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DYNAMIC SUB-GRID MODELLING OF AN
EVOLVING CBL AT GREY-ZONE
RESOLUTIONS
George Efstathiou1
R. S. Plant2 , M. M. Bopape2,3 and R. J. Beare1
1 Department of Mathematics, University of Exeter2 Department of Meteorology, University of Reading3 South African Weather Service
Shedding light on the greyzone ECMWF Workshop, Reading
13-16 November 2017
Modelling zone oundary ayer
Motivation
• Numerical Weather Prediction at O(100m) is now possible
• Dominant turbulence length scales ~ zi (100 m – 3 km)
• Boundary Layer (BL) turbulence becomes partially
resolved
Shedding light on the greyzone ECMWF Workshop, Reading
13-16 November 2017
How do we parametrize sub-grid processes in the BL grey-zone?
Spectral view of the grey-zone (Beare, 2014)
• LES : Resolved field -
scales for production (lp)
and dissipation (ld) of TKE
are well separated
• Grey zone : Dissipation
has an impact on TKE
production – Partially
resolved field
Partially-Resolved Boundary-Layer Turbulence Simulations
the second moment of the TKE power spectrum, with the aim of separating the effects of
different subgrid models and advection schemes.
2 Method
Figure 1 illustrates our approach of using the TKE power spectrum (Se) to define the grey zone.
From that spectrum we identify three key length scales. The peak of the spectrum is given by lpand is typically controlled by the largest eddies of the turbulence, for example the boundary-
layer depth. For a horizontal wavenumber (k) above that of the largest eddies, the ideal
spectrum follows the inertial sub-range and varies as the well-established k− 5/ 3 Kolmogorov
law (Davidson 2004). Above a certain wavenumber, the spectrum of the simulation will
typically have more dissipation than that associated with the Kolmogorov law. In the vicinity
of the dissipation scale (ld), above wavenumber 2π/ ld, the simulation’s spectrum deviates
increasingly from the ideal k− 5/ 3 spectrum. Note that ld does not need to lie at the turning
point from the ideal spectrum as in the schematic; however it does need to change in response
(a) LES
k
2l d1l p
1
Se
f1
IDEAL k 5/3
(b)
Grey zone
k
2
l p1
Se
f1
IDEAL k 5/3
l d1
Fig. 1 A schematic showing the TKE spectrum (Se) against horizontal wavenumber (k) for a simulation (black
line) and an ideal k− 5/ 3 law (grey line). The length-scales annotated are: the spectral peak (lp), the dissipation
length scale (ld) and the filter width ( f ). Illustrations of these are given for: a a large-eddy simulation, b a
simulation in the grey zone
123
Author's personal copy
(Beare, 2014)
A working definition for the grey-zone
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
Scales
0.020
Most of the TKE is
resolved
Part of the TKE is
resolved – Mostly
controlled by sub-
grid mixing
No Resolved TKE
GREY ZONE
0.4 4
LES
Convergent
MESOSCALE (RANS)
VLES –
NEAR GREY ZONE
Δx/Λ
ere
s/e
tota
l
1
0
(Sullivan and Patton, 2011) (Beare, 2014)
ECMWF Workshop, Reading
13-16 November 2017
(Honnert and Masson, 2014)Transition from 3D to 1D turbulence
(Efstathiou and Beare, 2015)
Shedding light on the greyzone
Research Tools
• Numerical simulations with the LEM (Large-Eddy Met Office Model)
• Quasi-steady state CBL (zi=1000 m)
• Evolving CBL (Wangara case study)
• A range of horizontal resolutions (LES-Greyzone-Mesoscale)
• Compare with filtered LES
• Smagorinsky type eddy-viscocity model
KM,H = l2 S fM,H (Ri)
l-2 = (k z)-2 +λ0-2
λ0 = cs Δx
Control : cs = 0.23
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
Steady State Simulations (Free Convection)
6ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
Quantifying sub-grid diffusion in the grey-zone
• Reducing sub-grid
diffusion ?
• Increasing vertical
resolution ?
7
z/zi = 0.5
How much resolved TKE?
ECMWF Workshop, Reading
13-16 November 2017
(Efstathiou and Beare, 2015)
Shedding light on the greyzone
Parametrization approaches
• Modifying Smagorinsky
• BOUND approach (Efstathiou and Beare, 2015)
• Dynamic Smagorinsky Modelling
• Dynamic Blending (Preliminary results)
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
Evolution of Scales – Wangara CBLN
O R
ES
OLV
ED
Wangara Day 33 – Filtered Fields
During the morning CBL
development simulations
of different Δx go
through different
regimes
(Efstathiou et al., 2016)
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
Dynamic sub-grid modelling
• Using “resolved” scales to estimate CS
• Apply a test filter (GαΔ) to diagnose sub-filter
scales
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
Charles Meneveau (2010), Scholarpedia, 5(1):9489.
Second filter (G2αΔ) to account for scale dependence
CS averaged over path lines (LASD)
τ : sub-grid stress
T : interactions between sub-grid - sub-filter
L : “smallest” resolved scales (Leonard stress)
Wangara CBL development
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
Comparison with the filtered fieldsΔx = 100 m
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
Comparison with the filtered fieldsΔx = 200 m
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
Comparison with the filtered fieldsΔx = 400 m
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
Met Office Blending Scheme
• Blending Scheme (Boutle et al., 2014)
• Implemented in the LEM (Efstathiou et al., 2016)
KH = max [W1D KH(1D), KH(SMAG)]
1D BLSMAG
W1D
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
(based on Hong et al., 2006)
Wangara CBL development
Δx = 400 m
SMAG BLEND
LASD BLEND
LES
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
Wangara CBL development
SMAG BLEND
LASD BLEND
LES
Δx = 800 m
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone
282 284 286 288 290 292
500
1000
1500
2000
Potential Temperature (K)
z (
m)
1100 LST
1300 LST
1530 LST
Summary• The grey-zone imposes practical limitations in very high resolution NWP
•
• Representing coherent structures
• Quantify the resolved TKE – Energetics – TKE spin-up
• Form of transition
• Shape and form of the coherent structures in the CBL would affect the representation of shallow Cu convection
• Implications with deep convection and convective parametrizations
•
• Dynamic Smagorinsky a better alternative than Standard Smagorinsky
• Improves spin-up / Representation of mean quantities and turbulence statistics
• Relies on dynamics (unable to resolve for Δx/zi > 2) – Usability limit
• Modified 1D schemes suffer from delayed spin-up
• Dynamic Blending extends the benefits of dynamic modelling further into the grey-zone
Beare, R. J., 2014: A length scale defining partially-resolved boundary-layer turbulence simulations. Boundary-Layer Meteorol. 151: 39–55.
Efstathiou, G. A. and R. J. Beare, 2015: Quantifying and improving sub-grid diffusion in the boundary-layer grey zone. Quarterly Journal of the Royal Meteorological
Society, 141, 3006–3017.
Efstathiou, G. A., R. J. Beare, S. Osborne, A. P. Lock, 2016: Grey zone simulations of the morning convective boundary layer development, Journal of Geophysical Research:
Atmospheres, 121, 9
Efstathiou, G. A., Plant R. S., and M. M. Bopape, 2017: Simulation of an evolving convective boundary layer using a scale-dependent dynamic Smagorinsky model at near
grey-zone resolutions. Journal of Applied Meteorology and Climatology, submitted.
Should any convective overturning be allowed in the grey-zone?
Papers
ECMWF Workshop, Reading
13-16 November 2017Shedding light on the greyzone