The Pennsylvania State University
The Graduate School
College of Earth and Mineral Sciences
PRACTICAL PREDICTABILITY OF TROPICAL CYCLONES:
HURRICANES KARL (2010), SANDY (2012), AND EDOUARD (2014)
A Dissertation in
Meteorology
by
Christopher Lee Melhauser
Submitted in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
May 2016
The dissertation of Christopher Melhauser was reviewed and approved* by the following:
Fuqing Zhang Professor of Meteorology Dissertation Advisor Chair of Committee
Eugene E. Clothiaux Professor of Meteorology
Jerry Y. Harrington Associate Professor of Meteorology
Steven J. Greybush Assistant Professor of Meteorology
Zhibiao Zhao Associate Professor of Statistics
Hans Verlinde Professor of Meteorology Associate Head, Graduate Program in Meteorology
*Signatures are on file in the Graduate School
iii ABSTRACT
Various aspects of the practical predictability – the limit on atmospheric prediction using the current optimal analysis procedures to derive the initial state and the best available atmospheric model forecast – of tropical cyclones (TC) are examined using Hurricane Karl
(2010), Hurricane Sandy (2012), and Hurricane Edouard (2014) as case studies. The practical predictability of TCs is limited by uncertainties in the forecast model and initial conditions. The uncertainties include the adequacy of observations (i.e. accuracy, spatial and temporal coverage, and usability), data assimilation procedures, and deficiencies in the forecast models. This dissertation is partitioned into three parts that explore: (I) model uncertainties by examining the sensitivity of a model pre-genesis environment of a developing TC to the radiation parameterization, (II) the use of wind retrievals for TC prediction by creating a simplified wind retrieval algorithm using tail-Doppler radar measurements of TCs and generating low error wind field estimates for the purpose of TC data assimilation, and (III) model uncertainties by examining the impact of model dynamic core and physics configurations on the ensemble mean and spread using identical initial conditions to initialize three TC-tuned regional models.
In Part I, if was found that the pre-genesis environmental stability and intensity of deep moist convection associated with a TC can be considerably modulated by the diurnal extremes in radiation. In Part II, it was found that assimilating u-wind and v-wind from a new simplified coplane retrieval algorithm can impact track and intensity forecasts differently compared to assimilating direct radial velocity even though similar information is being assimilated. The computational efficiency and real-time low error wind field retrieval of the new simplified coplane retrieval algorithm make this a competitive method for observation generation for TC prediction. Finally, the findings in Part III suggest that model physical parameterizations are a dominant source of model error and can drastically impact ensemble forecast statistics. It is
iv hypothesized that for the two case studies presented, an ensemble can be constructed using a single model core that has similar forecast error characteristics as an ensemble constructed from a multiple model cores.
v TABLE OF CONTENTS
LIST OF FIGURES ...... vii
LIST OF TABLES ...... xiv
ACKNOWLEDGEMENTS ...... xv
Chapter 1 Introduction ...... 1
Chapter 1 Figures ...... 5
Chapter 2 Diurnal Radiation Cycle Impact on the Pre-Genesis Environment of Hurricane Karl (2010) ...... 6
Introduction ...... 6 Model Setup and Experimental Design ...... 9 Forecast Model ...... 9 Initial and Boundary Conditions ...... 11 Sensitivity Experiment Design ...... 12 Storm Tracking, Storm Development Criteria, and Vertical Profile Radial Averages ...... 13 Evolution of the Local Environment ...... 14 Case in Study: Hurricane Karl (2010) ...... 14 Original Ensemble Members ...... 15 Sensitivity Experiments ...... 16 Impact of Diurnal Radiation Cycle on Local and Large-Scale Environment ...... 19 Concluding Remarks ...... 27 Chapter 2 Figures ...... 30
Chapter 3 Application of a Simplified Coplane Wind Retrieval Using Dual-Beam Airborne Doppler Radar Observations for Tropical Cyclone Prediction ...... 43
Introduction ...... 43 Data and Methodology ...... 47 Case in Study: Hurricane Karl (2010) ...... 47 A Simplified Review of the Coplane Methodology ...... 48 A Simplified Coplane Algorithm for Tropical Cyclone Initialization ...... 49 Error Analysis Using a Simulated Tropical Cyclone ...... 52 Testing the Impact of the Simplified Coplane Analysis Observations on Forecast Track and Intensity: Data Assimilation Methodology, Model Setup, and Initial and Boundary Conditions ...... 54 Simplified Coplane Analysis: Flight-Level and Dropsonde Error Analysis ...... 54 Flight-Level Wind Validation ...... 55 Dropsonde Wind Validation ...... 57 Error Analysis of the Coplane Algorithm through Simulated NOAA P3 TDR Data ...... 58 Impact of Assimilating Coplane Observations on Track and Intensity Forecasts ...... 63
vi Concluding Remarks ...... 66 Chapter 3 Tables ...... 70 Chapter 3 Figures ...... 73
Chapter 4 A Multiple-Model Ensemble Examination of the Probabilistic Prediction of Hurricane Sandy (2012) and Hurricane Edouard (2014) ...... 87
Introduction ...... 87 Methodology ...... 90 Cases in Study: Hurricanes Sandy (2012) and Edouard (2014) ...... 90 Models ...... 92 Initial and Boundary Conditions ...... 93 Single-Core Multi-Physics and Stochastic Physics Sensitivity Experiments ...... 94 Results and Discussion ...... 95 Inter-Model Comparison: Evolution of Ensemble Track and Intensity ...... 95 Inter-Model Comparison: Multi-Core Ensemble ...... 97 Inter-Model Comparison: Multi-Physics Ensemble ...... 99 Inter-Model Comparison: Stochastic Physics and Inflated Initial Condition Ensembles ...... 102 Initial Condition Error Versus Model Error: Track and Intensity Measures ...... 104 Initial Condition Versus Model Error: Domain Integrated Measures ...... 105 Ensemble Composite and Correlation Analysis for Hurricane Edouard (2014) ...... 108 Concluding Remarks ...... 111 Chapter 4 Tables ...... 115 Chapter 4 Figures ...... 117
Chapter 5 Summary and Conclusions ...... 134
REFERENCES ...... 137
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LIST OF FIGURES
Figure 1-1: Idealized schematic illustrating the reduction of initial condition error by reducing the ensemble spread highlighting: (a) the practical predictability representative of a 9-10 Jun 2003 squall line and bow echo and (b) intrinsic predictability representative of a theoretical ensemble forecast with the ensemble forecast having equally favorable solutions. [Schematic details: solid shading - flow regime #1; striped pattern - flow regime #2; black dots - ensemble members; white dots – ensemble means; white cross - forecast truth]. Source: Figure 18 from Melhauser and Zhang (2012)...... 5
Figure 2-1: (a) Model domain setup (outer domain D01 not shown) for the original ensemble and sensitivity experiment simulations. Overlaid are the vortex center tracks for developing members (thin grey) for the full original ensemble with highlighted member 16 (thick red) and member 39 (thick blue) and the National Hurricane Center (NHC) best track (NHC Best Track; thick black). (b) Vortex center tracks for member 16 sensitivity experiments: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta) plotted on D02. All model simulation tracks are plotted every 3 hours for 120 h starting at 0000 UTC 12 September. The NHC Best Track is plotted every 6 hours for 78 hours starting at 1800 UTC 13 September...... 30
Figure 2-2: Geostationary Operational Environmental Satellite (GOES) 13 channel 4 (~11 microns) enhanced thermal infrared imagery at (a) 12/1200 UTC, (b) 13/0000 UTC, (c) 13/1200 UTC, (d) 14/0000 UTC. (e) Time-radius diagram of cloud-top temperature (75th percentile temperature within successive 20 km radial rings) derived from GOES infrared radiances (adapted from Figure 3b of Davis and Ahijevych (2012)). The dashed line indicates the time Karl reached tropical storm status...... 31
Figure 2-3: The evolution of the maximum 10 m wind speeds [m s-1] within 225 km of the average vortex center over the first 120 h of the simulation for (a) the original ensemble, (b) developing member 16, (c) developing member 39, and (d) non- developing member 11 sensitivity experiments with CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta). Note: in panel (a), member 16 CNTL is colored red, member 39 CNTL is colored blue, the NHC Best Track is bold black, and remaining developed members light grey; the highlighting scheme is identical to Figure 2-1a...... 32
Figure 2-4: Vertical profiles of the local environment relative humidity (left) and relative vorticity (right) averaged within 225 km of the vortex center for each member of the original ensemble over a 24 h period beginning at 0000 UTC 12 September (top row) and 0000 UTC 13 September (bottom row). Developing (non-developing) members are colored blue (red), with the mean profile of each group bolded...... 33
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Figure 2-5: Vertical profiles of the average local environment hourly model output within 225 km of the vortex center of relative humidity (left, shaded every 5%), combined cloud water and ice mixing ratio (center, starting at 0.05 g kg-1; shaded every 0.15 g kg-1), and relative vorticity (right, thick black line denotes 0, shaded every 5x10-5 s-1) for member 16 sensitivity experiments CNTL (top row), DayOnly (middle), and NightOnly (bottom). The black dashed lines indicate genesis time for the corresponding sensitivity experiment...... 34
Figure 2-6: Temporal evolution of the average 850-500 hPa relative vorticity [x10-5 s-1] within a 225 km radius of the vortex center for all member 16 sensitivity experiments CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta)...... 35
Figure 2-7: Filtered relative vorticity (wavelengths < 300 km removed) contoured every 4x10-5 s-1 (starting at 2x10-4 s-1) at the 850 hPa (red) and 500 hPa (blue) pressure levels for developing member 16 sensitivity experiments (a-d) CNTL, (e-h) DayOnly, and (i-l) NightOnly. Sea level pressure is shaded every 8 hPa starting at 1004 hPa...... 36
Figure 2-8: Vertical profiles of the clear-air large-scale environmental moist static energy (MSE) hourly departure (shaded every 1 kJ) from the initial conditions (0000 UTC 12 September) for member 16 sensitivity experiments: (a) CNTL, (b) DayOnly, (c) NightOnly, (d) NoRad, and (e) Offset. The large-scale cloud fraction is provided for reference in (f) for the sensitivity experiments: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta)...... 37
Figure 2-9: Clear-air and cloudy-air (a-c) large-scale and (d-f) local environment 0-16 km vertical profiles of (a,d) net radiative heating [K day-1], (b,e) shortwave radiative heating [K day-1], and (c,f) longwave radiative heating [K day-1] averaged over a 24 h period starting at 0000 UTC 12 September for member 16. Solid lines are clear-air averages and dashed lines are cloudy-air averages. The sensitivity experiments are colored: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta)...... 38
Figure 2-10: Clear-air local environment 24 h average starting at 0000 UTC 12 September 0-16 km vertical profiles for CNTL (black) and sensitivity experiment departures from CNTL (solid) of (a) potential temperature [K], (b) water vapor mixing ratio [g kg-1], and (c) relative humidity [%]; the corresponding cloud fraction is provided in (d). Both sensitivity experiment departures and actual values are colored: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta)...... 39
Figure 2-11: Clear-air large-scale environment 0-2 km vertical profiles for (a) potential temperature [K], (b) saturation equivalent potential temperature [K], (c) relative humidity [%], (d) water vapor [g kg-1], and vertical gradient profiles of the local environment (e) potential temperature with height [K km-1], (f) saturation equivalent potential temperature with height [K km-1], (g) temperature with height [K km-1], and (h) relative humidity with height [% km-1] averaged over a 24 h period starting
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at 0000 UTC 12 September for member 16. The sensitivity experiments are colored: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta)...... 40
Figure 2-12: Clear-air large-scale environment (a) Convective available potential energy (MCAPE) [J kg-1] and convective inhibition (MCIN) [J kg-1] for a parcel (defined as a 500 m vertical layer average) with the highest equivalent potential temperature below 3000 m AGL over a 48 h period starting at 0000 UTC 12 September for member 16 sensitivity experiments. The sensitivity experiments are colored: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta)...... 41
Figure 2-13: Schematic depiction of the diurnal radiation cycle impact on the clear-air local and large-scale environment for the genesis of Hurricane Karl during the first 24 h of the simulation. The red (blue) background shading of Day (Night) indicates net large-scale environmental heating (cooling). The vertical profile of net clear-air radiation tendency for sensitivity experiments NightOnly (red), DayOnly (blue), and CNTL (black) are depicted on the left for reference. Arrows indicate the local environment clear-air net radiative cooling (solid) for the entrainment zone; the size indicates relative magnitude. The schematic is drawn to scale. During the nighttime, net cooling of the cloud-free large-scale environment from longwave emission reduces static stability with a corresponding net increase in relative humidity. A large net cooling of the entrainment zone reduces stability of the low-level entrainment stable layer in the local environment. The combined impact is an overall environment more conducive for vigorous deep moist convection. During the daytime, the clear-air large-scale environmental heating from shortwave radiation is larger in magnitude than the cooling from longwave radiation above approximately 3 km, causing a net stabilization of the clear-air large-scale environment. Within the entrainment zone, a relatively smaller net cooling occurs due to the combined effect of shortwave radiation from above and increased longwave radiative emission from the relatively moist PBL below. The increased stability of the entrainment stable layer and stabilization of the local environment leads to the suppression of convective activity during the first 12-18 hours of the simulation, altering the subsequent evolution of tropical cyclone development. Note: the cloud distributions and stable layers for the first 12-18 hours are shown for reference. Schematic adapted from Johnson et al. (1999); first documented by Malkus (1956)...... 42
Figure 3-1: Spatial configuration of a plane flying north for (a) a dual-beam airborne fore/aft scan of radial velocities at an arbitrary radial distance, each dot represents a simulated radial velocity; (b) the coplane scanning geometry in natural cylindrical coordinates (x,l,α); (c) fall speed component of radial velocity along an arbitrary coplane point (xm,lm,αm); (d) retrieved wind components along track (Γ ) and perpendicular to track (Ψ ), geometrically derived from Vfore and Vaft with beam orientation (θfore,α) and (θaft,α), respectively...... 73
Figure 3-2: Diagram of WRF domains used for the Hurricane Karl Observation Simulation Experiment (black; D1-D4), WRF domains used for ensemble Kalman Filter data assimilation experiments (red; D1’-D3’), NOAA P3 flights on September 12, 13, and 16 with numbered flight legs (blue shaded lines), and dropsondes used
x
for coplane and HRD analysis validation (pink dots). Note: D1 and D1’ are the same domains...... 74
Figure 3-3: Schematic of an arbitrary radial velocity fore/aft bin indicating the geometric center (black x), the constituent fore/aft radial velocity observations (gray dots), and volume swept out by the coplane observation (yellow shading)...... 75
Figure 3-4: Wind speed retrievals from the (a) simplified coplane analysis and (b) HRD analysis, and (c) radial velocity super observations from flight leg 2 of the 20100916H NOAA P3 mission...... 76
Figure 3-5: Flight level comparison of closest coplane observations to the flight track (<
2000 m) on α-plane 0˚, 180˚ (blue colored lines), HRD analysis wind speeds closest to flight level (~3km) and flight track (magenta line), and flight level values (black line) from the aircraft of (a) wind speed, (b) u-wind, (c) ν-wind, (d) gamma, (e) psi, and (f) wind direction from flight leg 2 of the 20100913H NOAA P3 mission...... 77
Figure 3-6: Same as Figure 3-5, but from flight leg 2 of the 20100916H NOAA P3 mission...... 78
Figure 3-7: Root-mean-squared error binned by α-plane bin and distance from flight track for (a) u-wind and (b) ν-wind. Flight Level indicates wind component comparison of closest coplane observations to the flight track (< 2000 m) for all available NOAA P3 flights (20100912I, 20100913I, 20100913H, and 20100916H) and Dropsonde indicates comparison of closest coplane observations to the available dropsonde observations for all available NOAA P3 flights and GRIP/PREDICT missions...... 79
Figure 3-8: Distributions of (a) distance between dropsonde observations and coplane observations, (b) u-wind errors, and (c) ν-wind errors used to calculate dropsonde comparison statistics...... 80
Figure 3-9: WRF simulated fields of (a) maximum radar reflectivity, (b) 10-m wind speed, (c) 10-m u-wind and (d) 10-m ν-wind at 0000 UTC 17 September 2010. The black arrows in panel (a) indicate the flight track legs used to simulate coplane observations...... 81
Figure 3-10: WRF model simulated retrieved coplane observations of (a) u-wind, (b) ν- wind, (c) maximum reflectivity, (d) u-wind error, (e) ν-wind error, and (f) HRD fall speed for flight leg 1 on α-plane 0˚, 180˚...... 82
Figure 3-11: Root-mean-square error of the simulated simplified coplane analysis by (a) perpendicular distance from aircraft track and (b) α-plane bin for all simulated flight legs using no vertical component (EXP_NOW; cyan), model w as vertical component (EXP_PERW; blue), HRD terminal fall speed correction to vertical component (EXP_FALL; black), and HRD terminal fall speed correction to vertical component without temporal change in model fields (EXP_FALL_S; black asterix) when calculating the simulated radial velocity...... 83
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Figure 3-12: Root-mean-squared error binned by α-plane bin and distance from simulated flight track for (a) u-wind and (b) ν-wind...... 84
Figure 3-13: PSU-WRF-EnKF data assimilation experiments forecast (a) track, (b) maximum 10-m wind speed [m s-1], and (c) root-mean-squared error of track [km] and maximum 10-m wind speed [m s-1] validated against the National Hurricane Center best track data from 0000 UTC to 1800 UTC 17 September 2010. All experiments assimilate NHC best track and intensity for the first 18 hours, except the no data assimilation experiment (NODA), and the remaining simulations assimilate airborne observations including: coplane observations (TDRCP), coplane observations with error specified by distance from track and α-plane (TDRCPU), HRD analysis observations (TDRHD), radial velocity super observations (TDRSO), and raw fore and aft radial velocities used to derive the coplane observations (TDRVR). The NODA and hurricane position and minimum sea level pressure (PI) only experiments are included for reference...... 85
Figure 3-14: Model increment (analysis minus background) difference for the first airborne TDR data assimilation cycle at 1900 UTC 16 September 2010 on WRF eta level 10 (~2250 m) for (a,d) u-wind, (b,e) ν-wind, and (c,f) potential temperature between TDRCPU and TDRSO (left column) and TDRCPU and TDRVR (right column)...... 86
Figure 4-1: Domain setup for WRF-ARW (APSU; green), HWRF (cyan), and COAMPS-TC (COTC; magenta). Domain 1 (D01) is globally fixed for APSU and COTC, but centers on the TC for HWRF at initialization and fixed for the remainder of the forecast. D02 and D03 are two-way nested, vortex following for all models, centered on the TC at initialization. Note: APSU and COTC domains are nearly identical and thus substantially overlap. Detailed domain settings can be found in Table 4-1...... 117
Figure 4-2: Ensemble track spread for (a) APSU (green), HWRF (cyan), and COTC (magenta) (only 20 ensemble members shown for clarity). Ensemble mean track for (b) APSU (green), HWRF (cyan), COTC (magenta), the combined single-core multi-physics ensemble MPHY (gray), and the combined multi-core ensemble MCOR (black), (c) single-core single-physics ensembles APS1 (light gray) through APS5 (dark navy), and (d) stochastic physics experiments SKEB (maroon) and SPPT (purple) and inflated initial perturbation experiments I20P (yellow) and I50P (blue) for Hurricane Sandy initialized at 0000 UTC 26 October 2012. The NHC best track data (black line) is plotted every 6 hrs. The solid dots in (b-d) indicate the position and every 6 hrs...... 118
Figure 4-3: Ensemble intensity spread [m s-1] for (a) APSU (green), HWRF (cyan), and COTC (magenta) (only 20 ensemble members shown for clarity). Ensemble mean intensity [m s-1] for (b) APSU (green), HWRF (cyan), COTC (magenta), the single- core multi-physics ensemble MPHY (gray), and the multi-core ensemble MCOR (black), (c) single-core single-physics ensembles APS1 (light gray) through APS5 (dark navy), and (d) stochastic physics experiments SKEB (maroon) and SPPT (purple) and inflated initial perturbation experiments I20P (yellow) and I50P (blue)
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for Hurricane Sandy (2012) initialized at 0000 UTC 12 September 2012. The NHC best track data (black line) is plotted every 6 hrs. The solid dots in (b-d) indicate the intensity and every 6 hrs...... 119
Figure 4-4: Same as Figure 4-2, but for Hurricane Edouard (2014) initialized at 1200 UTC 11 September 2014...... 120
Figure 4-5: Same as Figure 4-3, but for Hurricane Edouard (2014) initialized at 1200 UTC 11 September 2014...... 121
Figure 4-6: Root-mean-squared error (RMSE) verified with NHC best track data (solid line) and the ensemble spread [m s-1] (dotted line) at 6-hourly lead times for track (a,c,e) [km] and intensity (b,d,f) [ms-1] of (a,b) APSU (green), HWRF (cyan), COTC (magenta), the single-core multi-physics ensemble MPHY (gray), and the multi-core ensemble MCOR (black), (c,d) single-core single-physics APS1 (light gray) through APS5 (dark navy), and (e,f) stochastic physics experiments SKEB (maroon) and SPPT (purple) and inflated initial perturbation experiments I20P (yellow) and I50P (blue) ensembles for Hurricane Sandy initialized at 0000 UTC 26 October 2012. The asterisks in panels (a,b,e,f) corresponding to the aforementioned ensembles indicate the lead times when the ensemble spread is statistically different from the MCOR ensemble spread at the 95% significance level...... 122
Figure 4-7: Same as Figure 4-6, but for Hurricane Edouard (2014) initialized at 1200 UTC 11 September 2014...... 123
Figure 4-8: Pairwise root-mean-squared difference (RMSD) of (a,c) track [km] and (b,d) maximum 10-m wind speed [m s-1] at 6-hourly lead times between HWRF and COTC (red), HWRF and APSU (cyan), COTC and APSU (magenta), and APS1 and APSU (light gray) through APS5 and APSU (navy). Panels (a,b) are for Hurricane Sandy initialized at 0000 UTC 26 October 2012 and (c,d) are for Hurricane Edouard at 1200 UTC 11 September 2014...... 124
Figure 4-9: Domain integrated Difference Total Energy (DTE) [m2 s-2] for (top row) Hurricane Sandy initialized at 0000 UTC 26 September 2012 and (bottom row) Hurricane Edouard initialized at 1200 UTC 11 September 2012 for (a,c) single-core single-physics ensembles APSU (green), HWRF (cyan), and COTC (magenta), (b,d) single-core single-physics ensembles APS1 to APS5 (gray to navy), SKEB (maroon), and SPPT (purple)...... 125
Figure 4-10: Vertically integrated root-mean difference total energy (RMDTE; m s-1) for Hurricane Sandy (2012) at 12 h lead time for the simulation initialized at 0000 UTC 26 October 2012. The top row is the RMDTE of the ensemble spread for (a) APSU, (b) HWRF, (c) COTC, and (d) APS5 and the bottom row is the RMDTE between multi-core ensembles (d) APSU and HWRF, (e) APSU and COTC, (f) HWRF and COTC, and (h) APS5 and APSU. All panels show the static 50˚x50˚ common domain at 0.25˚x0.25˚ horizontal resolution for which each model cores 27 km D01 is interpolated to calculate all DTE analyses...... 126
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Figure 4-11: Same as Figure 4-10, but for 36 hr lead time initialized at 0000 UTC 26 October 2012...... 127
Figure 4-12: Same as Figure 4-10, but for Hurricane Edouard (2014) initialized at 12 UTC 11 September 2014...... 128
Figure 4-13: Same as Figure 4-10, but for Hurricane Edouard (2014) at 36 h lead time initialized at 12 UTC 11 September 2014...... 129
Figure 4-14: HWRF-poor ensemble members D01 composite simulated maximum radar reflectivity (cloud water and rain water only) and mean sea level pressure for (a,e,i) APSU, (b,f,j) COTC, (c,g,k) HWRF, and (d,h,l) APS5 at lead times (top row) 24 h, (middle row) 48 h, and (bottom row) 72 h initialized at 1200 UTC 11 September 2014. The deep layer (200- to 850-hPa) shear vector (red arrow) and (850- to 500- hPa) tilt vector (magenta arrow) are overlaid on each panel...... 130
Figure 4-15: HWRF-poor ensemble members D01 composite deep-layer 200- to 850-hPa shear vector (a) magnitude and (b) direction and 500- to 850-hPa tilt vector (c) magnitude and (d) direction for 4-days lead time every 12 hours starting at 1200 UTC 11 September 2014 for APSU (green), COTC (magenta), HWRF (cyan), and APS5 (navy)...... 131
Figure 4-16: HWRF-poor ensemble members D01 composite 700-hPa relative humidity for (a,e,i) APSU, (b,f,j) COTC, (c,g,k) HWRF, and (d,h,l) APS5 at lead times (top row) 24 h, (middle row) 48 h, and (bottom row) 72 h initialized at 1200 UTC 11 September 2014...... 132
Figure 4-17: D01 composite COTC, HWRF, and APSU of HWRF-poor ensemble members 700-hPa relative humidity at lead times (a) 24 h, (b) 48 h, and (c) 72 h initialized at 1200 UTC 11 September 2004. Grid point correlations with the 96 h max 10-m wind speed are contoured at 0.5 (weak), 0.7 (moderate), and 0.9 (strong) with solid contours indicating positive and dotted contours indicating negative correlations...... 133
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LIST OF TABLES
Table 3-1: Individual and combined flight-level mean error (ME), mean absolute error (MAE), and root-mean-squared error (RMSE) of the retrieved u- and ν-wind components of the (a) simplified coplane analysis and (b) HRD analysis compared with NOAA P3 flight-level winds...... 70
Table 3-2: Individual and combined dropsonde mean error (ME), mean absolute error (MAE), and root-mean-squared error (RMSE) of the retrieved u- and ν-wind components of (a) the simplified coplane analysis and (b) HRD analysis compared with available dropsondes from NOAA P3 flights, GRIP, and PREDICT missions...... 71
Table 3-3: Simulated simplified coplane analysis mean error (ME), mean absolute error (MAE), and root-mean-squared error (RMSE) of the u- and ν-wind components for flight level (closest coplane observations to the simulated flight track), all coplane observations on parallel planes with the simulated aircraft wings (alpha = 0˚, 180˚), coplane observations available between +/- 50˚ α-plane deviations and perpendicular distance less than 20 km from flight track, and coplane observations available between +/- 50˚ α-plane deviations at all perpendicular distances...... 72
Table 4-1: Model domain and physical parameterization settings for pseudo-operational versions of WRF-ARW (APSU), HWRF, and COAMPS-TC (COTC)...... 115
Table 4-2: Model physical parameterization differences from APSU configuration for sensitivity experiments APS1 through APS5. Dashed line indicates same scheme as APSU...... 115
Table 4-3: Stochastic physics parameters settings ...... 116
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ACKNOWLEDGEMENTS
Completing this work has been an adventure and a learning experience. It would not have been possible without the encouragement of many, especially my adviser Fuqing Zhang and the rest of my committee, Eugene Clothiaux, Jerry Harrington, Steven Greybush, and Zhibiao Zhao, and past and present members of the Zhang research group. Overarching all, without the support, guidance, and inspiration of my mom Paula Melhauser-Schuermann and stepdad Randy
Schuermann, I would not be the person I am today capable of completing this dissertation. Thank you!
For Part I of this dissertation, the author would like to thank Yonghui Weng for performing the real-time ensemble data assimilation and forecasts that are used in this study and
Xiaqiong Zhou for initiating some preliminary analysis of the diurnal cycle. Computing was primarily conducted at the Texas Advanced Computing Center (TACC) and the Jet supercomputer cluster at NOAA’s Earth System Research Laboratory. This research was partially supported by ONR Grant N000140910526, NOAA (HFIP), NASA Grant NNX12AJ79G and
NSF Grant 0840651.
For Part II the author thanks NOAA/HRD for the real-time quality-controlled radial velocities, NOAA P3 flight-level data, and hurricane radar analysis (available at http://www.aoml.noaa.gov/hrd/data_sub) with special thanks to John Gamache for his help with the HRD datasets and methodologies. This work has benefited from discussions with and presentations by Anthony Didlake, who implemented a dual-Doppler retrieval in cylindrical coordinates using mass-continuity for the High-Altitude Imaging Wind and Rain Airborne
Profiler (HIWRAP). Computing was performed at the Texas Advanced Computing Center
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(TACC). This work was supported by the Office of Naval Research Grant N000140910526, the
National Science Foundation Grant AGS-1305798, and NASA Grant NNX12AJ79G.
Finally, for Part III, the author thanks Yi Jin, Hao Jin, and Allen Zhao at the Naval
Research Laboratory in Monterey, California, for their help debugging and running the Coupled
Ocean and Atmosphere Mesoscale Prediction System and Judith Berner at the National Center for
Atmospheric Research for her help implementing SKEBS and SPPT within the WRF-ARW model. Computing was performed on Jet at the National Center for Atmospheric Research under the Hurricane Forecasting and Improvement Project. This work was supported by the Office of
Naval Research Grant N000140910526, the National Science Foundation Grant AGS-1305798, and NASA Grant NNX12AJ79G.
1
Chapter 1
Introduction
Model and initial condition errors are an inherent issue in NWP that will never be eliminated, but can be quantified and reduced. These two sources of error arise from the inability to perfectly represent the initial state of the atmosphere – initial condition error – and truthfully represent the dynamical and physical processes occurring in the atmosphere – model error. Initial condition error can be reduced through improvements in the data assimilation (DA) methodology and observations used to generate the atmospheric analysis. Model error is both spatially and temporally dependent, with different scales and flow regimes exhibiting varying error growth properties (Zhang et al. 2003; Meng and Zhang 2007). The accumulation of model error can significantly degrade forecast accuracy. The presented research focuses on understanding the role of observations, initial condition error, and forecast model error on the predictability of Hurricane
Karl (2010), Hurricane Sandy (2012), and Hurricane Edouard (2014).
Understanding sources of TC forecast uncertainty and error growth are crucial to the improvement of TC forecasts. Substantial improvements in skill for position forecasts of TCs have been observed over the past 30 years; today’s 48 h position forecasts have as much skill as the 24 h position forecasts 10 years ago (Cangialosi and Franklin 2014). Unfortunately, the improvements in skill of intensity forecasts have remained stagnant and improvements still remain a significant challenge. The movements of TCs are generally governed by synoptic-scale horizontal winds, a feature of the atmosphere that is well modeled. The intensity forecasts, however, are dependent on convective-scale moist processes, an atmospheric feature that is a challenge to predict (Zhang et al. 2002, 2003). Despite the inherent challenge for TC intensity prediction, recent studies have shown that some TCs have higher predictability, indicating that
2 convective-scale moist processes don’t always dominate the evolution of cyclone strength
(Majumdar and Finocchio 2010; Snyder et al. 2010; Hamill and Whitaker 2011). The less predictable TCs are generally associated with increased convection near the center of circulation in favorable environments for TC maintenance. The more predictable TCs are hypothesized to be controlled by their large-scale environments or by strong forcing from the mean secondary circulation of the parent vortex, modulating the high error growth associated with moist convection.
To better understand TC predictability, one must first understand some fundamental concepts of general atmospheric predictability. The atmosphere is a chaotic system, hypothesized to have a finite limit of predictability. Using an idealized toy model to represent atmospheric convection, Edward Lorenz set the foundation for chaos theory and the study of atmospheric predictability. He discovered that small errors in the initial state of non-linear dynamic systems can grow, rapidly causing the solutions to diverge. In his pioneering 1963 publication
Deterministic Nonperiodic Flow, Lorenz concluded the atmosphere may have an inevitable limit to predictability, stating:
“… [atmospheric] prediction of the sufficiently distant future is impossible by any method, unless the present conditions are known exactly. In view of the inevitable inaccuracy and incompleteness of weather observations, precise very-long range forecasting would seem to be non-existent”.
Atmospheric predictability can be divided into two types: (1) intrinsic predictability: the limit on atmospheric prediction if the initial state is near1 perfect and a near perfect model is used and (2) practical predictability: the limit on atmospheric prediction using the current optimal analysis procedures to derive the initial state and the best available atmospheric forecast model.
1 Near refers to the limit of resolving the initial state and dynamical and physical processes of the atmosphere given the fundamental principles of physics.
3
The practical predictability is limited by uncertainties in the forecast model and initial conditions.
These uncertainties can include the adequacy of observations (i.e. accuracy, spatial and temporal coverage, and usability), DA procedures, and deficiencies in the forecast models.
Practical and intrinsic predictability and the impact of initial condition error on forecast error for various weather phenomena have been studied in the literature for full non-linear mesoscale cloud-resolving NWP models, ranging from synoptic scale snowstorms (Zhang et al.
2002, 2004), to TCs (Zhang and Sippel 2009; Sippel and Zhang 2008, 2010), to smaller scale mesoscale convective vortices (Hawblitzel et al. 2007) and bow-echoes (Melhauser and Zhang
2012). A common theme in this literature is the error growth at small scales from moist convection and the potential intrinsic limit to predictability of the weather events. Small errors in the initial conditions are exacerbated by the models’ moist physics, causing a cascading error growth from small- to large-scales and a divergence in modeled solutions.
Melhauser and Zhang (2012) created a schematic that describes the practical and intrinsic predictability for a mesoscale convective system (Figure 1-1) and this schematic can be extended to TCs. The larger circles represent the spread of an ensemble analysis (uncertainty in the initial conditions) generated from a DA system, the ensemble mean is the white dot in the center, the individual ensemble members are the black dots scattered around the ensemble mean, the truth is the white cross, and the different shading of the larger circles represents two different flow regimes, e.g. a developing and non-developing TC. The practical and intrinsic predictability are flow-dependent and are limited during regime transition (i.e. developing to non-developing TC).
Most of the loss of predictability in the simulation forecasts arises from chaotic behavior near this regime transition. If a simulations’ initial conditions that represent the correct flow regime of the weather phenomenon of interest are known, improvements in the initial conditions will cause the ensemble to converge towards the truth and the practical predictability can be improved.
Conversely, if the truth were to straddle the flow regimes, no matter how well the initial
4 conditions of the simulation are known, the predictability cannot be improved. Thus the predictability is intrinsically limited by the system. One of the goals of the proposed research is to examine how the practical predictability of TCs can be improved by reducing the initial condition errors through improved observations.
This dissertation is segmented into three parts. Chapter 2 focuses on the diurnal cycle impact on the pre-genesis environment of Hurricane Karl (2010). Chapter 3 focuses on TC radar observations, observation errors, and the impact on forecast uncertainty assimilating these observations using an ensemble Kalman filter for Hurricane Karl (2010). Chapter 4 focuses on model uncertainties and their impact on ensemble mean and spread forecasts using three pseudo- operational TC tuned regional models for Hurricanes Sandy (2012) and Edouard (2014).
5
Chapter 1 Figures
(b) Intrinsic Predictability (a) Practical Predictability
Figure 1-1: Idealized schematic illustrating the reduction of initial condition error by reducing the ensemble spread highlighting: (a) the practical predictability representative of a 9-10 June 2003 squall line and bow echo and (b) intrinsic predictability representative of a theoretical ensemble forecast with the ensemble forecast having equally favorable solutions. [Schematic details: solid shading - flow regime #1; striped pattern - flow regime #2; black dots - ensemble members; white dots – ensemble means; white cross - forecast truth (verifyin atmospheric state)]. Source: Figure 18 from Melhauser and Zhang (2012).
6 Chapter 2
Diurnal Radiation Cycle Impact on the Pre-Genesis Environment of Hurricane Karl (2010)
Introduction
In the tropics, cloud and water vapor distributions in the troposphere – primarily due to deep moist convection and clear-air subsidence – provide important pathways for solar and terrestrial radiation to modify the transient tropospheric thermodynamic structure. An observational study by Johnson et al. (1996, 1999) using soundings from the west Pacific warm pool confirmed the previously documented dominant cloud layers in the tropics by Malkus
(1956): low-level cumulus capped by a trade inversion stable layer and deep layer cumulonimbus capped by the tropopause. Johnson et al. (1999) also documented a third dominant cloud type and stable layer: low- to mid-level cumulus congestus with tops near the 0˚C melting stable layer.
These stable layers can inhibit cloud growth and prevent deep moist convection. Generally, enhanced gradients in relative humidity (RH) from the detrainment of moist convection are found near the base of the stable layers. A recent study by Posselt et al. (2008) using a tropical environment in radiative convective equilibrium successfully modeled the three distinct stable layers.
Mapes and Zuidema (1996) found dry, stable layers and associated RH gradients at the interface with moist air below provide a layer of anomalous longwave radiative heating and stabilization at the base of the dry layer and a layer of anomalous longwave radiative cooling of the moist layer below. The moist layer below the dry layer emits relatively larger amounts of longwave radiation, heating the base of the dry layer. Pakula and Stephens (2009) examined the cloud distributions in regions of active tropical convection also using a radiative-convective equilibrium cloud-resolving model. They simulated increased stable layers and produced similar
7 moisture, stability, and cloud structures to those observed by Johnson et al. (1996, 1999).
Moreover, radiation influenced stable layers in the vicinity of RH gradients by the same mechanism studied by Mapes and Zuidema (1996). Pakula and Stephens (2009) found convectively active and convectively suppressed phases in simulations using realistic and modified radiative heating profiles in a cloud resolving radiative equilibrium model. During convectively suppressed phases, clouds were capped at lower levels, supporting the development of lower level stable layers with associated RH gradients providing additional stabilization.
Many previous studies also examined the impact of radiative processes on the evolution and precipitation patterns of both tropical and mid-latitude mesoscale convective systems (MCSs)
(Tao et al. 1996; Miller and Frank 1993). Tao et al. (1996) examined the longwave radiation mechanisms of cloud top cooling and cloud base heating, differential cooling between cloudy and clear regions, and large-scale environmental cooling. They found that for an MCS observed during the Equatorial Mesoscale Experiment (EMEX), large-scale environmental cooling played a dominant role with regards to storm organization and total precipitation. Longwave radiation provided clear-air cooling throughout the troposphere, reducing the temperature and increasing the RH. In the moist tropics, this reduces the impact of entrainment on developing and organizing deep moist convection, allowing condensation to occur more efficiently, similar to findings by
Dudhia (1989). Miller and Frank (1993) also found that the domain-wide destabilization caused by radiative processes modifies the evolution of tropical MCSs.
There have been attempts to study the impact of radiation on tropical cyclone development using idealized simulations. Sundqvist (1970) used an axisymmetric balanced primitive equation model to simulate the development of tropical cyclones and found that the idealized tropical cyclone grew much more rapidly when radiative cooling of clear-air2 only was
2 Clear-air was defined in the study as all grid points where condensation was not taking place; clouds are implicit since cooling only occurred where clouds are not present.
8 included, but there was no impact on the final intensity. Hack (1980) used a similar modeling approach, but with prescribed clear-air and cloudy-air radiative heating profiles. It was found that the tropical cyclone growth rate was similar between experiments with and without radiation, but the experiment with radiation started to intensify at an earlier time and had a greater final intensity, which is also confirmed in Craig (1996). However, following a similar approach to
Hack (1980), Baik et al. (1990) found the rate of intensification and final storm intensity was not impacted.
The lack of consensus among these aforementioned idealized studies calls for real-data studies to examine the impact of radiation on tropical cyclone genesis, which will be the focus of the current study. An observational study of hurricanes and tropical cyclones by Steranka et al.
(1984) found significant diurnal and semidiurnal cloud cycles in observations of satellite derived cloud top temperatures. Kossin (2002) confirmed the diurnal oscillations and hypothesized that radiative cooling induced subsidence at night in the region of the hurricane canopy reduces the spatial coverage of high cirrus clouds producing the observed reduction in cloud top heights. Both studies found the diurnal and semidiurnal cycle impact was more pronounced farther from the core of the tropical cyclone. Using idealized tropical cyclone simulations, Fovell et al. (2010) found a track sensitivity to radiation through a radiative-cloud feedback, driven by differences in hydrometeor species and number concentration distributions generated through microphysical processes. The amount of longwave emission and absorption from the microphysical differences impacted the storm thermodynamics and dynamics, altering the tropical cyclone structure, development, and track.
This study uses Hurricane Karl (2010) as a case study to focus on the impact of the diurnal radiation cycle on the pre-genesis environment of a developing tropical cyclone.
Hurricane Karl was the eleventh named storm and fifth major hurricane of the 2010 Atlantic hurricane season, reaching tropical storm strength at 1800 UTC 14 September. Genesis forecasts
9 of Karl were challenging, driven by many factors including a lack of organized convection near the center of low pressure and the misalignment of the low- and mid-level circulations. Karl was observed during the PRE-Depression Investigation of Cloud-systems in the Tropics (PREDICT) field experiment (Montgomery et al. 2012; Davis and Ahijevych 2012). The goal of PREDICT was to obtain extensive pre-genesis environmental observations of potential tropical cyclones to better understand why some tropical waves develop into hurricanes while others do not
(Montgomery et al. 2012). Davis and Ahijevych (2012), hereafter DA12, profiled the pre-genesis environment of Karl and found the storm was characterized by strong diurnal variations in deep moist convection, with a maximum in the mid- to late-morning and a minimum in the late evening; only immediately before genesis did deep moist convection become constant and extensive.
Model Setup and Experimental Design
Forecast Model
This study uses the non-hydrostatic Advanced Research Weather Research and
Forecasting model (WRF-ARW) Version 3.1.1 (Skamarock et al. 2008) with three domains; the inner domains (D02 and D03) are two-way nested. The horizontal grid spacing and coverage, from coarse to fine, are D01: 40.5 km – 253x163, D02: 13.5 km – 364x253 and D03: 4.5 km –
601x391 (Figure 2-1a; D01 not shown). All three domains have 35 vertical terrain following Eta levels and a model top at 10 hPa. Note that the resolution of the model in the lower troposphere, given only 35 total vertical model levels, might not fully resolve the convectively mixed layer and entrainment zone; the entrainment zone is the layer between the convectively mixed layer, herein mixed layer, and the free atmosphere. The WRF Single-Moment 6-class microphysics scheme
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(WSM6; Hong and Lim 2006), Yonsei University (YSU) planetary boundary layer (PBL) scheme
(Hong et al. 2006), thermal diffusion surface physics scheme, rapid radiation transfer model longwave radiative scheme (RRTM; Mlawer et al. 1997), and Dudhia shortwave radiation scheme
(Dudhia 1989) are employed for all domains. The Grell-Devenyi ensemble cumulus scheme
(Grell and Devenyi 2002) is used for D01; no cumulus parameterization is used for D02 and D03.
The model domains are two-way nested such that all forecast variables in D03 are directly passed into D02. The use of cumulus parameterization in D02 will make little or no difference due to the two-way nesting. Nearly all convective activity associated with the development of Karl is within
D03. Also, cumulus parameterization was not included in D02 to avoid spurious gradients in water vapor at the boundary of D02 and D03.
The Dudhia shortwave and RRTM longwave radiation schemes and the WSM6 microphysics scheme within WRF interact implicitly. Heating from the radiation schemes modifies the thermodynamics of the environment, impacting cloud processes and vice versa. At any given grid point in a model column, the net heating is a summation of the shortwave and longwave heating from their respective schemes. Each radiation scheme uses the cloud fraction to determine if the scheme is calculating a cloudy or clear-air heating rate. The cloud fraction for the
Dudhia and RRTM radiation schemes are determined from the cloud mixing ratio (qc) or summation of cloud mixing ratio and ice mixing ratio (qci). If qc or qci is greater than the set threshold of 10-6 [kg kg-1], the cloud fraction is set to 1 and the cloudy heating rates are calculated; otherwise the cloud fraction is set to 0 and clear-air heating rates are calculated. The qc and ice mixing ratio (qi ) are prognostic variables within the WSM6 microphysics scheme; the other prognostic variables in the scheme are the mixing ratios of water vapor (qv), snow (qs), rain
(qr), and graupel (qG). The Dudhia and RRTM radiation schemes are calculated every 30 minutes while the WSM6 microphysics scheme is calculated every time step for time steps less than 120 s and every 120 s if the model time step is larger.
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The Dudhia (1989) shortwave radiation scheme calculates the downward column shortwave clear-air and cloudy-air heating rates, accounting for clear-air scattering, clear-air water vapor absorption, cloudy-air scattering (albedo effects), and cloudy-air absorption; the calculation is dependent on the binary cloud fraction at each level in the column. A cloud fraction of 1, cloudy air, instructs the model to use cloud radiation parameters of cloud scattering and absorption. Clear-air scattering and water vapor absorption are calculated when the cloud fraction is 0. For cloudy-air, the microphysical quantities at each grid point are taken into account through the liquid water path (LWP). The LWP is used to describe optical properties of the cloud due to its availability in the WRF and relationship to optical thickness. The LWP is computed in the
Dudhia SW scheme in WRF using a density-weighted summation of the weighted cloud-mixing ratio (100%), ice mixing ratio (10%), rain water-mixing ratio (5%), snow mixing ratio (2%), and graupel mixing ratio (5%). The LWP is subsequently used in combination with the cosine of the zenith angle of the solar irradiance to determine the cloud scattering and absorption; interpolated from tabulated values from Stephens (1978a,b) theoretical results. Stephens (1978a) showed that the details of the drop size distribution within the cloud are of secondary importance to the vertical distribution of liquid water content within the cloud when calculating the SW radiative flux. The effective radius for the various drop size distributions seen in the cloud types defined by
Stephens (1978a) are inherently taken into account when determining the relationship between
LWP and optical thickness when deriving the SW parameterization. The reader is directed to
Stephens (1978a,b) for further details on the theory and parameterization details.
Initial and Boundary Conditions
The initial conditions are generated from the Pennsylvania State University (PSU) limited-area mesoscale ensemble prediction system using a cycling ensemble Kalman Filter
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(EnKF; Meng and Zhang 2008a,b; Zhang et al. 2009, 2011b; Weng and Zhang 2012). The system was used during PREDICT as part of the forecast guidance and assimilated all data used by the
National Centers for Environmental Prediction (NCEP), excluding satellite radiances
(Montgomery et al. 2012). For further details on the PSU-EnKF system, the reader is directed to
Zhang et al. (2009) and Weng and Zhang (2012). The 30-member ensemble used in this study is initialized from the 0000 UTC 12 September posterior of the real-time analysis from the PSU-
EnKF used during PREDICT. The model is integrated for 144 hours for each ensemble member without any additional data being assimilated. The boundary conditions for D01 are updated every 12 h from the Global Forecast Model (GFS) forecast initialized at 0000 UTC 12 September.
The WRF 3-Dimensional Variational Data Assimilation (WRF-3DVAR; Barker et al. 2004) is used to perturb the GFS forecast boundary condition tendencies using balanced random perturbations derived using the “cv3” option for the background error statistics. For further details on the boundary condition generation methodology, the reader is directed to Meng and
Zhang (2008b).
Sensitivity Experiment Design
To test the effect of diurnal cycle on storm development, multiple sensitivity simulations are generated to isolate various parts of the diurnal radiation cycle. These experiments include an endless daytime (solar insolation set at local noon, DayOnly), an endless nighttime (no solar insolation, NightOnly), and the disabling of both longwave and shortwave radiation (NoRad).
Normal diurnal cycle experiments are also performed with unmodified radiation (CNTL) and with a reversal of the diurnal cycle that shifts the model time (for shortwave radiative forcing only) backwards by 12 h (Offset). General conclusions cannot be adequately drawn from only the analysis of the CNTL forecast and the associated vertical radiation profiles; it is necessary to use
13 the various sensitivity experiments to isolate the extremes of the diurnal cycle. Due to computational restrictions, the sensitivity experiments are performed for two developing (member
16 and member 39; subjectively chosen due to their similarity in track to observations) and two non-developing (member 11 and member 37) members of the initial PREDICT ensemble.
Storm Tracking, Storm Development Criteria, and Vertical Profile Radial Averages
The pre-storm dislocation of the lower- and mid-level circulations associated with Karl made it difficult to define and track the pre-genesis vortex center. For this study, a 2-D low pass fast Fourier transform (FFT) filter is used on the 850- and 500-hPa relative vorticity fields to filter wavelengths less than 300 km prior to application of the tracking algorithm. Composite best track data from PREDICT is used at 0000 UTC 12 September (local time is -5 h offset from UTC) to constrain the initial search for the maxima of the 850- and 500-hPa relative vorticity fields. The vortex center is set as the average of the locations of the 850- and 500-hPa relative vorticity maxima. Subsequent searches use the location of the prior vortex center as the initial search point.
Vertical profiles of model variables are generated for the local environment3 by horizontally averaging each model level within a circle of radius 225 km, and for the large-scale environment by averaging over an annulus from 300 km to 450 km, both using the 850-500 hPa average vortex center. Storm intensity is defined by the maximum 10 m wind speed within 225 km of the vortex center. A simulation is considered developed when the 10 m maximum wind speed is over 18 m s-1. All diagnostic analyses are performed on D03 unless otherwise noted.
3 The local environment here refers to the inner-core area centered on the incipient vortex center.
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Evolution of the Local Environment
Case in Study: Hurricane Karl (2010)
A trough over northern South America merged with a westward moving tropical wave on
8 September to form an area of low pressure east of the Windward Islands (Stewart 2010). Prior to cyclogenesis, the disturbance was characterized by strong diurnal variations in deep moist convection, discernable in Figure 2-2e, a Geostationary Operational Environmental Satellite
(GOES) infrared data derived time-radius diagram of cloud-top temperature (adapted from
DA12). Pulsations in cloud top temperature from deep moist convection coincide well with the diurnal cycle; coldest cloud tops occurred near the circulation center around approximately 0600
UTC each cycle, extending radially outward through time with the largest radial extent occurring at approximately 1200 UTC. GOES infrared imagery every 12 hfrom 1200 UTC 12 September through 0000 UTC 14 September (Figure 2-2a-d) depict the spatial distribution of the deep moist convection, the largest concentration of cold cloud tops occurring at approximately 1200 UTC 12 and 13 September to the northwest of the vortex center. DA12 found that the pulsations in deep moist convection helped overcome the negative effects of friction and vertical wind shear produced during the convectively inactive periods. They concluded that deep moist convection and the vertical alignment of the relative vorticity were key environmental factors in the genesis of Karl. Using dropsonde data from PREDICT, DA12 found that in the 4 days prior to genesis, the average environment within 3o of the 900 hPa storm center had RH values between 75-80% below 500 hPa, dropping off rapidly to approximately 40% by 200 hPa (DA12, their Figure 13b).
A large reduction in low-level circulation with a smaller associated reduction in mid-level circulation occurred between 1800 UTC 11 September and 0000 UTC 13 September. The mid-
15 level circulation regained much of its strength by 1200 UTC 13 September, with the low level circulation (between 900 and 700 hPa) rapidly increasing just prior to genesis on 14 September.
Original Ensemble Members
The 30-member ensemble forecasts initialized from 0000 UTC 12 September cycling
PSU-EnKF produced 11 developing and 19 non-developing storms. Figure 2-1a shows the 120 h storm tracks of the developing members and the National Hurricane Center (NHC)’s Best Track, with the accompanying storm intensity in Figure 2-3a. The spread in the intensity exposes the low predictability for the genesis of Karl, with a few members showing immediate genesis and others not until later in the period between 14-15 September.
The composite environments of the developing and non-developing ensemble members at initialization (0000 UTC 12 September) indicate statistically significant differences in RH, relative vorticity, and deep layer shear; these fields, either individually or in aggregate potentially impact Karl’s genesis. The developing members initially have higher 700 hPa to 500 hPa RH
(71.3% vs. 65.9%), larger 850 hPa relative vorticity (3.2x10-5 s-1 vs. 2.7x10-5 s-1), and stronger
850 hPa to 200 hPa deep layer wind shear (8.8 m s-1 vs. 6.4 m s-1) calculated at the vortex center.
DA12 found that the displacement of the low- and mid-level circulations was the main contributor to the observed wind shear in Karl, while the background environmental wind shear was a secondary contributor. A large displacement of the vortex centers is observed in the initial conditions generated by the PSU-EnKF system for Karl, a contributor to the observed wind shear.
Figure 2-4 shows vertical profiles of the local environment RH (calculated with respect to ice below 0˚ C) and relative vorticity, averaged over 24 h starting at 0000 UTC 12 September
(Figure 2-4a,b) and 0000 UTC 13 September (Figure 2-4c,d) for developing (blue) and non- developing (red) ensemble members. The mean of the developing and non-developing ensemble
16 members are bolded. Consistent with past studies (e.g., McBride and Zehr 1981; Zhang and
Sippel 2009; Sippel and Zhang 2010; Torn and Cook 2013), during both periods before cyclogenesis, the developing members, on average, have higher RH as well as larger low- to mid- level relative vorticity.
Sensitivity Experiments
The effect of the diurnal cycle on storm development is analyzed by sensitivity experiments that modify the radiation applied to a given simulation in an attempt to isolate the extremes of the diurnal cycle. The impact on the intensification can be seen in Figure 2-3b,c,d with the intensities of two developing members (16 and 39) and one non-developing (member 11; member 37 not shown due to its similarity with member 11), spanning 12-17 September. Member
16 and 39’s CNTL and NightOnly all develop; the NightOnly simulations are generally more intense compared with the CNTL runs. Member 16’s Offset develops while Member 39’s Offset does not develop, even though both receive the same additional period of solar radiation post initialization. All DayOnly and NoRad experiments do not develop. Some of the non-developing sensitivity experiment members attain marginal tropical storm wind speeds, but develop broad and less organized convection with weaker low- to mid-level circulation; as such the maximum wind speed overstates the development of these storms.
It should be noted that the switch from local late evening, when the sun is nearly set, to local noon in the DayOnly experiments at simulation initialization generates no discernible transient response in the initial model fields. The initial fields minimally vary between sensitivity members during the first 6 h, distinguishable differences are not evident until approximately 10 h.
The impact of radiation is an integrated effect, taking time to substantially alter the simulations.
17
Additional tests were performed using initial conditions at 1800 UTC 11 September with the same DayOnly radiative forcing; all exhibit similar behavior early on(not shown).
All sensitivity experiments vortex centers throughout the first 24 h are near 15oN latitude with the tracks staying within +/- 2o latitude as the simulations progresses; DayOnly makes the largest deviation of member 16’s track. Within the first 24 h, land-modified air from the north of
South America and islands surrounding the eastern Caribbean Sea minimally interact with the local environment of the circulation. Therefore, the analysis of the pre-genesis environment is focused on the first 24 h in order to minimize complications induced by land, including enhanced sea breeze circulations, and overproduced convection due to increased surface heating of land in the DayOnly experiments.
To examine the pre-development environment and subsequent evolution of the sensitivity experiments for the developing members, the analysis focuses on member 16 for simplicity.
Member 39 showed very similar evolution for each sensitivity experiment except for Offset; the nature of this experiment will be discussed in the next section. Unless otherwise noted, the remaining discussion and figures all reference member 16. Vertical profiles of the average local environment hourly model output from 0000 UTC 12 September to 1200 UTC 15 September of
RH (%), cloud water and ice mixing ratio (g kg-1), and relative vorticity (x10-4 s-1) are shown in
Figure 2-5 for CNTL, DayOnly, and NightOnly. The cloud water and ice mixing ratios for CNTL and NightOnly (Figure 2-5b,h) indicate three local cloud maxima: above the mixed layer of the
PBL in the entrainment zone (~1.5 km), near the 0˚ C melting level (~5 km), and below the tropopause (~12 km). During the first 24 h, CNTL and NightOnly both produce deep moist convection, hypothesized to be a precursor for aiding in the development of a deep vortex later in the simulation, as seen in Zhang and Sippel (2009). DayOnly does not exhibit strong vertical development during the first 24 h.
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Focusing on the RH in Figures 2-5a,d,g, DayOnly had a decrease in RH from 2 km up to the tropopause compared with CNTL and NightOnly, although a weak signal of drier mid- to upper-level air is present in CNTL and NightOnly from 6 km to 10 km. In DayOnly, the constant bombardment of shortwave radiation increased the temperature above the boundary layer and entrainment zone (see moist static energy discussion and corresponding Figure 2-8), dropping the
RH; there is a pronounced decrease in RH seen by the end of the first 24 h from 8 km to 14 km in
DayOnly. The warmed local environment for DayOnly reduces the initial convective burst mid- day on 12 September that occurs in developing members CNTL, NightOnly, and marginally in
Offset.
The relative vorticity is similar for CNTL, DayOnly, and NightOnly during the first 12 h, but by 1800 UTC 12 September, CNTL and NightOnly diverge from DayOnly with increased mid- to upper-level relative vorticity (Figures 2-5c,i). Increased mid-level relative vorticity is evident in CNTL and NightOnly by 1200 UTC 13 September. The average 850- to 500-hPa local environment relative vorticity for the first 3 days of the simulation is shown in Figure 2-6. The strength of NightOnly over CNTL is evident after 0000 UTC 14 September and corroborates that seen in Figures 2-5c,i. After 0000 UTC 14 September, NightOnly maintains the largest average magnitude over the other sensitivity experiments. There is a delay in the development and intensification of Offset, lagging NightOnly and CNTL by approximately 18 hours. Once intensification begins, the rate of intensification of NightOnly is the largest, CNTL and Offset are similar, and DayOnly and NoRad do not develop. These results are similar to Sundqvist (1970) who found an increased intensification rate when clear-air cooling was included.
The alignment of the low- and mid-level circulations was found to be instrumental in the genesis of Karl (DA12). The alignment of the low- (850 hPa) and mid-level (500 hPa) relative vorticity is evident in Figure 2-7. At 1200 UTC 12 September (Figure 2-7a,e,i), all three simulations have similar alignment of low- and mid-level circulations. As the simulation
19 progresses, the strength of both low- and mid-level circulations for DayOnly remains weak and the misalignment much larger than that of CNTL and NightOnly (Figure 2-7c,g,k). By 1200 UTC
14 September, approximately 3 h before tropical cyclogenesis, CNTL and NightOnly are well aligned with a surface depression evident in the sea level pressure fields and strong low- and mid- level relative vorticity.
An analysis of the radial and vertical mass flux (not shown) of the local environment prior to storm genesis shows strong inward radial mass flux at the surface for CNTL and
NightOnly. The strongest vertical mass flux was found near deep moist convection. Minimal low- level convergence and vertical mass flux was observed for DayOnly, with net subsidence from 2 km extending through the tropopause from 1200 UTC 12 September through 0000 UTC 13
September. As expected, the simulations with strong deep moist convection – CNTL and
NightOnly – showed stronger low-level convergence and vertical mass flux.
Impact of Diurnal Radiation Cycle on Local and Large-Scale Environment
Previous studies (Tao et al. 1996; Craig 1996) show that large-scale clear-air cooling impacts storm development, both for MCSs and tropical cyclones. For this study, radiative heating and cooling differences for each sensitivity experiment are hypothesized to impact the local and large-scale environment, altering the evolution of the overall pre-genesis environment.
It should be noted that the environment and radiative heating profiles examined herein are clear-air only. Clear-air is defined as any grid point in the model with a cloud mixing ratio or cloud and ice mixing ratio less than a threshold of 1x10-6 [kg kg-1]. The clear-air assumption does not take into account the impact of clouds in the modification of the local and large-scale environment, except implicitly through the detrainment and transport of cloud water.
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The impact of diurnal radiation can be seen by examining the 24-h departure of moist static energy (MSE) in the clear-air large-scale environment of each sensitivity experiment from the initial conditions (Figure 2-8). MSE is a thermodynamic variable derived from the first law of thermodynamics (see page 86 of Wallace and Hobbs [2006]) that is approximately conserved following air parcels. It is the sum of the moist enthalpy and gravitational potential energy per unit mass; in other words, it is the total energy content of the air excluding kinetic energy. MSE in a closed system can only be changed by surface fluxes of latent and sensible heat and/or radiative heating. Focusing on DayOnly (Figure 2-8b) during the first 24 h, it is clear that the
MSE in the PBL is increasing over the initial condition, driven by latent and sensible heat flux.
There is a large increase in MSE in the mid- to upper-troposphere, caused by shortwave radiative heating of the large-scale environment. NightOnly (Figure 2-8c) shows a decrease in MSE above approximately 3 km extending to the tropopause, driven by the clear-air radiative cooling of the large-scale environment. The MSE panels of Figure 2-8 indicate the dominant impact radiation has on the large-scale mid- to upper-level temperature of the environment. A similar MSE departure was found for the local environment of the clear-air (not shown).
To help explain the impact of longwave and shortwave radiation on the large-scale environment, the net (Figure 2-9a,c), shortwave (Figure 2-9b), and longwave (Figure 2-9c) clear- air and cloudy-air radiative heating tendency profiles are averaged over the first 24 h. The focus is on the large-scale clear- and cloudy-air vertical profiles; the cloudy-air vertical profiles for the large-scale environment and the similar net (Figure 2-9d), shortwave (Figure 2-9b,e), and longwave (Figure 2-9c,f) vertical profiles for the local environment are provided for reference.
The net clear-air large-scale radiative heating profiles (Figure 2-9a; solid lines) show a clear net heating for DayOnly from approximately 3 km through 12 km with the other experiments having a net cooling above the surface layer (first few model levels) to the tropopause; NightOnly has the largest net cooling. Focusing on the components of the net
21 radiative heating tendency, the clear-air longwave and shortwave radiative heating tendencies, over the first 24 h, DayOnly has a positive shortwave (Figure 2-9b; solid lines) heating component throughout the entire troposphere, with a peak at approximately 9 km. A local maximum is seen at approximately 600 m at the top of the PBL. CNTL and Offset have similar positive heating profiles, but are smaller in magnitude compared to DayOnly. NightOnly and
NoRad do not have shortwave heating by experimental design. The clear-air longwave heating profiles (Figure 2-9c; solid lines) show DayOnly with the largest magnitude of longwave cooling at all levels below 9km and NightOnly and CNTL with the smallest longwave cooling; Offset splits the difference, although closer to NightOnly and CNTL. The constant bombardment of shortwave radiation is a dominant contributor to the heating (cooling) of the clear-air atmospheric column for DayOnly (NightOnly). The clear-air will therefore emit relatively larger (smaller) amounts of longwave radiation.
The net radiative heating summarizes the impact of radiation on the large-scale, clear-air environment. DayOnly has a reduced cooling below approximately 3 km and net heating from approximately 3 km to 12 km, stabilizing the large-scale clear-air environment. NightOnly has net radiative cooling above the surface layer through the entire troposphere, destabilizing the large-scale clear-air environment. CNTL and Offset have similar profiles as NightOnly, but smaller magnitudes. These results are consistent with past studies including Dudhia (1989),
Miller and Frank (1993), and Tao et al. (1996).
The vertical radiative heating profiles for the local environment are similar to those of the large-scale; the largest differences occur in mid- to upper-tropospheric cloudy-air. Comparing
Figures 2-9a-c and Figures 2-9d-e, between 9-12 km, there is an evident increase in both the shortwave and longwave heating. This coincides with a 10-15% (Figures 2-8f and 2-10d) increase in cloud fraction, associated with increased cloud coverage in the local environment. The increased water content produces larger heating rates and an overall near neutral heating (Figure
22
2-9d) from 9-12 km. The detailed impacts of cloud processes are out-of-scope of this study, but an area of focus for future research.
To study the evolution of the local environment for the first day of the simulation (0000
UTC 12 September to 0000 UTC 13 September), vertical profiles of the clear-air 24 h sensitivity experiment departures from CNTL are presented for potential temperature (Figure 2-10a), water vapor mixing ratio (Figure 2-10b), and RH (Figure 2-10c), with the cloud fraction presented in
Figure 2-10d. The CNTL 24-h averages for each variable are included for reference.
Figure 2-10a shows the average potential temperature departure over the first 24 hours.
Given the net radiative heating profiles described above, it is no surprise that DayOnly
(NightOnly) has the highest (lowest) potential temperature throughout the averaged tropospheric profile when compared with CNTL; the remaining members fall in between these bounds. The largest spread lies between the top of the entrainment zone and the tropopause, aligning with vertical layers of net radiative cooling associated with NightOnly and radiative heating associated with DayOnly. The water vapor mixing ratio departures in Figure 2-10b are driven by slightly different mechanisms, depending on the altitude. Below approximately 1.5 km, the largest departure of water vapor from CNTL is DayOnly, Offset, and NoRad, driven by larger fluxes of water vapor into the mixed layer of the PBL. Aloft, the spread is driven by the increased deep moist convection in NightOnly and NoRad. The impact of the net radiative heating and cooling on the large-scale environment can also be examined by looking at the 24-h average RH departure profiles in Figure 2-10c. Above the PBL, DayOnly has a lower RH, also seen in Figure
2-5d. The increase in the potential temperature of DayOnly over the first 24 hours above the mixed layer is the dominant mechanism that drives the spread in RH between DayOnly and
NightOnly. Tropical environments with larger RH are less detrimental to developing moist convection by diminishing the impact of entrainment. Also, larger RH in the low- to mid-
23 troposphere reduces the local stabilization of the PBL by evaporation of precipitation and the transport of low equivalent potential temperature air towards the surface.
Above the entrainment zone extending to the tropopause, the RH for NightOnly is slightly larger in comparison to CNTL (Figure 2-10c). The moister environment in NightOnly is more conducive for deep moist convection relative to CNTL. Although there is no systematic difference between NightOnly and CNTL in the maximum surface (10 m) wind speed (Figure 2-
3b), the circulation associated with CNTL is not as strong as NightOnly in terms of low-to-mid level vorticity as shown in the Hovmöller diagrams of Figure 2-5c versus Figure 2-5i, likely as a direct consequence of enhanced convective activity in NightOnly than CNTL. A systematic intensification rate is seen in both Figure 2-3b,c between NightOnly and CNTL, also seen in
Figure 2-6 in the average relative vorticity.
To expose why the convection in DayOnly and Offset is suppressed during the first 12 hours of the simulation – as seen as a reduction in RH and cloud water and ice in Figure 2-5d,e for DayOnly – the clear-air local environmental stability above the mixed layer in the entrainment zone is examined. Figure 2-11 shows a 0-2 km vertical profile of the average local environment
∗ potential temperature (Figure 2-10a), saturation equivalent potential temperature (� ) (Figure 2-
11b), RH (Figure 2-11c), and water vapor (Figure 2-11d). Also shown in Figure 2-11 are the 0-2 km vertical profile of the clear-air local average of vertical gradients of potential temperature
∗ (Figure 2-11e), saturation equivalent potential temperature (Figure 2-11f),
temperature (Figure 2-11g), and RH (Figure 2-11h). Within the PBL4, the local environment is fairly well mixed with gradients in potential temperature, saturation equivalent potential temperature, temperature, and RH fairly uniform, although some deviations between
4 The PBL heights for the sensitivity experiments (not shown) range from 500 m to 600 m. NoRad has the largest PBL height followed by DayOnly, Offset, CNTL, and NightOnly. There is a decreasing trend in height for experiments throughout the first 24 hours.
24
sensitivity experiments exist. The local environmental lapse rate Γ = − is close to dry adiabatic below 200 m and sufficiently mixed up to the top of the PBL where it approaches moist adiabatic (Figure 2-11g). The lack of vertical resolution of the model in the PBL is conjectured to be the culprit for a departure from dry adiabatic profiles in the mixed layer.
Focusing on the potential temperature (Figure 2-11a), it is clear that DayOnly has the largest value within the PBL and accompanying entrainment zone. The gradient in the potential temperature is a useful diagnostic to determine stability to dry vertical motion. Below 100 m (the
first two model levels), < 0 for all experiments; the lowest layer of the PBL is absolutely unstable. This is driven by the fixed ocean surface temperature in the model having a temperature slightly above that of the overlying air. Above this shallow layer, the remaining PBL and
entrainment zone is stable to dry motions with > 0 for all sensitivity experiments.
Combining the information provided by the gradient of the local environment saturation equivalent potential temperature (Figure 2-11f) and lapse rate (Figure 2-11g) and the gradient in potential temperature, discussed above, the environment is found to be conditionally unstable below approximately 650 m and above approximately 2000 m with enhanced stability to moist
∗ motions in between. The gradient in saturation equivalent potential temperature is negative, <
0 , for all experiments indicating the environment is unstable to moist motions. Above the PBL mixed layer in the entrainment zone, the sensitivity experiments have decreased environmental lapse rates, signifying a relatively stable layer. The local environment lapse rate of DayOnly and
Offset are relatively smaller than that of NightOnly and CNTL, also evident in the large-scale environment, but to a lesser degree.
To assess the impact of the relatively more stable entrainment zone for DayOnly and
Offset during the first 12-18 h, the average clear-air large-scale environment (similar values were derived for the local environment) most unstable convective inhibition (MCIN; Figure 2-12b) and
25 most unstable convective available potential energy (MCAPE; Figure 2-12a) are plotted for the first 48 h for each sensitivity experiment. The MCAPE and MCIN are for a parcel5 with the highest equivalent potential temperature below 3000 m AGL. The MCIN for DayOnly, Offset, and NoRad has a relatively larger magnitude than that of NightOnly and CNTL for the first approximately 12-18 h. Focusing on the MCAPE, the instability grows in NoRad and DayOnly after the first 18 hours; the increase in MCAPE for DayOnly is a result of the heating and moistening of the DayOnly PBL coupled with the stabilization of the entrainment zone. NoRad is driven by a combination of the heating of the PBL through sensible and latent heat and a lack of heating or cooling in the clear-air large-scale environment. As the simulations progress,
NightOnly is continuously convectively active, consuming CAPE and maintaining the low
MCAPE values (not shown).
A potential contribution to the stabilization of the entrainment zone is the impact of differential radiative heating and cooling at the RH gradient (Mapes and Zuidema 1996; Pakula and Stephens 2009). Moist air below relatively drier air cools at a larger rate than the drier air above, heating the base of the drier air thus aiding in the stabilization of that relatively drier layer.
This may help to maintain and/or strengthen the stability above the PBL in the entrainment zone.
DayOnly has the largest gradient in RH at the entrainment zone (Figure 2-11h), with reduced RH above approximately 2 km. The enhanced mixing in the PBL and an increase in water vapor in
DayOnly, Offset, and NoRad provides additional sharpening of the moisture gradient at the top of the mixed layer of the PBL. CNTL and NightOnly have weaker gradients in RH below the entrainment zone. A peak in the longwave radiative heating near the top of the PBL (~500-650 m) is associated with the moist mixed layer in the PBL environment. There is a local maximum in shortwave heating at the top of the PBL (Figure 2-10b) extending into the entrainment zone for
DayOnly, around approximately 650 m. The gradient in RH (Figure 2-11h) associated with the
5 A parcel is defined as a 500 m vertical layer average at each horizontal grid point.
26 base of the entrainment zone produces a longwave cooling stratification that may aid in the impact on the local vertical temperature profile of each sensitivity experiment. The net effect of the differential longwave cooling and additional shortwave heating (in experiments with daytime) at and below the entrainment zone is to modify the stability of the entrainment zone, enhancing the stability in DayOnly and to a lesser extent, Offset, relative to that in CNTL and NightOnly. It is clear that DayOnly has increased stability to moist vertical motions during the initial 12 hours, which suppresses convection during the initial 12-18 hours of the simulation.
The diurnal radiation cycle impacts the pre-genesis local and large-scale environment for
Karl by modifying the deep-layer stability and the stability in the entrainment zone, resulting in variations in the amount and timing of deep moist convection during the initial development of the simulation. The relative vorticity, RH, and deep moist convection are coupled, with TC developing sensitivity experiments CNTL, NightOnly, and Offset have a period of strong deep moist convection during the second half of the first 24 h. The associated burst of deep moist convection is hypothesized to be the catalyst driving the increased relative vorticity at the surface and mid-levels (Figure 2-5c,i) and moistening of the low- and mid-levels (Figure 2-5a,c) that leads to the eventual development of the tropical cyclone. Our finding is consistent with DA12 who observed the relationship between deep moist convection modulated by a strong diurnal cycle and the intensification of the pre-genesis circulation of Karl.
A schematic depiction of diurnal radiation cycle impacts is shown in Figure 2-13, displaying the NightOnly and DayOnly radiative differences of the combined local and large- scale environment and stable layers; CNTL is provided for reference. During nighttime, the net cooling of the clear-air local and large-scale environment from longwave emission reduces static stability with a corresponding net increase in RH; the overall environment is more conducive to vigorous convection that precedes the genesis of Karl. During the daytime, the heating from shortwave radiation is larger in magnitude than the cooling from longwave radiation in the mid-
27 to upper-level clear-air local and large-scale environment, leading to a net stabilization. An enhancement in stability of the entrainment zone (due to the shortwave radiative heating and the differential radiative heating of the relatively drier air at the interface between the top of the PBL and the entrainment zone) produces a smaller cooling rate in the entrainment zone, leading to increased stability and an initial period of suppressed convective activity in the local environment. For the full diurnal cycle (CNTL), the shortwave heating of the local and large- scale environment offsets a portion of the cooling seen in the nighttime only experiment throughout the troposphere, producing a relatively closer to neutral cooling vertical profile, but still providing net destabilization.
Concluding Remarks
This study examined the effect of the diurnal radiation cycle on the pre-genesis environment of Hurricane Karl (2010). The sensitivity experiments are intended to isolate various parts of the diurnal radiation cycle, which include endless daytime, endless nighttime, no radiation, a normal diurnal cycle, and a reversal of the diurnal cycle that shifts the model time backwards by 12 h. The initial conditions were taken from a 30-member ensemble analysis perturbation generated during the PREDICT field campaign from the cycling PSU WRF-EnKF system; two developing and two non-developing systems were chosen.
Potential tropical cyclogenesis was found to be sensitive to the periodic cycle of heating and cooling associated with the diurnal cycle and its impact on deep moist convection. The nighttime phase of the diurnal radiation cycle provides critical destabilization in the pre-genesis local and large-scale clear-air environment, promoting deep moist convection and increased relative humidity throughout the troposphere, thus improving chances for cyclogenesis. The daytime phase of the diurnal radiation cycle is critical in reducing the local and large-scale
28 relative humidity and increasing the stability, making the overall environment less conducive to deep moist convection thus altering the local environmental evolution and subsequent tropical cyclone development. The impact of radiation was found to be an integrated effect, taking time
(~10 h) for the radiation scheme modifications to noticeably alter the local and large-scale environment and evolution.
Relative humidity gradients at the base of dry layers in the troposphere can provide a region of anomalous longwave radiative heating and stabilization at the base of the dry layer and a layer of anomalous longwave radiative cooling of the moist layer below. This is hypothesized to play a role in enhancing the stability associated with the entrainment zone in this study. During the initial period, DayOnly and Offset sensitivity experiments produce larger relative humidity gradients at the top of the PBL, driven by increased boundary layer mixing from absorption of shortwave radiation in DayOnly and Offset. Note that the sea surface temperature is fixed.
NightOnly and CNTL experiments have reduced relative humidity gradients due to reduced heating and moistening of the PBL. The stability within the entrainment zone above the PBL top is crucial to the development of deep moist convection during the first 12-18 hours. Experiments with only the daytime phase have enhanced stability from additional shortwave heating of the entrainment zone, increasing the convective inhibition and preventing moist convection during the initial 12-18 hours. The daytime phase of the diurnal cycle is conjectured to play a role in stabilizing the entrainment zone. Experiments including a nighttime phase of the diurnal cycle have reduced stability of the entrainment zone and reduced convective inhibition, enhancing the development potential of deep moist convection.
The analysis of sensitivity experiments performed on two original TC developing ensemble members found radiation may impact the rate of intensification, but no discernable difference in timing of intensification was discovered. The nighttime only simulations, with only longwave cooling, were more intense by the end of the 120 h simulation period and intensified
29 the quickest compared with the simulations that included shortwave radiation. The simulations were not run to a steady-state, therefore the impact on final intensity could not be determined.
The findings herein are preliminary and the robustness of the results need to be verified with additional case studies. This study focused on one cyclogenesis case, one tropical cyclone basin, and emphasis was placed on the first 24 h of the model simulations. Only one PBL scheme was used in the construction of the experiment and the robustness of the results to different PBL schemes was not examined. The YSU PBL scheme explicitly models entrainment in the entrainment zone; this may have an impact on the stability of the entrainment zone and deep moist convective development. Future work is needed to stress test these results using different pairings of PBL schemes, radiation schemes, and microphysics schemes available in the WRF model.
30
Chapter 2 Figures
90° W 60° W (a) D02 Member 16
30° N Member 39 NHC Best Track Dev. Members D03
15° N
90° W 60° W (b) CNTL DayOnly
30° N NightOnly Offset NoRad
15° N
Figure 2-1: (a) Model domain setup (outer domain D01 not shown) for the original ensemble and sensitivity experiment simulations. Overlaid are the vortex center tracks for developing members (thin grey) for the full original ensemble with highlighted member 16 (thick red) and member 39 (thick blue) and the National Hurricane Center (NHC) best track (NHC Best Track; thick black). (b) Vortex center tracks for member 16 sensitivity experiments: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta) plotted on D02. All model simulation tracks are plotted every 3 hours for 120 h starting at 0000 UTC 12 September. The NHC Best Track is plotted every 6 hours for 78 hours starting at 1800 UTC 13 September.
31
(a) 12/1200 UTC (b) 13/0000 UTC (c) 13/1200 UTC
10/00 11/00 12/00 13/00 14/00 15/00 16/00 UTC (d) 14/0000 UTC km (e) 600 400 200 0 [oC] 255 245 195 [K] -90 -70 -50 -30 -10 10 30 235 225 215 205 185 175 165 Figure 2-2: Geostationary Operational Environmental Satellite (GOES) 13 channel 4 (~11 microns) enhanced thermal infrared imagery at (a) 12/1200 UTC, (b) 13/0000 UTC, (c) 13/1200 UTC, (d) 14/0000 UTC. (e) Time-radius diagram of cloud-top temperature (75th percentile temperature within successive 20 km radial rings) derived from GOES infrared radiances (adapted from Figure 3b of Davis and Ahijevych (2012)). The dashed line indicates the time Karl reached tropical storm status.
32
12/00Z 14/00Z 16/00Z 0
70 10 (a) Original Ensemble 60 Member 16
] -1 20 Member 39 50 NHC Best Track
4030 Dev. Members
3040
2050 WindSpeed s [m
1060
700 12/00Z(b) Member 1614/00Z 16/00Z 60 CNTL ]
-1 DayOnly 50 NightOnly 40 Offset NoRad 30
20 WindSpeed s [m 10
700 12/00Z(c) Member 3914/00Z 16/00Z 60 ] -1 50
40
30
20 WindSpeed s [m 10
700 12/00Z(d) Member 1114/00Z 16/00Z 60 ] -1 50
40
30
20 WindSpeed s [m 10
0 09/1212/00Z 09/13 09/1414/00Z 09/15 16/00Z09/16 09/17 00 UTC 00 UTC 00 UTC 00 UTC 00 UTC 00 UTC
Figure 2-3: The evolution of the maximum 10 m wind speeds [m s-1] within 225 km of the average vortex center over the first 120 h of the simulation for (a) the original ensemble, (b) developing member 16, (c) developing member 39, and (d) non-developing member 11 sensitivity experiments with CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta). Note: in panel (a), member 16 CNTL is colored red, member 39 CNTL is colored blue, the NHC Best Track is bold black, and remaining developed members light grey; the highlighting scheme is identical to Figure 2-1a.
33
20 20 (a) (b) 18 18
16 16
14 14
12 12
10 10
Height [km] 8 8
6 6 12/0013/00 UTCto 4 4 Developed 2 Non-Developed 2 20 20 0 50 100 −5 0 5 (c) (d) −5 18 18 x 10
16 16
14 14
12 12
10 10
Height [km] 8 8
6 6 13/0014/00 UTCto
4 4
2 2
0 50 100 −5 0 5 Relative humidity [%] Relative Vorticity [x10-5 s-1]− 5 x 10 Figure 2-4: Vertical profiles of the local environment relative humidity (left) and relative vorticity (right) averaged within 225 km of the vortex center for each member of the original ensemble over a 24 h period beginning at 0000 UTC 12 September (top row) and 0000 UTC 13 September (bottom row). Developing (non-developing) members are colored blue (red), with the mean profile of each group bolded.
Pressure [Pa] 12/00Z Pressure [Pa] 10 Pressure [Pa] 9 8 7 6 5 4 3 2 1 12/00Z 10 12/00Z 10
9 8 7 6 5 4 3 2 1 x 10 9 8 7 6 5 4 3 2 1
x 10
x 10 4 4 4 13/00Z 13/00Z 13/00Z 34 Forecast Time Forecast Time Forecast Time 14/00Z 14/00Z 14/00Z
Relative Humidity Cloud + Ice Mixing Ratio Relative Vorticity -1 -4 -1
[%] 15/00Z [g kg ] 15/00Z [x10 s ] 15/00Z
0 20 40 60 80 0 0.4 0.8 1.2 -8 -4 0 4 8 x 10 − − 0 1 2 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 2 1 −
20 20 20 4 (a) CNTL (b) (c) 18 18 18 16 16 16 14 14 14 12 12 12 10 10 10 8 8 8 Height [km] 6 6 6 4 4 4 2 2 2 20 20 20 12/00Z(d) DayOnly13/00Z 14/00Z 15/00Z12/00Z(e) 13/00Z 14/00Z 15/00Z12/00Z(f) 13/00Z 14/00Z 15/00Z 18 18 18 16 16 16 14 14 14 12 12 12 10 10 10 8 8 8 Height [km] 6 6 6 4 4 4 2 2 2 20 20 20 12/00Z(g) NightOnly13/00Z 14/00Z 15/00Z12/00Z(h) 13/00Z 14/00Z 15/00Z12/00Z(i) 13/00Z 14/00Z 15/00Z 18 18 18 16 16 16 14 14 14 12 12 12 10 10 10 8 8 8 Height [km] 6 6 6 4 4 4 2 2 2
12/00Z09/12 13/00Z 14/00Z09/14 15/00Z12/00Z09/12 13/00Z 14/00Z09/14 15/00Z12/00Z09/12 13/00Z 14/00Z09/14 15/00Z 00 UTC 00 UTC 00 UTC 00 UTC 00 UTC 00 UTC
Figure 2-5: Vertical profiles of the average local environment hourly model output within 225 km of the vortex center of relative humidity (left, shaded every 5%), combined cloud water and ice mixing ratio (center, starting at 0.05 g kg-1; shaded every 0.15 g kg-1), and relative vorticity (right, thick black line denotes 0, shaded every 5x10-5 s-1) for member 16 sensitivity experiments CNTL (top row), DayOnly (middle), and NightOnly (bottom). The black dashed lines indicate genesis time for the corresponding sensitivity experiment.
35 −5 x 10 8
77 CNTL 66 DayOnly
] NightOnly -1
s Offset 5 -5 5 NoRad
[x10 44
33 Vorticity
22 Relative 11
00 09/12 09/13 09/14 09/15 09/16 09/12 09/13 09/14 09/15 09/16 00 UTC 00 UTC 00 UTC 00 UTC 00 UTC
Figure 2-6: Temporal evolution of the average 850-500 hPa relative vorticity [x10-5 s-1] within a 225 km radius of the vortex center for all member 16 sensitivity experiments CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta).
36
12/1200 UTC 13/1200 UTC 14/1200 UTC 15/1200 UTC
140 140 140 140 1000 (a) CNTL (b) (c) 140 (d) 1000
120 120 120 120 120 990990 100 100 100 100
80 80 80 100 80 980
60 60 60 60 80
40 40 40 40 970 60 20 20 20 20 960 40 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 140 (e) DayOnly 140 (f) 140 (g) 140 (h) 950950 20 120 120 120 120
100 100 100 100 940940 50 100 150 [hPa] 80 80 80 80
60 60 60 60
40 40 40 40
20 20 20 20
20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 140 (i) NightOnly 140 (j) 140 (k) 140 (l)
120 120 120 120
100 100 100 100
80 80 80 80
60 60 60 60 300km
40 40 40 40
20 20 20 20
20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 Figure 2-7: Filtered relative vorticity (wavelengths < 300 km removed) contoured every 4x10-5 s-1 (starting at 2x10-4 s-1) at the 850 hPa (red) and 500 hPa (blue) pressure levels for developing member 16 sensitivity experiments (a-d) CNTL, (e-h) DayOnly, and (i-l) NightOnly. Sea level pressure is shaded every 8 hPa starting at 1004 hPa.
37
16 (a) CNTL (b) DayOnly (c) NightOnly [kJ][kJ] 14 4 12
10 2
8 0
Height [km] 6 -2-2 4
-4-4 2
16 16 (d) NoRad (e) Offset (f) 14 14
12 12
10 10
8 8
Height [km] 6 6 CNTL 4 4 DayOnly NightOnly Offset 2 2 NoRad
0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 09/12 09/12 09/12 09/12 09/12 09/12 09/12 09/12 0 0.2 0.4 0.6 00 UTC 06 UTC 12 UTC 18 UTC 00 UTC 06 UTC 12 UTC 18 UTC Cloud Fraction
Figure 2-8: Vertical profiles of the clear-air large-scale environmental moist static energy (MSE) hourly departure (shaded every 1 kJ) from the initial conditions (0000 UTC 12 September) for member 16 sensitivity experiments: (a) CNTL, (b) DayOnly, (c) NightOnly, (d) NoRad, and (e) Offset. The large-scale cloud fraction is provided for reference in (f) for the sensitivity experiments: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta).
38
1616 (a) (b) (c)
1414
1212
1010
8
Height [km] 66 CNTL 44 DayOnly NightOnly 2 Offset NoRad 0 1616−10 −5 0 5 100 5 −1010 −5 0 5 10 (d) (e) (f) 1414
1212
1010
88
Height [km] 66
44
22
0 −010 −5 0 5 100 5 −1010 −5 0 5 10 -10 0 10 0 5 10 -10 0 10 Net Radiative Heating SW Radiative Heating LW Radiative Heating [K day-1] [K day-1] [K day-1]
Figure 2-9: Clear-air and cloudy-air (a-c) large-scale and (d-f) local environment 0-16 km vertical profiles of (a,d) net radiative heating [K day-1], (b,e) shortwave radiative heating [K day-1], and (c,f) longwave radiative heating [K day-1] averaged over a 24 h period starting at 0000 UTC 12 September for member 16. Solid lines are clear-air averages and dashed lines are cloudy-air averages. The sensitivity experiments are colored: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta).
39
Potential Water Vapor Relative Temperature Mixing Ratio Humidity [K] [g kg-1] [%]
300300 320 340340 360 00 10 2020 40 60 8080 1616 (a) (b) (c) (d)
1414
1212
1010
88
Height [km] 66
CNTL 44 DayOnly NightOnly 22 Offset NoRad 0 −-22 0 2 −-0.50.5 0 0.5 −20-20 0 2020 0 0.2 0.4 0.6 0.8 Potential Water Vapor Relative Cloud Temperature Mixing Ratio Humidity Fraction Departure Departure Departure [K] [g kg-1] [%]
Figure 2-10: Clear-air local environment 24 h average starting at 0000 UTC 12 September 0-16 km vertical profiles for CNTL (black) and sensitivity experiment departures from CNTL (solid) of (a) potential temperature [K], (b) water vapor mixing ratio [g kg-1], and (c) relative humidity [%]; the corresponding cloud fraction is provided in (d). Both sensitivity experiment departures and actual values are colored: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta).
40
20002 (a) (b) (c) (d) CNTL 18001.8 DayOnly
16001.6 NightOnly Offset 14001.4 NoRad
12001.2
10001
Height [m] 8000.8
6000.6
4000.4
2000.2
00 302302 304 306306 308 310310 312335335 340 345345 35035535570 70 8080 90900.01 10 0.01515 0.0220 Potential Sat. Equiv. Relative Water Vapor Temp. [K] Pot. Temp. [K] Humidity [%] [g kg-1] 20002 (e) (f) (g) (h) 18001.8
16001.6
14001.4
12001.2
10001
0.8 Height [m] 800
6000.6
4000.4
2000.2
00 −-55 0 5 −20-20 −-1010 04 6 8 1010 −-2020 00 2020 ∂θ δθ * ∂T ∂RH [K km-1] e [K km-1] − [K km-1] [% km-1] δz δz δz δz Figure 2-11: Clear-air large-scale environment 0-2 km vertical profiles for (a) potential temperature [K], (b) saturation equivalent potential temperature [K], (c) relative humidity [%], (d) water vapor [g kg-1], and vertical gradient profiles of the local environment (e) potential temperature with height [K km-1], (f) saturation equivalent potential temperature with height [K km-1], (g) temperature with height [K km-1], and (h) relative humidity with height [% km-1] averaged over a 24 h period starting at 0000 UTC 12 September for member 16. The sensitivity experiments are colored: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta).
41
24002400 (a) 22002200
20002000 ]
-1 18001800
16001600
14001400 MCAPE [J kg MCAPE[J
12001200
10001000
800800
600600 25 5 10 15 20 25 30 35 40 45 (b) CNTL DayOnly NightOnly 2020 Offset NoRad ]
-1 1515
1010 MCIN [J kg MCIN[J
55
00 09/12 5 1009/1215 20 09/1325 30 3509/1340 45 09/14 00 UTC 12 UTC 00 UTC 12 UTC 00 UTC
Figure 2-12: Clear-air large-scale environment (a) Convective available potential energy (MCAPE) [J kg-1] and convective inhibition (MCIN) [J kg-1] for a parcel (defined as a 500 m vertical layer average) with the highest equivalent potential temperature below 3000 m AGL over a 48 h period starting at 0000 UTC 12 September for member 16 sensitivity experiments. The sensitivity experiments are colored: CNTL (black), DayOnly (blue), NightOnly (red), Offset (green), and NoRad (magenta).
42
Day Night Full Cycle NET ENVIRONMENTAL WARMING NET ENVIRONMENTAL COOLING NET ENVIRONMENTAL COOLING NET DECREASE RELATIVE HUMIDITY NET INCREASE RELATIVE HUMIDITY NET DESTABILIZATION NET LARGE-SCALE STABILIZATION NET LARGE-SCALE DESTABILIZATION
Tropopause
NightOnly
CNTL CNTL DayOnly
Melting Layer Heating Tendency Tendency Heating Radiative Entrainment Zone
Clear-airNet - + PBL Top Figure 2-13: Schematic depiction of the diurnal radiation cycle impact on the clear-air local and large- scale environment for the genesis of Hurricane Karl during the first 24 h of the simulation. The red (blue) background shading of Day (Night) indicates net large-scale environmental heating (cooling). The vertical profile of net clear-air radiation tendency for sensitivity experiments NightOnly (red), DayOnly (blue), and CNTL (black) are depicted on the left for reference. Arrows indicate the local environment clear-air net radiative cooling (solid) for the entrainment zone; the size indicates relative magnitude. The schematic is drawn to scale. During the nighttime, net cooling of the cloud-free large-scale environment from longwave emission reduces static stability with a corresponding net increase in relative humidity. A large net cooling of the entrainment zone reduces stability of the low-level entrainment stable layer in the local environment. The combined impact is an overall environment more conducive for vigorous deep moist convection. During the daytime, the clear-air large-scale environmental heating from shortwave radiation is larger in magnitude than the cooling from longwave radiation above approximately 3 km, causing a net stabilization of the clear-air large-scale environment. Within the entrainment zone, a relatively smaller net cooling occurs due to the combined effect of shortwave radiation from above and increased longwave radiative emission from the relatively moist PBL below. The increased stability of the entrainment stable layer and stabilization of the local environment leads to the suppression of convective activity during the first 12-18 hours of the simulation, altering the subsequent evolution of tropical cyclone development. Note: the cloud distributions and stable layers for the first 12-18 hours are shown for reference. Schematic adapted from Johnson et al. (1999); first documented by Malkus (1956).
43
Chapter 3
Application of a Simplified Coplane Wind Retrieval Using Dual-Beam Airborne Doppler Radar Observations for Tropical Cyclone Prediction
Introduction
Recent studies demonstrate that ingestion of Doppler velocity observations from the Tail
Doppler Radar (TDR) onboard the NOAA P3 aircraft into convection-permitting hurricane prediction models can considerably improve tropical cyclone (TC) forecasts, especially the intensity (Aksoy et al. 2010; Zhang et al. 2011b; Weng and Zhang 2012; Zhang and Weng 2015) .
Doppler velocity observations only provide information about the wind magnitude and direction along the radar beam, but the scanning strategy of the NOAA TDR can be exploited to derive the cross-beam component of the wind field. This additional cross-beam information is advantageous for improving forecasts when assimilated from land based radars (Li et al. 2013; Wang et al.
2014) and airborne radars (Li et al. 2014).
The TDR is a conically scanning radar mounted on the tail of the NOAA P3 aircraft with
a tilt angle θfore/aft of 20˚ from a plane normal to the flight track, scanning forwards (fore) and backwards (aft) using the Fore/Aft Scanning Technique (Frush et al. 1986; Hildebrand et al.
1986; Gamache et al. 1995). Since the aircraft is moving, each radar sweep traces out a helical pattern (Figure 3-1a). A dual-Doppler analysis (Armijo 1969) can exploit the fore/aft scanning technique geometry, combining the mass continuity equation, a fall speed correction based on radar reflectivity, and multiple Doppler velocity observations interpolated to a common grid to derive a three-dimensional wind field.
44
Doppler velocity measurements from precipitation radars, such as the NOAA P3 TDR, are the horizontal and vertical motions of scatters (e.g. hydrometeors, insects, debris) in the wind field, not the actual air motions. The horizontal motions of the scatters are assumed to be comparable to that of the horizontal air motion, but the vertical motion of the scatters is a combination of the fall speed of the hydrometeors and the vertical air motion (Figure 3-1c). Using the bulk estimate of the precipitation fall speed (Rogers 1964), a relationship between the reflectivity and height can be specified (e.g. Marks et al. 1987) above, at, and below the melting layer to estimate bulk fall speeds for rain (Joss and Waldvogel 1970) and snow (Atlas et al. 1973;
Gunn and Marshall 1958). This bulk vertical fall speed correction is applied to derive the true vertical air motion, introducing uncertainties in the retrieved vertical velocities.
Jorgensen et al. (1996) formulated the dual- and quad-Doppler retrieval methodology in
Cartesian coordinates for the airborne TDR fore/aft scanning technique geometry. Their study quantified the three-dimensional error variance as a function of geometric viewing angle, taking into account uncertainties in the raw radial velocity estimates. There is additional error associated with raw airborne radial velocity measurements over ground-based measurements, stemming from the errors in the radar pointing angles due to the aircraft motion (Jorgensen et al. 1983). The error variance for this mechanism was estimated to be approximately 0.7-1.1 m s-1, larger than the ground based result of approximately 0.03 m s-1. Combing radar pointing angles and geometric viewing angle errors, the root-mean squared error (RMSE) associated with the airborne TDR radial velocity observation is estimated as approximately 1.5 m s-1 (Jorgensen et al. 1996).
Although dual-Doppler analyses are routinely preformed in Cartesian space (e.g. Frisch et al. 1974; Ray et al. 1975; Mohr et al. 1981), the geometry of the airborne fore/aft scanning technique is naturally expressed in cylindrical coordinates. A dual-Doppler analysis using the coplane scanning technique (Lhermitte and Miller 1970) – originally designed to be used with two ground-based radars – provides a natural extension of deriving a dual-Doppler analysis for
45 the airborne TDR (Figure 3-1b) in cylindrical coordinates. Chong and Testud (1996) applied the coplane scanning technique to airborne TDR Doppler velocity observations of a tropical squall line, demonstrating the advantages over traditional methods, not requiring an iterative process to solve for the wind field and mathematically describing a well-posed solution for determining the three-dimensional wind field. Their study found that the coplane technique provides high-quality dual-Doppler wind estimation, but errors derived from boundary condition assumptions and the anelastic mass continuity equation constraint increases the uncertainty in the three-dimensional wind field retrieval, especially near the boundaries of the analysis. A recent study by Didlake et al. (2015) applied the coplane dual-Doppler wind retrieval technique to the NASA High-Altitude
Wind and Rain Airborne Profiler (HIWRAP) dual-beam conically scanning, downward-pointing airborne radar. Errors for the coplane technique applied to the HIWRAP geometry for the along- aircraft track component, the cross-aircraft track component, and the derived vertical component were examined using a model-simulated TC and HIWRAP radar observations for Hurricane
Ingrid (2013). This study showed a strong dependence of the errors in the retrieved three- dimensional wind field on the quality of the boundary conditions.
Early dual-Doppler analysis approaches interpolated radial velocities to a common grid and solve the dual-Doppler projection equations, using set boundary conditions and integrating mass continuity from the boundary throughout the analysis domain (Bohne and Srivastava 1975;
Ray et al. 1980; Marks and Houze 1984; Didlake et al. 2015). Another approach is to solve an optimization problem, minimizing a cost function that describes the misfit between the radial velocity observations and the radial velocity equation. This optimization problem can be a simple least-squares approach or a variational approach including additional constraints such as mass continuity and boundary conditions to improve the three-dimensional wind field retrieval (e.g.
Ziegler 1978; Chong and Campos 1996; Gao et al. 1999; Guimond et al. 2014). The variational optimization approach bypasses the issue of integrating mass continuity and directly propagating
46 boundary errors throughout the analysis domain, but substantial errors from the boundaries can still be propagated throughout the domain during the minimization process (Gao et al. 1999). This approach is used by the Hurricane Research Division (HRD) to produce the dual-Doppler radar
TC analysis from the NOAA P3 TDR (Gamache et al. 1997).
For TCs, it has been shown that the vertical wind component has a small correlation with other state variables (Poterjoy and Zhang 2011) with most of the information provided in the u- and ν-wind field. Generally, the goal of any dual-Doppler analysis is to produce the lowest error estimate of the three-dimensional wind field. Generating only the u- and ν-wind components without potentially adding additional error by applying mass continuity is advantageous when producing u- and ν-wind observations to assimilate into a numerical weather prediction models for TC prediction. This study will use the dual-Doppler projection equations formulated in cylindrical coordinates for the airborne fore/aft scanning TDR (Chong and Testud 1996) to estimate only the horizontal wind components, helping to specify errors associated with fall speed contamination and fore/aft scanning technique scan time differences.
The authors wish to explore the use of the fore/aft scanning technique geometry and coplane technique without applying the mass-continuity equation to derive a low error wind estimate of the two-dimensional u- and ν-wind field for the sole purpose of data assimilation and
TC prediction. The questions motivating the study are: (a) What are the temporal errors in the retrieved u- and ν-wind field due to the time lag between fore/aft scans? (b) What is the impact of the fall speed correction on the retrieved u- and ν-wind field? (c) How does the retrieved u- and
ν-wind field from the simplified coplane analysis compare to the variational HRD dual-Doppler analysis? (d) What is the appropriate value of error for the u- and ν-wind for this simplified coplane analysis for data assimilation purposes? (e) Can the simplified coplane analysis observations help improve track and intensity forecasts?
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An overview of the simplified coplane methodology and simulated radial velocity methodology including model simulations used to generate a simulated TC u- and ν-wind field are described in Section 2. Section 3 presents the results comparing the simplified coplane analysis and the conventional HRD hurricane wind field analysis with in-situ flight-level data and dropsondes, and Section 4 extends the comparison using simulated radial velocities for the simplified coplane analysis. Section 5 describes forecast experiments assimilating simplified coplane analysis observations. Concluding remarks are given in Section 6.
Data and Methodology
Case in Study: Hurricane Karl (2010)
Hurricane Karl (2010) which formed during the Pre-Depression Investigation of Cloud-
Systems in the Tropics (PREDICT) experiment (Montgomery et al. 2012), the NASA’s Genesis and Rapid Intensification Processes (GRIP) experiment (Braun et al. 2013), and the NOAA's
Intensity Forecast Experiment (IFEX, Rogers et al. 2006) is used as a case study to test the simplified coplane u- and ν-wind retrievals using the TDR radial velocity observations. Karl was the eleventh named storm of the 2010 Atlantic hurricane season becoming a TC at 1800 UTC 14
September 2010 before making first landfall over the Yucatan Peninsula and moving into the Bay of Campeche the morning of the 16 September 2010. Once over the Bay of Campeche, it quickly intensified in the favorable high sea surface temperature and low vertical wind shear environment, intensifying into a Category 3 hurricane on the 17 September 2010, just prior to landfall in central Mexico. Both NOAA 42 and NOAA 43 P3 aircraft flew a total of 4 flights, each of which were comprised of two or three flight legs (Figure 3-2). Three of the flights were during the pre-genesis phase on the 12 and 13 of September 2010 and one during the post-genesis
48 phase just prior to rapid intensification on 16 September 2010. We will validate the simplified coplane observations of this study with flight-level measurements onboard the NOAA P3 aircraft and dropsonde data from each NOAA P3 aircraft, the NOAA G-IV, and multiple
PREDICT/GRIP aircraft platforms during Hurricane Karl (2010) (Figure 3-2).
A Simplified Review of the Coplane Methodology
A detailed derivation of the coplane methodology, including all assumptions and equations can be found in Chong and Testud (1996) Section 2b. For this study, the coordinate convention of Chong and Testud (1996) is used to describe the relevant geometry of the coplane methodology.
The fore/aft scanning technique generates radial velocities in a helical geometry around the flight track at each specified range gate – a single radial distance is diagramed in Figure 3-1a.
Assuming the aircraft track has minimal deviations in heading and altitude, a series of fore/aft radar beams can be structured into a half-plane about the flight track axis (Figure 3-1b). A point on the half-plane can be described by (xm, lm, αm), where x is the distance along the flight track, l is the perpendicular distance from the flight track, α is the elevation angle of the tilted half-plane, and the m subscript corresponds to a single point. An angle α=0˚ describes the half-plane parallel to the Earths surface on the port side of the aircraft and monotonically increases in value clockwise. Focusing on a single intersection of the fore/aft beam on an arbitrary α-plane (Figure
3-1d), the distance of a radial bin along radar beam r from the aircrafts TDR and the tilt angle θ of the TDR (the departure of TDR antennae from perpendicular to the aircraft track, + is towards the nose) fore/aft radar beams are important for defining the geometry of the coplane scanning technique.
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The aircraft relative along track component Γ and perpendicular to track component Ψ
(defined positive away from the aircraft track; Figure 3-1d) wind components can be evaluated by geometrically combining two radial velocity wind vectors Vfore and Vaft (positive defined toward the radar) at an intersecting point (xm, lm, αm) on an α-plane. When the α-plane deviates from parallel with the Earths surface, the fall speed of hydrometeors in the radar sampling volume must be accounted for in the Γ and Ψ components. The simplified methodology of this study differs from Chong and Testud (1996) since the fall speed is already accounted for in the raw radial velocities and not explicitly accounted for in the Γ and Ψ calculation (Eq. (4), Chong and Testud
1996). The retrieved Γ- and Ψ-wind components can subsequently be converted to aircraft and ground-relative Cartesian u- and ν-wind components.
A Simplified Coplane Algorithm for Tropical Cyclone Initialization
The retrieved wind field for the simplified coplane analysis in the manuscript is intended for TC initialization, thus, the radial velocity data is statistically thinned and quality controlled prior to the coplane retrieval and the vertical velocity is neglected. As previously discussed, the vertical velocity has small correlations with other state variables in TCs (Poterjoy and Zhang
2011). By their nature, radar radial velocity data have high spatial and temporal resolutions, generating more observations than can be efficiently ingested by current data assimilation systems. Generating super observations (“super-obbing” or SO) can greatly reduce the number of observations by removing partially redundant observations while minimizing the information lost and reducing observation random and representativeness errors (Lorenc 1981; Purser et al. 2000;
Weng and Zhang 2012). A thinning and quality control procedure is applied using similar quality control procedures as Weng and Zhang (2012) for radial velocity observations, generating radial
50 velocity super observations before applying the coplane algorithm to retrieve the u- and ν-wind components.
Typical NOAA P3 flight parameters – aircraft ground speed of 115 m s-1, radar altitude of
3 km, radar antenna speed of 10 rpm, and radar tilt angle of 20˚ – produce a spacing between consecutive fore scans along the x-axis (Figure 3-1b) of 1400 m. Based on the coplane geometry, the spacing between offset coplane observations along the x-axis is 700 m and along the l-axis is
1100 m. The temporal resolution is highly dependent on the distance from the aircraft track. The coplane observation closest to the aircraft on a given α-plane (~700 m) uses fore/aft scan data that are 10 s apart, but this increases to approximately 360 s by 60 km. Prior to the statistical thinning of the radial velocity data, the flight radials are first quality controlled for noisy data, ground reflection, aliasing, corrected for aircraft velocity and attitude, and corrected for hydrometeor fall speeds by the HRD (Gamache et al. 1997). The processed radial velocities are further quality controlled and statistically thinned before calculating the coplane observations using the following steps:
i. Flight-level data and HRD processed radials are aligned with flight data based on flight
time and radar radial time.
ii. The aircraft relative azimuth and elevation angle are used to calculate θ and α (Figure 3-
1b) for each radar beam, the location (xm, lm, αm) of each radial bin is calculated on each
α-plane, and each radar beam is then binned by α-angle using a user-specified bin width
(Figure 3-3b).
iii. The intersection of each fore/aft scan defines the center of each coplane α-plane bin with
mean values of the intersecting radial bins radar geometry (α,θ) and radar beam flight
data (lat, lon, altitude) used to define the center position (lat, lon, altitude) of the coplane
observation.
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iv. The radial velocities of the closest three radial bins on either side of the fore/aft beam
crossing (Figure 3-3a) and the closest α-plane within the coplane α-plane bin width
(Figure 3-3b) are used for quality control and Vfore and Vaft selection. Within the group of
fore/aft radial velocities, radial velocities are removed that are: missing, have values less
than 2 m s-1 which are indistinguishable from radar noise or have values greater than the
unambiguous radial velocity of the TDR (71 m s-1; both these constraints are in addition
to the HRD real-time radar processing), and are greater than 2x the standard deviation of
the group. Subsequently, if the group has less than 4 fore/aft radial velocity values
remaining, that coplane observation is discarded.
v. The Γ-wind and Ψ-wind are calculated using the median of the quality-controlled fore/aft
radial velocities and rotated to ground-relative u- and ν-wind components.
vi. All coplane observations with fore/aft radial velocity standard deviations 2x the standard
deviation of the radial velocities in each complete fore/aft radar sweep are removed.
vii. All coplane observations that occur during flight track changes of greater than 0.5 o/sec
are removed.
This algorithm is used to generate the simplified coplane observations for both the simulated and the real NOAA P3 TDR data in this study. It should be noted that beam broadening has not been taken into account. Therefore, distances further from the aircraft will represent a larger volume and thus representativeness errors will likely increase with increasing distance from the aircraft track, partially mitigated by the radial velocity super observation process.
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Error Analysis Using a Simulated Tropical Cyclone
Model Setup and Initial and Boundary Conditions
The Advanced Research Weather Research and Forecasting Model (WRF-ARW) v3.6
(Skamarock et al. 2008) is used to generate a convection-permitting simulation of Hurricane Karl
(2010) and for the data assimilation experiments. Four two-way nested domains are used (Figure
3-2) with horizontal grid spacing of 27 km (200x150; D1), 9 km (202x151; D2), 3 km (256x256;
D3), and 1 km (430x430; D4), all with 61 vertical levels. Model physics include the WRF 6-class single-moment bulk microphysics scheme (Hong and Lim 2006), modified Tiedtke cumulus parameterization (Zhang et al. 2011a) for the coarse 27 km domain only, Yonsei University planetary boundary layer scheme (Hong et al. 2006), 5-layer thermal diffusion land surface model, and Rapid Radiation Transfer Model shortwave and longwave radiation schemes (Iacono et al. 2008). The lack of cumulus parameterization in D2 will make little difference owing to the two-way nesting; nearly all convective activity associated with the development of Karl is within
D3 and D4.
The initial and boundary conditions are generated from the Global Forecasting System
(GFS) Final (FNL) Analysis initialized at 1200 UTC 16 September 2010 with 6-h boundary tendency updates over the 36 h simulation duration. A 60-member ensemble is generated using the WRF Data Assimilation (WRFDA) System v3.6 (Barker et al. 2004) for assimilation of airborne radial velocity super observations at 1900, 2000, and 2100 UTC 16 September 2010 using the Penn State University (PSU) WRF ensemble Kalman Filter (EnKF) system described in
Weng and Zhang (2012). The use of airborne radial velocity super observations helps constrain the vortex, simulating a more realistic, rapidly intensifying TC from 0000 to 1200 UTC 17
September 2010 compared with the no data assimilation simulation.
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Generating Simulated Radial Velocities
To simulate the NOAA P3 flight through the simulated TC, a three-leg butterfly-type pattern is flown using the high-resolution mean simulation for D4 starting at 1200 UTC 17
September 2010. The data are updated every 5 min during the simulated flight to account for storm evolution. The simulated aircraft is flown at 115 m s-1 at an altitude of 3000 m, similar to typical NOAA P3 aircraft flight. For simplicity, the attitude parameters (roll, pitch, and drift) are assumed to be 0˚ and the track angle is adjusted for each flight leg heading to generate the simulated butterfly legs.
The simulated TDR uses fore/aft scanning with a tilt angle (θfore = θaft; Figure 3-1d) of
20˚, a rotation rate of 10˚ s-1 with an azimuthal resolution of 0.75o, and a radial gate-to-gate resolution of 150 m, all typical parameters of the operational NOAA P3 TDR. The aircraft relative azimuth and elevation angles of each radial beam are projected into ground-relative coordinates of radar azimuth and elevation angle; the standardized methodology is documented in
Lee et al. (1994). Each radial bin position is corrected for refraction and Earths curvature by applying a standard factor of 4/3 when calculating the radial bin height from the radar.
Using the aircraft position within the simulated ground-relative domain and ground- relative radial beam azimuth γ and elevation ϕ angles, the position of each radial bin is computed and radial velocity νr calculated as:
�� = ��� � ��� � � + ��� � ��� � � + ��� � (� − ��), (3-1)
where u, ν, and w are the model winds and νt the model derived fall speed correction linearly interpolated to the radial bin location. To simulate realistic airborne radial velocities, the model simulated reflectivity (Stoelinga 2005) is calculated at each model grid point, linearly interpolated to the radial bin location, and used to filter out any radial bins with a simulated reflectivity less than 15 dBZ. The model-simulated reflectivity is calculated and linearly interpolated to the radial bin
54 location to compute the mean terminal fall speed of the hydrometeors using the fall speed correction described by Marks et al. (1987). The algorithm is used on the modeled data to estimate the hydrometeor fall speed instead of the diagnostic fall speed calculated in the model microphysics scheme to keep consistency with the processing of the real-time and modeled data.
Testing the Impact of the Simplified Coplane Analysis Observations on Forecast Track and Intensity: Data Assimilation Methodology, Model Setup, and Initial and Boundary Conditions
The WRF model configuration including model physics and dynamics are the same as those used for the error analysis using the simulated TC, but the three two-way nested domains
(Figure 3-2) are slightly modified using horizontal grid spacing’s of 27 km (200x150; D1’), 9 km
(202x151; D2’), and 3 km (256x256; D3’) with 43 vertical levels. A 1 km domain is not used for these experiments.
The initialization, boundary conditions, and data assimilation procedure is the same as those used for the error analysis using the simulated TC, except the experiments are initialized at
0000 UTC on the 16 September 2010 and the National Hurricane Center (NHC) best track position and intensity data is assimilated every six hours to constrain the 60-member ensemble until the airborne observation assimilation at 1900 UTC 16 September 2010.
Simplified Coplane Analysis: Flight-Level and Dropsonde Error Analysis
The horizontal and vertical spatial coverage of the simplified coplane observations are highly dependent on the quality of the fore/aft radial velocity observations. Any violation of the simplified coplane algorithm assumptions or data outside of specific thresholds discussed in the previous section will result in a degradation of quality (e.g. unrepresentative radial velocities
55 contaminating the radial velocities) or complete removal of the retrieved winds since the minimum number of observations in the fore/aft bin is not met. Comparing the flight level horizontal coverage of retrieved winds from the NOAA P3 flight leg 2 on 16 September 2010 between the simplified coplane analysis (Figure 3-4.a) and the HRD analysis (Figure 3-4b), a reduction in coplane observation coverage is evident at large distances perpendicular to the flight track and locations of large flight track heading changes – particularly in the eye. The HRD analysis inherently smoothens the retrieved winds due to the variational technique used in its generation, thus small-scale details are removed. This is evidenced by the lack of detail in the wind speed, especially in the asymmetric maximum in wind speed in the northeast quadrant of
Karl. This smoothing effect was discussed in Didlake et al. (2015) in terms of their global solver.
The radial velocity super observations of Weng and Zhang (2012) have a more complete spatial coverage (Figure 3-4c) compared with that of the simplified coplane analysis due to the stricter quality control constraints on flight track and the need of both a fore/aft scan at each coplane observation location for the simplified coplane analysis.
Flight-Level Wind Validation
The NOAA P3 aircraft have onboard instrumentation to provide in-situ measurements of flight-level winds; useful to compare with retrieved u- and ν-wind components closest to the aircraft track. The 10-s flight-level aircraft in-situ u- and ν-wind observation with the smallest temporal deviation from each coplane and HRD observation that falls within 2 km of the flight track are compared, effectively thinning the flight-level data to the analysis data. Each in-situ measurement is used only once on each α-plane. Flight-level wind comparison with retrieved wind components for pre-genesis flight leg 2 on 13 September 2010 (Figure 3-5) and post-genesis flight leg 2 on 16 September 2010 (Figure 3-6) indicate strong agreement between both airplane
56 relative (Γ- and Ψ-wind) and ground-relative (u- and ν-wind) winds for the α-planes parallel to
Earths surface (α=0˚,180˚) and the HRD analysis. For the second leg of the flight on the 13
September 2010 and 16 September 2010 (heading of approximately 315˚; Figure 3-2), a slight bias of approximately 0.5 m s-1 exists in the Ψ-wind for both pre- and post-genesis flights, which translates into both u- and ν-wind components when rotated. The bias is a result of the airplane heading departure from the track due to the southwest then northeast winds as the plane traverses the TC. This results in an overestimate of the observed winds when the radar beam is corrected for aircraft attitude. The sign of the bias depends on the α-plane and increases in magnitude, up to
1 m s-1 for stronger circulations on 16 September 2010 compared with the earlier flights on the 12 and 13 September 2010. Chong and Testud (1996) showed random errors in aircraft attitude parameters (pitch, roll, and drift) and systematic deviations to the aircraft track can increase errors in the coplane dual-Doppler analysis horizontal winds by as much as 0.5 m s-1.
Focusing on the u- and ν-wind components, Table 3-1a provides the mean error (ME), mean absolute error (MAE), and RMSE statistics for each full flight and combined flights for the simplified coplane analysis; the same statistics for the HRD analysis are presented in Table 3-1b.
The ground-relative wind component ME of all flights for both the coplane and the HRD analyses have a minimal bias and are generally consistent among all flights. The RMSE is generally smaller for the coplane observations compared with the HRD for individual flights and is 0.15-
0.25 m s-1 smaller on average for all NOAA P3 flights into Karl. Given the small bias, a larger variance is present in errors for the HRD retrieved wind components compared to the simplified coplane analysis. The simplified coplane analysis is more accurate compared to the HRD analysis when retrieving the u- and ν-wind components closest to the aircraft. Reasor et al. (2009) presented a flight-level error analysis between 10 flight passes over the TC inner core of
Hurricane Guillermo (1997) and an airborne dual-Doppler analysis following Gamache (1997),
57 the same base method used in the HRD analysis. The bias of the HRD method in Table 3-1 is consistent between studies, although the RMSE of the current study is approximately 1-2 m s-1 less, a substantial improvement. These results elucidate the benefits of the simplified coplane method.
As the α-plane deviates from parallel with the Earths surface, a vertical component is introduced into the Ψ-wind component and will contaminate the rotated ground-relative u- and ν- wind components. An analytical derivation of this geometric error was described in Jorgensen et al. (1996) and corresponds well with the flight-level results. The Ψ-wind is a function of the inverse cosine, thus increasing alpha will reduce the observed along-beam component, underestimating the ground-relative u- and ν-wind components. Comparing the flight-level winds to the coplane u- and ν-wind observations closest to the flight track while varying the α-plane
(Flight Level; Figure 3-7), a large increase in RMSE is observed as the radar beam attains a larger vertical component. The lowest error retrievals are at small �-plane deviations, quickly exceeding
5 m s-1 by +/- 50˚ α-plane deviation; Jorgensen et al. (1996) recommended using observations within +/- 45˚.
Dropsonde Wind Validation
During each flight, the NOAA P3 aircrafts drop multiple dropsondes, an in-situ instrument that can be used to validate radar retrievals below flight level far from the aircraft
(Figure 3-2). Also, aircraft from the GRIP and PREDICT field experiments, flying at higher altitudes, have dropsondes during each NOAA P3 flight that can be used to validate coplane observations at higher altitudes. In general, the RMSE for the simplified coplane analysis retrieved winds are smaller closer to the aircraft track and for smaller α-plane deviations from 0˚
58 and 180˚, but no clear trend in errors exists for coplane observations retrieved farther from the aircraft (Figure 3-7). When calculating errors between the coplane observations and each dropsonde observation, all dropsonde observations are smoothed and less than 2 km away from a specific coplane observation – by design – with a majority between 1-1.5 km (Figure 3-8a). Due to the limited availability of dropsonde for comparison, the maximum perpendicular distance of observations from the aircraft is 22 km, only approximately 1/3 the distance the coplane algorithm assumptions allow. The increase in RMSE for coplane observations retrieved far from the aircraft due to the fore/aft time delay assumption cannot be validated with this data source.
The dropsonde comparison errors for the simplified coplane analysis u- and ν-wind components are normally distributed (Figure 3-8b,c), with a general positive bias in the u- and ν- wind (Table 3-2a) wind components. Calculating errors using the same dropsonde observations for both the simplified coplane analysis (Table 3-2a), and the HRD analysis (Table 3-2b), the
HRD analysis has a smaller RMSE for the u-wind, but similar ν-wind component. The HRD error results of approximately 2-3 m s-1 are in agreement with a synthetic data study by Lorsolo et al.
(2013) who found less than 2 m s-1 RMSE for the tangential wind not including errors introduced by aircraft attitude. Given the disparity in u- and ν-wind dropsonde error statistics for both methods, a future study with more cases will need to be performed to better ascertain accurate dropsonde results. The statistics presented herein should be interpreted as a general estimate of approximately 1.5 to 2.75 m s-1 error in either component.
Error Analysis of the Coplane Algorithm through Simulated NOAA P3 TDR Data
The spatial deficiency in flight-level and dropsonde observations used for validation can be supplemented by simulating a NOAA P3 flight and radar data from a NWP simulation of a
TC. The simulated radial velocities are processed using the simplified coplane algorithm,
59 retrieving the u- and ν-wind components and compared with the true values at each coplane observation location interpolated from the true model simulation used to generate the simulated radials. The errors calculated using the simulated coplane observations do not include errors introduced by aircraft attitude, radar pointing angle, or beam broadening, but provide an estimate of the fall speed assumption and temporal fore/aft timing assumption errors associated with the simplified coplane algorithm.
The simulated radial velocities are generated along three legs of a typical butterfly pattern flown by the NOAA P3 aircraft through a mature TC (Figure 3-9a). The flight track is ground relative, following a fixed path relative to the Earth. The intersection of the three legs is the mean location of the eye during the simulated flight. The WRF simulation of Karl generates a realistic structure of the rapidly intensifying TC, albeit the simulation has a slightly weaker maximum 10- m wind speed and slightly higher minimum seal level pressure than the NHC best track data. The wind speed and u- and ν-wind components at the beginning of the simulated radial velocity period for leg 1 at 0000 UTC 17 September 2010 (Figure 3-9b,c,d) indicate a relatively small eye and mean circulation, both observed with Karl. A spatially similar spiral band structure for the observed storm is present in the simulated radar reflectivity field (Figure 3-9a); the similarity is most notable in the southwest quadrant. Examining the simplified coplane analysis u- and ν-wind components from the simulated radial velocities of leg 1 for the 0˚ and 180˚ α-planes (Figure 3-
10a,b), the algorithm successfully retrieves an approximately homogenous and spatially dense set of observations. The retrieved u- and ν-wind components have a similar spatial pattern as the retrieved simulated reflectivity (Figure 3-10c) used to filter out non-representative low dBZ retrievals. The algorithm correctly captures the clear eye and breaks in-between spiral bands in the southeast quadrant.
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The errors in the simulated u- and ν-wind components can be broken into four primary sources, stemming from (a) the geometric errors of the coplane methodology, (b) the radial velocity super observation process, (c) introduction of fall speed corrections, and (d) the temporal assumptions associated with the use of fore/aft scans at different times. Interpolation errors introduced from the discrete simulation grid are assumed small due to the high horizontal and vertical spatial resolution of the simulation. The analytical geometric errors for airborne dual-
Doppler radar retrievals have been thoroughly documented by Jorgensen et al. (1996), the real data errors in this study closely match the documented analytical results. The radial velocity super observation process may generate a representativeness error due to the use of a median fore/aft radial velocity to describe a radar volume that spans 18 fore/aft range gates (Figure 3-3a,b). The two median values are then used to derive the Γ- and Ψ-wind. For this study, this source of error is not separated from the other three errors. The remainder of this section examines the fall speed and temporal assumption errors.
The spatial distribution of errors for the 0˚ and 180˚ α-planes – these α-planes minimize the contribution of errors due to fall speed contamination – exhibit the spatial error distribution expected from the temporal fore/aft assumption used in the coplane algorithm (Figure 3-10d,e).
Errors increase with increasing perpendicular distance from the aircraft track, a result of temporal representativeness error using aft radials valid further in the relative future compared with the fore scans valid time. It should be noted that since the simulated wind field is updated every 5 min with new simulation data fed to the coplane algorithm, artificial dislocation errors are present due to storm motion. The errors are exacerbated near regions with large gradients in wind speed.
The coplane geometry fully resolves winds parallel to the aircraft track although winds perpendicular to the track have a vertical component. Even though the coplane observations depicted in Figure 3-10 are on horizontal α-planes, each coplane observation is a binning of the
61 closest radials within +/- 1.5o of the specified α-planes. The radial velocity super observation process implicitly introduces a vertical component for the horizontal planes. For flight leg 1, the largest errors in the u-wind (Figure 3-10d) fall to the left side of the aircraft heading and to the right side for the ν-wind (Figure 3-10e) due to the backing from a predominantly easterly to northerly wind on the right side and flipping from an east-southeasterly to a west-southwesterly wind on the left side of the simulated aircraft. Due to the track heading, the simulated aircraft track has many more observations with large Ψ-wind components, manifested as larger errors on the right side of the plane heading when on the northern side and left side of the track when on the southern side of the simulated eye in the retrieved u- and ν-wind fields.
The coplane observations presented in Figure 3-10 use simulated radials that include the
HRD fall speed correction. The higher fall speeds νt (Figure 3-10e) for each coplane observation correspond to higher simulated maximum reflectivity (Figure 3-10c) values, but given the small
α-plane deviations, this only contributes to a small portion of the error in the u- and ν-wind components for low α-plane deviation. Based on the simple geometry of the coplane algorithm, as the α-plane deviation increases from horizontal, the impact of vertical velocities becomes larger in the retrieved winds. Since the purpose of this study is for TC data assimilation purposes, the focus is how the fall speed correction error propagates into the components. Three additional experiments using temporally updated model fields were performed to isolate the impact of fall speed correction on the u- and ν-wind components: assuming no vertical velocity (EXP_NOW), using the model vertical velocity (EXP_PERW), and subtracting the simulated HRD fall speed
(EXP_FALL). The EXP_NOW simulation errors are a result of interpolation and the temporal disparity between fore/aft scans. Examining the impact of perpendicular distance from aircraft track by aggregating all α-planes for all simulated flight legs (Figure 3-11a), EXP_NOW has the
62 lowest error of the temporal simulations, minimizing close to the aircraft track around 0.5 m s-1 and increasing to 1.75 m s-1 by 40 km where the largest disparity in timing arises.
Adding in the vertical motion in both EXP_PERW and EXP_FALL increases the RMSE over 1 m s-1 at all range bins, with the coplane observations within 10 km and large α-plane deviations dominating the error statistics. A drastic increase in RMSE is observed closest to the aircraft, a direct result of the coplane geometry. At larger α-plane deviations, the vertical velocity dominates the radial velocities, but is not retrieved by the coplane algorithm; the w-wind is assumed to be null and the ν-wind error increases by cos-1α. As the range increases from 10 km, valid quality-controlled radial velocities are constrained at smaller α-plane deviations and the errors associated with the null vertical velocity assumption in the coplane algorithm become irrelevant. An additional experiment keeping the fall speed correction, but holding the model fields static at the initial simulation time when retrieving the radial velocities (EXP_FALL_S) isolates the temporal disparity errors, reducing the errors by 2 to 3 m s-1 at all perpendicular distances from the aircraft.
Examining the combined errors of the u- and ν-wind coplane observations by α-plane bins (Figure 3-11b) also exposes the high error dependence on the α-plane deviation. Below an
α-plane deviation of +/- 40˚, the fore/aft temporal disparity is the primary contributor to the error, but the exclusion of the vertical velocity dominates at larger α-plane deviations. The local maxima in all temporal simulations (EXP_NOW, EXP_PERW, EXP_FALL) is close to α-planes parallel to the Earths surface and arises from the increased perpendicular distance from the aircraft, thus an increased time between fore/aft scans. As expected, EXP_FALL_S minimizes at these angles. Breaking apart the EXP_FALL errors by bin and range for the u-wind (Figure 3-
12a) and ν-wind (Figure 3-12b) over all simulated legs, the aforementioned patterns of increasing error by α-plane deviation and perpendicular distance emerges. Strong regional fluctuations in the
63
RMSE appear in the u- and ν-wind error, an artifact of the limited grid spacing impacting the interpolation of model variables and the α-plane binning process.
The RMSEs for the u- and ν-wind components (Table 3-3) of all simulated flight legs quantify the general error associated with the simplified coplane retrieval. The retrievals closest to the simulated aircraft at α-planes of 0˚ and 180˚ at flight level have small errors of approximately 0.02-0.2 m s-1, predominantly interpolation errors. Extending to all coplane observations out to 40 km, the errors jump to approximately 2.2-2.3 m s-1, driven by the inclusion of the temporal fore/aft disparity assumption. Extending to α-plane deviations of +/-50˚ and introducing the impacts of vertical motion minimally increases the RMSE, approximately 0.1 m s-
1. Restricting the perpendicular distance from the aircraft while maintaining the +/-50˚ α-plane deviations slightly decreases the RMSE by approximately 0.1 m s-1.
Impact of Assimilating Coplane Observations on Track and Intensity Forecasts
The simplified coplane analysis only uses geometry and does not require iterative algorithms or minimization techniques to derive the wind field, thus uses minimal computing to generate low uncertainty u- and ν-wind retrievals from the airborne TDR. Additionally, it does not require a full flight of radar data to generate the analysis and therefore can be used in real- time. To test the viability of these observations for TC prediction, a data assimilation experiment using airborne NOAA P3 TDR data of Karl between 1900 UTC and 2100 UTC on 16 September
2010 is performed. Seven experiments initialized at 0000 UTC 16 September 2010 and ending
0000 UTC 18 September 2010 are examined, including a no data assimilation experiment
(NODA), a cycling position and intensity only experiment with NHC best track position and intensity assimilated at 0600, 1200, and 1800 UTC 16 September 2010 to constrain the vortex,
64 and five cycling airborne experiments using position and intensity for the first 18 h and various airborne TDR observations with a prescribed error of 3 m s-1 (error used for the operational radial velocity super observations) unless otherwise stated, including: coplane observations (TDRCP), coplane observations with dynamic error assignment (TDRCPU), fore/aft radial velocity observations used to generate the coplane observations (TDRVR), radial velocity super observations, (TDRSO), and HRD observations (TDRHD).
The error used for the TDRCPU experiment incorporates the error analysis of Section 4 to constrain the error based on the α-plane dependent geometric errors inherent in the coplane methodology and raw radial velocity observations, contamination of the retrieved winds from vertically falling hydrometeors, and the temporal errors associated with the distance from the aircraft perpendicular to the aircraft track. These values are ad hoc, providing an error distribution similar to what was found in Figure 3-7 andFigure 3-12, minimizing closest to the aircraft with a value of 1.5 m s-1 and maximizing furthest from the aircraft at the largest α-plane deviation from
0˚ or 180˚ with a value of 4 m s-1. All airborne data assimilation experiments use coplane observations with maximum α-plane deviation of +/- 20˚ from 0˚ or 180˚ and within 30 km of the flight track as the errors within this data subset are similar across all methods.
For the three flight legs of the 16 September 2010 flight (Figure 3-2), the simplified coplane analysis is applied and the observations thinned to the model grid resolution (3 km), with the observations valid at 1900, 2000, and 2100 UTC 16 September 2010. Using the position of the thinned coplane data, the closest HRD observation and radial velocity super observation is found to each coplane observation along with the corresponding fore/aft radial velocity used to derive the coplane observation, thus TDRCP, TDRCPU, TDRHD, and TDRVR use the same number of observations and TDRSO uses half.
Examining the forecast track, the coplane experiments tracks are close to the actual storm track (Figure 3-13a), making landfall by 1800 UTC 17 September 2010 while TDRSO and
65
TDRVR had much slower translation and TDRHD a more northerly track. The RMSE of the forecast track (Figure 3-13c) indicates improved performance of TDRCP, TDRCPU, and
TDRHD compared to direct radial velocity observations of TDRSO and TDRVR for this case.
Focusing on the maximum 10-m wind speed (Figure 3-13b), all experiments underestimate the intensity at all lead times, but generally capture the strengthening of Karl as it moves into middle of the Bay of Campeche. The TDRVR and TDRCPU forecasts provide realistic estimates of the rapid strengthening of Karl with TDRVR having the best estimates of the intensification and weakening rates. TDRHD performs well from 21 to 27 h and at longer lead times from 36 to 45 h just before and during landfall, but weaker during the strongest stage of the storm, not capturing the rapid strengthening. At longer lead times, the TDRCP and TDRCPU forecasts weaken more rapidly due to their faster translation, interacting with land before
TDRHD, TDRSO, and TDRVR.
The analysis increment – the difference between the analysis and prior model field after the assimilation of observations – provides information about how observations and associated uncertainties in the observations and prior model field correct the prior model field. Figure 3-14 shows the difference in the analysis increment at a height of approximately 2250 m for the first data assimilation cycle between the TDRCPU - TDRSO and TDRCPU - TDRVR. Examining the difference in analysis increment between TDRCPU - TDRSO, the benefit of using both u- and ν- wind at each observation point is evident, with a stronger vortex (Figure 3-14a,b) and more prominent warm core (Figure 3-14c) in the analysis. This same trend continued through the remaining cycles (not shown) and accounts for the weaker vortex, evident in Figure 3-13b, with a much weaker TC for TDRSO. However, even though the TDRSO analysis intensity was inferior to all other airborne experiments at 2100 UTC 16 September 2010, the model dynamics were able to generate a coherent and realistic vortex over the first 6 h of the forecast and produce a competitive forecast. The inclusion of two independent fore and aft radial velocities at each
66 observation point in TDRVR (Figure 3-14d,e,f) substantially improves the vortex in the analysis field. The differences in analysis increments cannot be used to statistically diagnose large-scale differences between the two observation types since it is only one case, but the additional independent information provides a more representative vortex in the analysis, improved track, and improved intensity forecast compared to the operational radial velocity super observations.
The RMSE of maximum 10-m wind speed in Figure 3-13c indicates that the experiments assimilating direct radial velocity observations reduces the intensity forecast error over experiments assimilating processed u- and ν-wind components.
For this particular case, the assimilation of u- and ν-wind components – particularly the user-specified error TDRCPU experiment – can improve track forecasts over radial velocities.
For intensity, the experiments assimilating radial velocities provide improved 10-m wind speed forecasts with two independent radial velocity observations at each point providing the lowest error intensity forecast. It should be noted that the reduction in track and intensity forecast error between the TDRCPU and TDRCP experiments compared with the TDRHD and TDRSO experiments was not statistically significant. A multiple-season study is required to definitively address the improvement in forecast errors and is beyond the scope of this study. However, these findings are in agreement to those of Li et al. (2014) who found that assimilating radial velocities enhance convective development and better resolve the inner core structure of a TC improving the intensity forecast and assimilating both u- and ν-wind components improves the environmental flows surrounding the TC inner core, improving the track forecast.
Concluding Remarks
The coplane dual-Doppler technique is applied without the use of the mass continuity equation to quality-controlled airborne fore/aft radial velocities from the NOAA P3 TDR to
67 derive low error estimate u- and ν-wind components. This simplified coplane analysis requires minimal computational resources and does not require a full flight leg (or multiple flight legs) to calculate retrievals, thus it could be applied in real-time. The coplane algorithm provides two independent observations at a given point in space, providing two pieces of information about the wind field, estimating both along- and cross-beam wind information. The error is quantified in the retrieved along- and cross-beam winds through verification against independent in-situ flight- level and dropsonde observations and through simulated observation experiments with a convection-permitting NWP model for Hurricane Karl (2010). The WRF model simulation provides a controlled error analysis, focusing on the errors induced by the vertical fall speed correction assumption and temporal fore/aft valid time assumption. For comparison, in-situ flight- level and dropsonde observations are also used to generate errors for the HRD variational analysis. The temporal errors in the coplane retrieved u- and ν-wind field due to the time lag between fore/aft scans and a systematic analysis of the impact of the vertical velocity correction on the u- and ν-wind field were the main focus of the study, not documented in previous literature on airborne dual-Doppler retrievals.
A super observation algorithm was described and applied to the Doppler radial velocity observations to quality control the derived u- and ν-wind fields. The vertical hydrometeor fall speed correction was used to remove vertical fall speed contamination from the radial velocities before the coplane dual-Doppler projection equations were applied. Due to the high spatial resolution of airborne radial velocity data, operationally, the data are thinned before ingesting into a NWP model.
Validating the coplane u- and ν-wind observations against flight-level and dropsonde data for all pre- and post-genesis NOAA P3 flights into Hurricane Karl (2010) showed a strong dependence of error on α-plane deviation (Jorgensen et al. 1996). The simplified coplane analysis
68
RMSE ranges from 1.5 m s-1 for flight-level data closest to the aircraft track to 2.75 m s-1 for dropsonde validation for α-plane deviations of +/- 50˚ from horizontal. The HRD variational dual-Doppler analysis showed a slightly higher RMSE error of approximately 1.75 m s-1 for flight-level data, hypothesized to be consequence of the HRD analysis using mass continuity as a constraint to solve for the full three-dimensional wind field, introducing additional uncertainty.
The dropsonde validation showed a lower RMSE for the u-wind retrieval, but similar ν-wind retrieval ranging from approximately 2.0 to 2.5 m s-1. Common in both coplane and HRD validation is the dependence of RMSE errors on the strength of the storm. The pre-genesis storms generally have smaller RMSE errors than the post-genesis storms, largely a result of the temporal fore/aft radial assumption.
A simulated NOAA P3 flight for the post-genesis Karl was examined to fill in gaps due to limited in-situ observations. It validated the strong dependence of error on α-plane deviation and helped quantify the error in the zero vertical velocity and temporal fore/aft valid time assumptions. At perpendicular distances from the aircraft of less than 20 km, the errors are small and generally less than 1.5 m s-1. As the distance increases, the RMSE rises to 2.0-4.0 m s-1.
The real and simulated radial velocity validation of the coplane algorithm showed that the coplane algorithm u- and ν-wind components are best used within +/- 50˚ deviation in α-plane to minimize the impact of fall speed errors and within 40 km of the aircraft to minimize temporal fore/aft errors. For purposes of assimilating the coplane u- and ν-wind observations into NWP models for TC initialization, errors should be assigned with values ranging from a minimum of approximately 1 to 1.5 m s-1 close to the aircraft and small α-plane deviations to approximately 4 to 5 m s-1 at higher α-plane deviations (+/- 50˚) and further distance from the aircraft (40 km).
Performing a trial data assimilation experiment with the cycling PSU-WRF-EnKF for a
NOAA P3 flight into Karl on 16 September showed that assimilating simplified coplane analysis
69 observations provided similar improvements in track and intensity forecasts compared to assimilating similar HRD analysis observations, radial velocity super observations, and both fore/aft radial velocities for a single TC case. Applying a user-specified error based on the error investigated in this study improved the track forecast when applied to the coplane observation, however, the improvements were not statistically significant. The results of this single case study suggest that it may be beneficial to include additional independent observations at each location compared to current operational radial velocity super observations to improve track forecasts, but additional case studies are needed. The results also suggest it may be beneficial to combine both u- and ν-wind and radial velocities to utilize both their strengths to improve both track and intensity forecast.
Future work needs to be performed to extend the analysis of the potential benefits of using the simplified coplane observations described herein for TC vortex initialization in NWP models. A systematic comparison of analysis and forecast errors needs to be performed for a number of TC seasons, assimilating the simplified coplane analysis observations along with previously documented retrieval methods (e.g. Jorgensen et al. 1996; Chong and Testud 1996;
Gao et al. 1999) and radial velocity super observations. The dynamic error specification should be further evaluated and additional errors included such as storm motion and beam broadening for an optimum configuration of parameters to minimize the error in TC analyses and forecasts. In addition, it would be worth exploring if an optimal combination of radial velocity and u- and ν- wind components could be found that takes into account the benefit of both observations types. Li et al. (2014) found using both observation types can improve TC forecasts over each observation type individually, but they did not combine both observation types in one assimilation step.
Finally, the observations should be tested using variational data assimilation methodologies to assess any benefit in the variational framework over the purely statistical EnKF framework.
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Chapter 3 Tables
Table 3-1: Individual and combined flight-level mean error (ME), mean absolute error (MAE), and root- mean-squared error (RMSE) of the retrieved u- and ν-wind components of the (a) simplified coplane analysis and (b) HRD analysis compared with NOAA P3 flight-level winds.
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Table 3-2: Individual and combined dropsonde mean error (ME), mean absolute error (MAE), and root- mean-squared error (RMSE) of the retrieved u- and ν-wind components of (a) the simplified coplane analysis and (b) HRD analysis compared with available dropsondes from NOAA P3 flights, GRIP, and PREDICT missions.
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Table 3-3: Simulated simplified coplane analysis mean error (ME), mean absolute error (MAE), and root- mean-squared error (RMSE) of the u- and ν-wind components for flight level (closest coplane observations to the simulated flight track), all coplane observations on parallel planes with the simulated aircraft wings (alpha = 0˚, 180˚), coplane observations available between +/- 50˚ α-plane deviations and perpendicular distance less than 20 km from flight track, and coplane observations available between +/- 50˚ α-plane deviations at all perpendicular distances.
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Chapter 3 Figures
Figure 3-1: Spatial configuration of a plane flying north for (a) a dual-beam airborne fore/aft scan of radial velocities at an arbitrary radial distance, each dot represents a simulated radial velocity; (b) the coplane scanning geometry in natural cylindrical coordinates (x,l,α); (c) fall speed component of radial velocity along an arbitrary coplane point (xm,lm,αm); (d) retrieved wind components along track (Γ ) and perpendicular to track (Ψ ), geometrically derived from Vfore and Vaft with beam orientation (θfore,α) and (θaft,α), respectively.
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Figure 3-2: Diagram of WRF domains used for the Hurricane Karl Observation Simulation Experiment (black; D1-D4), WRF domains used for ensemble Kalman Filter data assimilation experiments (red; D1’- D3’), NOAA P3 flights on September 12, 13, and 16 with numbered flight legs (blue shaded lines), and dropsondes used for coplane and HRD analysis validation (pink dots). Note: D1 and D1’ are the same domains.
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Figure 3-3: Schematic of an arbitrary radial velocity fore/aft bin indicating the geometric center (black x), the constituent fore/aft radial velocity observations (gray dots), and volume swept out by the coplane observation (yellow shading).
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Figure 3-4: Wind speed retrievals from the (a) simplified coplane analysis and (b) HRD analysis, and (c) radial velocity super observations from flight leg 2 of the 20100916H NOAA P3 mission.
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Figure 3-5: Flight level comparison of closest coplane observations to the flight track (< 2000 m) on α- plane 0˚, 180˚ (blue colored lines), HRD analysis wind speeds closest to flight level (~3km) and flight track (magenta line), and flight level values (black line) from the aircraft of (a) wind speed, (b) u-wind, (c) ν- wind, (d) gamma, (e) psi, and (f) wind direction from flight leg 2 of the 20100913H NOAA P3 mission.
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Figure 3-6: Same as Figure 3-5, but from flight leg 2 of the 20100916H NOAA P3 mission.
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Figure 3-7: Root-mean-squared error binned by α-plane bin and distance from flight track for (a) u-wind and (b) ν-wind. Flight Level indicates wind component comparison of closest coplane observations to the flight track (< 2000 m) for all available NOAA P3 flights (20100912I, 20100913I, 20100913H, and 20100916H) and Dropsonde indicates comparison of closest coplane observations to the available dropsonde observations for all available NOAA P3 flights and GRIP/PREDICT missions.
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Figure 3-8: Distributions of (a) distance between dropsonde observations and coplane observations, (b) u- wind errors, and (c) ν-wind errors used to calculate dropsonde comparison statistics.
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Figure 3-9: WRF simulated fields of (a) maximum radar reflectivity, (b) 10-m wind speed, (c) 10-m u- wind and (d) 10-m ν-wind at 0000 UTC 17 September 2010. The black arrows in panel (a) indicate the flight track legs used to simulate coplane observations.
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Figure 3-10: WRF model simulated retrieved coplane observations of (a) u-wind, (b) ν-wind, (c) maximum reflectivity, (d) u-wind error, (e) ν-wind error, and (f) HRD fall speed for flight leg 1 on α-plane 0˚, 180˚.
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Figure 3-11: Root-mean-square error of the simulated simplified coplane analysis by (a) perpendicular distance from aircraft track and (b) α-plane bin for all simulated flight legs using no vertical component (EXP_NOW; cyan), model w as vertical component (EXP_PERW; blue), HRD terminal fall speed correction to vertical component (EXP_FALL; black), and HRD terminal fall speed correction to vertical component without temporal change in model fields (EXP_FALL_S; black asterix) when calculating the simulated radial velocity.
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Figure 3-12: Root-mean-squared error binned by α-plane bin and distance from simulated flight track for (a) u-wind and (b) ν-wind.
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Figure 3-13: PSU-WRF-EnKF data assimilation experiments forecast (a) track, (b) maximum 10-m wind speed [m s-1], and (c) root-mean-squared error of track [km] and maximum 10-m wind speed [m s-1] validated against the National Hurricane Center best track data from 0000 UTC to 1800 UTC 17 September 2010. All experiments assimilate NHC best track and intensity for the first 18 hours, except the no data assimilation experiment (NODA), and the remaining simulations assimilate airborne observations including: coplane observations (TDRCP), coplane observations with error specified by distance from track and α-plane (TDRCPU), HRD analysis observations (TDRHD), radial velocity super observations (TDRSO), and raw fore and aft radial velocities used to derive the coplane observations (TDRVR). The NODA and hurricane position and minimum sea level pressure (PI) only experiments are included for reference.
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Figure 3-14: Model increment (analysis minus background) difference for the first airborne TDR data assimilation cycle at 1900 UTC 16 September 2010 on WRF eta level 10 (~2250 m) for (a,d) u-wind, (b,e) ν-wind, and (c,f) potential temperature between TDRCPU and TDRSO (left column) and TDRCPU and TDRVR (right column).
87 Chapter 4
A Multiple-Model Ensemble Examination of the Probabilistic Prediction of Hurricane Sandy (2012) and Hurricane Edouard (2014)
Introduction
Every year tropical cyclones (TCs) take thousands of lives and cause billions of dollars of insured and economic losses. The substantial impacts on property and life make improvement of
TC forecasts, particularly TC track, intensity, and inland flooding, crucial for public safety.
Improving TC forecasts will require a combination of improved understanding of TC dynamics and inner-core processes and advanced dynamical weather models that incorporate remote and in- situ observations with advanced data assimilation techniques.
Many weather agencies, including the National Center of Environmental Prediction
(NCEP), the Geophysical Fluid Dynamics Lab (GFDL), and the United States Navy, run independent TC tuned regional dynamic and statistical forecast models along with global models to forecast track and intensity of high impact storms. Dynamic models explicitly consider the physics of the atmosphere, having complex methods to numerically represent what is occurring in the atmosphere. Each model has its own dynamic core (hereafter model-core), including, but not limited to, the prognostic variables to represent the atmospheric state, formulations of fundamental equations that govern how the atmosphere behaves, the model map projection, the model horizontal and vertical grid structure, and the model numerics.
Additionally, physical parameterizations that resolve sub-grid scale processes not explicitly resolved by the fundamental equations are formulated for each model-core. These physical parameterizations include shortwave and longwave radiation schemes, microphysical processes, cumulus parameterization for coarse model grids, planetary boundary layer (PBL) schemes, and surface physics representing moisture and energy fluxes. When parameterizing each
88 sub-grid scale physical process, various assumptions and levels of complexity can be chosen to generate various formulations of the physical parameterization. The choice of physical parameterization can have a substantial impact on TC structure, modifying many facets of the TC formation, evolution, and structure that ultimately impact the forecast track (e.g., Fovell and Su
2007; Fovell et al. 2009; Fovell et al. 2010; Bu et al. 2013), and/or intensity (e.g., Sundqvist
1970; Willoughby et al. 1984; Wang 1996; Braun and Tao 2000; Green and Zhang 2013).
The model errors induced by the model-core and/or physical parameterizations can be reduced through the use of ensemble forecasts. Generally, a consensus or ensemble of ensemble forecasts – either the same model-core while varying the initial conditions and/or model physics or a combination of multiple model-cores – provides a superior forecast over any individual ensemble member or individual independent model. The ensemble mean of a scalar forecast variable is the simplest parameter derived from the ensemble and generally provides the best- forecast estimate (e.g., Goerss 2000; Sampson et al. 2008), cancelling out random errors during the averaging process. Individual members of single-core ensembles are often weighted (i.e. corrected) during the averaging process to account for biases in the single-core model. The ensemble spread provides information about the uncertainty in the forecast (e.g., Tracton and
Kalnay 1993; Palmer 2002), measuring the confidence surrounding the ensemble mean.
For any ensemble prediction system, it is important that the ensemble spread is large enough to cover the forecast error so the ensemble is not underdispersive – the individual ensemble members trajectories do not correctly capture the forecast error. The ensemble spread - error relationship can be improved by reducing the ensemble mean forecast error or increasing the spread through various ensemble techniques including multi-core ensembles, single-core multi- physics ensembles, and/or stochastic physics ensembles. To account for deficiencies in the initial conditions and model error, previous studies have looked at the performance of single-core multi- physics or perturbed physics ensembles to account for: (1) errors in physical parameterizations
89
(e.g., Wang and Johnson 2012, Rao and Srinivas 2014), single-core single-physics ensembles with perturbed initial conditions to account for initial condition uncertainty (e.g., Yamaguchi et al. 2009; Yamaguchi and Majumdar 2010; Majumdar and Finocchio 2010), (2) both corrected and uncorrected ensembles of single-core single-physics ensembles to account for initial condition and/or model error (e.g., Leslie and Fraedrich 1990; Krishnamurti 1999; Aberson 2001;
Vijaya Kumar et al. 2003; Qi et al. 2013), and (3) stochastic physics to account for model error or the deterministic properties of physical parameterizations by injecting spatially and temporally correlated stochastic perturbations (Shutts 2005; Palmer et al. 2009) into the forecast model during integration.
The current study examines the impact of model error on ensemble forecasts of TC track and intensity, using identical initial conditions to initialize three state-of-the-art TC tuned regional models. To the best of the author’s knowledge, no previous study has tried to independently quantify the propagation of model error using multi-core ensembles while controlling for initial condition error between models. This study further analyzes the impact of model physical parameterizations and stochastic physics using a single-core to highlight the dominance of the model physical parameterizations in evolving the ensemble mean and spread. The main questions addressed in this study are: (1) How does the evolution of the ensemble mean and spread with the same initial conditions compare using different model-cores?, (2) Is a single-core multi-physics ensemble sufficient for representing model uncertainties in TC prediction, or is there a benefit using a multi-core ensemble?, and (3) Can a single-core single-physics ensemble with stochastic physics and/or inflated initial condition uncertainty impact ensemble mean and spread similar to a multi-physics ensemble?
This Chapter is structured into 4 sections. Section 2 provides an overview of the TC case studies, regional TC tuned models and physical parameterization configurations, initial and boundary condition generation methodology, single-core model physical parameterization
90 configurations, and stochastic physics configurations. Section 3 presents results and discusses the evolution of the ensemble mean and spread between single-core ensembles, multi-core and single-core multi-physics ensembles, single-core stochastic physics ensembles, and inflated initial condition ensembles for both TC case studies. Section 4 provides a summary and concluding remarks.
Methodology
Cases in Study: Hurricanes Sandy (2012) and Edouard (2014)
The TCs chosen for this study were picked for their unique track and/or intensity characteristics: Hurricane Sandy (2012) and Hurricane Edouard (2014). Hurricane Sandy (2012) is known for its track forecast sensitivity with its abnormal northwest track towards the US mid-
Atlantic during its journey up the east coast, a forecast challenge for both global and regional models. Hurricane Edouard (2014) was the first major hurricane in the Atlantic basin since
Hurricane Sandy (2012) that had a consistent strengthening that was well-observed with multiple airborne in-situ and remote platforms (NOAA P-3, NOAA Gulfstream IV, and NASA’s high- altitude Global Hawk drones during the Hurricane Severe Storm Sentinel (HS3) field experiment).
Sandy first developed into a tropical depression at 1200 UTC 22 October over the northwest Caribbean sea, accelerating north-northwest under the influence of an upper-level trough digging over the northwest Caribbean sea (Blake et al. 2013). It was named at 1800 UTC
22 October and made landfall in Jamaica as a Category 1, and Cuba as a Category 3 hurricane, before moving out over the Bahamas and turning northwestward, slowly weakening to a tropical storm by 0000 UTC 27 October. Sandy turned northeast just north of the Bahamas and
91 strengthened back into a Category 1 hurricane, paralleling the eastern seaboard, but made an abnormal turn to the northwest by 1200 UTC 29 October, briefly intensifying back into a
Category 2 hurricane.
The official NHC forecast guidance for Sandy’s track was well below the mean official errors for the previous 5-yr period, with the Global Forecasting System (GFS) ensemble performing slightly better than official guidance for the first 48 h and the European Center for
Medium-range Weather Forecasts (ECMWF) through 72 h (Blake et al. 2013). The ECMWF ensemble performed remarkably well in predicting the abnormal track of Sandy at 4- to 5-days out, with a large number of the ensemble members making the northwestward turn back towards the east coast 5-days out, while the GFS had most of the members heading out into the Atlantic.
In this study, forecasts were initialized at 0000 UTC 26 October when the storm was moving towards the northwest over the Bahamas, when ensemble forecasts had both land falling and out- to-sea solutions.
Edouard developed into a tropical depression at 1200 UTC 11 September and was subsequently named at 0000 UTC 12 September. The storm tracked around the southwestern side of a deep-layer subtropical ridge, embedded in an environment with favorable upper-level winds and sea-surface temperatures, but drier-than-normal mid-level air (Stewart 2014). The storm slowly strengthened in this environment, undergoing rapid intensification (RI)6 from 0600 UTC
14 September to 0600 UTC 15 September, increasing wind speed 25 knots; its peak intensity of
105 knots was reached at 1200 UTC 16 September. In this study, forecasts were initialized at
1200 UTC 11 September when the storm was fairly weak, and 0000 UTC 14 September, just prior to rapid intensification.
6 Rapid intensification (RI) in the Atlantic basin is commonly defined as a 25 knot increase in wind speed within 24 hours (Kaplan and DeMaria 2003).
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Models
This study uses pseudo-operational implementations of three state-of-the-art non-
hydrostatic TC tuned regional models, including the Navy’s Coupled Ocean/Atmospheric
Mesoscale Prediction System for Tropical Cyclones (COAMPS-TC; Hodur 1997), the Hurricane
Weather Research and Forecasting model (HWRF; Bernardet et al. 2013), and the Weather
Research and Forecasting (WRF-ARW; Skamarock et al. 2008). The 2014 Hurricane Forecast
Improvement Project (HFIP) configuration of COAMPS-TC, the 2013 pseudo-operational
configuration of HWRF, and the 2014 PSU-WRF-EnKF real time forecast system (Zhang et al.
2009, 2011b; Weng and Zhang 2012) configuration of WRF-ARW are used as the control
ensembles for each individual model-core. The model configurations control for differences
between model-cores, reducing sources of uncertainty in forecasts by using only the atmospheric
component of the model (the operational version of COAMPS-TC uses a 1D ocean model and
HWRF uses a 3D ocean model), fixing the sea surface temperatures in all models from the initial
input global data, and running COAMPS-TC at a higher horizontal grid resolution to match the
WRF-ARW configuration. All models use three domains, two-way nested, with vortex
following inner domains. The domain configurations can be found in Table 4-1. Both WRF-
ARW and COAMPS-TC are on an Arakawa C-grid, use a Mercator projection, and use a fixed
outer domain. HWRF is on an Arakawa E-grid, uses a rotated lat-lon projection, and adjusts the
outer domain to be centered on the TC at forecast initialization. The grid setup for Edouard at
1200 UTC 11 September can be found in Figure 4-1.
Each model has physical parameterizations that represent unresolved sub-grid scale
processes with some schemes similar across model-cores and others developed for a particular
model-core. The lack of consistent physical parameterizations across all model-cores is another
factor in choosing pseudo-operational settings that are tuned for TC forecasting (Table 4-1).
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More specific to each model-core are the numerical solver for the various prognostic variables
and model equations, model grid staggering and map projections, model vertical coordinates,
and treatment of diffusion and advection, among other model specific settings (for COAMPS see
Hodur 1997; for HWRF see Bernardet et al. 2013; for Skamarock et al. 2008). The tunable
model-core settings are set to their operational versions for this study.
Initial and Boundary Conditions
This study examines the evolution of initial condition and model error within and between model-cores, thus it is imperative that the initial conditions be identical and the boundary conditions as close as possible for each model-core, given the grid and domain limitations. To accomplish this task, each model is cold-started using the model-core specific initialization routine (e.g., real, real_nmm, or coama) to interpolate identical global model input data onto the model specific grids and generate boundary conditions for the forecast.
To generate the ensemble initial conditions, the Global Data Assimilation System
(GDAS) 0.5˚x0.5˚ lat-lon surface and standard pressure level analysis at a given initialization time is merged with the 60-member Pennsylvania State University WRF-ARW ensemble Kalman filter (PSU-WRF-EnKF; Weng and Zhang 2012) real-time 9- and 3-km analysis WRF domains on a common 0.1˚x0.1˚ lat-lon horizontal grid7 on standard vertical pressure levels. The PSU-
WRF-EnKF model output are linearly relaxed from 300- to 900-km from the vortex center8 to the
GDAS model output providing a smooth transition in the far-field TC environment. The PSU-
WRF-EnKF data provides 60 high-resolution variations of a flow-dependent TC vortex in the initial conditions with the GDAS data allowing for identical boundaries far from the TC-vortex in
7 0.1˚ horizontal spacing was chosen to reduce interpolation errors, but stay within computing resource constraints. 8 The PSU-WRF-EnKF only assimilates observations within 800 km of the TC center.
94 each ensemble. Given the grid and domain limitations for each dynamic core, the GDAS analysis at 0 h and the GFS deterministic forecast from 6-120 h is used for each ensemble member to help control for uncertainties when defining each dynamic cores boundary conditions. With this configuration, the TC circulation and near TC environment ( < 900 km from TC center) are perturbed for each ensemble member while the larger-scale, synoptic environment is identical.
Single-Core Multi-Physics and Stochastic Physics Sensitivity Experiments
To examine the impact of using a single-core with varying physical parameterizations, the APSU physical parameterization configuration within the WRF-ARW model was systematically modified. The cumulus parameterization (CP), microphysics scheme (MP), planetary boundary scheme (PBL), shortwave and longwave radiation schemes (RAD) and surface flux settings (SFC) were all changed incrementally from “APSU-like” (APS1) to
“HWRF-like” (APS5). The physical parameterization differences from APSU are listed in Table
4-2. The physics were additively modified, e.g., modifying SFC settings (APS1), modifying SFC settings and MP (APS2), modifying SFC settings, MP, and RAD (APS3), etc., to systematically sample physical parameterization schemes between the “APSU-like” and “HWRF-like” configurations.
To examine the impact of stochastic physics on ensemble mean and spread, the APSU ensemble configuration is modified with spatially and temporally correlated perturbations using either the Stochastic Kinetic Energy Backscatter Scheme (SKEBS; Shutts 2005; Berner et al.
2009) or Stochastically Perturbed Parameterization Tendencies (SPPT; Palmer et al. 2009;
Romine et al. 2014; Berner et al. 2015). SKEBS is an additive scheme, stochastically perturbing the model state, while SPPT is a multiplicative scheme, stochastically perturbing the physical parameterization tendency.
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SKEBS accounts for a model’s shortcoming in reproducing the turbulent energy cascade from unresolved sub-grid scale processes. This scheme generates random temporal and spatial stochastic forcing patterns and adds the perturbations to the rotational u- and v-wind components and potential temperature. For this study, the default configuration in WRF v3.6 is used (Table 4-
3) and the horizontal perturbations are constant with height.
SPPT accounts for the deterministic characteristic of existing sub-grid scale physical parameterization schemes, generating a probabilistic solution by multiplying the sub-grid scale physical parameterization total tendency with a stochastic forcing pattern. The pattern generator is similar to SKEBS. The pertinent SPPT parameters are listed in Table 4-3. Like SKEBS, the horizontal perturbations are assumed constant with height.
Results and Discussion
Inter-Model Comparison: Evolution of Ensemble Track and Intensity
As a first step, it is important to see if each regional TC model can evolve identical initial conditions to produce similar TC forecasts. A 20-member sample (60 member ensemble thinned for plotting clarity) of the 5 day ensemble track and maximum 10-m wind speed (hereafter intensity) forecasts for APSU, HWRF, and COTC are shown in Figure 4-2 and Figure 4-3, respectively, for Sandy and Figure 4-4 and Figure 4-5, respectively, for Edouard. The figures indicate that each pseudo-operational model can generally capture the track and spread for both cases. Systematic errors become evident at longer lead times. Recall that each model is initialized from the same blended global and regional analysis, thus, the evolution differences can be attributed to the different physical parameterizations and dynamical configurations.
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The evolution of the ensemble tracks for Sandy in Figure 4-2a are consistent across the three model-cores during the first 60 h, with systematic errors evident at longer lead times as
Sandy begins to curve back towards the northwest. The systematic track errors at longer lead times become clear when examining the ensemble means (Figure 4-2b). The COTC ensemble members track further east compared to APSU members, with HWRF ensemble members falling in between and remarkably close to the NHC best track. The HWRF ensemble is generally more diverse at longer lead times, covering both the APSU and COTC solutions. Overall, it is encouraging that all three model-cores capture the complex track of Sandy.
The ensemble intensity forecasts for Sandy are consistent before landfall (~96 h).
Afterward, the further east displacement of the COTC ensemble keeps the ensemble over water longer, not weakening as quickly as the APSU and HWRF ensembles (Figure 4-3a). Besides the low wind speeds of HWRF at initialization9, COTC generally has a lower intensity over the first
48 h compared with HWRF and APSU. At longer lead times prior to landfall (~60 h to 96 h), all three model-cores capture the secondary intensification of Sandy, evident in the ensemble mean
(Figure 4-3b), although APSU and COTC are 12 h early and slightly weaker compared with the
NHC best track and HWRF is 6 h late and slightly stronger.
The ensemble evolution of intensity for Edouard provides insight into the less predictable internal TC dynamics and convective processes handled by each model. The APSU and COTC solutions (Figure 4-5a) have a similar evolution throughout the 5-day forecast, strengthening the
TC with similar mean magnitudes (Figure 4-5b). The HWRF intensities have a much larger spread, with many not strengthening, and the strongest member remaining weaker than the NHC best track and many of the APSU and COTC members. The systematic low wind speed error is clearly evident in the ensemble mean. For this case, the pseudo-operational HWRF configuration
9 HWRF does not use the diagnosed 10-m wind speeds from the initial conditions during cold-start initialization, unlike APSU and COTC.
97 is not conducive for convective development, reducing the strengthening and maximum intensity of the TC. There is an apparent link between the intensity and track for this case with the weaker members tracking further west (Figure 4-4a). The weaker members in all ensembles track further west with the weak members in HWRF having the largest west track displacement. This relationship is evident in the ensemble mean (Figure 4-4b).
All three single model-core ensembles can generally reproduce the mean track and spread at earlier lead times, generally < 48 h, but the range of solutions from all three models cover a larger solution space than any single-core ensemble at longer lead times. Systematic errors in the ensemble track are evident at longer lead times for Sandy and for both track and intensity for
Edouard.
Inter-Model Comparison: Multi-Core Ensemble
To objectively quantify the relationship between the single-core single-physics ensembles and a multi-core ensemble, a 60-member ensemble (MCOR) is generated by randomly sampling
20 ensemble members without replacement from the APSU, HWRF, and COTC ensembles. The absolute error of the ensemble mean (hereafter error) and the spread of a multi-core ensemble provide an objective measure of the benefit, if any, of a multi-core ensemble. It is unwise to make conclusions about the spread/error relationship from case studies as the climatological errors and flow dependent forecast errors are unknown for the model configurations in this study, but analyzing the relative spread/error relationships between the single-core and multi-core ensembles provide useful insights for ensemble design. The track and intensity ensemble spread and error for each individual model and the MCOR ensemble is shown for Sandy in Figure 4-6a,b and Edouard in Figure 4-7a,b. The NHC best track is used for verification with a perfect observation assumption. Both figures show that the single-core ensemble forecasts for Sandy and
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Edouard are favorable with a small track error and the ensemble spread of all ensembles typically as large or larger than the error.
The intensity for all three single-core ensembles and the MCOR ensemble perform similarly (Figure 4-6b) for Sandy with no systematic difference between MCOR and the individual ensembles, except post landfall. For track, MCOR generally performs as well or better than the individual ensembles. At shorter lead times up to approximately 36 h, the ensemble spread of APSU, HWRF, and COTC and MCOR are all similar. After this period, MCOR covers a larger solution space, reflected in the increased combined ensemble spread. After APSU and
HWRF make landfall, the inclusion of the easterly tracks of COTC in MCOR shift the ensemble mean east, increasing the error.
Examining the ensemble spread and error for Edouard, MCOR has the largest spread in intensity (Figure 4-7b) after approximately 24 h compared with the component ensembles. A large divergence in the component ensembles after 48 h is observed with continued strengthening all APSU and COTC ensemble members, but not clear with HWRF. The spread of APSU and
COTC is generally consistent for the entire forecast, but a large range of intensity solutions for
HWRF exists after approximately 48 h with the ensemble spread and error continually increasing until the end of the forecast. The combined MCOR ensemble performs the best for the first 72 h with the smallest error and largest spread over any individual component model, but is systematically degraded after approximately 72 h by HWRF. For operational purposes, a component model of a multi-core ensemble cannot be excluded when underperforming, as the verification is unknown. For Edouard, the use of the multi-core ensemble forecast at long lead times is worse compared with using the individual APSU and COTC ensemble mean forecasts.
The track ensemble spread for Edouard (Figure 4-7a) is fairly consistent for all members within approximately 48 h, with a continued increase in spread for HWRF at longer lead times.
Including the HWRF model in the MCOR ensemble substantially increases the MCOR spread.
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For shorter lead times (< 48 h), the MCOR ensemble performs similarly to the better performing component single-core ensembles, but at longer lead times, performs better than both APSU and
HWRF. The component HWRF westward members and COTC further eastward members average out to a generally improved track forecast, similar to what was seen with Sandy. MCOR also has the largest ensemble spread at longer lead times, but whether this large of uncertainty is needed for TC ensemble prediction is beyond a single case study and beyond the scope of this study.
Overall, common between both case studies, the MCOR ensemble generally has the largest spread in both track and intensity compared with any component model at longer lead times, but the error is case and metric specific. The consistent benefit of increased ensemble spread at all lead times is evident for the multi-core ensemble.
Inter-Model Comparison: Multi-Physics Ensemble
Model physical parameterization schemes can strongly influence TC forecasts of intensity (e.g., Lord et al. 1984; Wang 2002; McFarquhar et al. 2006; Zhu and Zhang 2006) and track (e.g., Fovell et al. 2010; Bu et al. 2013). Given that APSU, HWRF, and COTC ensembles have different dynamic cores and physical parameterizations, it is worth exploring if a single-core ensemble with systematically varying physical parameterizations to represent two (limited by available physics parameterizations in WRF-ARW) of the component MCOR ensembles can perform similarly to the MCOR ensemble. To begin investigating this question, the WRF-ARW model is used to generate sensitivity experiments by varying the model physical parameterizations to range from “APSU-like” (APS1) to “HWRF-like” (APS5); the model physical parameterizations differences from APSU are outlined in Table 4-2. Also, a single-core
100 multi-physics 60-member ensemble (MPHY) is constructed by randomly sampling 12 members, without replacement, from APS1-5 for comparison with the MCOR ensemble.
The ensemble mean track forecast of the APS1-5 sensitivity experiments, Figure 4-2c for
Sandy and Figure 4-4c for Edouard, respectively, clearly indicate the sensitivity of track forecasts to the physical parameterizations. For Sandy (Figure 4-2c), the APS3-5 ensembles have a mean displacement further east in track after approximately 60 h relative to APSU, with APS5 closely resembling COTC rather than APSU at longer lead times. The APS1-5 experiments track ensemble spread (Figure 4-6c) have similar growth characteristics and magnitude as APSU throughout a majority of the simulation; APS3-5 diverge after approximately 72 h. APS5 is more similar to COTC than HWRF or APSU, having a similar track spread after approximately 96 h and increased error consistent with its further east displacement. Comparing the MPHYS error for
Sandy to APSU, HWRF, and COTC ensembles (Figure 4-6a), the MPHYS mean follows APSU with consistent increased error at approximately 24 h and 72 h lead times when APSU has a further westward track, but, the error is reduced due to the inclusion of eastward tracking members APS4-5 in the MPHYS ensemble. The spread of MPHYS remains as large or larger than APSU at longer lead times, generally closer to the MCOR spread. Statistically testing10 the track error distributions under the null hypothesis that MPHYS and MCOR are drawn from the same underlying error distribution, MPHYS and MCOR cannot be proven statistically different for most lead times; the times when the null hypothesis can be rejected are indicated with grey asterisks (Figure 4-6a).
For Edouard, both the track and intensity forecasts are sensitive to modifying the physical parameterizations. The ensemble mean tracks for APS2-5 track further west (Figure 4-4c) at longer lead times. A monotonic decrease in the intensity (Figure 4-5c) throughout a majority of
10 A 10,000 sample bootstrapped Komologorov-Smirnov two-sample test at the 95% significance level was performed between MPHY and MCOR at each 6 h lead time.
101 the 5-day forecast is evident from APS1 to APS5. The monotonic decrease is not linear; a larger decrease is found at longer lead times. A track-intensity feedback is present, with the weaker ensemble members having a farther westward displacement, which can feedback on intensity.
The HWRF-like physical parameterizations are hypothesized to impact the environment and the convection associated with the TC.
Statistically testing the track error distributions between MPHY and MCOR (gray asterisks Figure 4-7a) indicates the error distributions at lead times greater than 80 h have statistically different underlying error distributions; the MPHY is deficient in solutions similar to
COTC. The COTC ensemble has more members with an eastward track at longer lead times, closer to the NHC best track. The physical parameterization packages used in the APS1-5 configuration are different than the COTC configuration, likely not able to capture the solutions evident with the COTC configuration. It is hypothesized that a well-designed ensemble with a sampling of all available physical parameterizations would alleviate this issue11. The current
MPHY is not sampling the entire solution space, evident in the spread at longer lead times.
The APS1-5 intensities cover the APSU (and COTC since it was very similar to APSU) and HWRF solution space. MPHY behaves very similarly to MCOR, performing well at shorter lead times and is strongly influenced by the poor performing members of APS4-5 at longer lead times. The spread increases in tandem to error, similarly to MCOR, with a larger spread by the end of the forecast. The intensity error distributions between MPHY and MCOR cannot be statistically differentiated, except at the 120 h lead-time.
Generally, the single-core multi-physics ensemble error distributions of track and intensity cannot be shown to be statistically different from a multi-core ensemble for a majority
11 The COTC physical parameterizations have been developed independently from WRF-ARW and HWRF and have unique physics parameterizations based on different underlying assumptions (see Table 4-1), not available in WRF-ARW or HWRF.
102 of the lead-times and cases, but if the single-core multi-physics ensemble does not cover the full suite of physics of the multi-core ensemble, it can miss possible solutions.
Inter-Model Comparison: Stochastic Physics and Inflated Initial Condition Ensembles
A single-core ensemble comprised of members with multi-physics configurations can increase the ensemble spread compared with the single-core single-physics ensemble. A few other approaches commonly used to increase the ensemble spread to account for underdispersive ensembles are the use of stochastic physics and modifying the magnitude of the perturbations in the initial conditions. The first targets deficiencies in the forecast model while the other targets deficiencies in the initial conditions.
Stochastic physics are currently employed in some fashion at operational meteorological centers (e.g. NCEP and ECMWF) to account for model deficiencies. Two different methodologies, SKEBS and SPPT, that target slightly different model deficiencies are available in WRF-ARW and are used in this study to determine if the ensemble spread of a single-core single-physics ensemble can be inflated without degrading the mean forecast. Additionally, a simple, but effective multiplicative inflation of initial condition perturbations by 20% (I20P) or
50% (I50P) relative to the control APSU perturbations is performed to determine if modifying the initial condition perturbations is sufficient to cover similar spread compared to MPHY and
MCOR. The single-core stochastic physics and inflated initial condition experiments are performed using the WRF-ARW model with the APSU configuration (Table 4-1).
The SKEB, I20P, and I50P have minimal impact on mean track (Figure 4-2d) and intensity (Figure 4-3d) for Sandy, while SPPT shifts the ensemble mean east at lead times > 48 h, more similar to HWRF, and strengthens the system, substantially at longer lead times. Since
SPPT impacts the physical parameterizations directly, areas sensitive to active physical processes
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(e.g. moist convection) will be impacted. Many factors, including the size of Sandy and the complex interaction with the baroclinic system along the east coast of the US, make this system highly sensitive to fluctuations in the physical tendencies. Focusing on track ensemble spread
(Figure 4-6e), both stochastic physics and initial condition perturbations act to increase the ensemble spread. SKEB has minimal impact at all lead times, SPPT has the largest impact at longer lead times, and I50P drastically increases the spread throughout the entire experiment.
Statistically testing the track error distributions between the various experiments and MCOR
(asterisks Figure 4-6e) show an increased number of lead times in all experiments that can be statistically differentiated from MCOR. For the intensity (Figure 4-6f), it is clear that SPPT drastically increases the spread at all lead times, but severely overestimates the intensity, increasing the error. The I50P experiment shows a slight improvement in error as well as increased spread at a majority of lead-times.
A systematic impact of stochastic physics and inflated initial conditions was evident for
Edouard. The inflated initial condition experiments increased the ensemble track spread over the stochastic physics (Figure 4-7e), with SKEBS and SPPT having a similar impact. After approximately 36 h, the error of all sensitivity experiments increased relative to MCOR, with
SKEBS having minimal degradation and SPPT and I50P substantially degrading the forecast.
SPPT, I20P, and I50P had progressively westward tracks, which is evident in the ensemble mean
(Figure 4-4d). All stochastic physics and inflated initial condition ensembles had a similar deficiency in solutions as MPHYS, missing eastward solutions generated by the COTC ensemble at longer lead times. The error distributions of track are statistically different (asterisks in Figure
4-7e) from MCOR, similar to MPHYS, indicating these two methods of increasing ensemble spread were not capable of forcing ensemble members to cover the COTC solution space. For intensity (Figure 4-7f), SKEBS had little impact on ensemble spread with I50P and SPPT having the largest impact, although at longer lead times, I20P, I50P, and SPPT degraded the mean
104 forecast. Comparing the intensity error distributions to MCOR, both the I50P and SPPT had a majority of lead times that could not be statistically differentiated from MCOR. The reduced error at longer lead times of the sensitivity experiments compared with MCOR stems from a lack of ensemble members covering the HWRF solution space.
For both cases, the stochastic physics and inflated initial conditions increased the ensemble spread, but had inconclusive impacts on the error. SKEBS had the smallest and SPPT and I50P had the largest impact on ensemble spread. These two methods can both impact the ensemble spread and ensemble mean.
Initial Condition Error Versus Model Error: Track and Intensity Measures
The APSU, HWRF, and COTC ensembles are initialized with the same input data, thus, examining the evolution of the ensemble spread and pairwise ensemble differences of each ensemble member provides insight into how the initial condition perturbations evolve and how different models evolve each ensemble solution. The ensemble spread is the evolution of the initial conditions relative to a model with a constant configuration, whereas the pairwise root- mean-squared difference (RMSD) between the same ensemble member of different models controls for the initial condition differences and describes the relative error growth between the models.
The track RMSD for Sandy (Figure 4-8a) and both track and intensity for Edouard
(Figure 4-8c,d) indicate the different evolution of APSU, COTC, and HWRF. The systematic
RMSD difference between APS1-5 and APSU alludes to the error growth between models being reproduced by modifying physical parameterizations using a single-core. By modifying the physical parameterizations, the APSU ensemble can be forced to diverge similarly to COTC and
HWRF. A general monotonic increase in pairwise RMSD for both track (Figure 4-8c) and for
105 intensity (Figure 4-8d) for Edouard in APS1-5 is evident, the larger the divergence from APSU model physical parameterization configuration, the larger the pairwise RMSD magnitude and growth rate, especially at longer lead times. The rate and magnitude of pairwise RMSD appear to be highly dependent on the model physics parameterization for this case. However, the incremental changes in model physical parameterizations do not exhibit a linear relationship in the RMSD; a clear clustering of RMSD is evident for Edouard’s track forecasts. The relationship between initial condition error growth and pairwise RMSD for APS1-5 is qualitatively similar to that seen between HWRF-COTC, HWRF-APSU, and COTC-APSU, but generally not as large in magnitude as the multi-core ensemble pairwise RMSD. This suggests that dynamic core differences outside of model physical parameterizations play a role in the evolution of the ensemble members by different models, but a significant portion is the model physical parameterizations.
Initial Condition Versus Model Error: Domain Integrated Measures
The ensemble spread and pairwise ensemble error of track and intensity provide a measure of error growth and uncertainty for the TC track and intensity forecasts, but are scalars and do not provide an integrated measure of the error growth. This can be accomplished by examining the error growth in kinetic and available potential energy per unit mass at each model grid point between experiments, called the Difference Total Energy (DTE; Zhang et al. 2002, 2004) and calculated by
��� = � + � + ��′ , (4-1) , , , , , , , , , , , where the primes denote the difference between two experiments, i, j, and k correspond to the
Cartesian model grid indices of the model domain and n is the ensemble index, N is the total number of ensemble members, U and V are the model zonal and meridional wind components,
106
respectively, T is the air temperature, and � = � � (where � = 1005 , the specific heat ∙ capacity of dry air at 273 K and � = 273 � is a reference temperature used to define the reference state). The intra-ensemble DTE (ensemble spread) is calculated by differencing each ensemble member and the ensemble mean within a single ensemble (e.g., for the u-wind
component: � = � − � ) and the inter-ensemble DTE (pairwise difference) is calculated by differencing corresponding ensemble members between different ensembles (e.g.,
for u-wind component: � = � − � ). Since each model has its own domain configuration (Figure 4-1), all D01 (~27 km) analyses and forecasts are interpolated to a
0.25˚x0.25˚ grid with a common 50˚x50˚ static domain where all three model domains overlap.
The common domain encompasses each respective TC and its environment for the duration of the
5-day simulations allowing for consistent inter- and intra-ensemble DTE calculations.
The intra-ensemble domain integrated DTE (measure of ensemble spread about the mean) of the various single-core ensembles for Sandy (Figure 4-9a) and Edouard (Figure 4-9c) to the single-core varying single-physics ensembles for Sandy (Figure 4-9b) and Edouard (Figure 4-
9d) shows the systematic impact of physical parameterizations on the ensemble forecasts. The error growth characteristics of a single-core ensemble can be systematically modified to exhibit different error growth rates, timing of significant error growth, and overall DTE magnitudes. The
SKEB and SPPT sensitivity experiments substantially modify the intra-ensemble DTE due to the fundamental impact of the SKEBS/SPPT algorithm. The spatially and temporally correlated noise, different for each ensemble member, substantially increases the differences between ensemble members at each grid point.
Instead of integrating the DTE over all common grid dimensions, it is useful to examine the root-mean of the DTE (RMDTE) over the ensemble, n, and vertical, k, dimensions to generate a two dimensional spatial distribution of RMDTE. Taking the root-mean allows for comparison
107 with typical observation and forecast errors. The 12 h forecast RMDTE for Sandy (Figure 4-10) and Edouard (Figure 4-12) shows the spatial evolution of the intra-model RMDTE due to the initial perturbations from the ensemble Kalman filter surrounding the TC vortex (800 km from the TC, all ensemble members have the same IC; panels a-d) while the inter-model difference
(panels e-h) indicate error growth associated with the large-scale environment, in addition to the
TC. Coherent error structures are evident for the inter-model RMDTE for Sandy (Figure 4-10e-f) by 12 h, including the mid-latitude trough over the central US, the TC itself northeast of the
Bahamas, and a warm front and upper level ridge building to the northeast of the TC vortex. The intra-model RMDTE (Figure 4-10a-c) show structural differences associated with the TC and the surrounding environment but are limited to the spatial extent of the initial perturbations. By 36 h
(Figure 4-11a-c), the intra-model IC errors associated with the TC have also evolved environmental differences east of the mid-latitude trough over the US eastern seaboard and the warm front and ridge to the west. A substantial difference in the mid-latitude trough for COTC over the eastern seaboard can be seen in Figure 4-11f-g when comparing APSU and HWRF to
COTC; the evolution of this mid-latitude trough may have had an impact on the more eastward track of the COTC ensemble. The APS5 ensemble shows similar spatial error DTE as HWRF and
COTC compared to APSU, indicating by 36 h the model physical parameterizations have substantially altered the APSU solution.
The same intra- and inter-model relationships seen in Sandy can be found with Edouard.
Large-scale environmental error growth with coherent error structures in the Caribbean ocean associated with a tropical wave, the ITCZ off the coast of NE South America, and a tropical wave to the south of the Cape Verde islands are evident by 12 h (Figure 4-12e-h), more pronounced and developed by 36 h (Figure 4-13e-h). This same RMDTE analysis was performed for the SKEB and SPPT ensembles (not shown). The SPPT ensemble showed similar spatial error growth as the
108 inter-model RMDTE comparison, with SKEB having very little error growth outside of the IC perturbations, consistent with the scalar analyses of the previous section.
The integrated DTE and spatial RMDTE analysis indicates model physical parameterizations can substantially impact the evolution of the IC perturbations and the large-scale TC environment by as little as 12 h. Modifying the physical parameterizations can alter the evolution of identical initial conditions similarly to a completely different model core.
Ensemble Composite and Correlation Analysis for Hurricane Edouard (2014)
To start uncovering why HWRF performed so poorly in track and intensity for Hurricane
Edouard, ensemble composites were constructed to examine relevant dynamic and thermodynamic fields important for TC strengthening. Since all ensemble members in APSU and
COTC developed and strengthened over the 5-day forecast period, HWRF is used as the control and the 10 worst performing HWRF ensemble members (hereafter HWRF-poor) in terms of maximum 10-m wind speed at 96 h were selected and TC centered composites from D01 within each model’s ensemble were constructed. The storm centered mean environmental shear is calculated over a 3˚ ring from 2˚ to 5˚ from storm center on D02 and the tilt vector is calculated between the 500- and 850-hpa maximum potential vorticity center.
Relative humidity (e.g., Gray 1975; Gray et al. 1975) and environmental wind shear (e.g.,
Simpson et al. 1958; Gray 1968) impact tropical cyclogenesis and maintenance. This provides a starting point to examine relevant environmental fields. From Figure 4-5a, it is clear HWRF struggles to develop Edouard, and after 48-h, APSU and COTC begin a period of continual strengthening while many HWRF members marginally strengthen. Examining the HWRF-poor
109 composites of simulated maximum radar reflectivity12 from APSU, HWRF, and COTC at 24 h
(Figure 4-14a,b,c), it is clear that HWRF struggles to generate strong convection down shear (red vector) of the TC center. By 72-h (Figure 4-14i,j,k), the HWRF convection remains weak with substantially smaller area of low pressure and a tilt vector to the right of the shear vector. This indicates that the mid-level and lower-level circulation centers are misaligned, a sign of a moderately sheared system (Corbosiero and Molinari 2002; Rogers et al. 2003). The tilt magnitude between the low and mid-level circulations continually increase (Figure 4-15c) for
HWRF, while APSU and COTC become steadily aligned for these two systems (Zhang and Tao
2013; Tao and Zhang 2014). The shear magnitude between the various model composites (Figure
4-15a) are consistent throughout the entire simulation, with the shear direction (Figure 4-15b) diverging at 48 h between APSU/COTC and HWRF, a direct result of the stronger TC circulations in APSU/COTC impacting the local environment. The APSU and COTC ensembles have stronger convection associated with the main TC circulation, with the tilt of the TC decreasing, and subsequent strengthening ensuing. It appears that the difference in shear magnitude does not contribute to the divergence between APSU/COTC and the HWRF ensemble, but the reduced predictability present in the moderate shear regime likely has an impact on the differences that develop in a stationary rain band to the northeast of the TC.
Focusing back on the simulated radar reflectivity (Figure 4-14), a substantial difference in convection associated with a stationary rain band to the northeast of the storm center is evident by 48 h in HWRF (Figure 14-14g) compared with APSU (Figure 14-14e) and COTC (Figure 14-
14f). The rain band is along the horizontal shear region of the easterly winds associated with the sub-tropical high pressure stretched across the northern Atlantic and the southerly winds induced by the large-scale TC circulation. Examining the mid-level relative humidity (Figure 14-16), the
12 To generate comparable simulated radar reflectivity between models, only the cloud water and rain water mixing ratio were used due to differences in the microphysics schemes. This will impact the simulated radar reflectivity intensity, but the relative difference between models are the focus.
110 moisture associated with the stationary rain band is evident in all three models, but HWRF has the highest RH associated with this feature and active convection in this region. Compositing all of the HWRF-poor ensemble members from APSU, HWRF, and COTC and correlating each grid point RH value with the corresponding 96 h 10-m wind speed (Figure 14-16b), moderate (0.5) positive correlations appear by 48-h associated with relative humidity values surrounding the TC core to the south and moderate (0.5) negative values on the northern edge of the stationary rain band. The correlation with the northeastern stationary rain band is implying that a decrease in RH is linked to an increase in final intensity. Additionally, the increase in RH to the south of the TC center is linked to an increase in intensity. The correlations associated with the stationary rain band hint at a potential link of this feature and the intensity of the TC at 96 h.
Recalling that HWRF D02 is much smaller than APSU and COTC (Figure 4-1), approximately the same size as D03 of APSU and COTC, the stationary rain band lies outside of the high resolution nests in HWRF and thus, is being simulated with a lower resolution grid and convective parameterization. It is hypothesized that the convection associated with the stationary rain band in HWRF is impacting the larger-scale TC circulation. To investigate this further, the
APS5 simulation which behaves similarly to HWRF in intensity and uses similar physics to
HWRF (cumulus parameterization active in D02), is composited using the HWRF-poor members and compared to HWRF13. The reduced convection in the TC core (Figure 4-14d,h,l) and tilt vector magnitude (Figure 15c) is similar to that of HWRF, although the convection associated with the stationary rain band is not apparent in APS5. Examining the mid-level relative humidity
(Figure 4-15), it is clear the RH associated with this feature is much higher in APS5 compared to
APSU and COTC, which suggests stronger convection during the first 48 h. It has been shown in idealized and case studies that asymmetric convection of forming TC circulations can be
13 APS5 uses cumulus parameterization on D02, thus cumulus parameterization will be impacting a similar area surrounding the TC as HWRF.
111 detrimental to the mean symmetric TC circulation and thus weaken the vortex (e.g., Montgomery and Kallenbach 1997; Nolan and Grasso 2003; Nolan et al. 2007). It is hypothesized that the convection and latent heating associated with the enhanced convection along the stationary rain band to the northeast of the TC center evolves differently with the use of cumulus parametrization and choice of microphysics in HWRF and APSU over the first 48 h, altering the available energy to the symmetric TC circulation and keeping the TC circulation highly tilted (Figure 4-15c), preventing the strengthening of the HWRF and APS5 simulations.
Concluding Remarks
This study examined the mean and spread of ensembles using multiple TC tuned regional models, including the COAMPS-TC model, the HWRF model, and the WRF-ARW model. Each model dynamic core and physical parameterization configuration were set using their “pseudo- operational” settings with no ocean model (if applicable). The sea-surface temperatures were fixed for all ensembles. The three models were initialized with the same initial conditions from the real-time Penn State University WRF-ARW ensemble Kalman filter cycling data assimilation system blended with the Global Data Assimilation System analysis. Comparisons were made between the multiple TC tuned regional model and the mean and spread of ensembles using
WRF-ARW with multi-physics settings, stochastic physics, and inflated initial condition perturbations to determine if a multi-core ensemble could be reproduced with a single-core ensemble. Hurricane Sandy (2012) and Hurricane Edouard (2014) were used at 0000 UTC 26
October 2012 and 1200 UTC 26 September 2014, respectively, for case studies. The abnormal track of Sandy, the rapid intensification of Edouard, and the large number of observations for both cases make these ideal case studies.
112
Comparing the ensemble mean and spread of ensembles from different “pseudo-operational” configurations of regional TC tuned NWP models initialized with identical initial conditions showed each TC tuned regional model was capable of producing a similar ensemble mean track and spread for shorter lead times (< 36 h), but had systematic errors in the ensemble mean at longer lead times (> 48 h). For longer lead-times (> 60 h), the ensemble spread for both track and intensity from a multi-core ensemble is larger than any single-core single-physics ensemble.
To answer whether a single-core ensemble forecast could perform similarly to a multi-core ensemble with respect to the ensemble mean forecast error and ensemble spread, ensembles using the WRF-ARW model employing different physical parameterizations, stochastic physics, and inflated initial condition perturbations were compared. For the single-core ensembles with systematically varying physical parameterization experiments, the track and intensity ensemble mean can be systematically shifted by modifying physical parameterizations schemes. The track and intensity ensemble spread is less sensitive to physical parameterization scheme modifications than the ensemble mean, but can be modified at longer lead times.
Randomly sampling the single-core single-physics ensembles to generate a single-core multi- physics ensemble and comparing to the multi-core ensemble of pseudo-operational TC tuned models showed similar evolution of the ensemble mean and spread in track and intensity, except when the single-core multi-physics ensemble is deficient in certain model physical parameterizations. If an ensemble does not have the necessary physics to cover the range of possible forecast solutions, generating a single-core multi-physics ensemble without a complete suite of physics will result in a deficient ensemble. It is necessary to have many combinations of physical parameterizations to maximize the number of independent forecast solutions.
The SKEBS and SPPT stochastic physics algorithms in WRF-ARW both increase the ensemble spread in track and intensity using a single-core single-physics ensemble; the SPPT algorithm had a more pronounced impact with increases more in line with those of the single-core
113 multi-physics and multi-core ensembles. Although the SPPT had a larger impact on the ensemble spread, it also was detrimental to the ensemble mean forecast, sometimes drastically increases intensity and track errors, especially at longer lead times ( > 60 h). The inflated initial condition perturbation experiments also increased both the track and intensity ensemble spread, with the magnitude case specific. The larger 50% increase in initial condition perturbation had increases in spread more in line with those of the single-core multi-physics and multi-core ensembles.
Focusing on the evolution of the poor performing HWRF members between the various models and modified APSU physics configuration (APS5; “HWRF-like” physics), it is hypothesized the poor performance of the HWRF experiment is due to the use of a small inner- domain, with the combination of cumulus parameterization and microphysics in the HWRF and
APSU experiments enhancing convection along a stationary rain band in the larger primary TC circulation. This asymmetric convection was detrimental to the evolution of the TC vortex, compared with APSU and COTC. More analysis needs to be performed to examine the diabatic energy associated with this feature and the direct impact on the TC circulation. Additional experiments including running HWRF with a larger D02 and running APSU with a smaller D02 are proposed for future work.
For the two case studies presented, this study suggests that an ensemble can be constructed using a single-core in combination with one or more of the following: (1) varying the physical parameterization schemes, (2) using stochastic physics, and/or (3) inflating the initial perturbations to generate an ensemble mean and spread forecast similar to a multi-core ensemble.
These three methods increase the ensemble spread, some more profoundly than others. The results suggest the model physical parameterizations are a dominant source of model error and can drastically impact ensemble forecast uncertainty. This finding has far reaching implications for operational centers model development efforts, suggesting that focusing efforts and resources on model physical parameterization development, diversification, and refinement over model
114 dynamic core development is a good use of resources. The more combinations of TC tuned physical parameterizations available in an ensemble with tuned stochastic physics – addressing uncertainty for each physical parametrization independently – may provide a larger sample of possible solutions and a better representation of forecast uncertainty. Additionally, the evolution difference between APSU/COTC and HWRF provide additional insight into how model resolution (domain size) may have a substantial impact on large-scale environmental features that can alter the evolution of the TC.
This is a preliminary study, focusing on how ensemble spread and mean forecasts respond to the choice of model dynamic core and/or model physical parameterizations. Many questions still need to be addressed pertaining to the impact on TC dynamics and predictability. A follow-up study will focus on this data set for Sandy and Edouard, examining the ensemble error growth and predictability in more detail, the correlations between track position and intensity between model cores, and detailed physical analysis of the TC structure.
115
Chapter 4 Tables
Table 4-1: Model domain and physical parameterization settings for pseudo-operational versions of WRF- ARW (APSU), HWRF, and COAMPS-TC (COTC).
(Grell and Freitas 2013; Han and Pan 2011; Kain and Fritsch 1993; Hong and Lim 2006; Ferrier 1994; Rutledge and Hobbs 1983; Hong et al. 2006; Hong and Pan 1996; Mellor and Yamada 1982; Fels and Schwarzkopf 1981; Harshvardhan et al. 1987; Louis 1979)
Table 4-2: Model physical parameterization differences from APSU configuration for sensitivity experiments APS1 through APS5. Dashed line indicates same scheme as APSU.
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Table 4-3: Stochastic physics parameters settings.
117
Chapter 4 Figures
Figure 4-1: Domain setup for WRF-ARW (APSU; green), HWRF (cyan), and COAMPS-TC (COTC; magenta). Domain 1 (D01) is globally fixed for APSU and COTC, but centers on the TC for HWRF at initialization and fixed for the remainder of the forecast. D02 and D03 are two-way nested, vortex following for all models, centered on the TC at initialization. Note: APSU and COTC domains are nearly identical and thus substantially overlap. Detailed domain settings can be found in Table 4-1.
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Figure 4-2: Ensemble track spread for (a) APSU (green), HWRF (cyan), and COTC (magenta) (only 20 ensemble members shown for clarity). Ensemble mean track for (b) APSU (green), HWRF (cyan), COTC (magenta), the combined single-core multi-physics ensemble MPHY (gray), and the combined multi-core ensemble MCOR (black), (c) single-core single-physics ensembles APS1 (light gray) through APS5 (dark navy), and (d) stochastic physics experiments SKEB (maroon) and SPPT (purple) and inflated initial perturbation experiments I20P (yellow) and I50P (blue) for Hurricane Sandy initialized at 0000 UTC 26 October 2012. The NHC best track data (black line) is plotted every 6 hrs. The solid dots in (b-d) indicate the position every 6 hrs.
119
Figure 4-3: Ensemble intensity spread [m s-1] for (a) APSU (green), HWRF (cyan), and COTC (magenta) (only 20 ensemble members shown for clarity). Ensemble mean intensity [m s-1] for (b) APSU (green), HWRF (cyan), COTC (magenta), the single-core multi-physics ensemble MPHY (gray), and the multi-core ensemble MCOR (black), (c) single-core single-physics ensembles APS1 (light gray) through APS5 (dark navy), and (d) stochastic physics experiments SKEB (maroon) and SPPT (purple) and inflated initial perturbation experiments I20P (yellow) and I50P (blue) for Hurricane Sandy (2012) initialized at 0000 UTC 12 September 2012. The NHC best track data (black line) is plotted every 6 hrs. The solid dots in (b- d) indicate the intensity and every 6 hrs.
120
Figure 4-4: Same as Figure 4-2, but for Hurricane Edouard (2014) initialized at 1200 UTC 11 September 2014.
121
Figure 4-5: Same as Figure 4-3, but for Hurricane Edouard (2014) initialized at 1200 UTC 11 September 2014.
122
Figure 4-6: Root-mean-squared error (RMSE) verified with NHC best track data (solid line) and the ensemble spread [m s-1] (dotted line) at 6-hourly lead times for track (a,c,e) [km] and intensity (b,d,f) [ms- 1] of (a,b) APSU (green), HWRF (cyan), COTC (magenta), the single-core multi-physics ensemble MPHY (gray), and the multi-core ensemble MCOR (black), (c,d) single-core single-physics APS1 (light gray) through APS5 (dark navy), and (e,f) stochastic physics experiments SKEB (maroon) and SPPT (purple) and inflated initial perturbation experiments I20P (yellow) and I50P (blue) ensembles for Hurricane Sandy initialized at 0000 UTC 26 October 2012. The asterisks in panels (a,b,e,f) corresponding to the aforementioned ensembles indicate the lead times when the ensemble spread is statistically different from the MCOR ensemble spread at the 95% significance level.
123
Figure 4-7: Same as Figure 4-6, but for Hurricane Edouard (2014) initialized at 1200 UTC 11 September 2014.
124
Figure 4-8: Pairwise root-mean-squared difference (RMSD) of (a,c) track [km] and (b,d) maximum 10-m wind speed [m s-1] at 6-hourly lead times between HWRF and COTC (red), HWRF and APSU (cyan), COTC and APSU (magenta), and APS1 and APSU (light gray) through APS5 and APSU (navy). Panels (a,b) are for Hurricane Sandy initialized at 0000 UTC 26 October 2012 and (c,d) are for Hurricane Edouard at 1200 UTC 11 September 2014.
125
Figure 4-9: Domain integrated Difference Total Energy (DTE) [m2 s-2] for (top row) Hurricane Sandy initialized at 0000 UTC 26 September 2012 and (bottom row) Hurricane Edouard initialized at 1200 UTC 11 September 2012 for (a,c) varying single-core ensembles APSU (green), HWRF (cyan), and COTC (magenta), (b,d) single-core varying single-physics ensembles APS1 to APS5 (gray to navy), SKEB (maroon), and SPPT (purple) ensembles.
126
Figure 4-10: Vertically integrated root-mean difference total energy (RMDTE; m s-1) for Hurricane Sandy (2012) at 12 h lead time for the simulation initialized at 0000 UTC 26 October 2012. The top row is the RMDTE of the ensemble spread for (a) APSU, (b) HWRF, (c) COTC, and (d) APS5 and the bottom row is the RMDTE between multi-core ensembles (d) APSU and HWRF, (e) APSU and COTC, (f) HWRF and COTC, and (h) APS5 and APSU. All panels show the static 50˚x50˚ common domain at 0.25˚x0.25˚ horizontal resolution for which each model cores 27 km D01 is interpolated to calculate all DTE analyses.
127
Figure 4-11: Same as Figure 4-10, but for 36 hr lead time initialized at 0000 UTC 26 October 2012.
128
Figure 4-12: Same as Figure 4-10, but for Hurricane Edouard (2014) initialized at 12 UTC 11 September 2014.
129
Figure 4-13: Same as Figure 4-10, but for Hurricane Edouard (2014) at 36 h lead time initialized at 12 UTC 11 September 2014.
130
Figure 4-14: HWRF-poor ensemble members D01 composite simulated maximum radar reflectivity (cloud water and rain water only) and mean sea level pressure for (a,e,i) APSU, (b,f,j) COTC, (c,g,k) HWRF, and (d,h,l) APS5 at lead times (top row) 24 h, (middle row) 48 h, and (bottom row) 72 h initialized at 1200 UTC 11 September 2014. The deep layer (200- to 850-hPa) shear vector (red arrow) and (850- to 500-hPa) tilt vector (magenta arrow) are overlaid on each panel.
131
Figure 4-15: HWRF-poor ensemble members D01 composite deep-layer 200- to 850-hPa shear vector (a) magnitude and (b) direction and 500- to 850-hPa tilt vector (c) magnitude and (d) direction for 4-days lead time every 12 hours starting at 1200 UTC 11 September 2014 for APSU (green), COTC (magenta), HWRF (cyan), and APS5 (navy).
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Figure 4-16: HWRF-poor ensemble members D01 composite 700-hPa relative humidity for (a,e,i) APSU, (b,f,j) COTC, (c,g,k) HWRF, and (d,h,l) APS5 at lead times (top row) 24 h, (middle row) 48 h, and (bottom row) 72 h initialized at 1200 UTC 11 September 2014.
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Figure 4-17: D01 composite COTC, HWRF, and APSU of HWRF-poor ensemble members 700-hPa relative humidity at lead times (a) 24 h, (b) 48 h, and (c) 72 h initialized at 1200 UTC 11 September 2004. Grid point correlations with the 96 h max 10-m wind speed are contoured at 0.5 (weak), 0.7 (moderate), and 0.9 (strong) with solid contours indicating positive and dotted contours indicating negative correlations.
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Chapter 5
Summary and Conclusions
This dissertation focuses on the practical predictability of tropical cyclones, examining the impact of: (1) radiation on the pre-genesis environment of Hurricane Karl (2010), (2) tail
Doppler radar observations and observation error on track and intensity forecast uncertainty, (3) model uncertainties on ensemble track and intensity forecast statistics of Hurricanes Sandy (2012) and Edouard (2014). Although each chapter focused on a distinct component of the practical predictability of TCs, the overarching story is the examination of improving the initial conditions and/or investigating the impact of model uncertainties on TC track and intensity forecasts.
In Chapter 2, convection-permitting ensemble and sensitivity experiments were used to examine the impact of the diurnal radiation cycle on the pre-genesis environment of Hurricane
Karl (2010). It was found that the pre-genesis environmental stability and the intensity of deep moist convection can be considerably modulated by the diurnal extremes in radiation. Nighttime destabilization of the local and large-scale environment through radiative cooling may promote deep moist convection and increase the genesis potential, likely enhancing the intensity of the resultant TCs. Modified longwave and shortwave radiation experiments found TC development to be highly sensitive to the periodic cycle of heating and cooling, with suppressed formation in the daytime-only and no-radiation experiments, and quicker intensification compared with the control for nighttime-only experiments.
In Chapter 3, a new three-dimensional wind retrieval algorithm for tail Doppler radars – based on established coplane methodology – was developed to derive horizontal wind vectors of
TCs from radial velocity observations by the tail-Doppler radars onboard the NOAA P3 hurricane
135 reconnaissance aircraft. Observations generated with the new method were validated against independent in-situ flight-level and dropsonde observations before and after genesis of Hurricane
Karl (2010). The retrieved u- and ν-wind near the aircraft track have an average error of approximately 1.5 m s-1, which increases with the scanning angle and distance away from the aircraft track. Simulated radial velocities derived from a convection-permitting simulation of Karl are further used to systematically quantify errors of the coplane method. The accuracy of the method is strongly dependent on the time between forward and backward radar scans and to a lesser extent, the zero vertical velocity assumption at large angles relative to a plane parallel with the aircraft wings. Assimilating the coplane retrieved wind vectors with an ensemble Kalman filter showed improvements in track and intensity forecasts similar to assimilating radial velocity super observations. For this single-case study, the coplane retrieved wind vectors reduced the track, but degraded the intensity forecast error compared to the radial velocity super observations, however, this error reduction was not statistically significant. Nevertheless, the improvements in track and intensity forecasts for this single-case study are promising and the computational efficiency and real-time low-error wind field retrieval make this a competitive algorithm for observation generation for TC data assimilation.
Finally, in Chapter 4, a comparison of non-calibrated ensembles of multiple dynamic cores with distinct physics, a single dynamic core with varying physics, and a single dynamic core with stochastic physics were examined for the probabilistic prediction of Hurricane Sandy
(2012) and Hurricane Edouard (2014). The multiple dynamic cores include the Coupled
Ocean/Atmospheric Mesoscale Prediction System (COAMPS-TC) TC model, the Hurricane
Weather Research and Forecasting (HWRF) model, and a TC tuned Weather Research and
Forecasting (WRF-ARW) model. The Stochastic Kinetic Energy Backscatter Scheme (SKEBS) and Stochastically Perturbed Physics Tendencies (STTP) schemes are used within the WRF-
ARW core for the stochastic physics schemes. Each ensemble is initialized with identical initial
136 conditions derived from the Pennsylvania State University real-time cycling ensemble Kalman filter WRF-ARW data assimilation system (PSU WRF-EnKF) 60-member ensemble and provided deterministic boundary conditions from the Global Forecast System (GFS) forecasts.
A comparison of single-core distinct physics ensembles found that each model core was capable of generally reproducing the track mean and spread for the first approximately 48 h with biases evident at longer lead times. Systematically varying the physics options within the WRF-
ARW core from the WRF-ARW configuration to the HWRF configuration fundamentally changed the ensemble spread and forecast bias suggesting model physics may be more dominant than model core in defining a model. The spread of a multiple-core ensemble sampled from each individual model core model was statistically indistinguishable from the single-core distinct physics ensembles at shorter lead times. At longer lead times the multiple-core ensemble spread was larger than any single-core ensemble, which may provide a better estimate of the uncertainty.
The research results suggest that model physics may be the dominant mechanism for model error growth and a multi-physics ensemble can generally reproduce the forecast track uncertainty of a multi-core multi-physics ensemble. This research is the first systematic comparison performed for three state-of-the-art convection-permitting regional-scale TC-tuned hurricane prediction systems initialized with the same advanced data assimilation system initial conditions.
137
REFERENCES
Aberson, S. D., 2001: The ensemble of tropical cyclone track forecasting models in the North
Atlantic Basin (1976-2000). Bull. Amer. Meteorol. Soc., 82, 1895–1904.
Aksoy, A., D. C. Dowell, and C. Snyder, 2010: A Multicase Comparative Assessment of the
Ensemble Kalman Filter for Assimilation of Radar Observations. Part II: Short-Range
Ensemble Forecasts. Mon. Wea. Rev., 138, 1273–1292.
Armijo, L., 1969: A Theory for the Determination of Wind and Precipitation Velocities with
Doppler Radars. J. Atmos. Sci., 26, 570–573.
Atlas, D., R. C. Srivastava, and R. S. Sekhon, 1973: Doppler radar characteristics of precipitation
at vertical incidence. Rev. Geophys. Sp. Phys., 11, 1–35.
Baik, J.-J., M. DeMaria, and S. Raman, 1990: Tropical Cyclone Simulations with the Betts
Convective Adjustment Scheme. Part II: Sensitivity Experiments. Mon. Wea. Rev., 118,
529–541.
Barker, D. M., W. Huang, Y.-R. Guo, A. J. Bourgeois, and Q. N. Xiao, 2004: A Three-
Dimensional Variational Data Assimilation System for MM5: Implementation and Initial
Results. Mon. Wea. Rev., 132, 897–914.
Bernardet, L., V. Tallapragada, S. Bao, Y. Kwon, S. Trahan, M. Tong, Q. Liu, and X. Zhang,
2013: Hurricane WRF : 2013 operational implementation and community support.
Berner, J., G. J. Shutts, M. Leutbecher, and T. N. Palmer, 2009: A Spectral Stochastic Kinetic
Energy Backscatter Scheme and Its Impact on Flow-Dependent Predictability in the
ECMWF Ensemble Prediction System. J. Atmos. Sci., 66, 603–626.
——, K. R. Fossell, S.-Y. Ha, J. P. Hacker, and C. Snyder, 2015: Increasing the Skill of
Probabilistic Forecasts: Understanding Performance Improvements from Model-Error
Representations. Mon. Wea. Rev., 143, 1295–1320.
138
Blake, E. S., T. B. Kimberlain, R. J. Berg, J. P. Cangialosi, and J. L. B. Ii, 2013: Tropical
Cyclone Report Hurricane Sandy. 1-157 pp.
Bohne, A. R., and R. C. Srivastava, 1976: Random errors in wind and precipitation fall speed
measurement by a trible Doppler radar System. 17th Conference on Radar Meteorology,
Seattle, WA, Amer. Meteor. Soc., 7–14.
Braun, S. a., and W.-K. Tao, 2000: Sensitivity of High-Resolution Simulations of Hurricane Bob
(1991) to Planetary Boundary Layer Parameterizations. Mon. Wea. Rev., 128, 3941–3961.
Braun, S. A., R. Kakar, E. Zipser, and G. Heymsfield, 2013: NASA’s Genesis and Rapid
Intensification Processes (GRIP) field experiment. Bull. Amer. Meteorol. Soc., 94, 345–363.
Bu, Y. P., R. G. Fovell, and K. L. Corbosiero, 2013: Influence of cloud-radiative forcing on
tropical cyclone structure. J. Atmos. Sci., 71, 131127131123007.
Cangialosi, J. P., and J. L. Franklin, 2014: 2013 National Hurricane Center Forecast Verification
Report. 1-84 pp.
Chong, M., and C. Campos, 1996: Extended overdetermined dual-Doppler formalism in
synthesizing airborne Doppler radar data. J. Atmos. Oceanic Technol., 13, 581–597.
——, and J. Testud, 1996: Three-dimensional air circulation in a squall line from airborne dual-
beam Doppler radar data: A test of coplane methodology software. J. Atmos. Oceanic
Technol., 13, 36–53.
Corbosiero, K. L., and J. Molinari, 2002: The Effects of Vertical Wind Shear on the Distribution
of Convection in Tropical Cyclones. Mon. Wea. Rev., 130, 2110–2123.
Craig, G. C., 1996: Numerical experiments on radiation and tropical cyclones. Q. J. R. Meteorol.
Soc., 122, 415–422.
Davis, C., and D. A. Ahijevych, 2012: Mesoscale Structural Evolution of Three Tropical Weather
Systems Observed during PREDICT. J. Atmos. Sci., 69, 1284–1305.
Didlake, A. C., G. M. Heymsfield, L. Tian, and S. R. Guimond, 2015: The Coplane Analysis
139
Technique for Three-Dimensional Wind Retrieval Using the HIWRAP Airborne Doppler
Radar. J. Appl. Meteorol. Climatol., 54, 605–623.
Dudhia, J., 1989: Numerical Study of Convection Observed during the Winter Monsoon
Experiment Using a Mesoscale Two-Dimensional Model. J. Atmos. Sci., 46, 3077–3107.
Fels, S. B., and M. D. Schwarzkopf, 1981: An efficient, accurate algorithm for calculating CO 2
15 µm band cooling rates. J. Geophys. Res., 86, 1205.
Ferrier, B. S., 1994: A double-moment multiple-phase four-class bulk ice scheme. Part I:
Description. J. Atmos. Sci., 51, 249–280.
Fovell, R. G., and H. Su, 2007: Impact of cloud microphysics on hurricane track forecasts.
Geophys. Res. Lett., 34, 0–4.
Fovell, R. G., K. L. Corbosiero, and H.-C. Kuo, 2009: Cloud Microphysics Impact on Hurricane
Track as Revealed in Idealized Experiments. J. Atmos. Sci., 66, 1764–1778.
——, ——, A. Seifert, and K.-N. Liou, 2010: Impact of cloud-radiative processes on hurricane
track. Geophys. Res. Lett., 37, 1–6.
Frisch, A. S., L. J. Miller, and R. G. Strauch, 1974: Three-dimensional air motion measured in
snow. Geophys. Res. Lett., 1, 86–89.
Frush, C. L., P. H. Hildebrand, and C. Walther, 1986: The NCAR airborne Doppler radar. 23rd
Conference on Radar Meteorology, Snowmass, CO, Amer. Meteor. Soc., 151–154.
Gamache, J., P. Dodge, and N. Griffin, 1997: Automatic quality control and analysis of airborne
Doppler data: Realtime applications, and automatically post-processed analyses for
research. 28th Conference on Radar Meteorology, Austin, TX, Amer. Meteor. Soc., 422–
423.
Gamache, J. F., F. D. Marks, and F. Roux, 1995: Comparison of three airborne Doppler sampling
techniques with airborne in situ wind observations in Hurricane Gustav (1990). J. Atmos.
Oceanic Technol., 12, 171–181.
140
Gao, J., M. Xue, A. Shapiro, and K. K. Droegemeier, 1999: A variational method for the analysis
of three-dimensional wind fields from two Doppler radars. Mon. Wea. Rev., 127, 2128–
2142.
Goerss, J. S., 2000: Tropical Cyclone Track Forecasts Using an Ensemble of Dynamical Models.
Mon. Wea. Rev., 128, 1187–1193.
Gray, W. M., 1968: Global View of the Origin of Tropical Disturbances and Storms. Mon. Wea.
Rev., 96, 669–700.
——, 1975: Tropical Cyclone Genesis in the Western North Pacific.
——, E. Ruprecht, and R. Phelps, 1975: Relative Humidity in Tropical Weather Systems. Mon.
Wea. Rev., 103, 685–690.
Green, B. W., and F. Zhang, 2013: Impacts of Air–Sea Flux Parameterizations on the Intensity
and Structure of Tropical Cyclones. Mon. Wea. Rev., 141, 2308–2324.
Grell, G., and D. Devenyi, 2002: A generalized approach to parameterizing convection
combining ensemble and data assimilation techniques. Geophys. Res. Lett., 29, 1693.
Grell, G. A., and S. R. Freitas, 2013: A scale and aerosol aware stochastic convective
parameterization for weather and air quality modeling. Atmos. Chem. Phys. Discuss, 13,
823–845.
Guimond, S. R., L. Tian, G. M. Heymsfield, and S. J. Frasier, 2014: Wind Retrieval Algorithms
for the IWRAP and HIWRAP Airborne Doppler Radars with Applications to Hurricanes. J.
Atmos. Oceanic Technol., 31, 1189–1215.
Gunn, K. L. S., and J. S. Marshall, 1958: The distribution with size of aggregate snowflakes. J.
Meteorol., 15, 452–461.
Hack, J. J. J., 1980: The Role of Convective-Scale Processes in Tropical Cyclone Development.
Dissertation - Colorado State Univeristy,.
Hamill, T. M., and J. S. Whitaker, 2011: Global ensemble predictions of 2009’s tropical cyclones
141
initialized with an ensemble Kalman filter. Mon. Wea. Rev., 139, 668–688.
Han, J., and H.-L. Pan, 2011: Revision of Convection and Vertical Diffusion Schemes in the
NCEP Global Forecast System. Weather Forecast., 26, 520–533.
Harshvardhan, R. Davies, D. A. Randall, and T. G. Corsetti, 1987: A fast radiation
parameterization for atmospheric circulation models. J. Geophys. Res., 92, 1009.
Hawblitzel, D. P., F. Zhang, Z. Meng, and C. Davis, 2007: Probabilistic evaluation of the
dynamics and predictability of the mesoscale convective vortex of 10-13 June 2003. Mon.
Wea. Rev., 135, 1544–1563.
Hildebrand, P. H., C. Walther, and C. L. Frush, 1986: The NCAR Electra Doppler radar. Part I:
Evaluation of scientific needs. 23rd Conference on Radar Meteorology, Snowmass, CO,
Amer. Meteor. Soc., 147–150.
Hodur, R. M., 1997: The Naval Research Laboratory’s coupled ocean/atmosphere mesoscale
prediction system (COAMPS). Mon. Wea. Rev., 1414–1430.
Hong, S., and J. Lim, 2006: The WRF Single-Moment 6-Class Microphysics Scheme (WSM6). J.
Korean Meteorol. Soc., 42, 129–151.
——, Y. Noh, and J. Dudhia, 2006: A New Vertical Diffusion Package with an Explicit
Treatment of Entrainment Processes. Mon. Wea. Rev., 134, 2318–2341.
Hong, S.-Y., and H.-L. Pan, 1996: Nonlocal Boundary Layer Vertical Diffusion in a Medium-
Range Forecast Model. Mon. Wea. Rev., 124, 2322–2339.
Iacono, M. J., J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. a. Clough, and W. D. Collins,
2008: Radiative forcing by long-lived greenhouse gases: Calculations with the AER
radiative transfer models. J. Geophys. Res., 113, 1–8.
Johnson, R. H., P. E. Ciesielski, and K. A. Hart, 1996: Tropical Inversions near the 0°C Level. J.
Atmos. Sci., 53, 1838–1855.
——, T. M. Rickenbach, S. A. Rutledge, P. E. Ciesielski, and W. H. Schubert, 1999: Trimodal
142
Characteristics of Tropical Convection. J. Clim., 12, 2397–2418.
Jorgensen, D. P., P. H. Hildebrand, and C. L. Frush, 1983: Feasibility Test of an Airborne Pulse-
Doppler Meteorological Radar. J. Clim. Appl. Meteorol., 22, 744–757.
Jorgensen, D. P., T. Matejka, and J. D. DuGranrut, 1996: Multi-beam techniques for deriving
wind fields from airborne doppler radars. Meteorol. Atmos. Phys., 59, 83–104.
Joss, J., and A. Waldvogel, 1970: Raindrop size distribution and Doppler velocities. 14th
Conference on Radar Meteorology, Tucson, AZ, Amer. Meteor. Soc., 153–156.
Kain, J. S., and J. M. Fritsch, 1993: Convective Parameterization for Mesoscale Models: The
Kain-Fritsch Scheme. 165–170.
Kaplan, J., and M. DeMaria, 2003: Large-scale characteristics of rapidly intensifying tropical
cyclones in the North Atlantic basin. Weather Forecast., 18, 1093–1108.
Kossin, J. P., 2002: Daily Hurricane Variability Inferred from GOES Infrared Imagery. Mon.
Wea. Rev., 130, 2260–2270.
Krishnamurti, T. N., 1999: Improved Weather and Seasonal Climate Forecasts from Multimodel
Superensemble. Science (80-. )., 285, 1548–1550.
Lee, W.-C., P. Dodge, F. D. Marks, and P. H. Hildebrand, 1994: Mapping of Airborne Doppler
Radar Data. J. Atmos. Oceanic Technol., 11, 572–578.
Leslie, L. M., and K. Fraedrich, 1990: Reduction of tropical cyclone position errors using an
optimal combination of independent forecasts. Weather Forecast., 5, 158–161.
Lhermitte, R. M., and L. J. Miller, 1970: Doppler radar methodology for the observation of
convective storms. 14th Conference on Radar Meteorology, Tucson, AZ, Amer. Meteor.
Soc., 133–144.
Li, X., J. Ming, Y. Wang, K. Zhao, and M. Xue, 2013: Assimilation of T-TREC-retrieved wind
data with WRF 3DVAR for the short-term forecasting of typhoon Meranti (2010) near
landfall. J. Geophys. Res. Atmos., 118, 10361–10375.
143
Li, Z., Z. Pu, J. Sun, and W.-C. Lee, 2014: Impacts of 4DVAR Assimilation of Airborne Doppler
Radar Observations on Numerical Simulations of the Genesis of Typhoon Nuri (2008). J.
Appl. Meteorol. Climatol., 53, 2325–2343.
Lord, S. J., H. E. Willoughby, and J. M. Piotrowicz, 1984: Role of a Parameterized Ice-Phase
Microphysics in an Axisymmetric, Nonhydrostatic Tropical Cyclone Model. J. Atmos. Sci.,
41, 2836–2848.
Lorenc, A. C., 1981: A Global Three-Dimensional Multivariate Statistical Interpolation Scheme.
Mon. Wea. Rev., 109, 701–721.
Lorsolo, S., J. Gamache, and A. Aksoy, 2013: Evaluation of the Hurricane Research Division
Doppler Radar Analysis Software Using Synthetic Data. J. Atmos. Oceanic Technol., 30,
1055–1071.
Louis, J.-F., 1979: A parametric model of vertical eddy fluxes in the atmosphere. Boundary-Layer
Meteorol., 17, 187–202.
Majumdar, S. J., and P. M. Finocchio, 2010: On the ability of global ensemble prediction systems
to predict tropical cyclone track probabilities. Weather Forecast., 25, 659–680.
Malkus, J. S., 1956: On the Maintenance of the Trade Winds. Tellus A, 8, 335–350.
Mapes, B. E., and P. Zuidema, 1996: Radiative-Dynamical Consequences of Dry Tongues in the
Tropical Troposphere. J. Atmos. Sci., 53, 620–638.
Marks, F. D., and R. A. Houze, 1984: Airborne doppler radar observations in Hurricane Debby.
Bull. Amer. Meteorol. Soc., 65, 569–582.
——, ——, F. M. Jr, and R. H. Jr, 1987: Inner core structure of Hurricane Alicia from airborne
Doppler radar observations. J. Atmos. Sci., 44, 1296–1317.
McBride, J. L., and R. Zehr, 1981: Observational Analysis of Tropical Cyclone Formation. Part
II: Comparison of Non-Developing versus Developing Systems. J. Atmos. Sci., 38, 1132–
1151.
144
McFarquhar, G. M., H. Zhang, G. Heymsfield, J. B. Halverson, R. Hood, J. Dudhia, and F.
Marks, 2006: Factors Affecting the Evolution of Hurricane Erin (2001) and the
Distributions of Hydrometeors: Role of Microphysical Processes. J. Atmos. Sci., 63, 127–
150.
Melhauser, C., and F. Zhang, 2012: Practical and intrinsic predictability of severe and convective
weather at the mesoscales. J. Atmos. Sci., 69, 3350–3371.
——, and ——, 2014: Diurnal Radiation Cycle Impact on the Pregenesis Environment of
Hurricane Karl (2010). J. Atmos. Sci., 71, 1241–1259.
Mellor, G., and T. Yamada, 1982: Development of a turbulence closure model for geophysical
fluid problems. Rev. Geophys. Sp. Phys., 20, 851–875.
Meng, Z., and F. Zhang, 2007: Tests of an ensemble Kalman filter for mesoscale and regional-
scale data assimilation. Part II: Imperfect model experiments. Mon. Wea. Rev., 135, 1403–
1423.
——, and ——, 2008a: Tests of an Ensemble Kalman Filter for Mesoscale and Regional-Scale
Data Assimilation. Part IV: Comparison with 3DVAR in a Month-Long Experiment. Mon.
Wea. Rev., 136, 3671–3682.
——, and ——, 2008b: Tests of an Ensemble Kalman Filter for Mesoscale and Regional-Scale
Data Assimilation. Part III: Comparison with 3DVAR in a Real-Data Case Study. Mon.
Wea. Rev., 136, 522–540.
Miller, R. A., and W. M. Frank, 1993: Radiative Forcing of Simulated Tropical Cloud Clusters.
Mon. Wea. Rev., 121, 482–498.
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.
Mohr, C. G., L. J. Miller, and R. L. Vaughan, 1981: An interactive software package for the
145
rectification of radar data to three-dimensional Cartesian coordinates. 20th Conference on
Radar Meteorology, Boston, MA, Amer. Meteor. Soc., 690–695.
Montgomery, M. T., and R. J. Kallenbach, 1997: A theory for vortex rossby-waves and its
application to spiral bands and intensity changes in hurricanes. Q. J. R. Meteorol. Soc., 123,
435–465.
Montgomery, M. T., C. Davis, T. Dunkerton, Z. Wang, and C. Velden, 2012: The Pre-Depression
Investigation of Cloud-Systems in the Tropics (PREDICT) experiment: Scientific basis, new
analysis tools, and some first results. Bull. Amer. Meteorol. Soc., 93, 153–172.
Nolan, D. S., and L. D. Grasso, 2003: Nonhydrostatic, Three-Dimensional Perturbations to
Balanced, Hurricane-Like Vortices. Part II: Symmetric Response and Nonlinear
Simulations. J. Atmos. Sci., 60, 2717–2745.
——, Y. Moon, and D. P. Stern, 2007: Tropical Cyclone Intensification from Asymmetric
Convection: Energetics and Efficiency. J. Atmos. Sci., 64, 3377–3405.
Pakula, L., and G. L. Stephens, 2009: The Role of Radiation in Influencing Tropical Cloud
Distributions in a Radiative–Convective Equilibrium Cloud-Resolving Model. J. Atmos.
Sci., 66, 62–76.
Palmer, T., 2002: The economic value of ensemble forecasts as a too for risk assessment: from
days to decades. Q. J. R. Meteorol. Soc., 128, 747–774.
Palmer, T. N., R. Buizza, F. Doblas-Reyes, T. Jung, M. Leutbecher, G. Shutts, M. Steinheimer,
and A. Weisheimer, 2009: Stochastic Parametrization and Model Uncertainty. 42 pp.
Posselt, D. J., S. C. van den Heever, and G. L. Stephens, 2008: Trimodal cloudiness and tropical
stable layers in simulations of radiative convective equilibrium. Geophys. Res. Lett., 35,
L08802.
Poterjoy, J., and F. Zhang, 2011: Dynamics and Structure of Forecast Error Covariance in the
Core of a Developing Hurricane. J. Atmos. Sci., 68, 1586–1606.
146
Purser, R. J., D. F. Parrish, and M. Masutani, 2000: Meteorological observational data
compression; An alternative to conventional “super-Obbing.” 12 pp.
Qi, L., H. Yu, and P. Chen, 2013: Selective ensemble-mean technique for tropical cyclone track
forecast by using ensemble prediction systems. Q. J. R. Meteorol. Soc., 805–813.
Rao, D. V. B., and D. Srinivas, 2014: Multi-Physics ensemble prediction of tropical cyclone
movement over Bay of Bengal. Nat. Hazards, 70, 883–902.
Ray, P. S., R. J. Doviak, G. B. Walker, D. Sirmans, J. Carter, and B. Bumgarner, 1975: Dual-
Doppler observation of a tornadic storm. J. Appl. Meteorol., 14, 1521–1530.
——, C. L. Ziegler, W. Bumgarner, and R. J. Serafin, 1980: Single-and multiple-Doppler radar
observations of tornadic storms. Mon. Wea. Rev., 108, 1607–1625.
Reasor, P. D., M. D. Eastin, and J. F. Gamache, 2009: Rapidly Intensifying Hurricane Guillermo
(1997). Part I: Low-Wavenumber Structure and Evolution. Mon. Wea. Rev., 137, 603–631.
Rogers, R., S. Chen, J. Tenerelli, and H. Willoughby, 2003: A Numerical Study of the Impact of
Vertical Shear on the Distribution of Rainfall in Hurricane Bonnie (1998). Mon. Wea. Rev.,
131, 1577–1599.
——, and Coauthors, 2006: The Intensity Forecasting Experiment: A NOAA Multiyear Field
Program for Improving Tropical Cyclone Intensity Forecasts. Bull. Amer. Meteorol. Soc.,
87, 1523–1537.
Rogers, R. R., 1964: An extension of the ZR relation for Doppler radar. 11th Conference on
Radar Meteorology, Boulder, CO, Amer. Meteor. Soc., 158–161.
Romine, G. S., C. S. Schwartz, J. Berner, K. R. Fossell, C. Snyder, J. L. Anderson, and M. L.
Weisman, 2014: Representing Forecast Error in a Convection-Permitting Ensemble System.
Mon. Wea. Rev., 142, 4519–4541.
Rutledge, S. A., and P. Hobbs, 1983: The Mesoscale and Microscale Structure and Organization
of Clouds and Precipitation in Midlatitude Cyclones. VIII: A Model for the “Seeder-Feeder”
147
Process in Warm-Frontal Rainbands. J. Atmos. Sci., 40, 1185–1206.
Sampson, C. R., J. L. Franklin, J. a. Knaff, and M. DeMaria, 2008: Experiments with a Simple
Tropical Cyclone Intensity Consensus. Weather Forecast., 23, 304–312.
Shutts, G., 2005: A kinetic energy backscatter algorithm for use in ensemble prediction systems.
Q. J. R. Meteorol. Soc., 131, 3079–3102.
Simpson, R. H., U. S. W. Bureau, and H. Riehl, 1958: Mid-Tropospheric Ventilation as a
Constraint on Hurricane Development and Maintenance. Proceedings Technical Conference
on Hurricanes, Miami Beach, FL, D4.1–D4.10.
Sippel, J. A., and F. Zhang, 2008: A probabilistic analysis of the dynamics and predictability of
tropical cyclogenesis. J. Atmos. Sci., 65.
——, and ——, 2010: Factors affecting the predictability of Hurricane Humberto (2007). J.
Atmos. Sci., 67, 1759–1778.
Skamarock, W. C. W. C., and Coauthors, 2008: A Description of the Advanced Research WRF
Version 3. NCAR Tech Note NCAR/TN-475+STR, 113 pp.
Snyder, A. D., Z. Pu, and Y. Zhu, 2010: and verification of East Atlantic tropical cyclone genesis
in the NCEP global ensemble: Case studies during the NASA African Monsoon
Multidisciplinary Analyses. Weather Forecast., 25, 1397–1411.
Stephens, G. L., 1978a: Radiation profiles in extended water clouds. I: Theory. J. Atmos. Sci., 35,
2111–2122.
——, 1978b: Radiation Profiles in Extended Water Clouds. II: Parameterization Schemes. J.
Atmos. Sci., 35, 2123–2132.
Steranka, J., E. B. Rodgers, and R. C. Gentry, 1984: The Diurnal Variation of Atlantic Ocean
Tropical Cyclone aoud DistributionInferred from Geostationary Satellite Infrared
Measurements. Mon. Wea. Rev., 112, 2338–2344.
Stewart, S. R., 2010: Tropical Cyclone Report Hurricane Karl (2010). 1-17 pp.
148
——, 2014: Tropical Cyclone Report Hurricane Edouard (2014). 1-19 pp.
Stoelinga, M. T., 2005: Simulated equivalent reflectivity factor as currently formulated in RIP:
Description and possible improvements. 1-5 pp.
Sundqvist, H., 1970: Numerical simulation of the development of tropical cyclones with a ten-
level model. Part II. Tellus, 5, 504–510.
Tao, D., and F. Zhang, 2014: Effect of environmental shear, sea-surface temperature, and ambient
moisture on the formation and predictability of tropical cyclones: An ensemble-mean
perspective. J. Adv. Model. Earth Syst., 6, 384–404.
Tao, W.-K., S. Lang, J. Simpson, C.-H. Sui, B. Ferrier, and M.-D. Chou, 1996: Mechanisms of
Cloud-Radiation Interaction in the Tropics and Midlatitudes. J. Atmos. Sci., 53, 2624–2651.
Torn, R. D., and D. Cook, 2013: The Role of Vortex and Environment Errors in Genesis
Forecasts of Hurricanes Danielle and Karl (2010). Mon. Wea. Rev., 141, 232–251.
Tracton, M. S., and E. Kalnay, 1993: Operational Ensemble Prediction at the National
Meteorological Center: Practical Aspects. Weather Forecast., 8, 379–398.
Vijaya Kumar, T. S. V., T. N. Krishnamurti, M. Fiorino, and M. Nagata, 2003: Multimodel
Superensemble Forecasting of Tropical Cyclones in the Pacific. Mon. Wea. Rev., 131, 574–
583.
Wallace, J. M., and P. V. Hobbs, 2006: Atmospheric Science: An Introductory Survey. 2nd ed.
Academic Press, 504 pp.
Wang, M., M. Xue, K. Zhao, and J. Dong, 2014: Assimilation of T-TREC-Retrieved Winds from
Single-Doppler Radar with an Ensemble Kalman Filter for the Forecast of Typhoon Jangmi
(2008). Mon. Wea. Rev., 142, 1892–1907.
Wang, Y., 2002: An Explicit Simulation of Tropical Cyclones with a Triply Nested Movable
Mesh Primitive Equation Model: TCM3. Part II: Model Refinements and Sensitivity to
Cloud Microphysics Parameterization*. Mon. Wea. Rev., 130, 3022–3036.
149
Weng, Y., and F. Zhang, 2012: Assimilating airborne Doppler radar observations with an
ensemble Kalman filter for convection-permitting hurricane initialization and prediction:
Katrina (2005). Mon. Wea. Rev., 140, 841–859.
Willoughby, H. E., H.-L. Jin, S. J. Lord, and J. M. Piotrowicz, 1984: Hurricane Structure and
Evolution as Simulated by an Axisymmetric, Nonhydrostatic Numerical Model. J. Atmos.
Sci., 41, 1169–1186.
Yamaguchi, M., and S. J. Majumdar, 2010: Using TIGGE Data to Diagnose Initial Perturbations
and Their Growth for Tropical Cyclone Ensemble Forecasts. Mon. Wea. Rev., 138, 3634–
3655.
——, R. Sakai, M. Kyoda, T. Komori, and T. Kadowaki, 2009: Typhoon Ensemble Prediction
System Developed at the Japan Meteorological Agency. Mon. Wea. Rev., 137, 2592–2604.
Yuqing Wang, G. H., 1996: The Beta Drift of Baroclinic Vortices. Part II: Diabatic Vortices. J.
Atmos. Sci., 53, 3737–3756.
Zhang, C., Y. Wang, and K. Hamilton, 2011a: Improved Representation of Boundary Layer
Clouds over the Southeast Pacific in ARW-WRF Using a Modified Tiedtke Cumulus
Parameterization Scheme *. Mon. Wea. Rev., 139, 3489–3513.
Zhang, F., and J. A. Sippel, 2009: Effects of moist convection on hurricane predictability. J.
Atmos. Sci., 66, 1944–1961.
——, and D. Tao, 2013: Effects of Vertical Wind Shear on the Predictability of Tropical
Cyclones.
——, and Y. Weng, 2015: Predicting Hurricane Intensity and Associated Hazards: A Five-Year
Real-Time Forecast Experiment with Assimilation of Airborne Doppler Radar
Observations. Bull. Amer. Meteorol. Soc., 96, 25–33.
——, C. Snyder, and R. Rotunno, 2002: Mesoscale predictability of the “surprise” snowstorm of
24-25 January 2000. Mon. Wea. Rev., 130, 1617–1632.
150
——, ——, and ——, 2003: Effects of moist convection on mesoscale predictability. J. Atmos.
Sci., 60, 1173–1185.
——, ——, and J. Sun, 2004: Impacts of initial estimate and observation availability on
convective-scale data assimilation with an ensemble Kalman filter. Mon. Wea. Rev., 132,
1238–1253.
——, Y. Weng, and J. A. Sippel, 2009: Cloud-resolving hurricane initialization and prediction
through assimilation of Doppler radar observations with an ensemble Kalman filter. Mon.
Wea. Rev., 137, 2105–2125.
——, ——, J. F. Gamache, and F. D. Marks, 2011b: Performance of convection-permitting
hurricane initialization and prediction during 2008–2010 with ensemble data assimilation of
inner-core airborne Doppler radar observations. Geophys. Res. Lett., 38, 1–6.
Zhu, T., and D.-L. Zhang, 2006: Numerical Simulation of Hurricane Bonnie (1998). Part II:
Sensitivity to Varying Cloud Microphysical Processes. J. Atmos. Sci., 63, 109–126.
Ziegler, C. L., 1978: A dual Doppler variational objective analysis as applied to studies of
convective storms. University of Oklahoma, 115 pp.
VITA
Christopher Lee Melhauser
EDUCATION:
The Pennsylvania State University Doctor of Philosophy: Meteorology
The Pennsylvania State University, 05/2010 Masters of Science: Meteorology
University of Colorado at Boulder, 05/2008 Bachelors of Science: Mechanical Engineering
PUBLICATIONS:
Melhauser, C., F. Zhang, A. Zhao, Y. Jin, and H. Jin 2016: A Multiple-Model Ensemble Examination of the Probabilistic Prediction of Hurricane Sandy (2012) and Hurricane Edouard (2014), Weather and Forecasting, in-prep.
Melhauser, C., and F. Zhang, 2016: Application of a Simplified Coplane Wind Retrieval Using Dual-Beam Airborne Doppler Radar Observations for Tropical Cyclone Prediction. Monthly Weather Review, in-review.
Zhang, F., C. Melhauser, D. Tao, Y. Q. Sun, E. B. Munsell, Y. Weng and J. A. Sippel, 2015: Predictability of Severe Weather and Tropical Cyclones at the Mesoscales. To appear in Dynamics and Predictability of Large-scale, High- impact Weather and Climate Events (eds, J. Li, R. Swinbank, H. Volkert and R. Grotjahn). Cambridge University Press.
Melhauser, C., and F. Zhang, 2014: Diurnal radiation cycle impact on the genesis of Hurricane Karl (2010). Journal of the Atmospheric Sciences, 71, 1241-1259.
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.
PRESENTATIONS:
Melhauser, C., and F. Zhang, 2015: A Multiple-Model Examination of the Probabilistic Prediction of Hurricanes Sandy (2012) and Edouard (2014). Hurricane Forecasting and Improvement Project (HFIP) 2015 annual meeting. Miami, FL.
Melhauser, C. and F. Zhang, 2015: A Multiple-Model Ensemble Examination of the Probabilistic Prediction of Hurricane Sandy (2012) and Hurricane Edouard (2014). The 23rd Conference on Numerical Weather Prediction. Chicago, IL.
Melhauser, C., and F. Zhang, 2014: Airborne Tail Doppler Radar Coplanar Dual-Doppler Wind Velocity Retrievals For Use In Tropical Cyclone Numerical Model Initialization. The 2014 AMS Summer Community Meeting, Student Presentation. State College, PA.
Melhauser, C., F. Zhang, Y. Weng, and J. Sippel, 2013: The Use of Airborne Doppler Radar Radial Velocity Super Observations for Tropical Cyclone Prediction. The 36th Conference on Radar Meteorology. Breckenridge, CO.
Melhauser, C., F. Zhang, M. Weisman, and D. P. Jorgensen, 2009: Predictability and dynamics of a squall line and bow echo event during BAMEX. The 13th Conference on Mesoscale Processes. Salt Lake City, UT.