hwrf model sensitivity to non-hydrostatic effects 5.09/maclay.pdf · 2010. 4. 7. · hwrf model...

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.