Aspects of boundary layers in complex terrain and the ...

Aspects of boundary layers in complex terrain and the interaction to the free troposphere Mathias W Rotach University of Innsbruck, Austria

10th EMS Annual Meeting / 8th ECAC, Zürich Switzerland, 13-17 Sept 2010

Outline • Introduction  some general thoughts • Scaling - an example • Exchange between ‘complex surface’ - free troposphere • Summary and conclusions

Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)

Background In terms of numerical modelling: • Δx, Δy → 10km: hydrostatic assumption • Δx, Δy → O(1km): (deep) convection resolved  grey zone ‘terra incognita’ (Wyngaard, 2004) • Δx, Δy → < 1km: the next challenge


Boundary Layer challenges • BL/sfc exchange parameterization:  based on knowledge from flat horizontally homogenous terrain  do scaling regimes apply? • If the models were perfect:  what to reproduce?


The legendary ‘Kansas Experiment‘ (Haugen et al (1971)

Boundary Layer challenges • EMS2010-412: Juerg Schmidli  model intercomparison, highly idealized

Which is correct? Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)

Boundary Layer challenges • RANS models:  start to resolve part of the spectrum  1d-turbulence sufficient?  LES...

• Can (current) numerics stand steep terrain?  Rule of thumb: don’t stretch grid too much! b z tan 1 x  a = terrain slope, b ~ 1-5  Lundquist, Chow and Lundquist, AMS Conf on Mountain Met, 2010 Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)

Boundary Layer challenges • Grid stretching:  Zhou and Chow, AMS Conf on Mountain Met, 2010  LES (ARPS)

h / Lh = 1, TKE-1.5

+ Δx / Δzmin =1

Δx / Δzmin = 2


Δx / Δzmin = 5

Turb. Exchange: Complex Topography • Weather and climate modeling sensitive to parameterization of turbulent exchange • For applications such as hydrology, pollutant dispersion studies, ....: need the details FH,q,m FH,q,m

FH,q,m FH,q,m

Rotach and Zardi 2007 Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)

Turb. Exchange: Complex Topography • Weather and climate modeling sensitive to parameterization of turbulent exchange • For applications such as hydrology, pollutant dispersion studies, ....: need the details FH,q,m

FH,q,m

FH,q,m FH,q,m


Turb. Exchange: Complex Topography

(Xj+1,Yk+1) (Xj,Yk)

FH,q,m

FH,q,m

FH,q,m

(Xj+1,Yk+1) (Xj+1,Yk) FH,q,m FH,q,m


So what do we know?


Previous experience • Early observations: mainly mean conditions (valley wind, slope wind, etc) • Linearised theory (Jackson and Hunt, 1975, Hunt et al.1988) --> Askervein • Recent projects:  Riviera (Rotach et al. 2004): small narrow valley, 1999  VTMX (Doran et al 2002): Salt Lake Valley, 2000  T-Rex (Grubisic et al. 2008): Owen’s Valley, 2003-6  others... (various smaller projects)  joint efforts, 3d structure, remote sensing, observations and numerical modeling Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)

Scaling Behavior Convective boundary layer over flat topography

zi


Scaling Behavior Deardorff (1970,1972) similarity theory:

• Example:

TKE 2 w*

z f zi zi

• Velocity scale w* = w*(Ho, g/q, zi)

Sensible surface heat flux: Ho Aspects of boundary layers in complex terrain Buoyancy parameter: g/q | EMS 2010, ZÜRICH, 13-17 September 2010

Mathias Rotach (mathias.rotach [at] uibk.ac.at)

Riviera observations Scaled profiles of TKE - measured


Weigel and Rotach (QJRMS, 2004)

Energy flux Wm-2

Horizontal inhomogeneity 800 700 600 500 400 300 200 100 0 -100 -200

A1 H+LE+G B H+LE+G E2 H+LE+G A1 NRcor B NRcor E2 NRpar

0

4

8

12

Time [CET] Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)

16

20

24

Scaling Behavior Scaled profiles of TKE - simulated


Weigel et al (BLM, 2007)





How can this scaling behavior be understood? Mathias Rotach (mathias.rotach [at] uibk.ac.at) => Look into simulated TKE budget Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010


Production Mechanisms TKE budget (solved in ARPS’s 1.5 order TKE closure)

ADVECTION

SHEAR PRODUCTION

BUOYANCY PRESSURE CORRELATION, PRODUCTION TURB. TRANSPORT, DISSIPATION Mathias Rotach (mathias.rotach [at] uibk.ac.at) Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010

Production Mechanisms Evaluation of the TKE budget equation with ARPS Late morning

Example 22 August


Production Mechanisms Evaluation of the TKE budget equation with ARPS Early afternoon

Example 22 August


Production Mechanisms Evaluation of the TKE budget equation with ARPS Early afternoon Shear is dominant production mechanism

Turbulence not directly determined by buoyant processes from heated surface but by interaction of thermally driven valley flows Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)


Production Mechanisms Evaluation of the TKE budget equation with ARPS Late afternoon Shear is dominant production mechanism

Turbulence not directly determined by buoyant processes from heated surface but by interaction of thermally driven valley flows Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)


Production Mechanisms 21 August

Up-valley wind speed (averaged over valley volume)

w2* on eastern (sunlit) slope w2* on valley floor

22 August

25 August


Production Mechanisms Correlation between and w2* w2* from valley floor

w2* from sunlit slope 9-16 UTC

9-16 UTC

~ w2*

Coincidence? Problem with scaling: has wrong dimensions... Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)

Exchange BL - Free Troposphere Example: moisture transport out of Riviera Valley Essentially three processes: • Topography (valley gets smaller) • Local circulation • Turbulent exchange


Weigel et al (BLM, 2007b)

Exchange BL - Free Troposphere

‘Lmean’ Moisture flux associated with net vertical air flow --> valley narrowing --> local horizontal flow convergence

Lmean

w q

average('lid') Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)





‘Lfluc’ Moisture flux due to crossvalley circulations and mountain venting

Lfluc w'


w'q' qÕ 0





‘Lturb’ Moisture flux due to turbulent transport (turned out to be negligible)

Lturb

w'q'

(Integral of SGS flux) Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)


Example August 22 1999



asymmetric valley wind transition → local horizontal flow convergence.

Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010

Example August 21 1999 Example August 21 1999






What would a coarse model see?




‘E’ Valley topography not resolved --> moisture exchange estimated on basis of parameterized turbulent surface fluxes E


Total Moisture Exchange









Surface Flux good enough? Aspects of boundary layers in parameterization complex terrain Example August 25 1999 Example August 25 1999 needed…. Topography induced parameterization | EMS 2010, ZÜRICH, 13-17 September 2010


Summary • Next challenge when Δx → O(100m)  Boundary Layer dynamics in complex topography  need to understand processes  need to improve modelling

• Boundary layer parameterizations  scaling approaches  turbulent transport ⇔ geometric effects + unresolved circulations (+ turb. transport) • Exciting perspectives  new observations...  refined modelling Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)

Many thanks to Andreas Weigel, Pierluigi Calanca, Tina Chow, Juerg Schmidli, Dino Zardi, Alex Gohm, Marco Andretta, ... Aspects of boundary layers in complex terrain| EMS 2010, ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at)

Lior Perez, ‚Pyrenees Valley fog‘, EMS photo competition ‘09

MAP-Riviera Project


Numerical Modeling • High resolution, several nests


MAP-Riviera Project


Rotach et al 2004

MAP-Riviera Project

Biasca Riviera Valley

Bellinzona


Rotach et al (2008)

Production Mechanisms Buoyancy production of TKE [ m2 / s3 ]

1000 UTC

1400 UTC


Production Mechanisms Shear production of TKE [ m2 / s3 ]

1000 UTC

1400 UTC

TKE appears tolayers beindetermined of valley winds. But why Aspects of boundary complex terrain| EMSby 2010, strength ZÜRICH, 13-17 September 2010 Mathias Rotach (mathias.rotach [at] uibk.ac.at) does convective scaling approach nevertheless work ?