Entrainment and anisotropic turbulence inlarge-eddy simulation of the stratocumulus-topped
boundary layer
Jesper Grønnegaard Pedersen
Institute of Geophysics, Faculty of Physics, University of Warsaw
Workshop on numerical and computational methods for simulationof all-scale geophysical flows
ECMWF 06.10.2016
J. G. Pedersen (IGF UW) 06.10.2016 1 / 32
Motivation
“Only small changes in the coverage and thickness of stratocumulusclouds are required to produce a radiative effect comparable to thoseassociated with increasing greenhouse gases”R. Wood, Stratocumulus Clouds, Monthly Weather Review, 2012
Can we use LES to get improved understanding of e.g.entrainment?
Smallest eddies involved: O(0.1) m
Recent LES stratocumulus-topped boundary layer studies:I Horizontal grid spacing (∆x) between 5 and 120 mI Vertical grid spacing (∆z) between 2.5 and 25 m
Even at 5× 5× 2.5 m3 resolution we see grid-dependency(Yamaguchi et al., J. Atmos Sci., 2012)
J. G. Pedersen (IGF UW) 06.10.2016 2 / 32
Motivation
“Only small changes in the coverage and thickness of stratocumulusclouds are required to produce a radiative effect comparable to thoseassociated with increasing greenhouse gases”R. Wood, Stratocumulus Clouds, Monthly Weather Review, 2012
Can we use LES to get improved understanding of e.g.entrainment?
Smallest eddies involved: O(0.1) m
Recent LES stratocumulus-topped boundary layer studies:I Horizontal grid spacing (∆x) between 5 and 120 mI Vertical grid spacing (∆z) between 2.5 and 25 m
Even at 5× 5× 2.5 m3 resolution we see grid-dependency(Yamaguchi et al., J. Atmos Sci., 2012)
J. G. Pedersen (IGF UW) 06.10.2016 2 / 32
Pedersen et al., J. Adv. Model. Earth. Syst. 2016:
ILES of the DYCOMS-II Flight 1 stratocumulus case using“babyEULAG” going down to resolutions of 10× 10× 10 m3 and20× 20× 5 m3.
Decreasing horizontal grid spacing (reducing dx/dz) ⇒Smaller-scale isotropic turbulence at the cloud top ⇒Increased entrainment (initially) ⇒Reduced cloud cover and LWP ⇒Poor agreement with measurements
Decreasing vertical grid spacing ⇒Stronger inversion ⇒Less entrainment ⇒Increased cloud cover and LWP ⇒Good agreement with measurements
Increasing domain size has little effect
J. G. Pedersen (IGF UW) 06.10.2016 3 / 32
Pedersen et al., J. Adv. Model. Earth. Syst. 2016:
ILES of the DYCOMS-II Flight 1 stratocumulus case using“babyEULAG” going down to resolutions of 10× 10× 10 m3 and20× 20× 5 m3.
Decreasing horizontal grid spacing (reducing dx/dz) ⇒Smaller-scale isotropic turbulence at the cloud top ⇒Increased entrainment (initially) ⇒Reduced cloud cover and LWP ⇒Poor agreement with measurements
Decreasing vertical grid spacing ⇒Stronger inversion ⇒Less entrainment ⇒Increased cloud cover and LWP ⇒Good agreement with measurements
Increasing domain size has little effect
J. G. Pedersen (IGF UW) 06.10.2016 3 / 32
Pedersen et al., J. Adv. Model. Earth. Syst. 2016:
ILES of the DYCOMS-II Flight 1 stratocumulus case using“babyEULAG” going down to resolutions of 10× 10× 10 m3 and20× 20× 5 m3.
Decreasing horizontal grid spacing (reducing dx/dz) ⇒Smaller-scale isotropic turbulence at the cloud top ⇒Increased entrainment (initially) ⇒Reduced cloud cover and LWP ⇒Poor agreement with measurements
Decreasing vertical grid spacing ⇒Stronger inversion ⇒Less entrainment ⇒Increased cloud cover and LWP ⇒Good agreement with measurements
Increasing domain size has little effect
J. G. Pedersen (IGF UW) 06.10.2016 3 / 32
Pedersen et al., J. Adv. Model. Earth. Syst. 2016:
ILES of the DYCOMS-II Flight 1 stratocumulus case using“babyEULAG” going down to resolutions of 10× 10× 10 m3 and20× 20× 5 m3.
Decreasing horizontal grid spacing (reducing dx/dz) ⇒Smaller-scale isotropic turbulence at the cloud top ⇒Increased entrainment (initially) ⇒Reduced cloud cover and LWP ⇒Poor agreement with measurements
Decreasing vertical grid spacing ⇒Stronger inversion ⇒Less entrainment ⇒Increased cloud cover and LWP ⇒Good agreement with measurements
Increasing domain size has little effect
J. G. Pedersen (IGF UW) 06.10.2016 3 / 32
Simulation setupDYCOMS-II Flight 1 and POST Flight 13
3D
Non-hydrostatic
Anelastic
No supersaturation
No precipitation
No explicit subgrid-scale model (ILES)
MPDATA, IORD = 2
IMPLGW = 0
3.5× 3.5× 1.5 km3 domain with periodic lateral BC’s
DYCOMS: H0 = 15 W m−2, Q0 = 115 W m−2, and UG = 8.9 m s−1
POST: H0 = 5 W m−2, Q0 = 10 W m−2, and UG = 8.6 m s−1
Longwave radiative cooling based on qc
J. G. Pedersen (IGF UW) 06.10.2016 4 / 32
0 20 40 60 800
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
∆x [m]
LW
P∗
LWP∗ = 〈〈LWP〉〉4h−6h/LWPinitial
∆z = 5 m (DYCOMS)
∆z = 5 m (POST)
∆z = 10 m (DYCOMS)
∆z = 15 m (DYCOMS)
J. G. Pedersen (IGF UW) 06.10.2016 5 / 32
DYCOMS-II Flight 1 @ T = 0 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 6 / 32
DYCOMS-II Flight 1 @ T = 20 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 7 / 32
DYCOMS-II Flight 1 @ T = 40 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 8 / 32
DYCOMS-II Flight 1 @ T = 60 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 9 / 32
DYCOMS-II Flight 1 @ T = 120 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 10 / 32
DYCOMS-II Flight 1 @ T = 360 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 11 / 32
DYCOMS-II Flight 1
20
40
60
80
100
〈LW
P〉[
gm
−2]
0 1 2 3 4 5 60.5
0.75
1
Cloudco
ver
fraction
Time [h]
15 × 15 × 5m3
30 × 30 × 5m3
J. G. Pedersen (IGF UW) 06.10.2016 12 / 32
DYCOMS-II Flight 1 @ T = 40 min
Small ∆x ⇒ large cloud-top 〈w′w′〉 ⇒ high entrainment rate ⇒ disso-lution of cloud
0
0.7
1.4
z[m
]
15 × 15 × 5m3
0 0.05 0.1 0.15 0.2 0.250
0.7
1.4
Variance of vertical velocity
〈w′w′〉
[
m2 s−2]
z[m
]
0 0.8 1.6 2.4 3.20
0.7
1.4
z[m
]
30 × 30 × 5m3
x [m]
∆x= 15 m∆x= 30 m
J. G. Pedersen (IGF UW) 06.10.2016 13 / 32
DYCOMS-II Flight 1 @ T = 60 min
Dissolution of cloud ⇒ reduced cloud-top cooling ⇒ reduced TKE pro-duction ⇒ “decoupling” from surface layer (two maxima in 〈w′w′〉 pro-file)
0
0.7
1.4
z[m
]
15 × 15 × 5m3
0 0.2 0.4 0.6 0.8 10
0.7
1.4
Variance of vertical velocity
〈w′w′〉
[
m2 s−2]
z[m
]
0 0.8 1.6 2.4 3.20
0.7
1.4
z[m
]
30 × 30 × 5m3
x [m]
∆x= 15 m∆x= 30 m
J. G. Pedersen (IGF UW) 06.10.2016 13 / 32
DYCOMS-II Flight 1 @ T = 120 min
Quasi-steady state: The cloud “recovers” but still signs of decouplingwith ∆z = 15 m
0
0.7
1.4
z[m
]
15 × 15 × 5m3
0 0.05 0.1 0.15 0.2 0.250
0.7
1.4
Variance of vertical velocity
〈w′w′〉
[
m2 s−2]
z[m
]
0 0.8 1.6 2.4 3.20
0.7
1.4
z[m
]
30 × 30 × 5m3
x [m]
∆x= 15 m∆x= 30 m
J. G. Pedersen (IGF UW) 06.10.2016 13 / 32
DYCOMS-II Flight 1 @ T = 360 min
End of simulation: Still decoupled
0
0.7
1.4
z[m
]
15 × 15 × 5m3
0 0.05 0.1 0.15 0.2 0.250
0.7
1.4
Variance of vertical velocity
〈w′w′〉
[
m2 s−2]
z[m
]
0 0.8 1.6 2.4 3.20
0.7
1.4
z[m
]
30 × 30 × 5m3
x [m]
∆x= 15 m∆x= 30 m
J. G. Pedersen (IGF UW) 06.10.2016 13 / 32
DYCOMS-II Flight 1 @ T = 60 min and z = 300 m
102
103
10-2
10-1
100
101
102
103
λ [m]
15 × 15 × 5m3
[
m3s−
2]
102
103
λ [m]
30 × 30 × 5m3
Eu,v
Ew
κ−5/3
J. G. Pedersen (IGF UW) 06.10.2016 14 / 32
DYCOMS-II Flight 1 @ T = 60 min and z = 840 m
102
103
10-2
10-1
100
101
102
103
λ [m]
15 × 15 × 5m3
[
m3s−
2]
102
103
λ [m]
30 × 30 × 5m3
Eu,v
Ew
κ−5/3
J. G. Pedersen (IGF UW) 06.10.2016 15 / 32
DYCOMS-II Flight 1 @ T = 60 min and z = 840 m
102
103
10-2
10-1
100
101
102
103
λ [m]
Eu,v − Ew
[
m3s−
2]
15 × 15 × 5m3
30 × 30 × 5m3
J. G. Pedersen (IGF UW) 06.10.2016 16 / 32
DYCOMS-II Flight 1 @ T = 360 min and z = 840 m
102
103
10-2
10-1
100
101
102
103
λ [m]
Eu,v − Ew
[
m3s−
2]
15 × 15 × 5m3
30 × 30 × 5m3
J. G. Pedersen (IGF UW) 06.10.2016 17 / 32
0 20 40 60 800
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
?
∆x [m]
LW
P∗
LWP∗ = 〈〈LWP〉〉4h−6h/LWPinitial
∆z = 5 m (DYCOMS)
∆z = 5 m (POST)
J. G. Pedersen (IGF UW) 06.10.2016 18 / 32
Initial conditions
0
0.7
1.4
DYCOMS-II Flight 115 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
POST Flight 1315 × 15 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 19 / 32
POST Flight 13 @ T = 20 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 20 / 32
POST Flight 13 @ T = 40 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 21 / 32
POST Flight 13 @ T = 60 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 22 / 32
POST Flight 13 @ T = 120 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 23 / 32
POST Flight 13 @ T = 180 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 24 / 32
POST Flight 13 @ T = 240 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 25 / 32
POST Flight 13 @ T = 300 min
0
0.7
1.415 × 15 × 5m3
z[km]
0 0.8 1.6 2.4 3.20
0.7
1.4
x [km]
z[km]
30 × 30 × 5m3
0 0.8 1.6 2.4 3.2x [km]
q c[g/k
g]
0
0.5
1
q v[g/k
g]
1.5
4
6.5
9
J. G. Pedersen (IGF UW) 06.10.2016 26 / 32
POST Flight 13 @ T = 300 minNo decoupling in this case
0
0.7
1.4
z[m
]
15 × 15 × 5m3
0 0.02 0.04 0.06 0.08 0.10
0.7
1.4
Variance of vertical velocity
〈w′w′〉
[
m2 s−2]
z[m
]
0 0.8 1.6 2.4 3.20
0.7
1.4
z[m
]
30 × 30 × 5m3
x [m]
∆x= 15 m∆x= 30 m
J. G. Pedersen (IGF UW) 06.10.2016 27 / 32
0 20 40 60 800
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
?
?
∆x [m]
LW
P∗
LWP∗ = 〈〈LWP〉〉4h−6h/LWPinitial
∆z = 5 m (DYCOMS)
∆z = 5 m (POST)
J. G. Pedersen (IGF UW) 06.10.2016 28 / 32
Future work
Increase resolution, e.g. to 5× 5× 5 m3 or 2.5× 2.5× 2.5 m3
I Stratocumulus-top Ozmidov scale LO =(ε/N3
)1/2 ' 0.5 m (Jen-LaPlante et al., Atmos. Chem. Phys., 2016)
Will we see the same dependencies using conventional LES?I τij ∝ LSGSVSGSSij , but how to define LSGS when ∆x 6= ∆z?I LSGS = ∆xI LSGS = ∆zI LSGS = (∆x∆y∆z)
1/3
J. G. Pedersen (IGF UW) 06.10.2016 29 / 32
Future work
Increase resolution, e.g. to 5× 5× 5 m3 or 2.5× 2.5× 2.5 m3
I Stratocumulus-top Ozmidov scale LO =(ε/N3
)1/2 ' 0.5 m (Jen-LaPlante et al., Atmos. Chem. Phys., 2016)
Will we see the same dependencies using conventional LES?I τij ∝ LSGSVSGSSij , but how to define LSGS when ∆x 6= ∆z?I LSGS = ∆xI LSGS = ∆zI LSGS = (∆x∆y∆z)
1/3
J. G. Pedersen (IGF UW) 06.10.2016 29 / 32
Thank you
J. G. Pedersen (IGF UW) 06.10.2016 30 / 32
Some other issues:
IMPLGW 0/1
MPDATA3/MPDATM3
J. G. Pedersen (IGF UW) 06.10.2016 31 / 32
0
20
4060
80
100120
〈LW
P〉[
gm
−2]
30 × 30 × 10 m3
0 1 2 3 4 5 60
20
4060
80
100120
〈LW
P〉[
gm
−2]
75 × 75 × 10 m3
Time [h]
MPDATA3IMPLGW=0
MPDATA3IMPLGW=1
MPDATM3IMPLGW=0
MPDATA3IMPLGW=0
MPDATA3IMPLGW=1
MPDATM3IMPLGW=0
J. G. Pedersen (IGF UW) 06.10.2016 32 / 32
