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HWRF Model Sensitivity to Non-hydrostatic Effects Hurricane Diagnostics and Verification Workshop May 4, 2009 Katherine S. Maclay Colorado State University Department of Atmospheric Science
HWRF Model Sensitivity to Non-hydrostatic Effects
Hurricane Diagnostics and Verification Workshop
May 4, 2009
Katherine S. MaclayColorado State University
Department of Atmospheric Science
Outline
Motivations Model and data available Governing equations Energy principles Vertical velocity values Horizontal velocity values Epsilon values Conclusions Future Work
Looking for answers…
…via energy budget and PV field analysis of HWRF modeled Tropical Cyclone
Internal and external influences on TC structure change– Better understanding of heating and wind
structure relationships – Extratropical transition
Do the findings support/dispute observations and theories?
Tropical Cyclone Energy Cycle
P
K’
P’
K
Generation due to QDissipation via surface/internal friction
Azimuthal mean Variations from azimuthal mean
?
Kinetic Energy vs. Intensity
0
2E+16
4E+16
6E+16
8E+16
1E+17
1.2E+17
1.4E+17
1.6E+17
1.8E+17
0 20 40 60 80 100
Intensity (m/s)
KE
(J) HWRF
Recon
Hurricane Wilma October 18, 2005
00Z HWRF run
[Maclay (2008)]
HWRF 2007 Model
Moveable, 2-way nested grid
– 9 km inner grid spacing
– 27 km outer grid spacing
Advanced physics schemes from GFS and GFDL
Advanced vortex initialization (prototype GSI)
Ocean coupling using POM with the loop current (GFDL initialization)
Retrospective runs from the 2005 season
[Surgi (2008)]
Governing Equations
HFpvxkfdt
vd
)1(ˆ
VFgdt
dw
vtdt
d
Horizontal Momentum
Vertical Momentum
Material Derivative
Governing Equations (cont.)
0)(
)(
vt
Qc
TTv
t
T
p
Hydrostatic Balance
Continuity Equation
Thermodynamic Equation
A few definitions
1p̂
p
dt
dw
g
1
ppv
t
p ˆ)1(
v
tgw
1
Energy Principles
22
2
1wvK
dt
dww
dt
vdv
dt
dK
2
1
Kinetic Energy Definition
Kinetic Energy Principle
QcT
cTvct
Tc pppp
Potential Energy Principle
KE Principle Derivation
dt
dww
dt
vdv
VwFt
22
HFvpvt
v )(
)(
PROBLEM: Data provided in constant pressure vertical coordinate
∆t : 6 hours
How significant are the contributions from w and ε?
Vertical Velocity
Mean vertical velocity [m/s]
Standard Deviation Boundaries [m/s]
Horizontal Velocity
Mean horizontal velocity [m/s]
Standard Deviation Boundaries [m/s]
Epsilon (non-hydrostatic correction term)
Mean Epsilon value
Standard Deviation Boundaries
Conclusions
Non-hydrostatic effects make a negligibly small contribution
The energy principles derived from the hydrostatic approximated HWRF data are sufficient for our studies
What data is needed for a full
non-hydrostatic study…
Data in original sigma coordinates Horizontal and vertical momentum Geopotential height Pressure Temperature Radiative heat fluxes Momentum fluxes Condensate heating Relative humidity Specific humidity Absolute vorticity Cloud mixing ratio Total column ice, water, snow Sensible heat flux (sfc) Latent heat flux (sfc) Surface Precipitation: total, convective, large-scale
Data Needed for “full” study Data in original sigma coordinates Horizontal and vertical momentum Geopotential height Pressure Temperature Radiative heat fluxes Momentum fluxes Condensate heating Relative humidity Specific humidity Absolute vorticity Cloud mixing ratio Total column ice, water, snow Sensible heat flux (sfc) Latent heat flux (sfc) Surface Precipitation: total, convective, large-scale
Governing Equations: Part II
HFpvxkfdt
vd
)1(ˆ
VFgdt
dw
vtdt
d
Horizontal Momentum
Vertical Momentum
Material Derivative
Governing Equations II (cont.)
0)(
)(
vt
Qc
TTv
t
T
p
Hydrostatic Balance
Continuity Equation
Thermodynamic Equation
v
tgw
1
A few definitions
ppv
t
p ˆ)1(
1p̂
p
dt
dw
g
1
Energy Principles II
22
2
1wvK
dt
dww
dt
vdv
dt
dK
2
1
Kinetic Energy Definition
Kinetic Energy Principle
QcT
cTvct
Tc pppp
Potential Energy Principle
Hydrostatic Energy Principles
HFvt
vdt
vdv
)(
Kinetic Energy Principle
Potential Energy Principle
QcT
cTvct
Tc pppp
)()(
)(
The Next Steps…
Energy budget analysis:Use the methods of Tuleya and Kurihara (1975) as a guide.
Energy and PV Diagnostics
Stratosphere
Outflow Layer
Inflow Layer
Boundary Layer
Areas of interest indicated by the energy diagnostics will be further studied via analysis of the PV field.
References
• Maclay, K.S., M. DeMaria, T. Vonder Haar, 2008: Tropical cyclone size evolution. Mon. Wea. Rev., ???.
• Surgi, N, 2008: Advancement of the HWRF for next generation hurricane prediction at NCEP’s Environmental Modeling Center., 28th Conf. on Hurricanes and Trop. Meteor. http://ams.confex.com/ams/28Hurricanes/techprogram/paper_137876.htm.
• Tuleya, R., and Y. Kurihara, 1975: The energy and angular momentum budgets of a three-dimensional tropical cyclone model. J. Atmos. Sci., 32, 287-301.
