3Parametrization of PBL outer layer (overview) ApplicationOrder and Type of ClosureBulk modelsModels that treat PBL top as surface0th order non-localK-diffusionModels with fair resolution1st order localMass-flux1st order non-localED/MF (K& M)1st order non-localK-profileTKE-closureModels with high resolution1.5th order non-localHigher order closure2nd or 3rd order non-local
4Parametrization of PBL outer layer Overview of modelsBulk modelsLocal K-closureED/MF closureK-profile closureTKE closureCurrent closure in the ECMWF model
5Bulk - 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=hSolve rate equations for scaling parameters , and hThe mixed layer model of the day-time boundary layer is a well-known example of a bulk model.
6Mixed layer (bulk) model of day time BL energymassinversionentrainmentThis set of equations is not closed. A closure assumption is needed for entrainment velocity or for entrainment flux.
7Closure 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
8Parametrization of PBL outer layer Overview of modelsBulk modelsLocal K closureED/MF closureK-profile closureTKE closureCurrent closure in the ECMWF model
9Local K closure Levels in ECMWF model K-diffusion in analogy with molecular diffusion, but91-levelmodel31-levelmodelDiffusion coefficients need to be specified as a function of flow characteristics (e.g. shear, stability,length scales).
10Diffusion coefficients according to MO-similarity Use relation between andto solve for
11Stable boundary layer in the IFS: current problems underestimation of T2m and of wind turning (low level jet poorly represented)Increase the vertical diffusionSFMO1/l=1/kz+1/λ , λ=150mSFMO36R4Surface layer – SFMOAbove: f = α* fLTG + (1- α) * fMOα = exp(-H/150)
12GABLS 3 . Impact of the stability functions U200mT2MU10mhours since 12 UTChours since 12 UTChours since 12 UTC
13GABLS 3 : Impact of the mixing length U200mT2MU10mhours since 12 UTChours since 12 UTChours since 12 UTC
14K-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
15Parametrization of PBL outer layer Overview of modelsBulk modelsLocal K closureED/MF closureK-profile closureTKE closureCurrent closure in the ECMWF model
16K-diffusion versus Mass flux method K-diffusion method:analogy tomolecular diffusionMass-flux method:mass fluxentraining plume modeldetrainment rate
18BOMEX LES decomposition M-fluxsub-core fluxtotal fluxenv. fluxM-flux covers 80% of fluxSiebesma & Cuijpers, 1995
19Parametrization of PBL outer layer Overview of modelsBulk modelsLocal K-closureED/MF closureK-profile closureTKE closureCurrent closure in the ECMWF model
20K-profile closure Troen and Mahrt (1986) Heat fluxhProfile 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 resultsuch that:
21K-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 fluxeshMoisture fluxHeat fluxOriginal TM is too aggressive on inversionsEntrainment is specified implicitly for stability.ECMWF entrainment formulation:ECMWFTroen/MahrtCDCE
22K-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.
23Parametrization of PBL outer layer Overview of modelsBulk modelsLocal K closureED/MF closureK-profile closureTKE closureCurrent closure in the ECMWF model
24TKE closure (1.5 order)Eddy diffusivity approach:With diffusion coefficients related to kinetic energy:
25Closure of TKE equation Pressure correlationTKE from prognostic equation:StorageShear productionBuoyancyTurbulenttransportDissipationwith closure:Main problem is specification of length scales, which are usually a blend of , an asymptotic length scale anda stability related length scale in stable situations.
26TKE (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.
27Parametrization of PBL outer layer Overview of modelsBulk modelsLocal K closureED/MF closureK-profile closureTKE closureCurrent closure in the ECMWF model
28Current closure in the ECMWF model K-diffusion closure withdifferent f(Ri) for stable andunstable layersK-diffusion closure withdifferent f(Ri) for stable and unstable layersED/MF(K-profile + M flux)
29Reduced Diffusion above Surface Layer 1.00.80.60.40.210Monin-Obukhov(new)LTG momLTG heatLTG (old)8MO momMO heat6f(Ri)Height [km]4LTG (old & new)20.51.01.550100150Richardson Number RiTurbulent Length Scale l [m]Old large diffusion coefficients: Louis-Tiedtke-Geleyn (1982) empiricalNew small diffusion coefficients: Monin-Obukhov (1954) based on observations
30Z500 Activity increase due to K reduction K reducedcontrolFC Activity: wave number 0-3AN Activity: wave number 0-3Activity: wave number 4-14RMS error115 T399 runs
31Shear power spectrum: resolution dependence 101001000110-210-410-6Spectral Shear PowerHorizontal Wave Number202002000T1279T799T399T159T2047k-1.03z=1000mModel lacks shear powernear truncation.Flat spectrum suggests large missing shear at small scales.
32511 Forecasts ...even colder 2m T ...so basically the errors increase 2T error CTL – analysis , 72 h FC, 0 UTC2T difference SFMO – CTL , 72 h FC, 0 UTC...even colder 2m T2T error CTL – error SFMO , 72 h FC, 0 UTC...so basically theerrors increase
33Wind turning difference SFMO – CTL , 72 h FC, 0 UTC ...but better wind turning...Wind turning difference SFMO – CTL , 72 h FC, 0 UTC