Methods for Introducing VHTs

in Idealized Models:

Retrieving Latent Heat

Steve GuimondFlorida State University

Motivation

• Previous theoretical work on TC intensification• Many authors (i.e. Montgomery and Enagonio, 1998)

– Initialize with 2D, balanced vorticity or PV anomalies in barotropic/QG models

• Nolan and Montgomery (2002)– Dry simulations; initialize with 3D, unbalanced, weak,

prescribed θ’

• Nolan et al. (2007)– Dry, “equivalent heat injection”, 4D (time evolving θ’)

Attacking the problem

• What is the best way to characterize and introduce remotely sensed VHTs into an idealized simulation?– Latent Heating– Divergence (Mapes and Houze 1995)

• Observationally motivated simulation– Moist model– Consider evolution of latent heating into θ’

Latent Heating Algorithm

• Model testing…– Non-hydrostatic, full-physics, cloud-resolving (2-km) MM5

simulation of Hurricane Bonnie (1998; Braun 2006)

– Goal: saturation using production of precipitation (Gamache et al. 1993)

• Divergence, diffusion and offset are small and can be neglected

( ) ( ) ( )ZDQQ

z

Vq

z

wvq

z

wqvq

t

q tpp

pp

p ++−+∂

∂+⎟⎠

⎞⎜⎝

⎛∂

∂+•∇+

∂

∂−•−∇=

∂

∂−+

vv

( ) ( )net

tpp

p Qz

Vwqvq

t

q+

∂

+∂−•−∇=

∂

∂ −v

Structure of Latent Heat

total precipitation mixing ratio

horizontal winds

hydrometeor fallspeed

source of total precipitation

sink of total precipitation

net source of total precipitation

tu

p

t

net

q

v

V

Q

Q

Q

D

+

−

v

rbulent diffusion

model offset for numerical errorZ

Magnitude of Latent Heat

• Requirements– Temperature and pressure (mean dropsonde)– Vertical velocity (radar)

lnp

D JC

Dt T

θ=

ln c s

p

L qDw

Dt C T z

θ − ∂≅

∂

where s sc c

Dq qJ L L w

Dt z

∂=− ≅−

∂

gas constant

latent heat of condensation

T temperature

potential temperature

saturation mixing ratio

w vertical velocity

p

c

s

C

L

q

θ

– Net source of precipitation

– Positives• Full radar swath of latent heat in various types of clouds (sometimes 4-D)

– Negatives• Estimating local tendency term

– Steady-state ?– Guillermo (1997) ~34 mintue sampling

• Thermo based on mean dropsonde• Drop size distribution uncertainty and feedback on derived parameters

ln c s

p

L qDw

Dt C T z

θ ∂=−

∂)(saturated 0>netQ

ed)(unsaturat 0≤netQln c

netp

LDQ

Dt C T

θ=

Combining Structure and Magnitude

• Only care about condition of saturation for heating– Some error OK– Tendency, reflectivity-derived parameters, horizontal winds (excellent in P-3)

Testing algorithm in model

Testing algorithm in modelln c s

p

L qDw

Dt C T z

θ ∂=−

∂

Testing algorithm in model

P-3 Doppler Radar Results

Constructing Z-LWC Relationships

• Hurricane Katrina (2005) particle data from P-3– August 25, 27, 28 (TS,CAT3,CAT5)– Averaged for 6s ~ 1km along flight path

• Match probe and radar sampling volumes

Below melting level:

Z = 402*LWC1.47 n = 7067 RMSE = 0.212 g m-3

Above melting level (Black 1990):

Z = 670*IWC1.79 n = 1609 r = 0.81

P-3 Doppler Radar LH in Guillermo(1997)ln c s

p

L qDw

Dt C T z

θ ∂=−

∂

P-3 Doppler Radar LH in Guillermo(1997)ln c s

p

L qDw

Dt C T z

θ ∂=−

∂

P-3 Radar LH: Thermodynamic Sensitivity

• New method for LH retrievals– Ability to accept some errors in water budget

– Local tendency, radar-derived parameters

– LH magnitude relatively insensitive to thermo– Sensitive to vertical velocity (most important)

• Test mass continuity vertical velocity or use EDOP?

• ~30 minute radar sampling does nothing for water budget

• Local tendency à order of mag. less than Qnet• Incorporate WSR-88Ds for tendency, heating

evolution• Hybrid method

– Doppler radar and dropsonde

Conclusions and Future Work

LANL work

• End goal: find relationship between latent heating and lightning– TCs are diabatic systems– Satellite latent heating is crude (e.g. no winds)

– Doppler radar coverage sparse– To get lightning– cloud liquid water, graupel, ice collisions– Requires large updraft à latent heat– Lightning fills gap in convective monitoring– New sensors (precise 3-D lightning locations)

– Lightning type, what else?– Inject latent heating coincident with lightning

Taken from Richard Blakeslee TCSP ppt

-8 to -15 dB large, wet, asymmetric ice to large, wet snow aggregates

-13 to -17 dB medium, wet graupel or small hail

-18 to -26 dB small, dry ice particles to dry, low density snow

EYE

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Model Diabatic Heating Budget

• Non-hydrostatic, full-physics, cloud-resolving (2-km) MM5 simulation of Hurricane Bonnie (1998; Braun 2006)

Testing algorithm in model

( ) ( ) ( )ZDQQ

z

Vq

z

wvq

z

wqvq

t

q tpp

pp

p ++−+∂

∂+⎟⎠

⎞⎜⎝

⎛∂

∂+•∇+

∂

∂−•−∇=

∂

∂−+

vv

Acknowledgments

• Scott Braun (MM5 output)• Robert Black (particle processing)• Paul Reasor and Matt Eastin (Guillermo edits)• Paul Reasor and Mark Bourassa (advice)

References• Black (1990)• Braun et al. (2006), Braun (2006)• Gamache et al. (1993)• Heymsfield et al. (1999)• Reasor et al. (2008)• Satoh and Noda (2001)