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**Parametrization of PBL outer layer Irina Sandu and Martin Kohler**

Overview of models Bulk models Local K-closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

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Reynolds equations Reynolds Terms

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**Parametrization of PBL outer layer (overview)**

Application Order and Type of Closure Bulk models Models that treat PBL top as surface 0th order non-local K-diffusion Models with fair resolution 1st order local Mass-flux 1st order non-local ED/MF (K& M) 1st order non-local K-profile TKE-closure Models with high resolution 1.5th order non-local Higher order closure 2nd or 3rd order non-local

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**Parametrization of PBL outer layer**

Overview of models Bulk models Local K-closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

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**Bulk - Slab - Integral - Mixed Layer Models**

Bulk models can be formally obtained by: Making similarity assumption about shape of profile, e.g. Integrate equations from z=0 to z=h Solve rate equations for scaling parameters , and h The mixed layer model of the day-time boundary layer is a well-known example of a bulk model.

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**Mixed layer (bulk) model of day time BL**

energy mass inversion entrainment This set of equations is not closed. A closure assumption is needed for entrainment velocity or for entrainment flux.

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**Closure for mixed layer model**

The closure is based on the turbulent kinetic energy budget of the mixed layer: Buoyancy flux in inversion scales with production in mixed layer: CE is entrainment constant (0.2) Cs represents shear effects (2.5-5) but is often not considered

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**Parametrization of PBL outer layer**

Overview of models Bulk models Local K closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

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**Local K closure Levels in ECMWF model**

K-diffusion in analogy with molecular diffusion, but 91-level model 31-level model Diffusion coefficients need to be specified as a function of flow characteristics (e.g. shear, stability,length scales).

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**Diffusion coefficients according to MO-similarity**

Use relation between and to solve for

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**Stable boundary layer in the IFS: current problems**

underestimation of T2m and of wind turning (low level jet poorly represented) Increase the vertical diffusion SFMO 1/l=1/kz+1/λ , λ=150m SFMO 36R4 Surface layer – SFMO Above: f = α* fLTG + (1- α) * fMO α = exp(-H/150)

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**GABLS 3 . Impact of the stability functions**

U200m T2M U10m hours since 12 UTC hours since 12 UTC hours since 12 UTC

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**GABLS 3 : Impact of the mixing length**

U200m T2M U10m hours since 12 UTC hours since 12 UTC hours since 12 UTC

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**K-closure with local stability dependence (summary)**

Scheme is simple and easy to implement. Fully consistent with local scaling for stable boundary layer. A sufficient number of levels is needed to resolve the BL i.e. to locate inversion. Entrainment at the top of the boundary layer is not represented (only encroachment)! flux

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**Parametrization of PBL outer layer**

Overview of models Bulk models Local K closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

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**K-diffusion versus Mass flux method**

K-diffusion method: analogy to molecular diffusion Mass-flux method: mass flux entraining plume model detrainment rate

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**M ED/MF framework a sub-core flux env. flux M-flux**

Siebesma & Cuijpers, 1995

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**BOMEX LES decomposition**

M-flux sub-core flux total flux env. flux M-flux covers 80% of flux Siebesma & Cuijpers, 1995

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**Parametrization of PBL outer layer**

Overview of models Bulk models Local K-closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

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**K-profile closure Troen and Mahrt (1986)**

Heat flux h Profile of diffusion coefficients: Find inversion by parcel lifting with T-excess: Ri_c=0.25 is irrelevant for a mixed layer (any number will do). For stable layers, it gives a realistic result such that:

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**K-profile closure (ECMWF up to 2005)**

Inversion interaction was too aggressive in original scheme and too much dependent on vertical resolution. Features of ECMWF implementation: No counter gradient terms. Not used for stable boundary layer. Lifting from minimum virtual T. Different constants. Implicit entrainment formulation. Entrainment fluxes h Moisture flux Heat flux Original TM is too aggressive on inversions Entrainment is specified implicitly for stability. ECMWF entrainment formulation: ECMWF Troen/Mahrt C D CE

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**K-profile closure (summary)**

Scheme is simple and easy to implement. Numerically robust. Scheme simulates realistic mixed layers. Counter-gradient effects can be included (might create numerical problems). Entrainment can be controlled rather easily. A sufficient number of levels is needed to resolve BL e.g. to locate inversion.

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**Parametrization of PBL outer layer**

Overview of models Bulk models Local K closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

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TKE closure (1.5 order) Eddy diffusivity approach: With diffusion coefficients related to kinetic energy:

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**Closure of TKE equation**

Pressure correlation TKE from prognostic equation: Storage Shear production Buoyancy Turbulent transport Dissipation with closure: Main problem is specification of length scales, which are usually a blend of , an asymptotic length scale and a stability related length scale in stable situations.

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**TKE (summary) TKE has natural way of representing entrainment.**

TKE needs more resolution than first order schemes. TKE does not necessarily reproduce MO-similarity. Stable boundary layer may be a problem.

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**Parametrization of PBL outer layer**

Overview of models Bulk models Local K closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

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**Current closure in the ECMWF model**

K-diffusion closure with different f(Ri) for stable and unstable layers K-diffusion closure with different f(Ri) for stable and unstable layers ED/MF (K-profile + M flux)

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**Reduced Diffusion above Surface Layer**

1.0 0.8 0.6 0.4 0.2 10 Monin-Obukhov (new) LTG mom LTG heat LTG (old) 8 MO mom MO heat 6 f(Ri) Height [km] 4 LTG (old & new) 2 0.5 1.0 1.5 50 100 150 Richardson Number Ri Turbulent Length Scale l [m] Old large diffusion coefficients: Louis-Tiedtke-Geleyn (1982) empirical New small diffusion coefficients: Monin-Obukhov (1954) based on observations

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**Z500 Activity increase due to K reduction**

K reduced control FC Activity: wave number 0-3 AN Activity: wave number 0-3 Activity: wave number 4-14 RMS error 115 T399 runs

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**Shear power spectrum: resolution dependence**

10 100 1000 1 10-2 10-4 10-6 Spectral Shear Power Horizontal Wave Number 20 200 2000 T1279 T799 T399 T159 T2047 k-1.03 z=1000m Model lacks shear power near truncation. Flat spectrum suggests large missing shear at small scales.

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**511 Forecasts ...even colder 2m T ...so basically the errors increase**

2T error CTL – analysis , 72 h FC, 0 UTC 2T difference SFMO – CTL , 72 h FC, 0 UTC ...even colder 2m T 2T error CTL – error SFMO , 72 h FC, 0 UTC ...so basically the errors increase

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**Wind turning difference SFMO – CTL , 72 h FC, 0 UTC**

...but better wind turning... Wind turning difference SFMO – CTL , 72 h FC, 0 UTC

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