COSMO General Meeting, Moscow, Russia. 6-10 September 2010.

Further Single-Column Testing and Implementation into the COSMO Model of the TKE-Scalar Variance

Second-Order Turbulence-Convection Scheme

7 September 2010

Ekaterina Machulskaya and Dmitrii Mironov

German Weather Service, Offenbach am Main, Germany

(ekaterina.machulskaya@dwd.de, dmitrii.mironov@dwd.de)

COSMO General Meeting, Moscow, Russia. 6-10 September 2010.

Single-column tests: dry convective PBL, nocturnal stratocumuli, shallow cumuli, stably-stratified PBL

Modified statistical SGS cloud scheme: parallel experiments

TKE-scalar variance scheme within a full-fledged COSMO model: implementation, parallel experiment, problems

Conclusions and outlook

Outline

Single-Column Tests: Dry Convective PBL

Mean potential temperature in shear-free convective PBL.

Red – TKE scheme, blue – TKE-scalar variance scheme, black dashed – LES data.

Single-Column Tests: Nocturnal Stratocumuli

Fractional cloud cover (left) and cloud water content (middle) in DYCOMS-II.

Red – TKE scheme, blue – TKE-scalar variance scheme.

Black solid curve in the right figure shows LES data.

Single-Column Tests: Shallow Cumuli

Fractional cloud cover (upper row) and cloud water content (lower row) in BOMEX.

Red – TKE scheme, blue – TKE-scalar variance scheme. Black solid curves in the middle figures show LES data.

Gaussian

Gaussian

skewed

skewed

Single-column tests: shallow cumuli (cont’d)

Potential temperature variance (two left panels) and total water variance (two right panels) in BOMEX.

Red – TKE scheme, blue – TKE-scalar variance scheme.

Black solid curves in the middle figures show LES data.

1

0.5

0

Linear approximationof the error function

(Gaussian distribution)

Exponential tail

Cloud fraction

Normalised saturation deficit

Strong mean undersaturation =shallow cumuli case

Single-column tests: shallow cumuli (cont’d)

Important! Non-Gaussian correction is introduced into the expression for the buoyancy flux in the TKE equation

Modified Statistical SGS Cloud Scheme: Parallel Experiments

Exp 7680 – COSMO-EU model with modified SGS cloud scheme, January 2010

Exp 7692 – COSMO-EU model with modified SGS cloud scheme, June 2010

Pressure over COSMO-EU domain in June 2010 (00UTC forecasts).

Red – Exp7692, blue – COSMO-EU.

Modified Statistical SGS Cloud Scheme: Parallel Experiments (cont’d)

T2m TD2m deficit

Exp 7680, COMO-EU, January 2010 (00UTC forecasts)

Verification over COSMO-DE domain

Modified Statistical SGS Cloud Scheme: Parallel Experiments (cont’d)

red – Exp7692, blue – COSMO-EU routine

total cloud cover

low-level cloud cover

COSMO-EU domain, June 2010

TKE-scalar variance scheme within a full-fledged COSMO model

TKE-scalar variance scheme is implemented into full-fledged three-dimensional COSMO model

Parallel experiments are being performed

• Exp 7771 – with Gaussian SGS cloud scheme

• Exp 7778 – with modified (skewed) SGS cloud scheme

Problems

• numerical stability (hope to improve the situation using non-local formulation for turbulence length scale)

• more physically sound parameterisation of non-Gaussian effects within the SGS cloud scheme is needed

LES and Modelling of SBL over Heterogeneous and Homogeneous Surfaces

by D. Mironov, P. Sullivan (NCAR) and E. Machulskaya

Blue – homogeneous SBL,

red – heterogeneous SBL.

Tiled TKE-Temperature Variance Closure Model

• Transport (prognostic) equations for TKE and for the temperature variances including third-order transport

• Algebraic (diagnostic) formulations for temperature flux, for the Reynolds-stress components, and for turbulence length scale

• Tile approach where different tiles have different surface temperature

• Surface fluxes are computed as weighted means of fluxes over individual tiles

• <w’’2> is non-zero at the surface in heterogeneous SBL

• Input parameters of numerical experiments are similar to LES (except for piece-wise vs. sinusoidally varying surface temperature)

Tiled TKE-Temperature Variance Model: Results

Blue – homogeneous SBL,

red – heterogeneous SBL.

COSMO General Meeting, Moscow, Russia. 6-10 September 2010.

Single-column tests show that the use of TKE-scalar variance scheme brings about some improvements as to fractional cloud cover, second-moment profiles, and evolution of turbulence moments in time, although problems remain

Modified SGS statistical cloud scheme (effect of shallow cumuli à la Bechtold et al. 1995) is favourably tested through parallel experiments; scores are neutral to slightly positive

TKE-scalar variance scheme is implemented into full-fledged three-dimensional COSMO model, parallel experiment is being performed, performance is monitored, results of verification will be reported later

Comprehensive testing through parallel experiments (key issues: numerical stability, computational efficiency), preparation of documentation

Improve a parameterisation of the turbulence length/time scale (e.g. non-local vs. Blackadar)

Improve description of non-Gaussian effects within the SGS statistical cloud scheme (Bechtold et al. 1995, modifications do not seem to be sufficient)

Conclusions and Outlook

COSMO General Meeting, Moscow, Russia. 6-10 September 2010.

Thank you for your attention!

Acknowledgements: Vittorio Canuto, Peter Bechtold, Sergey Danilov, Evgeni Fedorovich, Jochen Förstner, Vladimir Gryanik, Thomas Hanisch, Donald Lenschow, Chin-Hoh Moeng, Ned Patton, Pier Siebesma, Peter Sulluvan, Jeffrey Weil, and Yun-Ichi Yano.