Bob Beare University of Exeter Thanks to Adrian Lock, John Thuburn and Bob Plant
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1 Modelling convective boundary layers in the terra-incognita m resolution 3.0 h m resolution 3.0 h y (m) y (m) x (m) x (m) Vertical wind ms Vertical wind ms -1 Bob Beare University of Exeter Thanks to Adrian Lock, John Thuburn and Bob Plant
2 Boundary layers in high resolution NWP MetUM forecasts at 1 km horizontal resolution but runs also at 100 m resolution. Convective boundary layer is partially resolved. Terra-incognita, Wyngaard How do we represent the boundary layer at these scales?
3 The boundary layer in the terra-incognita Energy Terra incognita Mesoscale LES 1/D mes 1/L 1/D LES Wavenumber Figure based on Wyngaard 2004
4 Background Analysis of arrays of surface layer data (HATS) to derive closures (e.g. Wyngaard 04, Hatlee and Wyngaard 07) Using LES models to derive similarity functions for sub-grid/total ratio of fluxes (Honnert et al 2011) My approach: role of both the advection and sub-grid scheme; behaviour of boundary layer top entrainment flux.
5 Large-eddy simulation Navier-Stokes decomposed into resolved and sub-grid components E(k) Kolmogorov k -5/3 Sub-grid model: 1 2Δx k (wavenumber)
6 Sources of diffusion in LES Explicit sub-grid model Implicit diffusion from advection scheme, e.g. 1D upstream advection
7 Experimental set up Initial mixed layer of depth 1 km Domain 10 km x 10 km x 5 km Surface sensible heat 150 Wm -2 Geostrophic wind 2 ms -1 Run at horizontal resolutions of 1600, 800, 400, 200, 100, 50, 25 m
8 Horizontal w cross-sections at 1km m resolution h h y (m) x (m) Vertical wind ms -1
9 Entrainment in Terra-incognita m 100 m m 800 m 400 m m 25 m z z <wb> (Wm -2 ) <wb> (Wm -2 )
10 Mass flux scaled (kgm -2s-1) time (h) Mass flux scaled (kgm -2s-1) time (h) Spin up in the terra-incognita Mass flux (kgm -2 s -1 ) Mass flux (kgm -2 s -1 ) time (h) time (h)
11 Experiments 2 types of experiment: Advection scheme fixed. Sub-grid model varied (e.g. backscatter on and off) Sub-grid model fixed. Advection scheme on potential temp. changed between: Centred-difference scheme (PW) Monotone, finite volume method (TVD) TVD more dissipative than PW.
12 Entrainment and advection scheme m P-W 25 m P-W m TVD m TVD z 1000 z <wb> (Wm -2 ) <wb> (Wm -2 )
13 Vertical velocity spectra at 1 km ww spectra at height 1000m at 3 hou m P-W 400 m TVD ww spectra at height 1000m at 3 hou m P-W 25 m TVD ks(k)/w * ks(k)/w * kz i kz i
14 Interaction of sub-grid and advection scheme SG/TOTAL <ww> TVD on scalars Centre-difference on scalars Horizontal grid length (m)
15 Sub-grid model vs advection scheme k -5/3 inertial sub-range Change in advection scheme Change in sub-grid model
16 Met Office advection scheme implicit diffusion Vertical velocity at 50 m resolution >1.5 m/s red; <1.5 m/s blue Identical sub-grid models, different advection schemes Beare et al 2007, Met Office report
17 Morning transition boundary layer Lapworth 2006
18 Relation of stable boundary layer depth to geostrophic wind Geostrophic wind Geostrophic wind
19 Entrainment in the early morning mixed layer Geostrophic wind
20 Framework for boundary-layer parametrization in terra-incognita 1. Scaling for turning off column scheme Scaling includes: Diffusion from sub-grid model, Diffusion from advection scheme Relevant integral scale 2. Modification for poor scale separation, e.g.: tensorial diffusion, stochastic backscatter or dynamic modelling?
21 Summary Terra-incognita for boundary layer modelling. Entrainment sensitive and non-linear function of grid length. Implicit diffusion from advection as important as sub-grid model diffusion. Implications for morning transition. Framework for parametrization.
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