HWRF Model Sensitivity HWRF Model Sensitivity to Non-hydrostatic to Non-hydrostatic

EffectsEffects

Hurricane Diagnostics and Verification Hurricane Diagnostics and Verification WorkshopWorkshop

May 4, 2009May 4, 2009

Katherine S. MaclayKatherine S. MaclayColorado State UniversityColorado State University

Department of Atmospheric ScienceDepartment of Atmospheric Science

OutlineOutline

MotivationsMotivations Model and data availableModel and data available Governing equationsGoverning equations Energy principlesEnergy principles Vertical velocity valuesVertical velocity values Horizontal velocity valuesHorizontal velocity values Epsilon valuesEpsilon values ConclusionsConclusions Future WorkFuture Work

Looking for answers…Looking for answers…

……via energy budget and PV field via energy budget and PV field analysis of HWRF modeled Tropical analysis of HWRF modeled Tropical CycloneCyclone

Internal and external influences on TC Internal and external influences on TC structure changestructure change– Better understanding of heating and wind Better understanding of heating and wind

structure relationships structure relationships – Extratropical transition Extratropical transition

Do the findings support/dispute Do the findings support/dispute observations and theories?observations and theories?

Tropical Cyclone Energy Tropical Cyclone Energy CycleCycle

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 Hurricane Wilma October 18, 2005 October 18, 2005

00Z HWRF run00Z HWRF run

[Maclay (2008)]

HWRF 2007 ModelHWRF 2007 Model

Moveable, 2-way nested gridMoveable, 2-way nested grid– 9 km inner grid spacing9 km inner grid spacing– 27 km outer grid spacing27 km outer grid spacing

Advanced physics schemes from GFS and Advanced physics schemes from GFS and GFDLGFDL

Advanced vortex initialization (prototype Advanced vortex initialization (prototype GSI)GSI)

Ocean coupling using POM with the loop Ocean coupling using POM with the loop current (GFDL initialization)current (GFDL initialization)

Retrospective runs from the 2005 seasonRetrospective runs from the 2005 season[Surgi (2008)]

Governing EquationsGoverning Equations

HFpvxkfdt

vd

)1(ˆ

VFgdt

dw

vtdt

d

Horizontal Momentum

Vertical Momentum

Material Derivative

Governing Equations Governing Equations (cont.)(cont.)

0)(

)(

vt

Qc

TTv

t

T

p

Hydrostatic Balance

Continuity Equation

Thermodynamic Equation

A few definitionsA few definitions

1p̂

p

dt

dw

g

1

p

pvt

p ˆ)1(

v

tgw

1

Energy PrinciplesEnergy 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 DerivationKE 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 VelocityVertical Velocity

Mean vertical velocity [m/s]

Standard Deviation Boundaries [m/s]

Horizontal VelocityHorizontal Velocity

Mean horizontal velocity [m/s]

Standard Deviation Boundaries [m/s]

Epsilon (non-hydrostatic Epsilon (non-hydrostatic correction term)correction term)

Mean Epsilon value

Standard Deviation Boundaries

ConclusionsConclusions

Non-hydrostatic effects make a Non-hydrostatic effects make a negligibly small contribution negligibly small contribution

The energy principles derived from the The energy principles derived from the hydrostatic approximated HWRF data hydrostatic approximated HWRF data are sufficient for our studiesare sufficient for our studies

What data is needed for a full What data is needed for a full

non-hydrostatic study…non-hydrostatic study…

Data in original sigma coordinatesData in original sigma coordinates Horizontal and vertical momentumHorizontal and vertical momentum Geopotential heightGeopotential height PressurePressure TemperatureTemperature Radiative heat fluxesRadiative heat fluxes Momentum fluxesMomentum fluxes Condensate heatingCondensate heating Relative humidityRelative humidity Specific humiditySpecific humidity Absolute vorticityAbsolute vorticity Cloud mixing ratioCloud mixing ratio Total column ice, water, snowTotal column ice, water, snow Sensible heat flux (sfc)Sensible heat flux (sfc) Latent heat flux (sfc)Latent heat flux (sfc) Surface Precipitation: total, convective, large-scaleSurface Precipitation: total, convective, large-scale

Data Needed for “full” Data Needed for “full” study study Data in original sigma coordinatesData in original sigma coordinates Horizontal and vertical momentumHorizontal and vertical momentum Geopotential heightGeopotential height PressurePressure TemperatureTemperature Radiative heat fluxesRadiative heat fluxes Momentum fluxesMomentum fluxes Condensate heatingCondensate heating Relative humidityRelative humidity Specific humiditySpecific humidity Absolute vorticityAbsolute vorticity Cloud mixing ratioCloud mixing ratio Total column ice, water, snowTotal column ice, water, snow Sensible heat flux (sfc)Sensible heat flux (sfc) Latent heat flux (sfc)Latent heat flux (sfc) Surface Precipitation: total, convective, large-scaleSurface Precipitation: total, convective, large-scale

Governing Equations: Governing Equations: Part IIPart II

HFpvxkfdt

vd

)1(ˆ

VFgdt

dw

vtdt

d

Horizontal Momentum

Vertical Momentum

Material Derivative

Governing Equations II Governing Equations II (cont.)(cont.)

0)(

)(

vt

Qc

TTv

t

T

p

Hydrostatic Balance

Continuity Equation

Thermodynamic Equation

v

tgw

1

A few definitionsA few definitions

p

pvt

p ˆ)1(

1p̂

p

dt

dw

g

1

Energy Principles IIEnergy 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 Hydrostatic Energy PrinciplesPrinciples

HFvtv

dt

vdv

)(

Kinetic Energy Principle

Potential Energy Principle

QcT

cTvct

Tc pppp

)(

)()(

The Next Steps…The Next Steps…

Energy budget analysis:Use the methods of Tuleya and Kurihara (1975) as a guide.

Energy and PV Energy and PV DiagnosticsDiagnostics

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.

ReferencesReferences

• Maclay, K.S., M. DeMaria, T. Vonder Haar, 2008: Tropical Maclay, K.S., M. DeMaria, T. Vonder Haar, 2008: Tropical cyclone size evolution. cyclone size evolution. Mon. Wea. Rev.Mon. Wea. Rev., , ??????..

• Surgi, N, 2008: Advancement of the HWRF for next generation Surgi, N, 2008: Advancement of the HWRF for next generation hurricane prediction at NCEP’s Environmental Modeling hurricane prediction at NCEP’s Environmental Modeling Center., Center., 28th Conf. on Hurricanes and Trop. Meteor28th 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 Tuleya, R., and Y. Kurihara, 1975: The energy and angular momentum budgets of a three-dimensional tropical cyclone momentum budgets of a three-dimensional tropical cyclone model. model. J. Atmos. Sci.J. Atmos. Sci., , 3232, 287-301., 287-301.