modelling convective boundary layers in the terra-incognita · • terra-incognita for boundary...
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![Page 1: Modelling convective boundary layers in the terra-incognita · • Terra-incognita for boundary layer modelling. • Entrainment sensitive and non-linear function of grid length](https://reader033.vdocuments.us/reader033/viewer/2022060311/5f0abef77e708231d42d233b/html5/thumbnails/1.jpg)
Bob Beare University of Exeter
Thanks to Adrian Lock, John Thuburn and Bob Plant
Modelling convective boundary layers in the terra-incognita
800 m resolution 3.0 h
-4800 -2400 0 2400 4800x (m)
-4800
-2880
-960
960
2880
4800
y (m
)
-4.4 -3.6 -2.8 -2.0 -1.2 -0.4 0.4 1.2 2.0 2.8 3.6 4.4Vertical wind ms-1
50 m resolution 3.0 h
-4800 -2400 0 2400 4800x (m)
-4800
-2880
-960
960
2880
4800
y (m
)
-4.4 -3.6 -2.8 -2.0 -1.2 -0.4 0.4 1.2 2.0 2.8 3.6 4.4Vertical wind ms-1
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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 2004. • How do we represent the boundary layer
at these scales?
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The boundary layer in the terra-incognita
Terra incognita
LES Mesoscale
Energy
Wavenumber 1/L 1/Dmes 1/DLES
Figure based on Wyngaard 2004
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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.
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Large-eddy simulation
Sub-grid model: Kolmogorov k-5/3
E(k)
k (wavenumber) xΔ21
Navier-Stokes decomposed into resolved and sub-grid components
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Sources of diffusion in LES Explicit sub-grid model
Implicit diffusion from advection scheme, e.g. 1D upstream advection
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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
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Horizontal w cross-sections at 1km 1600 m resolution 3.0 h
-4800 -2400 0 2400 4800x (m)
-4800
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-960
960
2880
4800
y (m
)
-4.4 -3.6 -2.8 -2.0 -1.2 -0.4 0.4 1.2 2.0 2.8 3.6 4.4Vertical wind ms-1
800 m resolution 3.0 h
-4800 -2400 0 2400 4800x (m)
-4800
-2880
-960
960
2880
4800
y (m
)
-4.4 -3.6 -2.8 -2.0 -1.2 -0.4 0.4 1.2 2.0 2.8 3.6 4.4Vertical wind ms-1
400 m resolution 3.0 h
-4800 -2400 0 2400 4800x (m)
-4800
-2880
-960
960
2880
4800
y (m
)
-4.4 -3.6 -2.8 -2.0 -1.2 -0.4 0.4 1.2 2.0 2.8 3.6 4.4Vertical wind ms-1
200 m resolution 3.0 h
-4800 -2400 0 2400 4800x (m)
-4800
-2880
-960
960
2880
4800
y (m
)
-4.4 -3.6 -2.8 -2.0 -1.2 -0.4 0.4 1.2 2.0 2.8 3.6 4.4Vertical wind ms-1
100 m resolution 3.0 h
-4800 -2400 0 2400 4800x (m)
-4800
-2880
-960
960
2880
4800
y (m
)
-4.4 -3.6 -2.8 -2.0 -1.2 -0.4 0.4 1.2 2.0 2.8 3.6 4.4Vertical wind ms-1
50 m resolution 3.0 h
-4800 -2400 0 2400 4800x (m)
-4800
-2880
-960
960
2880
4800
y (m
)
-4.4 -3.6 -2.8 -2.0 -1.2 -0.4 0.4 1.2 2.0 2.8 3.6 4.4Vertical wind ms-1
25 m resolution 3.0 h
-4800 -2400 0 2400 4800x (m)
-4800
-2880
-960
960
2880
4800
y (m
)
-4.4 -3.6 -2.8 -2.0 -1.2 -0.4 0.4 1.2 2.0 2.8 3.6 4.4Vertical wind ms-1
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Entrainment in Terra-incognita
-45 60 165<wb> (Wm-2)
0
500
1000
1500
2000
2500
z
25 m
50 m
100 m
200 m
-45 60 165<wb> (Wm-2)
0
500
1000
1500
2000
z
400 m800 m1600 m
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Spin up in the terra-incognita
0 1 2 3 4time (h)
0.00
0.05
0.10
0.15
Mass
flux
(kgm
-2s-1
)
0 1 2 3 4time (h)
0.00
0.05
0.10
0.15
Mass
flux
scale
d (k
gm-2s-1
)
0 1 2 3 4time (h)
0.0
0.1
0.2
0.3
0.4
Mas
s flu
x (k
gm-2s-1
)
0 1 2 3 4time (h)
0.0
0.1
0.2
0.3
0.4
Mas
s flu
x sc
aled
(kgm
-2s-1
)
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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.
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Entrainment and advection scheme
-45 60 165<wb> (Wm-2)
0
500
1000
1500
2000
z
400 m TVD
400 m P-W
-45 60 165<wb> (Wm-2)
0
500
1000
1500
2000
z
25 m TVD
25 m P-W
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Vertical velocity spectra at 1 km ww spectra at height 1000m at 3 hou
0.1 1.0 10.0 100.0kzi
0.1
1.0
10.0
100.0
1000.0
kS(k
)/w*2
400 m TVD
400 m P-W
ww spectra at height 1000m at 3 hou
0.1 1.0 10.0 100.0kzi
0.1
1.0
10.0
100.0
1000.0
kS(k
)/w*2
25 m TVD
25 m P-W
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Interaction of sub-grid and advection scheme
0 200 400 600 800 1000Horizontal grid length (m)
0.0
0.1
0.2
0.3
0.4
0.5
SG/TO
TAL <
ww>
TVD on scalars
Centre-difference on scalars
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Sub-grid model vs advection scheme
k-5/3 inertial sub-range
Change in advection scheme
Change in sub-grid model
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Met Office advection scheme implicit diffusion
Beare et al 2007, Met Office report
Vertical velocity at 50 m resolution >1.5 m/s red; <1.5 m/s blue
Identical sub-grid models , different advection schemes
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Morning transition boundary layer Lapworth 2006
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Relation of stable boundary layer depth to geostrophic wind
Geostrophic wind
Geostrophic wind
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Entrainment in the early morning mixed layer
Geostrophic wind
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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?
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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.