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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) ParametrizationApplicationOrder and Type of Closure Bulk modelsModels that treat PBL top as surface0 th order non-local K-diffusion Models with fair resolution1 st order local Mass-flux Models with fair resolution1 st order non-local ED/MF (K& M)Models with fair resolution1 st order non-local K-profileModels with fair resolution1 st order non-local TKE-closureModels with high resolution1.5 th order non- local Higher order closureModels with high resolution2 nd or 3 rd 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 This set of equations is not closed. A closure assumption is needed for entrainment velocity or for entrainment flux. energy mass inversion entrainment

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

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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 91-level model 31-level model Levels in ECMWF model K-diffusion in analogy with molecular diffusion, but 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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underestimation of T2m and of wind turning (low level jet poorly represented) Increase the vertical diffusion 1/l=1/kz+1/λ, λ=150m 36R4 Surface layer – SFMO Above: f = α* fLTG + (1- α) * fMO α = exp(-H/150) Stable boundary layer in the IFS: current problems SFMO

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GABLS 3. Impact of the stability functions T2M hours since 12 UTC U200m U10m

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GABLS 3 : Impact of the mixing length T2M hours since 12 UTC U200m U10m

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

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ED/MF framework a M M-fluxenv. fluxsub-core flux Siebesma & Cuijpers, 1995

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BOMEX LES decomposition total flux M-flux env. flux sub-core flux Siebesma & Cuijpers, 1995 M-flux covers 80% of 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-profile closure Troen and Mahrt (1986) Heat flux h Profile of diffusion coefficients: Find inversion by parcel lifting with T-excess: such that:

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K-profile closure (ECMWF up to 2005) Moisture flux Entrainment fluxes Heat flux h ECMWF entrainment formulation: ECMWFTroen/Mahrt C D C E 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.

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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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BuoyancyShear productionStorage Closure of TKE equation TKE from prognostic equation: 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. Turbulent transport Dissipation Pressure correlation

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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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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 f(Ri) Richardson Number Ri LTG mom LTG heat MO mom MO heat LTG (old & new) LTG (old) Monin-Obukhov (new) Height [km] 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 FC Activity: wave number T399 runs RMS error K reduced control AN Activity: wave number 0-3 Activity: wave number 4-14

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Shear power spectrum: resolution dependence Spectral Shear Power Horizontal Wave Number T1279 T799 T399 T159 T2047 k Model lacks shear power near truncation. Flat spectrum suggests large missing shear at small scales. z=1000m

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511 Forecasts 2T error CTL – analysis, 72 h FC, 0 UTC2T difference SFMO – CTL, 72 h FC, 0 UTC 2T error CTL – error SFMO, 72 h FC, 0 UTC...so basically the errors increase...even colder 2m T

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

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