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

Outline Motivations Motivations Model and data available Model and data available Governing equations Governing equations Energy principles Energy principles Vertical velocity values Vertical velocity values Horizontal velocity values Horizontal velocity values Epsilon values Epsilon values Conclusions Conclusions Future Work 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 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? Do the findings support/dispute observations and theories?

Tropical Cyclone Energy Cycle P K’ P’ K Generation due to Q Dissipation via surface/internal friction Azimuthal meanVariations from azimuthal mean ?

Hurricane Wilma October 18, Z HWRF run [Maclay (2008)]

HWRF 2007 Model Moveable, 2-way nested grid Moveable, 2-way nested grid –9 km inner grid spacing –27 km outer grid spacing Advanced physics schemes from GFS and GFDL Advanced physics schemes from GFS and GFDL Advanced vortex initialization (prototype GSI) Advanced vortex initialization (prototype GSI) Ocean coupling using POM with the loop current (GFDL initialization) Ocean coupling using POM with the loop current (GFDL initialization) Retrospective runs from the 2005 season Retrospective runs from the 2005 season [Surgi (2008)]

Governing Equations Horizontal Momentum Vertical Momentum Material Derivative

Governing Equations (cont.) Hydrostatic Balance Continuity Equation Thermodynamic Equation

A few definitions

Energy Principles Kinetic Energy Definition Kinetic Energy Principle Potential Energy Principle

KE Principle Derivation 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 Non-hydrostatic effects make a negligibly small contribution The energy principles derived from the hydrostatic approximated HWRF data are sufficient for our studies The energy principles derived from the hydrostatic approximated HWRF data are 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 coordinates Data in original sigma coordinates Horizontal and vertical momentum Horizontal and vertical momentum Geopotential height Geopotential height Pressure Pressure Temperature Temperature Radiative heat fluxes Radiative heat fluxes Momentum fluxes Momentum fluxes Condensate heating Condensate heating Relative humidity Relative humidity Specific humidity Specific humidity Absolute vorticity Absolute vorticity Cloud mixing ratio Cloud mixing ratio Total column ice, water, snow Total 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-scale Surface Precipitation: total, convective, large-scale Data Needed for “full” study Data in original sigma coordinates Data in original sigma coordinates Horizontal and vertical momentum Horizontal and vertical momentum Geopotential height Geopotential height Pressure Pressure Temperature Temperature Radiative heat fluxes Radiative heat fluxes Momentum fluxes Momentum fluxes Condensate heating Condensate heating Relative humidity Relative humidity Specific humidity Specific humidity Absolute vorticity Absolute vorticity Cloud mixing ratio Cloud mixing ratio Total column ice, water, snow Total 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-scale Surface Precipitation: total, convective, large-scale

Governing Equations: Part II Horizontal Momentum Vertical Momentum Material Derivative

Governing Equations II (cont.) Hydrostatic Balance Continuity Equation Thermodynamic Equation

A few definitions

Energy Principles II Kinetic Energy Definition Kinetic Energy Principle Potential Energy Principle

Hydrostatic Energy Principles Kinetic Energy Principle Potential Energy Principle

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., ???.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. htm.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. htm. htm htm Tuleya, R., and Y. Kurihara, 1975: The energy and angular momentum budgets of a three-dimensional tropical cyclone model. J. Atmos. Sci., 32, Tuleya, R., and Y. Kurihara, 1975: The energy and angular momentum budgets of a three-dimensional tropical cyclone model. J. Atmos. Sci., 32,