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Mesoscale impacts of explicit numericaldiffusion in a convection-permitting model

Wolfgang Langhans, Jürg Schmidli, Christoph Schär

Institute for Atmospheric and Climate Science, ETH Zurich

March 3, 2010

Wolfgang Langhans COSMO/CLM User Seminar 2010 March 3, 2010 1 / 21

Outline

1 Introduction

2 COSMO setup

3 Impact of explicit diffusionCloud structuresAlpine heat budgetSpectral analysis

4 The origin of small-scale energy

5 Conclusions


Introduction (1)

dχ

dt= · · · − ν

(∂4χ

∂x4 +∂4χ

∂y4

)4th-order diffusion operatoralong model surfaces

with χ = u, v , w , p′, T ′, qv , qc , qi

2 3 4 5 6 7 80

0.02

0.04

0.06

0.08

0.1

0.12

0.14

n = λ/∆ x

Dam

ping

/ tim

e st

ep

Explicit diffusive filter response

0.0608

0.032

0.02048

c4=1.2E−04 s−1

c4=6.7E−05 s−1

c4=4.2E−05 s−1

hd_coeff_χ=0.75

hd_coeff_χ=0.40

hd_coeff_χ=0.25


Introduction (2)

Upstream-biased advection → no explicit numerical filtersneeded (Wicker and Skamarock 2002)Still it is convenient to apply explicit numerical filters (Knievelet al. 2007)Effective resolution depends on filtering of shortwavelengths (Skamarock 2004) → Importance for CRMIdealized studies show strong influence of numerical andsub-grid turbulent filtering at kilometer-scales (Takemi andRotunno 2003; Bryan 2005)

Objectives and MotivationInvestigate kilometer-scale real-case simulations usingexplicit diffusionIs the bulk Alpine heat budget sensitive to explicit diffusion?How’s diffusion of specific prognostic variables related toconvective precipitation?


Introduction (2)




Introduction (2)




Introduction (2)




Introduction (2)




Introduction (2)




Introduction (2)




COSMO setup

Version: 4.3 & 4.8Dynamics:

split-explicit RK-3 scheme (Wickerand Skamarock, 2002)

p’, T’ dynamics

5th-order advection, Bott 2nd-order qxadvection

Monotonic 4th-order diffusion operator

Physics:

prognostic TKE-based 1D turbulencescheme (λ∞ = 100 m),

no cumulus scheme, TERRA_ML

one-moment graupel scheme

Large Alpine domain:

501× 451× 45

∆ϕ = ∆λ = 0.02◦, ∆t = 30 s

IC/BC:

ECMWF operational analysis


COSMO setup

Version: 4.3 & 4.8Dynamics:

split-explicit RK-3 scheme (Wickerand Skamarock, 2002)

p’, T’ dynamics

5th-order advection, Bott 2nd-order qxadvection

Monotonic 4th-order diffusion operator

Physics:

prognostic TKE-based 1D turbulencescheme (λ∞ = 100 m),

no cumulus scheme, TERRA_ML

one-moment graupel scheme

Large Alpine domain:

501× 451× 45

∆ϕ = ∆λ = 0.02◦, ∆t = 30 s

IC/BC:

ECMWF operational analysis

σ of 500 hPa geopotential height11.-20. July 2006

(gpdm)


COSMO budget diagnosis

What? Extracts model tendencies

∂θ

∂t= −ADV +

Lv

cpdSl +

Ls

cpdSf + MT + Qr + MHD

Saas-Fee

=∂∂t

TADV + HD + MIC + RAD + TUR = TOT

Leadtime →

Tend

ency→

O. Fuhrer (MeteoSwiss)


Cloud structures (4 km MSL)No Diffusion

16U

TC

uvwpt0.75

17U

TC


Cloud structures (4 km MSL)No Diffusion

16U

TC

uvwpt0.75

17U

TC


Cloud structures (vertical slice)11 UTC 13 UTC

15 UTC 17 UTC


Potential temperature tendencies (13 UTC)3d Advection Vertical advection

Microphysics Turbulence


Diurnal cycle of the heat budget

Net Advection

Turbulence Microphysics


. . . and the impact of explicit diffusion

Net Advection

Turbulence Microphysics


Diurnal cycle of precipitation

Switzerland Alps


Diurnal cycle of w-spectra no diffusion

4 km


Diurnal cycle of w-spectra with diffusion

4 km


Spectral damping

model

cloud scale

Alpine scaleMeso scale

4 km

model

cloud scale

Alpine scaleMeso scale

8 km


Diffusion applied to specific variables


















The origin of small-scale energy (1)

Diffusion on discrete levels

Modification of net heating

All levels

< 1 km AGL

> 1 km AGL


The origin of small-scale energy (2)

Moisture advection:Bott 2nd, Semi-Lagrangian,

van Leer

Modification of heating

Net

Advection

Latent heating


Conclusions

“Dilemma”: Strong explicit diffusion results in→ Less energy at poorly resolved scales

→ Reduced convective growth→ Modified impact on mesoscale

Diffusion of qv ,p’,w little influence, diffusion of u,v,T’ largeinfluenceOrigin of grid-scale perturbations at lowest model levelsPartly numerically generated grid-scale noiseSolutions (besides avoiding these scales):

Always a compromise with the current setup (e.g. weakdiffusion of momentum only)Monotonic schemes


Conclusions






Conclusions






Conclusions






Conclusions






Thanks for your attention


Reduction of preciptiation

RUN TOTCH PEAKCH TOTALPS PEAKALPSnone -00.58 -28.83uvwpt0.75 -37.94 -55.76 -37.26 -32.27uv0.75 -30.23 -51.08 -27.32 -24.13p0.75 -13.88 -17.97 +00.91 -01.25t0.75 -27.52 -43.59 -29.06 -27.56q0.75 -04.04 -34.17 -06.14 -04.17uvw0.4 -17.93 -46.14 -20.22 -15.86uvw0.25 -12.23 -35.32 -16.06 -14.21w0.75 -05.04 -32.24 -06.52 -08.37

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Mesoscale impacts of explicit numerical diffusion in ... - IAC Wiki