dynamic sub-grid modelling of an evolving cbl at grey …sws00rsp/research/blgrey/ecmwf17.pdf ·...

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)


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



Steady State Simulations (Free Convection)

6ECMWF Workshop, Reading


Quantifying sub-grid diffusion in the grey-zone

• Reducing sub-grid

diffusion ?

• Increasing vertical

resolution ?

7

z/zi = 0.5

How much resolved TKE?


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)



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)



Dynamic sub-grid modelling

• Using “resolved” scales to estimate CS

• Apply a test filter (GαΔ) to diagnose sub-filter

scales



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



Comparison with the filtered fieldsΔx = 100 m



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



(based on Hong et al., 2006)


Δx = 400 m

SMAG BLEND

LASD BLEND

LES




SMAG BLEND

LASD BLEND

LES

Δx = 800 m



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



dynamic sub-grid modelling of an evolving cbl at grey …sws00rsp/research/blgrey/ecmwf17.pdf ·...

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