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