The impact of valley geometry on thermallydriven flows and vertical heat fluxes

Johannes Wagner, Alexander Gohm, Mathias Rotach,Daniel Leukauf, Christian Posch

Institute of Meteorology and GeophysicsUniversity of Innsbruck, Austria

International Conference on Alpine Meteorology 2013

June 04, 2013

Outline

1 Introduction

2 Goals

3 Simulation results

4 Conclusion

Valley geometry and thermally driven flowsICAM 2013 2/18

Outline

1 Introduction

2 Goals

3 Simulation results

4 Conclusion

Valley geometry and thermally driven flowsICAM 2013 3/18

Atmospheric boundary layer (BL)

Convective boundary layer over flat terrain

Valley geometry and thermally driven flowsICAM 2013 4/18

Slope and valley winds ⇒ BL structure

Complex Terrain

?

Change of BL structure due to mesoscale slope/valley winds?Impact of thermally driven flows on vertical transport?Difference: valley BL ⇒ plain BL?

Valley geometry and thermally driven flowsICAM 2013 5/18

Slope and valley winds ⇒ BL structure

Complex Terrain

?

Change of BL structure due to mesoscale slope/valley winds?Impact of thermally driven flows on vertical transport?Difference: valley BL ⇒ plain BL?Operational NWP- and climate models do not resolve valleysproperly. ⇒ Error in vertical profiles ⇒ Parameterization

Valley geometry and thermally driven flowsICAM 2013 5/18

Outline

1 Introduction

2 Goals

3 Simulation results

4 Conclusion

Valley geometry and thermally driven flowsICAM 2013 6/18

Boundary layer over complex terrain

Systematically vary valley topography.Compute bulk flux profiles (heat, moisture, mass, ...).Impact of valley depth/width on bulk profiles?Difference between valley and plain profiles.

Valley geometry and thermally driven flowsICAM 2013 7/18

Outline

1 Introduction

2 Goals

3 Simulation results

4 Conclusion

Valley geometry and thermally driven flowsICAM 2013 8/18

Model set-up (Schmidli 2013)

x−Direction (km)

y−

Direction (

km

)

−20 −10 0 10 200

2

4

6

8

10

Altitude (

km

)

x−Direction (km)0

0.5

1

1.5

2

Altitude (

km

)0.2

0.4

0.6

0.8

1

1.2

1.4

Model set-up

WRF model (version 3.4)40 x 10 x 1.5 kmdx = dy = 50 (100) mdz = 8 to 50 mSGS turbulence: Deardorff-type TKEPeriodic lateral boundaries5 hours simulationOnline statistics module

Valley geometry and thermally driven flowsICAM 2013 9/18

Model set-up (Schmidli 2013)

x−Direction (km)

y−

Direction (

km

)

−20 −10 0 10 200

2

4

6

8

10

Altitude (

km

)

x−Direction (km)0

0.5

1

1.5

2

Altitude (

km

)0.2

0.4

0.6

0.8

1

1.2

1.4

Model set-up

WRF model (version 3.4)40 x 10 x 1.5 kmdx = dy = 50 (100) mdz = 8 to 50 mSGS turbulence: Deardorff-type TKEPeriodic lateral boundaries5 hours simulationOnline statistics module

Initialisation/Forcing

Atmosphere at rest∂θ∂z = 3 K km−1

Constant forcing: HFX = 150 W m−2

Valley geometry and thermally driven flowsICAM 2013 9/18

Model set-up (Schmidli 2013)A

ltitu

de

(km

)

x−Direction

BL−HeightPlain

0

0.5

1

1.5

2

2.5

x−Direction

Altitu

de

(km

)

BL−HeightPlain

0

0.5

1

1.5

2

2.5

Model set-up

WRF model (version 3.4)40 x 10 x 1.5 kmdx = dy = 50 (100) mdz = 8 to 50 mSGS turbulence: Deardorff-type TKEPeriodic lateral boundaries5 hours simulationOnline statistics module

Initialisation/Forcing

Atmosphere at rest∂θ∂z = 3 K km−1

Constant forcing: HFX = 150 W m−2

Valley geometry and thermally driven flowsICAM 2013 9/18

LES Output

Valley geometry and thermally driven flowsICAM 2013 10/18

Subgrid, resolved, mean variables

Fully turbulent variable: ψ̃Model-gridbox averaged variable: ψ

ψ̃ = ψ + ψ′︸︷︷︸SGS

LES output: ψ

ψ = <ψ>︸︷︷︸MEAN

+ ψ′′︸︷︷︸RES

Averaging operator (Schmidli 2013)

< > = 1TLy

∫ ∫ψdydt

T = 40 min, Ly = 10 kmValley geometry and thermally driven flowsICAM 2013 11/18

Reference run: mean flow

<U> <W>

Valley geometry and thermally driven flowsICAM 2013 12/18

Heat flux profile: plain ⇔ valley

MEAN+RES+SGS:

Vertical heat flux (W m−2

)

Altitu

de

(km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

MEAN

RES

SGS

TOT

x−direction (km)

z−

direction (

km

)

Time t = 5 h

303

REF

0 2 4 6 8 10 120

0.5

1

1.5

2

2.5

3

WP

TT

OT

(K

m s

−1)

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Vertical heat flux (W m−2

)

Altitu

de

(km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

MEAN

RES

SGS

TOT

Valley geometry and thermally driven flowsICAM 2013 13/18

Heat flux profile: plain ⇔ valley

MEAN:

Vertical heat flux (W m−2

)

Altitu

de

(km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

MEAN

RES

SGS

TOT

x−direction (km)

z−

direction (

km

)

Time t = 5 h

303

REF

0 2 4 6 8 10 120

0.5

1

1.5

2

2.5

3

WP

TM

EA

N (

K m

s−

1)

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Vertical heat flux (W m−2

)

Altitu

de

(km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

MEAN

RES

SGS

TOT

Valley geometry and thermally driven flowsICAM 2013 13/18

Variation of valley depth: <U>

x−direction (km)

z−

direction (

km

)

Time t = 5 h

302

303

303

304

305

306

H1250

−10 −8 −6 −4 −2 0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

U (

m s

−1)

−3

−2

−1

0

1

2

3

x−direction (km)

z−

direction (

km

)

Time t = 5 h

302

303

303

304

305

306

H1500

−10 −8 −6 −4 −2 0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

U (

m s

−1)

−3

−2

−1

0

1

2

3

Valley geometry and thermally driven flowsICAM 2013 14/18

Valley depth: bulk profiles

Heat Flux

Heat flux (W m−2

)

Altitude (

km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

Pot. Temperature

Theta (K)

Altitu

de

(km

)

BULK Theta

300 301 302 303 304 305 3060

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

Heating Rate

Heating Rate (10−3

K s−1

)

Altitude (

km

)

BULK Tend

−0.1 −0.05 0 0.05 0.1 0.15 0.20

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

Valley geometry and thermally driven flowsICAM 2013 15/18

Valley depth: bulk profiles

Heat Flux

Heat flux (W m−2

)

Altitude (

km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

Pot. Temperature

Theta (K)

Altitu

de

(km

)

BULK Theta

300 301 302 303 304 305 3060

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

Heating Rate

Heating Rate (10−3

K s−1

)

Altitude (

km

)

BULK Tend

−0.1 −0.05 0 0.05 0.1 0.15 0.20

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

Valley geometry and thermally driven flowsICAM 2013 15/18

Outline

1 Introduction

2 Goals

3 Simulation results

4 Conclusion

Valley geometry and thermally driven flowsICAM 2013 16/18

Conclusions

The deeper the valley the stronger the...valley inversionheat flux at mountain topsuperposed circulation cells

Valley geometry and thermally driven flowsICAM 2013 17/18

Conclusions

The wider the valley the...stronger the valley inversionweaker the heat flux at mountain topweaker the superposed circulation cells

Valley geometry and thermally driven flowsICAM 2013 17/18

Conclusions

Existence of along valley wind:stronger valley inversionstronger upslope-windsdeeper + colder valley BL

Valley geometry and thermally driven flowsICAM 2013 17/18

Literature

Thank you for your attention!

Schmidli, J., 2013: Daytime heat transfer processes over mountainous terrain , sub.

Valley geometry and thermally driven flowsICAM 2013 18/18

Heat flux profile: plain ⇔ valley

MEAN+RES+SGS:

Vertical heat flux (W m−2

)

Altitu

de

(km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

MEAN

RES

SGS

TOT

x−direction (km)

z−

direction (

km

)

Time t = 5 h

303

REF

0 2 4 6 8 10 120

0.5

1

1.5

2

2.5

3

WP

TT

OT

(K

m s

−1)

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Vertical heat flux (W m−2

)

Altitu

de

(km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

MEAN

RES

SGS

TOT

Valley geometry and thermally driven flowsICAM 2013 19/18

Heat flux profile: plain ⇔ valley

MEAN:

Vertical heat flux (W m−2

)

Altitu

de

(km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

MEAN

RES

SGS

TOT

x−direction (km)

z−

direction (

km

)

Time t = 5 h

303

REF

0 2 4 6 8 10 120

0.5

1

1.5

2

2.5

3

WP

TM

EA

N (

K m

s−

1)

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Vertical heat flux (W m−2

)

Altitu

de

(km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

MEAN

RES

SGS

TOT

Valley geometry and thermally driven flowsICAM 2013 19/18

Heat flux profile: plain ⇔ valley

RES+SGS:

Vertical heat flux (W m−2

)

Altitu

de

(km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

MEAN

RES

SGS

TOT

x−direction (km)

z−

direction (

km

)

Time t = 5 h

303

REF

0 2 4 6 8 10 120

0.5

1

1.5

2

2.5

3

WP

TR

ES

SG

S (

K m

s−

1)

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Vertical heat flux (W m−2

)

Altitu

de

(km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

MEAN

RES

SGS

TOT

Valley geometry and thermally driven flowsICAM 2013 19/18

Variation of valley width: <U>

x−direction (km)

z−

direction (

km

)

Time t = 5 h

301

301

301

302

302

303

304

305

306

F24

−20 −15 −10 −5 0 5 10 15 200

0.5

1

1.5

2

2.5

3

U (

m s

−1)

−3

−2

−1

0

1

2

3

x−direction (km)

z−

direction (

km

)

Time t = 5 h

302

302

303

303 303

303

304

305

306

F08

−10 −5 0 5 100

0.5

1

1.5

2

2.5

3

U (

m s

−1)

−3

−2

−1

0

1

2

3

x−direction (km)

z−

direction (

km

)

Time t = 5 h

302

302

303

303303

304

305

306

F12

−15 −10 −5 0 5 10 150

0.5

1

1.5

2

2.5

3

U (

m s

−1)

−3

−2

−1

0

1

2

3

x−direction (km)

z−

direction (

km

)

Time t = 5 h

302

303

303

304

305

306

F01

−10 −8 −6 −4 −2 0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

U (

m s

−1)

−3

−2

−1

0

1

2

3

Valley geometry and thermally driven flowsICAM 2013 20/18

Valley width: bulk profiles

Heat Flux

Heat flux (W m−2

)

Altitude (

km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

NARROW

WIDE

Pot. Temperature

Theta (K)

Altitu

de

(km

)

BULK Theta

300 301 302 303 304 305 3060

0.5

1

1.5

2

2.5

3

3.5

PLAIN

NARROW

WIDE

Heating Rate

Heating Rate (10−3

K s−1

)

Altitude (

km

)

BULK Tend

−0.1 −0.05 0 0.05 0.1 0.15 0.20

0.5

1

1.5

2

2.5

3

3.5

PLAIN

NARROW

WIDE

Valley geometry and thermally driven flowsICAM 2013 21/18

Valley-plain: bulk profiles

Heat Flux

Heat Flux (W m−2

)

Altitu

de

(km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H1500

VALPLA

Pot. Temperature

Theta (K)

Altitude (

km

)

BULK Theta

300 301 302 303 304 305 3060

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H1500

VALPLA

Heating Rate

Heating Rate (10−3

K s−1

)

Altitu

de

(km

)

BULK Tend

−0.1 −0.05 0 0.05 0.1 0.15 0.20

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H1500

VALPLA

Valley geometry and thermally driven flowsICAM 2013 22/18

Vertical profiles: <U>

Comparison WRF ⇐⇒ ARPS (Schmidli, 2013)

Valley

U (m s−1

)

z−

dire

ctio

n (

km

)

Position x = 2km at time = 5h

−3 −2 −1 0 1 2 30

0.5

1

1.5

2

2.5

3

WRF50

WRF100

ARPS

Slope

U (m s−1

)

z−

dire

ctio

n (

km

)

Position x = 5km at time = 5h

−3 −2 −1 0 1 2 30

0.5

1

1.5

2

2.5

3

WRF50

WRF100

ARPS

Ridge

U (m s−1

)

z−

dire

ctio

n (

km

)

Position x = 8km at time = 5h

−3 −2 −1 0 1 2 30

0.5

1

1.5

2

2.5

3

WRF50

WRF100

ARPS

Valley geometry and thermally driven flowsICAM 2013 23/18

Valley depth: bulk heat flux profiles

SGS

SGS Heat Flux (W m−2

)

Altitu

de

(km

)

BULK SGS−HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

RES

RES Heat Flux (W m−2

)

Altitu

de

(km

)

BULK RES−HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

MEAN

MEAN Heat Flux (W m−2

)

Altitu

de

(km

)

BULK MEAN−HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

Valley geometry and thermally driven flowsICAM 2013 24/18

Valley depth: bulk profiles

Heat Flux

Heat flux (W m−2

)

Altitude (

km

)

BULK HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

Pot. Temperature

Theta (K)

Altitu

de

(km

)

BULK Theta

300 301 302 303 304 305 3060

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

Heating Rate

Heating Rate (10−3

K s−1

)

Altitude (

km

)

BULK Tend

−0.1 −0.05 0 0.05 0.1 0.15 0.20

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H0500

H1000

H1250

H1500

H2000

Valley geometry and thermally driven flowsICAM 2013 25/18

Valley width: bulk heat flux profiles

SGS

SGS Heat Flux (W m−2

)

Altitu

de

(km

)

BULK SGS−HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

F01

F08

F12

F24

RES

RES Heat Flux (W m−2

)

Altitu

de

(km

)

BULK RES−HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

F01

F08

F12

F24

MEAN

MEAN Heat Flux (W m−2

)

Altitu

de

(km

)

BULK MEAN−HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

F01

F08

F12

F24

Valley geometry and thermally driven flowsICAM 2013 26/18

Valley-plain topography

Valley plain topography: evolution of along valley windssymmetric boundary conditions in along valley direction

x−Direction (km)

y−

Direction (

km

)

−20 −10 0 10 20−50

−30

−10

10

30

50

70

90

x−Direction (km)

y−

Dire

ctio

n (

km

)−20 −10 0 10 200

2

4

6

8

10

Valley geometry and thermally driven flowsICAM 2013 27/18

Valley-plain topography: <U>, <W><Θ>

Valley-plain

x−direction (km)

z−

direction (

km

)

Time t = 5 h

302

302

303

303

304

305

306

VALPLA

−10 −8 −6 −4 −2 0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

U (

m s

−1)

−3

−2

−1

0

1

2

3

x−direction (km)

z−

direction (

km

)

Time t = 5 h

302

302

303

303

304

305

306

VALPLA

−10 −8 −6 −4 −2 0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

WP

TM

EA

N (

K m

s−

1)

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Valley

x−direction (km)

z−

direction (

km

)

Time t = 5 h

302

303

303

304

305

306

REF

−10 −8 −6 −4 −2 0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

U (

m s

−1)

−3

−2

−1

0

1

2

3

x−direction (km)

z−

direction (

km

)

Time t = 5 h

302

303

303

304

305

306

REF

−10 −8 −6 −4 −2 0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

WP

TM

EA

N (

K m

s−

1)

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Valley geometry and thermally driven flowsICAM 2013 28/18

Valley-plain: bulk heat flux profiles

SGS

SGS Heat Flux (W m−2

)

Altitu

de

(km

)

BULK SGS−HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H1500

VALPLA

RES

RES Heat Flux (W m−2

)

Altitu

de

(km

)

BULK RES−HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H1500

VALPLA

MEAN

MEAN Heat Flux (W m−2

)

Altitu

de

(km

)

BULK MEAN−HFX

−50 0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

PLAIN

H1500

VALPLA

Valley geometry and thermally driven flowsICAM 2013 29/18