Evidence on non-self-similarity source scaling in cluster earthquakes
Local Similarity Scaling in the Nocturnal Boundary Layer...
Transcript of Local Similarity Scaling in the Nocturnal Boundary Layer...
Local Similarity Scaling in the NocturnalBoundary Layer over Heterogeneous Terrain
Karmen Babic1, Mathias W. Rotach2 and Zvjezdana Bencetic Klaic1
1 University of Zagreb, Faculty of Science, Department of Geophysics2 University of Innsbruck, Institute of Atmospheric and Cryospheric Sciences
22nd Symposium on Boundary Layers and Turbulence20 - 24 June 2016 Salt Lake City, UT, USA
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Introduction & Motivation
• Applicability of Monin-Obukhov similarity theory → still an openissue especially for stable conditions
• Nieuwstadt (1984) redefined MOST in terms of local scalingapproach
• Modest surface heterogeneity can lead to turbulence at higherRichardson numbers in comparison with homogeneous surfaces(Derbyshire 1995)
• Proper representation of turbulence important for parameterizationof surface-atmosphere exchange processes
Objective
• Examine the applicability of local similarity scaling in SBL over atruly heterogeneous terrain
• Investigate whether classical linear flux-gradient relationships can beapplied for non-homogeneous surfaces
2 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Introduction & Motivation
• Applicability of Monin-Obukhov similarity theory → still an openissue especially for stable conditions
• Nieuwstadt (1984) redefined MOST in terms of local scalingapproach
• Modest surface heterogeneity can lead to turbulence at higherRichardson numbers in comparison with homogeneous surfaces(Derbyshire 1995)
• Proper representation of turbulence important for parameterizationof surface-atmosphere exchange processes
Objective
• Examine the applicability of local similarity scaling in SBL over atruly heterogeneous terrain
• Investigate whether classical linear flux-gradient relationships can beapplied for non-homogeneous surfaces
2 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Data
Kutina (Croatia)
• 62 m tower
• Sonic anemometers:• 20, 32, 40, 55 and 62 m (20 Hz)
• Data (wintertime SBL):December 2008 - February 2009
• Nocturnal boundary layer:1800 - 0600 LST
• Walnut canopy ∼ 18 m
3 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Measurement site and surroundings
Topographic map Inhomogeneous landscape
Heterogeneous surface: variable roughness elements and variabletopography
4 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Influence of surface inhomogeneity on σw/u∗`
0 45 90 135 180 225 270 315 3600
1
2
3
Wind direction (deg)
σ w/u
*l(a)
Level 5 Level 4 Level 3 Level 2 Level 1
• Observed changes reflect the influence of surface inhomogeneity
5 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Influence of surface inhomogeneity on σw/u∗`
Kaimal and Finnigan (1994):σw/u∗` = φw(HHF ) = 1.25(1 + 0.2z/Λ)
0 45 90 135 180 225 270 315 3600.6
0.8
1
1.2
1.4
1.6
1.8
2
Wind direction (deg)
φ w/φ
w(H
HF)
(b)Level 1 Levels 2−5
• Level 1: Roughness sublayer
• Levels 2-5: Transition layer
6 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Flux-variance similarity functions
1
2
3
4
σ w/u
*l
ζ=(z−d)/Λ
Levels 2−5
(c)
10−3
10−2
10−1
100
101
102
1
2
3
4
σ w/u
*l
ζ=(z−d)/Λ
Level 1
Undistorted Distorted
• Kaimal and Finnigan (1994): σw/u∗` = 1.25(1 + 0.2z/Λ) (solid black line)
• Level 1: less dependence on the wind direction −→ rather local RSLinfluence
• Strongly stable regime (ζ > 1): z-less scaling
7 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Flux-gradient similarity
φm(ζ) = k(z−d)u∗`
∂U∂z , k=0.4 von Karman constant
• Dyer (1974): φm(ζ) = 1 + 4.8ζ
• Beljaars and Holtslag (1991):φm(ζ) = 1 + ζ + 0.667ζe−0.35ζ − 0.23ζ(ζ − 1.75)e−0.35ζ
10−3
10−2
10−1
100
101
10−1
100
101
Φm
ζ=(z−d)/Λ
0 0 0 2 6 26 32 36 37 61 68 60 50 19 6
6 12 7 14 11 11 19 4 9 6 1 0 0 0 0
Level 1Levels 2−5Dyer (1974)Beljaars and Holtslag (1991)
1
• Surface characteristics are influencing the strength of turbulent mixingand the wind gradient in the same way.
8 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Flux-gradient similarity
φm(ζ) = k(z−d)u∗`
∂U∂z , k=0.4 von Karman constant
• Dyer (1974): φm(ζ) = 1 + 4.8ζ
• Beljaars and Holtslag (1991):φm(ζ) = 1 + ζ + 0.667ζe−0.35ζ − 0.23ζ(ζ − 1.75)e−0.35ζ
10−3
10−2
10−1
100
101
10−1
100
101
Φm
ζ=(z−d)/Λ
0 0 0 2 6 26 32 36 37 61 68 60 50 19 6
6 12 7 14 11 11 19 4 9 6 1 0 0 0 0
Level 1Levels 2−5Dyer (1974)Beljaars and Holtslag (1991)
1
• Surface characteristics are influencing the strength of turbulent mixingand the wind gradient in the same way.
8 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Flux-gradient similarity
φm(ζ) = k(z−d)u∗`
∂U∂z , k=0.4 von Karman constant
• Dyer (1974): φm(ζ) = 1 + 4.8ζ
• Beljaars and Holtslag (1991):φm(ζ) = 1 + ζ + 0.667ζe−0.35ζ − 0.23ζ(ζ − 1.75)e−0.35ζ
10−3
10−2
10−1
100
101
10−1
100
101
Φm
ζ=(z−d)/Λ
Level 1
UndistortedDistorted
• Surface characteristics are influencing the strength of turbulent mixingand the wind gradient in the same way.
8 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Flux-gradient similarity
φm(ζ) = k(z−d)u∗`
∂U∂z , k=0.4 von Karman constant
• Dyer (1974): φm(ζ) = 1 + 4.8ζ
• Beljaars and Holtslag (1991):φm(ζ) = 1 + ζ + 0.667ζe−0.35ζ − 0.23ζ(ζ − 1.75)e−0.35ζ
10−3
10−2
10−1
100
101
10−1
100
101
Φm
ζ=(z−d)/Λ
Levels 2−5
Undistorted Distorted
• Surface characteristics are influencing the strength of turbulent mixingand the wind gradient in the same way.
8 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Flux Richardson number
10−3
10−2
10−1
100
101
10−3
10−2
10−1
100
101
102
Rfcr
=0.25
Rf
ζ=(z−d)/Λ
0 0 0 2 6 26 32 36 37 61 68 60 50 19 6
6 12 7 14 11 11 19 4 9 6 1 0 0 0 0
Level 1Levels 2−5
Grachev et al. (2013; ideal terrain):
• Subcritical: Ri ,Rf ≤ 0.20− 0.25 → Kolmogorov turbulence
• Supercritical: Ri ,Rf > 0.20− 0.25 → non-Kolmogorov turbulence
9 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Sub- vs supercritical regime
Grachev et al. (2013; ideal terrain):
• Subcritical: Ri ,Rf ≤ 0.20− 0.25 → Kolmogorov turbulence
• Supercritical: Ri ,Rf > 0.20− 0.25 → non-Kolmogorov turbulence
10−3
10−2
10−1
100
101
10−1
100
101
Rf ≤ 0.25
Φm
ζ=(z−d)/Λ
Dyer (1974)Beljaars and Holtslag (1991)
10 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Sub- vs supercritical regime
Grachev et al. (2013; ideal terrain):
• Subcritical: Ri ,Rf ≤ 0.20− 0.25 → Kolmogorov turbulence
• Supercritical: Ri ,Rf > 0.20− 0.25 → non-Kolmogorov turbulence
10−3
10−2
10−1
100
101
10−1
100
101
Rf ≤ 0.25
Φm
ζ=(z−d)/Λ
Dyer (1974)Beljaars and Holtslag (1991)Best fit
Best fit:φm(ζ) = 1 + 3.8ζ
↓consistency withz-less scaling
10 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Sub- vs supercritical regime
Grachev et al. (2013; ideal terrain):
• Subcritical: Ri ,Rf ≤ 0.20− 0.25 → Kolmogorov turbulence
• Supercritical: Ri ,Rf > 0.20− 0.25 → non-Kolmogorov turbulence
10−3
10−2
10−1
100
101
10−1
100
101
Rf ≤ 0.25Rf > 0.25
Φm
ζ=(z−d)/Λ
Dyer (1974)Beljaars and Holtslag (1991)Best fit
Best fit:φm(ζ) = 1 + 3.8ζ
↓consistency withz-less scaling
10 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Wind speed regimes
• Wind regime classification based on the mean wind speed• Strong regime: Ui ≥ U + 0.55σ• Intermediate regime: U− 0.55σ ≤ Ui ≤ U + 0.55σ• Weak-wind regime: Ui ≤ U− 0.55σ
0 2 4 6 80
2
4
6
8
10
12
Φm
ζ=(z−d)/Λ
Weak wind
Dyer (1974)Beljaars & Holtslag (1991)
0 2 4 6 80
2
4
6
8
10
12
Φm
ζ=(z−d)/Λ
Intermediate wind
0 2 4 6 80
2
4
6
8
10
12
Φm
ζ=(z−d)/Λ
Rf ≤ 0.25Rf > 0.25
Strong wind
Local stability parameter is sufficient predictor for flux-gradient relationship
11 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Wind speed regimes
• Wind regime classification based on the mean wind speed• Strong regime: Ui ≥ U + 0.55σ• Intermediate regime: U− 0.55σ ≤ Ui ≤ U + 0.55σ• Weak-wind regime: Ui ≤ U− 0.55σ
0 2 4 6 80
2
4
6
8
10
12
Φm
ζ=(z−d)/Λ
Weak wind
Dyer (1974)Beljaars & Holtslag (1991)
0 2 4 6 80
2
4
6
8
10
12
Φm
ζ=(z−d)/Λ
Intermediate wind
0 2 4 6 80
2
4
6
8
10
12
Φm
ζ=(z−d)/Λ
Rf ≤ 0.25Rf > 0.25
Strong wind
Local stability parameter is sufficient predictor for flux-gradient relationship
11 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Summary and Conclusions
• Local scaling promising even for highly non-homogeneous terrain
• Flux-variance and flux-gradient relationships respond differently toinhomogeneous surface characteristics
• Flux-gradient relationships are less influenced by surfaceinhomogeneity
• Classical Businger-Dyer linear expressions supported for Rf ≤ 0.25
• Deviations from linear expressions −→ due to the small-scaleturbulence (subcritical regime)
Babic, K., M. W. Rotach and Z. B. Klaic (2016): Evaluation of Local Similarity Theory in theWintertime Nocturnal Boundary Layer over Heterogeneous Surface, Agric. For. Meteorol. Inreview
12 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Introduction & Motivation Data Flux-variance Similarity Flux-gradient Similarity Conclusions
Summary and Conclusions
• Local scaling promising even for highly non-homogeneous terrain
• Flux-variance and flux-gradient relationships respond differently toinhomogeneous surface characteristics
• Flux-gradient relationships are less influenced by surfaceinhomogeneity
• Classical Businger-Dyer linear expressions supported for Rf ≤ 0.25
• Deviations from linear expressions −→ due to the small-scaleturbulence (subcritical regime)
Babic, K., M. W. Rotach and Z. B. Klaic (2016): Evaluation of Local Similarity Theory in theWintertime Nocturnal Boundary Layer over Heterogeneous Surface, Agric. For. Meteorol. Inreview
Thank you for your attention!
12 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Vertical structure
Conceptual sketch: idealized vertical layers at a step change in surfaceroughness
90 80 70 60 50 40 30 20 10
Hei
ght (
m)
IEL
Transition layer
hIBL
z01 z02
RSL
U
d
• RSL: RoughnessSublayer∗
• IEL: InternalEquilibriumLayer∗∗
• IBL: InternalBoundary Layer∗∗
∗ Raupach (1994): h∗−dhc−d
= 2
∗∗ Cheng and Castro (2002)
13 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Turbulent Kinetic Energy (TKE)
Sanz Rodrigo and Anderson (2013)(ideal horizontally homogeneous and flat terrain):
TKE
u2∗`
(ζ) =
{ 1α0
+ bEζ , ζ ≤ 101α0
+ bE10 , ζ > 10
α0 = 0.22 neutral limit value and bE = 0.5 (- - -)ζ = z/Λ - local stability parameter
10−3 10−2 10−1 100 1010
4
8
12
16
20
TKE
/u*l2
ζ=(z−d)/Λ
0 1 0 7 29 84 158
170
227
328
357
247
92 26 4
Level 1Levels 2−5
1
Best fit for levels 2-5:TKEu2∗`
(ζ) = 10.16
+ 0.8ζ
14 Karmen Babic : Local scaling in the SBL over heterogeneous terrain
Sub- vs supercritical regime
Grachev et al. (2013): φmφ−1w = k(z−d)
σw
dUdz
! not influenced by self-correlation
10−3 10−2 10−1 100 10110−1
100
101
ΦmΦ
w−1
ζ=(z−d)/Λ
(a)Level 1Levels 2−5
10−3 10−2 10−1 100 10110−1
100
101
ΦmΦ
w−1
ζ=(z−d)/Λ
Rf ≤ 0.25
(b)
All dataRSL influences σwprofile but not thewind shear profile
15 Karmen Babic : Local scaling in the SBL over heterogeneous terrain