The stable boundary layer parametrization problem Here is a nice picture of a stable bl in California. Dr Bob Beare © Crown copyright 2004

What is the stable boundary layer (SBL)? Overview What is the stable boundary layer (SBL)? Why is it important to the Met Office? SBL modelling in the UM and other GCMs. The GABLS stable boundary layer initiative. Comparison with Cardington observations. Fir © Crown copyright 2004

What is the stable boundary layer (SBL) Boundary layer is lowest 200m-2km of atmosphere, mainly turbulent. Over land is convective (driven by surface heating) by day and stable (driven by vertical wind shear) by night. Stable boundary layer also occurs when warmer air is advected over cold ocean surfaces (e.g. warm sector of Extra-tropical cyclone, some off-shore winds) and over the polar ice sheets. © Crown copyright 2004

Stable boundary layers in Global Model Land masses Red=stable Warm Sector © Crown copyright 2004

Why is simulating stable boundary layer (SBL) important? Basic understanding Surface temperature forecasting at night Drag on extra-tropical cyclones Fog forecasting Polar climate especially Antarctic winter, King et al. (2001) QJRMS Dispersion studies Wind power (low level jets) As motivation... boundary layer scheme and surface exchange scheme; important problem for variety of customers Fog (radiation) forms in stable conditions, small differences in T structure could be difference of saturation or not Areas like Antarctic in winter persitistent SBLs, King changing SBL and surface exchange dramatic effect of surface T.. Katabatic drainage flows. Dispersion: deviations of plume at night: variance parametrizations © Crown copyright 2004

Gradient Richardson number Stratification Shear Compactly represents the energetics: shear generation vs buoyancy consumption. Ri < 0.25 turbulence ‘turns on’. Represents local nature of stable turbulence. Fluxes of wind and heat as a diffusion model. Explain symbols K = boundary layer param. all about this mixing length deformation and a function of Richardson no. Ri no. is a measure of stability of turbulent flow stratification/shear^(2) It is local constistent with local scaling (c.gf convect bl) high shear and low stratification low stability low shear and high stratification high stability fundamental turb © Crown copyright 2004

NWP stability functions First order SBL scheme in Met Office NWP model: Long tails; Also sharp tails used in research As mentioned earlier, one of the motivations for GABLS is improving parametrizations, 1st order commonly used in operational NWP models and climate models. Cast the LES data in form for comparison. Simple but not simplistic: non-linear, local scaling. Numerical stability. © Crown copyright 2004

The enhanced mixing issue Stability dependence of operational schemes do not match theory and micrometeorological obs., with extended tails at high Richardson number. Possible reasons: Limiting runaway cooling when coupled to surface exchange scheme (Derbyshire 1999, BLM, Viterbo et al 1999 QJRMS). Representing intermittency at high Richardson number (van de Wiel et al 2002, JAS). Subgrid heterogeneties (Delage 1997, BLM). Compensating for biases elsewhere in the NWP system (King et al 2001, QJRMS). Convective boundary layer, resolution. On compensating errors: HADGEM= SHARP, GM = LONG, MES= LOUIS/SHARP. Resolution 3 or 4 points for mod stability (h=300m), 1 or 2 points for very high stability (h=50m)….. Woefully inadequate!!! © Crown copyright 2004

Sensitivity to SHARP tails (reduced mixing) Cooling over NH land with respect to analysis (DJF) This is the average of 5 NH winter forecasts (Paul Earnshaw’s suite) Similar negative bias over antartic in JJA © Crown copyright 2004

Vertical resolution issues Look how poor things are over land!! Land SBLs Sea SBLS © Crown copyright 2004

New formulations of SBL scheme New formulation of SBL scheme by Williams (2002), option in umui, so called ‘Equilibrium scheme’. However shares essential physics of old scheme: local stability dependence, first order closure, but within more complicated framework. Formulation involving SBL depth coupled to surface scheme being pursued (Anne McCabe). © Crown copyright 2004

Different SBL formulations Anne McCabe 50 equations 5 eqns Different constants Here is a comparison of different compliexity of the SBL formulation but that still share Same physics (local scaling) © Crown copyright 2004

12 hour fog forecast, 7 Z 18 Nov 2002 mesoscale model, Fog fraction 12 hour forecast using MES, overnight last Nov (current weather) High to w, Low to SE, light wind, surface cooling, stable conditions over land over night, radiation fog Fog fraction: fraction of grid box with. vis <1km Enhanced fog over Holland.. Consistent with observations from that time (see web site) Current scheme Scheme with less mixing © Crown copyright 2004

GEWEX atmospheric boundary layer study (GABLS) International collaboration to inform improvements of stable boundary layer parametrization with single column and Large-eddy models. Chaired by Prof. Bert Holtslag, Wagenigen Uni., Holland. Initial intercomparison for a simple case: prescribed geostrophic winds, surface cooling, akin to Arctic ocean case. Large-eddy study led by Met Office (Beare, McCabe, MacVean). Special issue to appear in Boundary Layer Met. 2005. Similar status to GCSS but newer © Crown copyright 2004

GABLS Single column model intercomparison Met Office Single column model © Crown copyright 2004

Large-eddy simulation (LES) of SBL LES of stable boundary layer is hard! : eddies of order 25m. Smagorinsky diffusion (blue) ; Stochastic backscatter (red) Brown et al. (1994) : Closer to surface layer similarity and stimulates stable turbulence Prescribed surface flux and surface cooling rate Domain 400m x 400m x 400m; grid lengths 10m to 1m LES equations: momentum, heat ,continuity dry, advection, coriolis, p-grad, buoyancy, SUB-GRID model… SBL LES hard resolution…. Intermitternt flows event more of a challenge Smagorinsky diffusion.. Not too different from param used in UM and then stoch backscatter, regions marginally resolved backscatter as well as dissipation of energy. Set ups of cooling:flux and dT.dt domain : note small grid-lengths and domains. © Crown copyright 2004

Mean potential temperature See: http://www.gabls.org Successful: generates resolved turbulence, spread not huge See web-site for more Spread but within bounds Positive curvature in PT, differences at BL top (partly BCs) GEWEX atmospheric boundary layer study (GABLS) on stable boundary layers. © Crown copyright 2004

Momentum stability functions And we find at coarse and fine resolution , that stability functions implied by LES are a lot sharper than the traditionally used LONG tails. What are the reasons? Physical: Sub-grid heterogenity – Mahrt and Delage… but the LES does provide an ensemble mean and thus accounts For variability, all be it for flat terrain. Pragmatic: compensating errors elsewhere in the climate/ NWP model It would be really good to understand this more in The future. © Crown copyright 2004

Comparison with Cardington observations Aim: To use Cardington balloon observations to provide a fair test of LES models and UM SBL scheme (collaboration with John Edwards). Simulation of SBL from 2030Z on 23 Sept 2003 till 0230Z 24 Sept 2003. Clear sky, Geostrophic wind 7m/s. Initialisation with observed wind and pot. Temp profiles, forced with observed 1.2m temp., geostrophic wind. © Crown copyright 2004

Balloon observations provided by Alan Lapworth, OBR Comparison of LES and tethered balloon observations for Cardington, Bedford Balloon observations provided by Alan Lapworth, OBR © Crown copyright 2004

Sensitivity to initial wind profile © Crown copyright 2004

Cardington case: sensitivity to stability function © Crown copyright 2004

Vertical velocity cross-section and spectra Distinct peak Red positive, blue down © Crown copyright 2004

Summary Stable boundary layer parametrizations in NWP/climate models tend to have more mixing than in Large-eddy simulations and observations. For a moderately stable case, LESs from different models compare well, providing useful guidance for NWP. Promising recent comparison with observations, highlighting importance of initial profile in simulating nocturnal boundary layer. © Crown copyright 2004

Future work Reassess the impact of SBL parametrization on synoptic flow in UM: cyclone evolution GABLS 2 intercomparison (Anne Mccabe) Reformulation of SBL scheme.. Mixing length, and boundary layer depth (Anne McCabe and John Edwards) Tackling the very stable limit with LES: decoupling, intermittence, heterogeneities. Beare and MacVean (2004), ‘Resolution sensitivity and scaling of large-eddy simulations of the stable boundary layer’, Boundary-Layer Meteorol. 112, 257-281. Beare et al (2005),’ An intercomparison of large-eddy simulations of the stable boundary layer’, to appear in Boundary-Layer Meteorol. (see www.gabls.org) © Crown copyright 2004