Parametrization of turbulent fluxes in the outer layer Irina Sandu Overview of models Bulk models Local K-closure K-profile closure ED/MF closure TKE closure Current closure in the ECMWF model 0 order 1st order non-local 1.5th order

Reynolds equations Reynolds Terms

Parametrization of turbulent fluxes in the outer layer Overview of models Bulk models Local K closure K-profile closure ED/MF closure TKE closure Current closure in the ECMWF model

Local K closure Levels in ECMWF model K-diffusion in analogy with molecular diffusion, but 137-level model Diffusion coefficients need to be specified as a function of flow characteristics (e.g. shear, stability,length scales).

Diffusion coefficients according to MO-similarity Use relation between and to solve for .

Stable boundary layer in the IFS: closure and caveats f(Ri) Long tails Short tails MO 1/l=1/kz+1/λ Long tails Recent years (36R4 – 38R2) Surface layer – Monin Obukhov Above: f = α* fLT + (1- α) * fST α = exp(-H/150) λ=150m short tails Long tails Short tails MO As in other NWP models the diffusion maintained in stable conditions is stronger than what LES or observations indicate Long tails short tails

Stable boundary layer in the IFS: closure and caveats Wind turning is underestimated Mean nocturnal bias over Europe 2m T is too low despite too strong diffusion obs 200m Mean annual wind speed at Cabaw model The strong diffusion maintained in stable conditions in the ECMWF model inherently translates in the type of biases pointed out in the GABLS framework. In the top plot you can see in red the bias in wind direction at the surface with respect to observations from 1992 to 2012. As you can see if this bias varied slightly along the years due to changes in the model, it always indicates an underestimation of the wind turning in the boundary layer, and this underestimation is even in recent years if approx. 10 degrees. The two plots below show the modeled and observed wind speed at 10, 80 and 200m at Cabauw for 1987 and 2011, from ERA-40 and OP. Again you can see that despite the model improvements between era-40 and the 2011 model, the low level jet is still underestimated at nighttime while the wind at the surface is slightly overestimated, which points again to a too strong mixing in stable PBL. 80 m 10 m 2011 OPERATIONAL Time (UTC)

Impact of reducing the diffusion in stable conditions ST: long tails short tails LT30: λ=150m λ=30m 1/l=1/kz+1/λ , λ=150m Almost halves the errors in low level jet, also increases the wind turning

+ Increase in drag over orography Stable boundary layer : changes to closure in 40R1 (Nov. 2013) Turbulence closure for stable conditions: Up to 38R2 long tails near surface, short tails above PBL λ =150m non-resolved shear term, with a maximum at 850hPa From 40R1 long tails everywhere λ = 10% PBL height in stable boundary layers λ = 30 m in free shear layers + Increase in drag over orography Increase in atm/surf coupling As in the past years, the bulk of the boundary layer activities focused on improving the representation of stable boundary layers. Just for reminder, as most of global NWP we are using too much diffusion in stable conditions, which leads to biases in key features of stable boundary layers, notably the near-surface winds. Building on the extensive study we did to investigate whether is possible to reduce the diffusion in stable conditions, summarized in a paper that came up this year, we came up with a solution which allows to reduce the diffusion and to improve the near-surface winds. This changes leads to a net red……In order to compensate the negative effects on the large-scale perf and the 2m temp of the changes to the turb closure, we combined them with an …. Consequence: net reduction in diffusion in stable boundary layers, not much change in free-shear layers, except at 850 hPa ECMWF Newsletter, no 138

Stable boundary layer : changes to closure in 40R1 (Nov. 2013) small changes in 2m temperature during nigh time in winter (~0.1 K over Europe) Reduction of wind direction bias over Europe by 3 in winter, 1  in summer (out of 10 ) Improvement in low level jets (next slide) Improvement of the large-scale performance of the model in winter N.Hemisphere Deterioration of tropical wind scores (against own analysis, not against observations)

Improvement of low level winds Cabauw Comparison with tower data T511L137 analysis runs JJA 2012, 0 UTC, step 24h Hamburg Improvement in both mean and RMSE in the upper part of stable boundary layers Falkenberg

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

Parametrization of turbulent fluxes in the outer layer Overview of models Bulk models Local K-closure K-profile closure ED/MF closure TKE closure Current closure in the ECMWF model

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:

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.

Parametrization of turbulent fluxes in the outer layer Overview of models Bulk models Local K closure K-profile closure ED/MF closure TKE closure Current closure in the ECMWF model

K-diffusion versus Mass flux method K-diffusion method - used to describe the small-scale turbulent motions: analogy to molecular diffusion Mass-flux method – used to describe the strong large-scale updraughts: mass flux entraining plume model detrainment rate

ED/MF framework a (neglected) The updraught: small fractional area a, containing the strongest upward vertical motions a   sub-core flux env. flux M-flux (neglected) Siebesma & Cuijpers, 1995

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

Parametrization of turbulent fluxes in the outer layer Overview of models Bulk models Local K closure K-profile closure ED/MF closure TKE closure Current closure in the ECMWF model

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

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.

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.

Parametrization of turbulent fluxes in the outer layer Overview of models Bulk models Local K closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

Current turbulence closure in the ECMWF model Stable surface layer Unstable surface layer K-diffusion closure (f(Ri) for stable/unstable layers) K-diffusion closure (f(Ri) for stable/unstable layers) ED/MF (K-profile + M flux) PBL_TYPE=0 PBL_TYPE=1,2,3

Unstable surface layer : ED/MF approach in the PBL K Shallow cumulus Deep cumulus Stratocumulus dry BL zcb zi Kbot Zi=W<0 Kentr Zi=Zcb Kprof+ Ktop Kprof Mixed layer Kprof K PBL_TYPE=1 PBL_TYPE=2 PBL_TYPE=3 EIS>7 EIS<7 Parcel method: If no cloud base IF cloud base

Caveats and challenges If stratocumulus (PBL_TYPE=2) no shallow convection Extra Kdiff due to cloud top radiative cooling mixing in thetal, qt, then qc computed with simple pdf scheme, and given to cloud scheme only scheme which gives explicitly dqc to cloud scheme If decoupled (PBL_TYPE=3) No top entrainment No mass flux from PBL PBL parcel different from shallow convection parcel Handling of stratocumulus to cumulus transitions Ongoing work towards a more unified treatment of diffusion, shallow convection and cloud