ice on the grid-scale, thus no cloud radiative effects D. Parameterized and resolved scale precipitation may predominate at different regions of an event (e.g. MCS  parameterize convection dominate convective region while microphysics scheme influences the stratiform rain region.) Select Parameterizations: Convection Relationship between parameterized sub-grid scale convection and resolved-scale convection (Warner, 2011) Partitioning of parameterized and resolved scale precipitation a function of meteorological event and convective parameterization scheme Select Parameterizations: Convection Important issues related to convective parameterization 1. ≥ 10-km: fully explicit approach (no convective parameterization) cannot successfully simulate mesoscale organization of convection (Molinari and Dudeck, 1992) ≤ 20-km: Fundamental assumption of convective parameterization begins to break down (Molinari and Dudeck, 1992) ≤ 20-km: Inclusion of convective parameterization may result in simultaneous implicit effects of subgrid scale convection and explicit convection (Molinari and Dudeck, 1992) 2. Convective parameterization removes excess instability and rainfall occurs as a byproduct of the process. Thus, do not rely on the timing and position of convective precipitation in NWP models with convective parameterization (UCAR, 2002) Select Parameterizations: Convection NWP Model skill when Convective Parameterization turned off (≤ 10-km)

5-10 km: Convective overturning develops/evolves too slowly; updraft/downdraft mass fluxes and precipitation rates too strong during mature phase (Weisman et al. 1997) 4-km: . Adequately resolve squall line mesoscale structures (Weisman et al. 1997) . Exaggerates scale of individual convective cells contributing to a high QPF bias (e.g. Deng and Stauffer, 2006) . Can accurately/skillfully predict convection occurrence and mode. Less skillful with regard to timing and position (Fowle and Roebber, 2003; Weisman et al. 2008) 4-km  2-km: Miniscule improvement in prediction skill; added value likely not worth the factor of 10 increase in computational expense (Kain, 2008) 2-km  0.25 km: Simulations of supercell very sensitive to grid spacing (2-km: steady state/unicellular ≤ 1-km: cyclic mesocyclogenesis (Adlerman and Droegemeier, 2002) NWP Model skill when Convective Parameterization turned off (≤ 10-km)

0901 UTC 4/14/2015 WSR-88D 0900 UTC 4/14/2015 HIRESW ARW WARM START 4.2 km

0900 UTC 4/14/2015 HRRR HOT START 0900 UTC 4/14/2015 NSSL COLD START 3.0 km 4.0 km NWP Model skill when Convective Parameterization turned off (≤ 10-km)

1000 UTC 4/14/2015 WSR-88D 1000 UTC 4/14/2015 HIRESW ARW WARM START 4.2 km

1000 UTC 4/14/2015 HRRR HOT 1000 UTC 4/14/2015 NSSL COLD START 3.0 km START 4.0 km NWP Model skill when Convective Parameterization turned off (≤ 10-km)

1100 UTC 4/14/2015 WSR-88D 1100 UTC 4/14/2015 HIRESW ARW WARM START 4.2 km

1100 UTC 4/14/2015 HRRR HOT 1100 UTC 4/14/2015 NSSL COLD START START 3.0 km 4.0 km Data Assimilation Methods: Continuous versus Sequential (Warner, 2011) Data Assimilation Methods: 3D- Variational (3D-Var) (Lorenc, 1986)

 Background 휲푏 (short-term NWP model prediction)

 Direct and indirect observations 휰표  Background and observations error covariances (휝, 푹)  Minimize scalar cost function J to determine an optimal

analysis 휲 = 휲푎:

푇 −1 푇 −1 2퐽 Χ = 휲 − 휲푏 휝 휲 − 휲푏 + 휰표 − 훨 휲 푹 휰표 − 훨 휲

 Iterative methods used to minimize J (Conjugate gradient, Quasi-Newton, etc.) Data Assimilation Methods: 3D-Var Minimization Graphical Depiction Example (Bouttier and Courtier, 1999) Data Assimilation Methods: Ensemble Kalman Filtering (EnKF) (e.g. Houtekamer et al., 1996)  Historically, 휝 computed via “NMC” method (Parrish and Derber, 1992): Τ 휝 ≈ 훼훦 Χ푓 48 ℎ − Χ푓 24 ℎ Χ푓 48 ℎ − Χ푓 24 ℎ  Major limitation: Isotropy of 휝.  EnKF: 휝 replaced by anisotropic/flow-dependent error covariances generated by an ensemble of concurrent K data assimilation cycles (Kalnay 2003): 1 Τ 푷푓 ≈ 휲푓 − 휲 푓 휲푓 − 휲 푓 푙 퐾 − 2 푘 푙 푘 푙 푘≠푙 • Hybrid EnKF: Hamill and Synder (2000) suggested a hybrid between 3D-Var and EnKF (Kalnay 2003):

푓(ℎ푦푏푟𝑖푑) 푓 푷푙 = 1 − 훼 휬푙 + 훼푩3퐷−푉푎푟 Data Assimilation Methods: Advantage of EnKF over 3D-Var (Pu et al. 2013)

3D-Var Data Assimilation Methods: Advantage of EnKF over 3D-Var (Pu et al. 2013)

EnKF Data Assimilation Methods: Method used in the GFS v13.0.2 (11 May 2016)

80 member ensemble of 9 h Predictions for background error covariance

9 h GSM prediction used in Hybrid 4DEnVar

The 00 (06,12,18) UTC cycle uses 9 h prediction from 18 (00,03,06) UTC GDAS cycle as the background. Assimilation window for the 00 (06,12,18) UTC cycle is from 21 (03,09,15) UTC to 03 (09,15,21) UTC Data Assimilation Methods: Method used in the ECMWF (12 May 2016) (ECMWF, 2016)

The 00 (12) UTC cycle uses 3 h prediction from 18 (06) UTC delayed cut-off analysis as the background. Assimilation window for the 00 (12) UTC cycle is from 21 (09) UTC to 09 (21) UTC Data Assimilation Methods: Method used in the NAM (2014) (EMC, 2016)

The 00,06,12,18 UTC cycle uses 6 h prediction from GDAS valid 12 h earlier as initial background. 12 h Assimilation window involving four 3 h NMMB predictions serving as background for subsequent GSI analysis and 3 h NMMB run (initialized with diabatic digital filter) Data Assimilation Methods: Method used in the RAPv3 (Benjamin et al., 2015) (23 August 2016) Data Initialization Methods

 Nonlinear Normal Mode Initialization Segregate high and low frequency components of initial input data via vertical and horizontal structure functions. High frequencies assumed to have no meteorological significance are removed (Daley, 1981)  Newtonian Relaxation (Nudging) NWP model runs during a pre-forecast period and is relaxed toward/constrained by observations and/or series of analyses; approximate dynamic balance develops during pre-forecast period as inertia-gravity waves associated with mass/momentum imbalance propagate away from domain (Hoke and Anthes, 1976)  Digital Filter Initialization Perform an adiabatic NWP model integration backward in time (short time period such as 3 h), then a diabatic integration forward in time (initialization time in center) and apply a digital filter to the resultant time series to remove high frequencies (Huang and Lynch, 1993) Specific Global, Mesoscale, and Cloud- allowing NWP models Select NWP Models to Support WFO Operations

GLOBAL  ECMWF  GFS  GDPS  NAVGEM (URL https://www.fnmoc.navy.mil/wxmap_cgi/index.html) LIMITED AREA MODELS [MESOSCALE]  12-km NEMS-NMMB (NAM)  13-km Rapid Refresh (RAP) LIMITED AREA MODELS [MESOSCALE AND CONVECTION ALLOWING/ PERMITTING]  4-km CONUS NAM nest  3-km High Resolution Rapid Refresh (HRRR)  3-4 km HIRESW (WRF-ARW and NEMS-NMMB)  4-km NSSL Realtime  4-km Texas Tech WRF The Mesoscale  2-20 km (γ) 20-200 km (β) 200-2000 km (α) (Orlanski, 1975)  “…horizontal spatial smaller than the conventional rawinsonde network, but significantly larger than individual cumulus clouds…” (Pielke, 2013)  “..horizontal extent large enough for the hydrostatic approximation to the vertical pressure distribution to be valid, yet small enough for the geostrophic and gradient winds to be inappropriate as approximations to the actual wind circulation above the planetary boundary layer…” (Pielke, 2013) “Convection-Allowing/Permitting” and “Convection-Resolving” NWP Models

CONVECTIVE ALLOWING/PERMITTING: Simulate deep convection without convective parameterization . ≤ 4 km grid spacing (Weisman et al. 1997)

CONVECTIVE RESOLVING: Resolving convective clouds without convective parameterization . ≤ 0.1 km grid spacing (Bryan et al. 2003; Petch 2006) . ≤ 0.5 km grid spacing (Jascourt S. 2010) NWP Model Configurations: RAPv2 versus RAPv3 (Scheduled for 23 August 2016) Model Domain Grid spacing Vertical Boundary Initialization levels condition Frequency RAPv3 North 13-km 50 GFS Hourly (cycled) American RAPv2 North 13-km 50 GFS Hourly (cycled) American

Model Dynamic Assimilation Radar DA Radiation Microphysics Core LW/SW RAPv3 ARW v3.6+ GSI Hybrid 3D- 13-km DFI + RRTMG Thompson- VAR/Ensemble low reflect v3.6 (Iacono et aerosol v3.6.1 (0.75/0.25) (Weygandt and al. 2008) (Thompson and Benjamin, 2007) Eidhammer, 2014)

RAPv2 ARW v3.4.1 GSI Hybrid 3D- 13-km DFI RRTM Thompson VAR/Ensemble (Weygandt and (Iacono et al. v3.4.1 (0.50/0.50) Benjamin, 2007) 2008) (Thompson et al. 2008) NWP Model Configurations: RAPv2 versus RAPv3

Model Cumulus Parameterization Planetary Land Initialization Boundary Surface (Balancing) Layer Model RAPv3 Deep: Grell and Freitas (2014) MYNN RUC Digital Filter Shallow: Grell-Freitas-Olson v3.6+ v3.6+ Initialization (DFI) (Nakanishi and (Smirnova (Weygandt and Niino, 2004, et al. 2008) Benjamin, 2007) 2009) RAPv2 G3 + Shallow MYNN RUC Digital Filter (Grell and Devenyi, 2002) (Nakanishi and (Smirnova Initialization (DFI) Niino, 2004, et al. 2008) (Weygandt and 2009) Benjamin, 2007) NWP Model Configurations: RAPv2 versus RAPv3 RAPv2 bias  insufficient cloud coverage  excessive downward solar radiation RAPv3 limits warm bias in RAPv2 (Benjamin et al. 2016) via shortwave radiation attenuation 1. Microphysics updated to include predictions for IN and CNN  increase clear-sky albedo 2. MYNN PBL scheme  improved sub-grid cloud representation (RH-based cloud fraction) and coupling to radiation scheme 3. Accounting for shallow cumulus clouds in the Grell-Freitas convective parameterization scheme NWP Model Configurations: RAPv3 versus HRRRv2

Model Domain Grid Vertical Boundary Initialization spacing levels condition Frequency RAPv3 North 13-km 50 GFS Hourly (cycled) American HRRR CONUS 3-km 50 RAP Hourly (cycled)

Model Dynamic Assimilation Radar DA Radiation Microphysics Core LW/SW RAPv3 ARW GSI Hybrid 3D- 13-km DFI + RRTMG Thompson- v3.6.1 VAR/ Ensemble low reflect v3.6 (Iacono aerosol v3.6.1 (0.75/0.25) (Weygandt and et al. 2008) (Thompson and Benjamin, 2007) Eidhammer, 2014) HRRR ARW GSI Hybrid 3D- 3-km 15 min RRTMG Thompson- V3.6.1 VAR/ Ensemble LH+ low reflect v3.6 (Iacono aerosol v3.6.1 (0.75/0.75) (Weygandt and et al. 2008) (Thompson and Benjamin, 2007) Eidhammer, 2014) NWP Model Configurations: RAPv3 versus HRRRv2

8 June 1993 – 19 June 2006 (Hydrostatic) Eta Model 20 June 2006 – 30 September 2011 Weather Research and Forecasting Non-hydrostatic Mesoscale Model: WRF-NMM WRF Modeling framework, NMM  dynamic core 1 October 2011 – Present NOAA Environmental Modeling System Non-hydrostatic Multiscale Model on the Arakawa B-grid: NEMS-NMMB NEMS  Modeling framework, NMMB  dynamic core WRF Modeling Framework NEMS Modeling Framework NWP Model Configurations: RAPv3 versus NEMS-NMMB (NAM)

Model Domain Grid Vertical Boundary Initialization spacing levels condition Frequency NEMS-NMMB North 12-km 60 (27 in 0- GFS 3-hr (cycled) American (Parent) 3km layer) RAPv3 North 13-km 50 GFS Hourly (cycled) American

Model Dynamic Assimilation Radar DA Radiation Microphysics Core LW/SW NEMS- NMMB Hybrid ensemble Yes LW: RRTM Ferrier-Aligo NMMB 3DVar (Iacono, et al. 2008) (Aligo et al. 2014) SW: RRTM (Mlawer, et al. 1997) RAPv3 ARW GSI Hybrid 3D- 13-km DFI + RRTMG v3.6 Thompson- v3.6+ VAR/ Ensemble low reflect (Iacono et al. 2008) aerosol v3.6.1 (0.75/0.25) (Weygandt and (Thompson and Benjamin, 2007) Eidhammer, 2014) NWP Model Configurations: RAPv3 versus NEMS-NMMB (NAM)

Model Cumulus Planetary Land Surface Initialization Parameterization Boundary Model (Balancing) Layer NEMS- BMJ (Janjic 1994) MYJ Level 2.5 Noah LSM (Ek et al. 2003) Diabatic Digital NMMB (Janjic 1994, 2001) (20 MODIS-IGBP land Filter use categories) RAPv3 Deep: MYNN v3.6+ RUC v3.6+ Digital Filter Grell and Freitas (2014) (Nakanishi and (Smirnova et al. 2008) Initialization Shallow: Niino, 2004, 2009) (DFI) Grell-Freitas-Olson (Weygandt and Benjamin, 2007) NWP Model Configurations: HIRESWINDOW v6.1.5 (CONUS) versus NAMCONUSNEST

Model Domain Grid Vertical levels Boundary Initialization spacing condition Frequency HIRESW(CONUS): CONUS (1) 3.6-km 50 RAP (IC) 3-hr (cycled) (1) NEMS-NMMB (2) 4.2-km (16 in lowest 120 hPa) GFS (BC) (2) WRF-ARW NAMCONUSNEST: CONUS 4-km 60 NAM 3-hr (cycled) NEMS-NMMB (27 in 0-3km layer)

Model Dynamic Assimilation Radar Radiation Microphysics Core DA LW/SW HIRESW(CONUS): (1) NMMB Hybrid Yes LW: RRTM (1) Ferrier-Aligo (1) NEMS-NMMB (2) ARW ensemble (Iacono, et al. 2008) (Aligo et al. 2014) SW: RRTM (2) Modified WSM6 (2) WRF-ARW v3.6.1 3DVar (Mlawer, et al. 1997) (Grasso et al. 2014) NAMCONUSNEST: NMMB Hybrid Yes LW: RRTM Ferrier-Aligo NEMS-NMMB 1/2015 ensemble (Iacono, et al. 2008) (Aligo et al. 2014) SW: RRTM 3DVar (Mlawer, et al. 1997) NWP Model Configurations: HIRESWINDOW v6.1.5 (CONUS) versus NAMCONUSNEST

Model Cumulus Planetary Land Surface Model Initialization Parameteri Boundary (Balancing) zation Layer HIRESW(CONUS): NONE MYJ Level 2.5 Noah LSM (Ek et al. 2003) (1) Diabatic (1) NEMS-NMMB (Janjic 1994, 2001) (20 MODIS-IGBP land Digital (2) WRF-ARW use categories) Filter

NAMCONUSNEST: NONE MYJ Level 2.5 Noah LSM (Ek et al. 2003) Diabatic NEMS-NMMB (Janjic 1994, 2001) (20 MODIS-IGBP land Digital Filter use categories)

NWP Model Configurations: NSSL Realtime WRF versus Texas Tech WRF

Model Domain Grid Vertical Boundary Initialization spacing levels condition Frequency NSSL Realtime CONUS 4-km 35 NAM 12 h WRF TexasTech WRF South Central 3-km 38 GFS 6 h CONUS

Model Dynamic Assimilation Radar Radiation Microphysics Core DA LW/SW NSSL Realtime ARW NAM Analysis No LW:RRTM WSM6 WRF (40-km) only (Mlawer, et al. 1997) (Hong and Lim 2006) SW: Dudhia TexasTech ARW GFS Analysis only No LW: RRTM Thompson WRF v3.5.1 (Mlawer, et al. 1997) (Thompson et al. SW: Dudhia 2008) NWP Model Configurations: NSSL Realtime WRF versus Texas Tech WRF

Model Cumulus Planetary Land Initialization Parameterization Boundary Surface (Balancing) Layer Model NSSL Realtime NONE MYJ (local) Noah NONE WRF (Janjic 1994, 2001) (Ek et al. 2013)

TexasTech WRF NONE YSU (nonlocal) Noah NONE (Hong et al. 2006) (Ek et al. 2013) NWP Model Configurations: GFS versus European Centre for Medium-Range Weather Forecasts (ECMWF) Model Domain Grid spacing Vertical Boundary Initialization levels condition Frequency GFS Global ~13-km 64 layers N/A 6 h (cycled) (Equator; days 0-10) ECMWF IFS Global 9-km 137 N/A 12 h (cycled) HRES 5/2016

Model Dynamic Assimilation Radar Radiation Microphysics Core DA LW/SW GFS 5/2016 Hydrostatic GDAS: Hybrid Yes Optimized RRTM Prognostic cloud SI/SL 4DEnVar (Mlawer et al. 1997; scheme Iacono et al. 2000; 0.875/0.125 (Zhao and Carr, 1997) Clough et al. 2005) (3-h window) ECMWF IFS Hydrostatic 4DVar REF RRTM Prognostic cloud HRES SI/SL (12-hr window) (Mlawer et al. 1997; scheme 5/2016 Iacono et al. 2008) (Tiedke 1993) NWP Model Configurations: GFS versus European Centre for Medium-Range Weather Forecasts (ECMWF)

Model Cumulus Planetary Boundary Land Initialization Parameterization Layer Surface (Balancing) Model GFS Deep: Simplified Strongly unstable PBL Noah LSM Digital Filter Arakawa-Schubert (SAS) Hybrid Eddy Diffusivity (Ek et al. 2003) Initialization Shallow: Mass Flux Mass Flux (EDMF) (DFI) (cloud depth ≤ 150 hPa) Weakly unstable PBL EDCG ECMWF Bulk mass flux Surface layer HTESSLE 4DVar IFS HRES (Tiedtke, 1989; Bechtold 1st order K-diffusion (12-hr window) 5/2016 et al. 2008, 2014) Above Surface layer Stable PBL: 1st order K- diffusion Unstable PBL: EDMF (Köhler et al., 2011) NWP Model Configurations: GFS versus Global Deterministic Prediction System (GDPS)

Model Domain Grid spacing Vertical Boundary Initialization levels condition Frequency GFS Global ~13-km 64 layers N/A 6 h (cycled) (Equator; days 0-10) GDPS Global 17.2 – 25 km 80 N/A 6 h (cycled)

Model Dynamic Assimilation Radar Radiation Microphysics Core DA LW/SW GFS 5/2016 Hydrostatic GDAS: Hybrid Yes Optimized Prognostic cloud SI/SL 4DEnVar to 0.875 RRTM scheme (Zhao & 6 h window (Mlawer et al. 1997; Carr, 1997) Iacono et al. 2000; Clough et al. 2005) GDPS v5.0.0 GEM v4.7.2 Hybrid 4DEnVar No Correlated-k Sundquist 12/15/2015 (Hydrostatic) 6 h window distribution (Li scheme & Barker, 2005) NWP Model Configurations: GFS versus Global Deterministic Prediction System (GDPS)

Model Cumulus Planetary Boundary Land Initialization Parameterization Layer Surface (Balancing) Model GFS Deep: Simplified Arakawa- Strongly unstable Noah LSM Digital Filter Schubert (SAS) PBL (Ek et al. Initialization Shallow: Mass Flux (cloud Hybrid EDMF 2003) (DFI) depth ≤ 150 hPa) Weakly unstable PBL EDCG GDPS Deep: Kain & Fritsch Based on TKE Mosaic 4D-IAU (Kain and Fritsch, 1990; 1993) (McTaggart-Cowan & (Bélair et al (Incremental Shallow: KuoTransient Zadra, 2015) 2003) Analysis Scheme (Bélair eta al., 2005) Update) NWP Model Configurations: GFS versus Navy Global Environmental Model (NAVGEM)

Model Domain Grid spacing Vertical Boundary Initialization levels condition Frequency GFS Global ~13-km 64 layers N/A 6 h (cycled) (Equator; days 0-10) NAVGEM v1.2 Global ~37 km 50 layers N/A 6 h (cycled) 11/6/2013

Model Dynamic Assimilation Radar Radiation Microphysics Core DA LW/SW GFS 5/2016 Hydrostatic GDAS: Hybrid Yes Optimized Prognostic cloud SI/SL 4DEnVar to 0.875 RRTM scheme 6 h window (Mlawer et al. 1997; (Zhao & Carr, 1997) Iacono et al. 2000; Clough et al. 2005) NAVGEM v1.2 Hydrostatic NAVDAS-AR No RRTMG Prognostic cloud 11/6/2013 SI/SL (4DVAR) (Xu et al., Clough et al. 2005) and ice scheme 2005; Rosmond and Xu, (Zhao and Carr, 1997; 2006; Chua et al.,2009) Sundqvist et al. 1989) NWP Model Configurations: GFS versus Navy Global Environmental Model (NAVGEM)

Model Cumulus Planetary Boundary Land Initialization Parameterization Layer Surface (Balancing) Model GFS Deep: Simplified Strongly unstable PBL Noah LSM Digital Filter Arakawa-Schubert (SAS) Hybrid EDMF (Ek et al. Initialization Shallow: Mass Flux Weakly unstable PBL 2003) (DFI) (cloud depth ≤ 150 hPa) EDCG NAVGEM Deep: Simplified Eddy Diffusion (local) Hogan (2007) NAVDAS-AR v1.2 Arakawa-Schubert (SAS) /Mass Flux (nonlocal) (4DVAR) (Xu et 11/6/2013 Shallow: Han and Pan (Louis et al., 1982) al., 2005; Rosmond (2011) (Suselj et al. 2012) and Xu, 2006; Chua et al.,2009 Select parameterizations and NWP skill based on limited literature search; implications for operational NWP models Select Parameterizations and NWP model predictive skill: PBL/Turbulence

Hu et al (2010)  The MYJ—a local PBL scheme—produced colder and more moist biases than nonlocal YSU and ACM2 schemes (Texas)

Cohen et al (2015)  Nonlocal mixing necessary to more accurately predict 0-3 km lapse rates  Nonlocal mixing did not unrealistically smooth the strong vertical wind shear, thus retaining large low-level SRH (although less than from local scheme)  Both local and nonlocal schemes overestimate MLCAPE Select Parameterizations and NWP model predictive skill: Microphysics

Wheatley et al 2014: Sensitivity of a bowing MCS to microphysics parameterizations • Thompson and double-moment NSSL  produces greater rainwater mixing ratio aloft resulting in a stronger cold pool (lower surface temperature bias) relative to single moment • Thompson  greater snow production likely explains ability to produce more realistic stratiform precipitation regions, consistent with Yang and Houze (1995) who attribute stratiform rain to melting of snow • Thompson and double-moment NSSL  more realistic rear-to- front flow owing to stronger magnitude of horizontal buoyancy gradients produced along back edge of rearward-tilted MCS Select Parameterizations: Microphysics

Wheatley et al 2014: Sensitivity of a bowing MCS to microphysics parameterizations: Implications for NWP models used at WFO CRP

• Relative to single moment microphysical schemes, double moment schemes more likely to accurately depict severe MCS • The NSSL Realtime uses WSM6, a single moment scheme Select Parameterizations and NWP model predictive skill: Convection Deng and Stauffer (2006): Adjusting Convection parameterization, PBL, and data assimilation/ initialization schemes to improve 4-km simulations • Use of explicit convection (no convective parameterization) on a 4-km grid likely generates updrafts larger (4-km x 4- km) than observed in nature (~2-km) resulting in spurious high QPF values • Use of a convective parameterization scheme on a 4-km grid improved precipitation and low-level wind (violation of CP assumption notwithstanding.) • Combining observational-nudging FDDA with a convective parameterization scheme produced the best results Select Parameterizations and NWP model predictive skill: Convection Deng and Stauffer (2006): Adjusting Convection parameterization, PBL, and data assimilation/ initialization schemes to improve 4-km simulations: Implications for NWP models used at WFO CRP:

• HIRESW (3.6-km, 4.2-km), NAM CONUS NEST (4-km), NSSL Realtime and Texas Tech WRF (3-km) do not use convective parameterization, which may result in overestimate of precipitation. • However, NSSL Realtime uses positive definite advection of moisture to limit high QPF bias (Skamarock and Weisman 2009) Select Parameterizations and NWP model predictive skill: Convection Pimonsree et al 2016: Sensitivity of QPF to convective parameterizations (BMJ, KF, GD, no CP, Ensembles) at 3-km resolution in complex terrain • All schemes have capability to reasonably reproduce main character of spatial distribution of precipitation • Grell-Devenyi schemes and ensemble of the 3 schemes yield better performance of simulated precipitation pattern • Simulating precipitation at grey-zone resolutions (2-10 km grid spacing) should account for convective precipitation scheme for better simulated precipitation in high resolution grid scales over complex terrain Select Parameterizations and NWP model predictive skill: Convection Pimonsree et al 2016: Sensitivity of QPF to convective parameterizations (BMJ, KF, GD, no CP, Ensembles) at 3-km resolution in complex terrain: Implications for NWP models used at WFO CRP:

• NSSL Realtime and Texas Tech WRF do not have CP, thus less than optimal with regard to pattern of convection over Sierra Madre Oriental in Mexico. Data Assimilation and NWP model predictive skill: Incorporation of radar data to improve QPF

 Assimilation of reflectivity via diabatic digital filter (DFI) within the RAP improves QPF (Weygandt, 2008; Benjamin et al. 2016)  Assimilation of Doppler radial velocities (3D-Var) improved 6 h QPF of heavy rainfall event (10-km NWP model grid spacing) (Xiao et al., 2015)  Indirect assimilation of radar reflectivity (retrieved rain water and estimated in-cloud water vapor) (3D-Var) improved short-term QPF skill up to 7 h during four summertime convective events (3-km NWP model grid spacing.) (Wang et al., 2013) Data Assimilation and NWP model predictive skill: The issue of Spin up

Spin-up: “…Post-initialization development of realistic three- dimensional features during the model integration…” (Warner, 2011)

 Cold Start: No spin up processes in initial condition: no vertical motions/ageostrophic circulations. Model initialized with an analysis from another model (static initialization)  Warm Start: Partially spun-up processes: vertical motions/ ageostrophic circulations. Model initialized from an NWP model prediction (dynamic initialization)  Hot Start: Completely spun-up processes/spin up eliminated: vertical motions/ageostrophic circulations. Initial values for all microphysical species/variables and latent heat. Model initialized from NWP model prediction (dynamic initialization) Data Assimilation and NWP model predictive skill: The issue of Spin up

0003 UTC 4/14/2015 WSR-88D 0000 UTC 4/14/2015 HIRESW ARW WARM START

0000 UTC 4/14/2015 HRRR HOT 0000 UTC 4/14/2015 NSSL COLD START START Data Assimilation and NWP model predictive skill: The issue of Spin up

0100 UTC 4/14/2015 WSR-88D 0100 UTC 4/14/2015 HIRESW ARW WARM START 4.2 km

0100 UTC 4/14/2015 HRRR HOT 0100 UTC 4/14/2015 NSSL COLD START START 3.0 km 4.0 km

Artificial high frequency waves?? Data Assimilation and NWP model predictive skill: The issue of Spin up

0200 UTC 4/14/2015 WSR-88D 0200 UTC 4/14/2015 HIRESW ARW WARM START 4.2 km

0200 UTC 4/14/2015 HRRR HOT START 0200 UTC 4/14/2015 NSSL COLD START

3.0 km 4.0 km Data Assimilation and NWP model predictive skill: The issue of Spin up

0300 UTC 4/14/2015 WSR-88D 0300 UTC 4/14/2015 HIRESW ARW WARM START 4.2 km

0300 UTC 4/14/2015 HRRR HOT START 0300 UTC 4/14/2015 NSSL COLD START 3.0 km 4.0 km Data Assimilation and NWP model predictive skill: The issue of Spin up

0400 UTC 4/14/2015 WSR-88D 0400 UTC 4/14/2015 HIRESW ARW WARM START 4.2 km

0400 UTC 4/14/2015 HRRR HOT 0400 UTC 4/14/2015 NSSL COLD START START 3.0 km 4.0 km Data Initialization and NWP model predictive skill: Mass/Momentum Imbalances (Stull, 2015)

Mass/momentum balance

Mass/momentum imbalance

Adjustment toward new balanced state

New mass/momentum balanced state Data Initialization and NWP model predictive skill: Mass/Momentum Imbalances

4-km NSSL exhibits unbalanced MSLP pattern during 0-7 h period

Warner (2011) What phenomena can be simulated/resolved by a particular NWP Model? What phenomena can be simulated/resolved by a particular NWP Model?

Grid point models: 8-10 grid points are needed to adequately resolve and maintain a feature during model integration (Lewis and Toth, 2011)

Example: 20-km Thunderstorm. Can the HRRR resolve it? HRRR: 3-km grid spacing 3-km X 8 = 24 km. Cannot resolve and maintain phenomena smaller than 24 km Thus, the HRRR cannot resolve and maintain the 20-km Thunderstorm Predictability Practical and Intrinsic Predictability

Practical Predictability  Ability to predict based on procedures currently available (Lorenz, 1969)  Can improve predictability by decreasing errors in initial conditions via better data assimilation methods and higher quality observations, or improve the NWP model parameterizations (e.g. Zhang et al. 2006) Practical and Intrinsic Predictability

Intrinsic Predictability  “Extent to which prediction is possible if an optimum procedure is used” (Lorenz, 1969)  Predictability given both nearly perfect knowledge of the initial atmospheric state and a nearly perfect NWP model (Lorenz, 1969)  Small amplitude errors such as undetectable random noise can rapidly grow and contaminate deterministic prediction Practical and Intrinsic Predictability

(Melhauser and Zhang, 2012) NWP Models: Predictability of Convection

Intrinsic Predictability: Specific studies

 Small, undetectable perturbations grew rapidly and contaminated a mesoscale prediction of a heavy rainfall event, resulting in intrinsic predictability to ≤ 36 h (Zhang et al. 2006)  Small, undetectable perturbations too small to modify the initial mesoscale environmental moisture and instability fields, grew rapidly and contaminated a storm scale prediction of a tornadic thunderstorm, reducing intrinsic predictability to ≤ 3-6 h (Zhang et al. 2013) NWP Models: Predictability of Convection

Intrinsic Predictability: Specific studies  Similar NWP model Skew- T structure (differences approximately undetectable) produced divergence storm lifetimes (Elmore et al. 2002) Predictability of Convective Storms (Sun et al. 2014) Summary: Issues Relevant to WFO CRP Forecast Operations

1. Understand specific parameterization schemes and data assimilation methods used in NWP models 2. Planetary Boundary Layer (PBL) parameterization  Local (nonlocal) turbulence closure: Relate unknown variables to known variables at nearby (any number of) vertical grid points  Majority of turbulent energy found in largest eddies with depth characteristic of PBL depth  more consistent with nonlocal closure  Local schemes tend not to match heat flux observations  Local (Nonlocal) schemes tend to predict too shallow/moist (deep/dry) deep of a PBL Summary: Issues Relevant to WFO CRP Forecast Operations 2. Planetary Boundary Layer (PBL) parameterization continued  Local scheme examples: YSU, MRF, ACM2  Nonlocal scheme examples: MYJ, QNSE, MYNN 3. Cloud Microphysics Parameterization  Parameterize phase changes and interactions between particle species  Single moment  Predict only particle mixing ratio  Double moment  Predict particle mixing ratio and number concentration (more realistic particle size distribution/size sorting)  Triple moment  Predict mixing ratio, number concentration, and reflectivity Summary: Issues Relevant to WFO CRP Forecast Operations 3. Cloud Microphysics Parameterization continued

Thompson-aerosol (Thompson and Eidhammer, 2014) 1-moment predictions of snow, graupel 2-moment predictions of cloud ice, rain, CCN, IN, cloud water (owing to 2-moment prediction of CCN and IN) Thompson (Thompson et al. 2008) 1-moment predictions of cloud water, snow, graupel 2-moment predictions of cloud ice, rain Ferrier and Aligo (Aligo et al. 2014) 1-moment predictions of cloud water, rain, snow WSM6 (Hong and Lim, 2006) 1-moment predictions of cloud water, cloud ice, graupel, rain, snow, water vapor Summary: Issues Relevant to WFO CRP Forecast Operations 3. Cloud Microphysics continued

Modified WSM6 (Grasso et al. 2014) Adjustment to WSM6 (Hong and Lim, 2006) to reduce excessive graupel production to increase ice cloud mass to more reasonable quantities Prognostic Cloud scheme (Zhao and Carr, 1997) 1-moment predictions of cloud water, cloud ice, rain, snow, water vapor Prognostic Cloud and ice scheme (Zhao and Carr, 1997; Sundqvist et al. 1989) 1-moment predictions of cloud water, cloud ice, rain, snow, water vapor Sundqvist et al. (1989) 1-moment prediction of cloud water Summary: Issues Relevant to WFO CRP Forecast Operations

4. Convective Parameterization . Parameterize sub-grid scale convection and remove excessive instability Convective component of total precipitation is simply a byproduct of the activated convective scheme . Precipitation can be simultaneously produced as a byproduct of the activation of moist convection by the convective parameterization scheme and by explicit prediction of grid-scale precipitation by cloud microphysical parameterization . Parameterized precipitation is generated within a sub-saturated grid box (since convection parameterized is of sub-grid scale), while resolved scale precipitation in the microphysics scheme requires grid box saturation Summary: Issues Relevant to WFO CRP Forecast Operations 5. When Convective Parameterization (CP) Turned Off [As of 1 September 2016, CP turned off in the 3-km HRRR, 4-km NSSL Realtime WRF, 3-km Texas Tech WRF, 4-km NAM CONUS Nest, 4.2-km HIRES CONUS WRF-ARW, 3.6-km CONUS NEMS-NMMB] . Precipitation can only occur due to grid scale microphysics and only after grid box is saturated; sub-grid scale convection not accounted for . For NWP model grid spacing ≥ 4-km, subsequent exaggerated scale of individual convective cells likely will contribute to a high QPF bias (NSSL RealtimeWRF uses positive definite advection of moisture to limit high QPF bias.) . Adequate resolution of squall line mesoscale mesoscale structures require NWP model grid spacing ≤ 4-km . For grid spacing range 0.25-km to 4-km, NWP models can skillfully predict convective initiation (CI) and mode (supercell, MCS, multi-cells, etc.), yet less skillful with regard to timing and position. During convective forecast operations, use NWP models for CI and convective mode, not for timing and position Summary: Issues Relevant to WFO CRP Forecast Operations

6. Data Assimilation 3D-Variational (3D-Var) with use of background error covariances calculated from NWP model ensembles (EnKF) are flow- dependent/anisotropic and result in more realistic analysis increments over complex topography than those developed via the “NMC” method. 3D- Var/EnKF data assimilation resulted in more accurate 6 h predictions.

7. Data Initialization NWP model initial condition with mass/momentum imbalances [4-km NSSL RealtimeWRF, 3-km Texas Tech WRF] will generate artificial inertia- gravity waves which can adversely affect 0-6 h (or more) of the simulation; MSLP especially vulnerable since gravity waves adjust mass field to the wind field on the mesoscale. Summary: Issues Relevant to WFO CRP Forecast Operations

8. RAPv2 versus RAPv3 RAPv3 decreased the warm bias in RAPv2 by reducing excessive downward solar radiation 9. Select Parameterizations and NWP model predictive skill . Local PBL/turbulence closure schemes tend to produce cooler/lower/moister PBL than nonlocal schemes . Nonlocal mixing necessary to more accurately predict 0-3 km lapse rates . 2-moment microphysics more accurately depict structure of bowing MCS (rear-to-front flow, cold pool strength) than 1-moment schemes . Use of a convective parameterization scheme on a 4-km grid (and on a 3-km in complex terrain) improved QPF Summary: Issues Relevant to WFO CRP Forecast Operations

10. Data Assimilation and NWP model predictive skill . Assimilation (via 3D-Var) of radar reflectivity and Doppler radial velocities improves QPF skill during the 0-6 h period of the simulation . NWP models with a cold start [4-km NSSL RealtimeWRF; 3-km Texas Tech WRF] will take awhile to spin up vertical velocities and ageostrophic circulations. Thus, the evolution of atmospheric processes will be delay relative to nature

11. To adequately resolve and maintain a feature during model integration, the feature must span 8-10 grid points. Summary: Issues Relevant to WFO CRP Forecast Operations

12. Predictability Practical Predictability . “Ability to predict based on what is currently available” . Can increase Practical Predictability by improving data assimilation techniques, incorporating higher quality observations, or improving NWP model parameterizations Intrinsic Predictability . “Extent to which prediction is possible if an optimum procedure is used” . Predictability given both nearly perfect knowledge of initial atmospheric state and nearly perfect NWP model Summary: Issues Relevant to WFO CRP Forecast Operations

12. Predictability continued Intrinsic Predictability continued . Small undetectable perturbations can rapidly grow and contaminate deterministic prediction . Cannot improve intrinsic predictability given chaotic atmosphere THE END References Continued

• Adlerman, E. J., and K.K. Droegemeir, 2002: The sensitivity of numerically simulated cyclic mesocyclogenesis to variations in model physical and computational parameters. Mon. Wea. Rev., 130, 2671-2691.

• Aligo E., B. Ferrier, J. Carley, M. Pyle, D. Jovic, and G. DiMego, 2014:High-Resolution NMMB Simulations of the 29 June 2012 Derecho, AMS 27th WAF/23rd NWP Conference, Atlanta, GA.

• Arakawa, A., and J. M. Chen, 1987: Closure Assumptions in the cumulus parameterization problem. Short & Medium Range Numerical Weather Prediction. T. Matsuno, Ed., Meteor. Soc. Japan, Universal Academy Press, 107-131

• Arakawa, A., 1993: Closure assumptions in the cumulus parameterization problem. In The Representation of Cumulus Convection in Numerical Models of the Atmosphere, eds. K. A. Emanuel and D. J. Raymond. Meteorological Monograph, No. 46, American Meteorological Society: Boston. Pp 1-15.yyy

• Bjerknes, 1904: V. Das Problem der Wettervorhersage, betrachtet vom Stanpunkt der Mechanik und der Physik. Meteor. Zeits. 21: 1-7.yyy References Continued

• Benjamin, S. G., Weygandt, S. S., Brown, J.M., Hu, Ming, Alexander C. R., SmirnovaT. G., Olson, J. B., James, E. P., Dowell, D. C., Grell, G. A., Lin, H., Peckham, S. E., Smith T. L., MoningerW. R., Kenyon J. S., and G. S. Manikin, 2016: A North American Hourly Assimilation and Model Forecast Cycle: The Rapid Refresh, Mon. Wea. Rev., 144, 1669-1694.

• Bluestein, H. B. 1992. Synoptic-Dynamic Meteorology in Midlatitudes. Volume 1: Principles of Kinematic and Dynamics. Oxford University Press: New York, NY; 431

• Bouttier, F., and P. Courtier, 1999: Data assimilation concepts and methods. http://www.ecmwf.int/en/learning/education-material/lecture-notes (accessed 24 August 2016)

• Bryan, G. H., J. C. Wyngaard, and J. M. Fritsch, 2003: Resolution requirements for the simulation of deep moist convection. Mon. Wea. Rev., 131, 2394–2416. References Continued

• Cheng, W. Y. Y., and W. R. Cotton, 2004: Sensitivity of a cloud-resolving simulation of the genesis of a mesoscale convective system to horizontal heterogeneities in soil moisture initialization. J. Hydrometeor., 5, 934 – 958.

• Chua, B., L. Xu, T. Rosmond, and E. Zaron. 2009. Preconditioning representer-based variational data assimilation systems: Application to NAVDAS-AR. Pp. 307-320 in Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications. Springer-Verlag.

• Clark, A. J., Coniglio, M. C., Coffer, B. E., Thompson, G., Xue, M., and F. Kong, 2015: Sensitivity of 24- h Forecast Dryline Position and Structure to Boundary Layer Parameterizations in Convection-Allowing WRF Model Simulations, Wea. Forecast.

• Clough, S. A., M. W. Shephard, E. J. Mlawer, J.S. Delamere, M. J. Iacono, K, Cady-Pereira, S. Boukabara, and P. D. Brown, 2005: Atmospheric radiative transfer modeling: A summary of the AER codes, J. Quant. Spectrosc. Radiat. Transfer, 91, 233-244, doi:10.1016/j.jqsrt.2004.05.058. J. Geophys. Res., 97, 15761- 15785

• Cohen A. E., Cavallo, S.M., Coniglio, M.C., and H. E. Brooks, 2015: A Review of Planetary Boundary Layer Parameterization Schemes and Their Sensitivity in Simulating Southeastern U.S. Cold Season Severe Weather Environments, Wea. Forecast., 30, 591-612.

• Daley, R., 1981: Normal mode initialization. Rev. Geophys. Space Phys., 19, 450-468. References Continued

• Deng, A., and D. R. Stauffer, 2006: On Improving 4-km Mesoscale Model Simulations. Journal of Applied Meteorology and Climatology, 45, 361-381.yyy

• Ek, M.B., K. E. Mitchell, Y. Lin, E. Rogers, P. Grunmann, V. Koren, G. Gayno, and J. D. Tarpley, 2003: Implementation of Noah land surface model advances in the National Centers for Environmental Prediction operational mesoscale Eta model. J. Geophys. Res., 108 (D22), 16, doi:10.1029/2002JD003296.

• EMC, 2016. North American Mesoscale (NAM) Analysis and Forecast System Characteristics. http://www.emc.ncep.noaa.gov/mmb/mmbpll/misc/nam_2014_specs/index.html

• ECMWF. 2016. IFS Documentation. http://www.ecmwf.int/en/forecasts/documentation-and- support/changes-ecmwf-model/ifs-documentation (accessed 23 August 2016)

• Fowle MA, Roebber PJ. 2003. Short-range (0–48 h) numerical predictions of convective occurrence, model and location. Weather Forecast. 18: 782–794.yyy

• Glickman, TS. Glossary of Meteorology. 2nd ed. Boston: American Meteorological Society; 2011. 1132 p. yyy

• Grasso L., D. T. Lindsey, K.-S. Lim, A. Clark, D. Bikos, and S. R. Dembek, 2014: Evaluation of and Suggested Improvements to the WSM6 Microphysics in WRF-ARW Using Synthetic and Observed GOES- 13 Imagery, Mon. Wea. Rev., http://dx.doi.org/10.1175/MWR-D-14-00005.1 References Continued  Grell, G. A., and D. Devenyi, 2002: A generalized approach to parameterizing convection combining ensemble and data assimilation techniques. Geophys. Res. Lett., 29, 2002, doi:10.1029/2002GL015311.

 -----, and S. Fretis, 2014: A scale and aerosol aware stochastic convective parameterization for weather and air quality modeling. Amos. Chem. Phys., 14, 5233-5250, doi:10.5194/acp- 14-5233-2014.  Han, J., and H.-L. Pan. 2011. Revision of convection and vertical diffusion schemes in the NCEP Global Forecast System. Wea. Forecast. 26:520-533.  Hogan, T.F. 2007. Land surface modeling in the Navy Operational Global Atmospheric Prediction System. Paper presented at AMS 22nd Conference on Weather Analysis and Forecasting/189th Conference on Numerical Weather Prediction, June 2007, Park City, Utah.  Hoke, J. E., and R. A. Anthes, 1976: The initialization of numerical models by a dynamic- initialization technique. Mon. Wea. Rev., 104, 1551-1556.  Hong, S. –Y., S. Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 2318-2341. References Continued

 Hong, S.-Y., and J.-O. J. Lim, 2006: The WRF Single-Moment 6-Class Microphysics Scheme (WSM6), Journal of the Korean Meteorological Society, 42: 129-151  Hu, X.-M., Nielsen-Gammon, J.W., and F. Zhang, 2010: Evaluation of Three Planetary Boundary Layer Schemes in the WRF Model. Journal of Applied Meteorology and Climatology, 49, 1831-1844.yyy  Huang X.-Y., and P. Lynch, 1993: Diabatic Digital-Filtering Initialization: Application to the HIRLAM Model, Mon. Wea. Rev., 121: 589-603.  Iacono, M. J., Delamere J. S., Mlawer E. J., Shephard M. W., Clough, S.A., and W. D. Collins, 2008: Radiative Forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models. J. Geophys. Res., 113, D13103, doi:10.1029/2008JD009944.  Janjic, Z. I., 1994: The Step-mountain Eta Coordinate Model: Further developments of the convection, viscous sublayer and turbulence closure schemes, Mon. Wea. Rev., 122, 927-945  Janjic, Z. I., 2001: Nonsingular implementation of the Mellor-Yamada level 2.5 scheme in the NCEP meso model. NCEP Office Note, 91 pp. [437]. References Continued

 Jascourt S. 2009. University Corporation for Atmospheric Research/Cooperative Program for Meteorological Education and Training: Effecive Use of High-resolution Models. http://www.meted.ucar.edu (accessed 20 July 2016)  Kain, J. S., Weiss S. J., Bright D. R., Baldwin M. E., Levit J. J., Carbin G. W., Schwartz C. S., Weisman, M. L., Droegemeier, K. K., Weber, D. B., and K. W. Thomas. 2008. Some Practical Considerations Regarding Horizontal Resolution in the First Generation of Operational Convection-Allowing NWP. Wea. Forecast. 23:931-952.  Kalnay E. Atmospheric Modeling, Data Assimilation and Predictability. Cambridge: Cambridge University Press; 2003.  Köhler, M., Ahlgrimm,M. and Beljaars,A.(2011). Unified treatment of dry convective and stratocumulus- topped boundary layers in the ECMWF model. Q. J. R. Meteorol. Soc., 137, 43-57  Laplace, P. S. 1996: A Philosophical Essay on Probabilities (republication of the edition published by John Wiley and Sons, New York, 1902). Dover Publications: New York.yyy  Lewis P, Toth G. 2011. University Corporation for Atmospheric Research/Cooperative Program for Meteorological Education and Training: Ten Common NWP Misconceptions. http://meted.ucar.edu/norlat/tencom (accessed 9 December 2011).  Lorenc, A., 1986: Analysis methods for numerical weather prediction. Quart. J. Roy. Meteor. Soc., 112, 1177-1194  Louis, J.F., M. Tiedtke, and J.F. Geleyn. 1982. A short history of the operational PBL parameterization at ECMWF. Pp. 59-79 in ECMWF Workshop on Planetary Boundary Parameterizations. European Center for Medium-range Weather Forecasts References Continued

 Lorenz, E. N. 1993. The Essence of Chaos. University of Washington Press: Seattle, WA; 227 p.  Melhauser, C., and F. Zhang, 2012: Practical and Intrinsic Predictability of Severe and Convective Weather at the Mesoscales, Journal of the Atmospheric Sciences, 69: 3350-3371  Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res.,102, 16663-16682.  Molinari, J. M., and M. Dudek, 1986: Implicit versus explicit convective heating in numerical weather prediction models. Mon. Wea. Rev., 114, 326-344.  --,--, 1992: Parameterization of Convective Precipitation in Mesoscale Numerical Models: A Critical Review. Mon. Wea. Rev., 120, 326-344.  Morrison, H., 2010: An overview of cloud and precipitation microphysics and its parameterization in models. WRF Workshop, June 21, 2010. Boulder CO. References Continued

 Nakanishi, M. and H. Niino, 2004: An improved Mellor-Yamada level-3 model with condensation physics: Its design and verification. Bound. Layer Meteor. , 112, 1-31.  ----, and ----, 2009: Development of an improved turbulence closure model for the atmospheric boundary layer. J. Meteor. Soc. Japan, 87, 895-912. • Orlanski I. 1975. A rational subdivision of scales for atmospheric processes. Bull. Am. Meteorol. Soc. 56: 527–530. • Peckham, S.E., T. G. Smirnova, S. G. Benjamin, J. M. Brown, and J. S. Kenyon, 2016: Implementation of a digital filter initialization in the WRF model and it’s application in the Rapid Refresh. Mon. Wea. Rev. 144, 99-106. • Pielke RA. 2013. Mesoscale Meteorological Modeling. International Geophysics Series, Vol. 78. Academic Press: San Diego, CA; 726. • Pimonsree, S., P. Ratnamhin, P. Vongruang, and S. Sumitsawan, 2016: Impacts of Cumulus Convective Parameterization Schemes on Precipitation at Grey-Zone Resolutions: A Case Study over Complex Terrain in upper Northern Thailand. International Journal of Environmental Science and Development, Vol. 7, No. 5, May 2016.yyy References Continued

 Petch, J. C., 2006: Sensitivity studies of developing convection in a cloud-resolving model. Quart. J. Roy. Meteor. Soc., 132, 345–358.yyy  ——, A. R. Brown, and M. E. B. Gray, 2002: The impact of horizontal resolution on the simulations of convective development over land. Quart. J. Roy. Meteor. Soc., 128, 2031–2044  Randall, D. A., J. A. Abeles, and T. G. Corsetti, 1985: Seasonal simulations of the planetary boundary layer and boundary-layer stratocumulus clouds with a general circulation model. J. Atmos. Sci., 42, 641-675.yyy  Randall, D. A., M. F. Khairoutdinov, A. Arakawa, and W. W. Grabowski, 2003: Breaking the cloud parameterization deadlock. Bull. Amer. Meteor. Soc. 84, 1547 – 1564.  Rosmond, t., and L. Xu. 2006. Development of NAVDAS-AR: Non-linear formulation and outer loop tests. Tellus 58A:45-58  Ross BB. 1986. An overview of numerical weather prediction. In Mesoscale Meteorology and Forecasting. American Meteorological Society: Boston, MA; 793.  Smirnova, T. G., Brown J. M., Benjamin S. G., and J. S. Kenyon, 2016: Modifications to the Rapid Update Cycle Land Surface Model (RUC LSM) available in the Weather Research and Forecasting (WRF) Model. Mon. Wea. Rev., 144, 1851-1865  Stull, R. B., 1991: Static stability: An update. Bull. Amer. Meteor. Soc., 72, 1521-1529. References Continued

 Stull R. Meteorology for Scientists and Engineers. 3rd ed. Pacific Grove: Brooks Cole; 2015.  Skamarock, W. C., and M. L. Weisman, 2009: The Impact of Positive-Definite Moisture Transport on NWP Precipitation Forecasts. Mon. Wea. Rev., 137: 488-494.  Song, X., G. J. Zhang, and J.-L. F. Li, 2012: Evaluation of microphysics parameterization for convective clouds in the NCAR 2011:Community Atmosphere Model CAM5. J. Climate, 25, 8568–8590, doi:10.1175/JCLI-D-11-00563.1.  Stensrud, DJ. 2007. Parameterization Schemes, Keys to Understanding Numerical Weather Prediction Models. Cambridge University Press: New York. 459 p.  Sundqvist, H., Berge, E., and J.E. Kristjansson. 1989. Condensation and cloud parameterization studies with mesoscale numerical weather prediction model. Mon. Wea. Rev., 117:1641-1757.  Suselj, K., J. Teixeira, and G. Matheou. 2012. Eddy diffusivity/mass flux and shallow cumulus boundary layer: An updraft PDF multiple mass flux scheme. Journal of Atmospheric Sciences, 69:1513-1533  Talagrand, O., 1997: Assimilation of observations, an introduction. J. Met. Soc. Japan Special Issue 75, 1B, 191-209. References Continued

 Thompson, G., Field, P. R., Rasmussen, R. M., and W. D. Hall, 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136: 5095-5115.  ------, G. and T. Eidhammer, 2014: A study of aerosol impacts on clouds and precipitation development in a large winter cyclone. J. Atmos. Sci., 71, 3636-3658.  Tiedtke, M. (1989). A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Mon. Wea. Rev. 117, 1779-1800.  UCAR. 2002. University Corporation for Atmospheric Research/Cooperative Program for Meteorological Education and Training: How Mesoscale Models Work. http://www.meted.ucar.edu/mesoprim/models/frameset.htm (accessed 28 April 2016).yyy  Wang, H., J. Sun, S. Fan, and X. Huang, 2013: Indirect Assimilation of Radar Reflectivity with WRF 3D-Var and Its Impact on Prediction of Four Summertime Convective Events. Journal of Applied Meteorology and Climatology., 52, 889-902.  Warner, T. T., 2011: Numerical Weather and Climate Prediction. Cambridge University Press: New York. 526 p.yyy References Continued

 KW, Klemp JB. 2008. Experiences with 0-36-h explicit convective forecasts with the WRF-ARW model. Weather Forecast. 23: 407–437.yyy  Weisman M. L., Droegemeier K. K., Weber D. B., and K. W. Thomas, 2008: Some Practical Considerations Regarding Horizontal Resolution in the First Generation of Operational Convection-Allowing NWP, Weather Forecast., 23, 931-952.  Weisman, M. L., W. C. Skamarock, and J. B. Klemp, 1997: The resolution dependence of explicitly modeled convective systems. Mon. Wea. Rev., 125, 527–548.yyy  Weygandt, S. S., and S. Benjamin, 2007: Radar reflectivity-based initialization of precipitation systems using a diabatic digital filter within the Rapid Update Cycle. 22nd Conf. on Weather Analysis and Forecasting/18th Conf. on Numerical Weather Prediction, Park City, UT, Amer. Meteor. Soc., 1B.7. [Available online at https://ams.confex.com/ams/22WAF18NWP/techprogram/paper_124540.htm.] References Continued

 Wheatley, D. M., Yussouf N., and D. J. Stensrud, 2014: Ensemble Kalman Filter Analyses and Forecasts of a Severe Mesoscale Convective System Using Different Choices of Microphysics Schemes. Mon. Wea. Rev., 142: 3243-3263.yyy  Xiao Q., Y. Kuo, J. Sun, W. Lee, E. Lim, Y. Guo, and D. M. Barker, 2005: Assimilation of Doppler Radar Observations with a Regional 3DVAR System: Impact of Doppler Velocities on Forecasts of a Heavy Rainfall Case. Journal of Applied Meteorology, 44: 768- 788.  Xu, L., Rosmond, T., and R. Daley. 2005. Development of NAVDAS-AR: Formulation and initial tests of the linear problem. Tellus 57A:546-559.yyy  Yang, M.-H., and R. A. Houze, 1995: Sensitivity of squall-line rear inflow to ice microphysics and environmental humidity. Mon. Wea. Rev., 123, 3175-3193.yyy  Zhao, Q., and F.H. Carr. 1997. A prognostic cloud scheme for operational NWP models. Mon. Wea. Rev., 125:1931-1953.yyy