TURBULENCE OVER OROGRAPHY

Ivana Stiperski

University of Innsbruck

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• Name: Ivana Stiperski
• Prof. of atmospheric turbulence at University of Innsbruck
• From: Zagreb, Croatia

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• Croatia (very small) is famous for:
• Invention of tie, parachute, mechanical pen, meglite..
• Moho layer
• Coast with 2000 islands
• Sports (soccer, basketball, handball, skiing, tennis …)
• Game of Thrones..

About me

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Croatia is home of bora winds

Orography of Croatia

Bora winds (signature downslope windstorm along the coast)

Strongest gust ever recorded: 69 m/s (official), 85 m/s (unofficial)

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Convection

• Undergrad degree (Diploma) in Physics/Geophysics at University of Zagreb, Croatia, 2004
• Topic of my Diploma thesis: Tornadogenesis (measurements/simulations)

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Mountain meteorology (mesoscale simulations)

• PhD in Physics of the Atmosphere and Ocean at University of Zagreb, 2010
• Topic: Katabatic flows, mountain waves and downslope windstorms (advisor V. Grubišić, DRI)
• Also worked on implementation of new convection parametrization into ALARO model (MeteoFrance, Czech weather service)
• Research stays in DRI, NCAR, University of Vienna

My (changing) research interests

Terrain-induced Rotor Experiment

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Turbulence in complex terrain (measurements)

• University of Innsbruck
• Postdoc (2011 - 2015): Innsbruck-Box (i-Box) (advisor M. Rotach)
• Postdoc on my own grant (2015 – 2018): Scale interactions in stable boundary layer

My (changing) research interests

• Professor (2019 – now):
• Similarity theory in complex terrain “Developing a novel framework for understanding near-surface turbulence in complex terrain (Unicorn)” (ERC Grant)
• Just for fun: Glacier boundary layers and turbulence, Katabatic flows, Cold pool dynamics, Turbulence in a cave

i-Box

i-Box

HEFEX

Ice-cave

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Importance of ceasing opportunities

• Applying for scholarships, awards, grants
• Networking at conferences – collaborations (UoU, UCLA, University of Balearic Islands, Wageningen, Duke, Oregon State, SLF, Oslo, Virginia)
• Know what is your main selling product: data, modelling, specific topic?

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Do what you love, but learn to love what you do

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Do your best but be aware that luck plays a role

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Cease the opportunities

→ How do mountains modify atmospheric processes at different scales

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Serafin et al. (2018)

Research question

Earth’s land surface

• 70% Complex terrain
• 25% Mountains

How does turbulence over orography differ from flat terrain?

→ All Earth system models still assume Earth is flat in turbulence parametrizations of surface exchange

→ Focus: Stratified flow over mountains – “truly complex terrain”

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Turbulence over flat terrain

Turbulence over HHF terrain

→ shows common, consistent and repeatable behavior �→ is determined by a few key processes (variables)

• Surface vertical sensible heat flux
• Surface vertical momentum flux
• Height above the surface

→ basis of Monin-Obukhov Similarity Theory

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Assumptions:

• Fluxes are constant with height (SL)
• Horizontally homogeneous and flat terrain
• Only relevant processes are buoyancy and vertical wind shear
• Turbulence eddies scale with z
• Stationary conditions
• No subsidence

Turbulence over flat terrain

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Effect of Mountains

https://www.youtube.com/watch?v=pZA4xTWE_H8

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AHATS – CA

Cabauw – NL

• All major assumptions of similarity theory are broken over mountains
• Orography affects turbulent variances differently to the turbulent fluxes and gradients
• Strong implications for similarity theory

Turbulence over mountains

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• Data do not collapse onto a single curve
• Scaling curves are site specific
• Large scatter within each dataset
• Large deviations for strong stratification (momentum) and neutral (temperature)

Similarity Theory in mountainous terrain

Flux-variance relations

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For stratified flows over topography:

• Fluxes are non-constant with height
• Only local scaling applies

Babić N et al. (2016)

Assumption: Fluxes are constant with height

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Lehner et al. (2021)

i-Box

→ Inherent heterogeneity

• Surface characteristics
• Heterogeneity increases variances

Assumption: Homogeneity

i-Box turbulence network (Rotach et al. 2017)

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Lehner et al. (2021)

Heterogeneity

→ Inherent heterogeneity

• Slope angle, Exposition – different solar insolation
• Differences in flow dynamics over short distances

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→ Gravity acts in the flow direction

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→ Obstacles to synoptic flow:

• Speed up at mountain top
• Flow separation in the lee
• Gravity waves
• Downslope windstorms

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→ Elevated heat sources: thermally driven circulations (gravity flows)

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Mountains are more than just heterogeneity

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BL height

Plain – mountain circulation

Valley winds

Slope flows

Mountain venting

Rotach et al. (2017)

Synoptically undisturbed conditions: no large scale pressure gradient, clear sky

→ Thermally driven circulations

Assumption: Flat terrain

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Defant (1949)

Valley and slope winds

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Schmidli (2013)

• With the same input of heat at the bottom valley atmosphere warms more than the plain due to smaller volume of air that needs to be warmed
• Where does the energy come from?

Valley and slope winds

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Schmidli (2013)

Local valley heat budget

• Cold horizontal advection and warm vertical advection through slope flows
• Subsidence warming at the valley core but source of heat is from local slope, not FA
• Vertical sensible heat flux divergence warms the entire valley atmosphere
• Slope flows export heat: 10 – 57% of surface sensible heat is exported (Leukauf et al. 2015)

Valley and slope winds

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Difference to Flat Terrain: Daytime

• Large difference in PBL structure in conditions of low synoptic forcing

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Over flat terrain:

• Buoyancy production of turbulence

→ Convective cells in the horizontal

Horizontal

Vertical

Wagner et al. (2014)

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Full TKE budget

Assumption: Only vertical exchange is important

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1D parametrization fail in complex terrain

• Appropriate for Buoyancy > Shear
• Underestimate TKE for

Shear > Buoyancy

Goger et al. (2018)

Difference to Flat Terrain: Daytime

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3D parametrization necessary for terrain

• horizontal shear production
• Advection

more accurately representation

Goger et al. (2018)

Difference to Flat Terrain: Daytime

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Difference to Flat Terrain: Nighttime

Over flat terrain:

• Large stratification leads to die-down of turbulence

→ Very stable stratification and intermittency

On sloping terrain (or over glaciers):

• Large stratification leads to katabatic flows (gravity current)

→ persistent turbulence

• Driver: negative buoyancy
• Retardation: surface friction and entrainment from above

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Finnigan et al. (2020)

Difference to Flat Terrain: Nighttime

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Above jet maximum:

• Scaling is not MOST (Nadeau et al. 2013)

Difference to Flat Terrain: Nighttime

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Katabatic flows:

• Dominant eddies have constant scale

Assumption: dominant eddies scale with z

Canonical boundary layer flows:

• Dominant eddies scale with height z

Stiperski et al. (2020)

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Difference to Flat Terrain: Directional shift

• Rotation of wind with height causes mis-alignment of shear vector and stress
• Frictional stress and directional stress are equally important (Andratta et al. 2001)

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Difference to Flat terrain: Directional dependence

Better match with MOST

• Along valley flows (de Franceschi et al. 2009)
• Flows with a more uniform fetch (Babić K et al. 2016)

Babić K et al. (2016)

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Extending Similarity Theory to complex terrain

Departure of the wind profile from logarithmic due to stratification:

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Associated with anisotropy

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Turbulence can be:

• Isotropic – equal in all directions

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• Anisotropic – stronger in some directions than in others

What is anisotropy?

Anisotropy – directional dependence of turbulence

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What is anisotropy

Isotropic turbulence

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Turbulence forcing is anisotropic

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• Horizontal: Shear driven turbulence
• Vertical: Buoyancy driven turbulence

Why is turbulence anisotropic?

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• Characteristic of Reynolds stress tensor:

6 independent components

Quantifying anisotropy

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y_B

x_B

prolate

oblate

Anisotropy invariant map

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Similarity theory and anisotropy

Stiperski and Calaf (2023)

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Ensemble of different datasets

Including anisotropy allows extending MOST to complex terrain – anisotropy encodes complexity

Similarity theory and anisotropy

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Stiperski and Calaf (2018)

Vercauteren et al. (2021)

Stiperski et al. (2021)

Gucci et al. (2022)

• In models: TKE is isotropic

Causes of anisotropy in flat terrain

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• Majority of Earth’s land surface is characterized by orography (small or large)
• In the numerical models the Earth’s surface is still represented as flat and Monin-Obukhov similarity theory (MOST) is used to parametrize the exchange
• Over mountains almost all assumptions underlying MOST do not hold:
• Fluxes are non-constant with height
• Turbulence is strongly influenced by heterogeneity, and variances and gradients are affected differently than fluxes
• Shear and stress tensors are mis-aligned
• All terms of the TKE budget are important
• Turbulence is strongly impacted by unresolved thermal circulations, and flow is strongly directionally dependent
• “Despite highly complex and heterogeneous structure mountain flows, characteristic and transferable patterns in the turbulence structures and larger-scale flow patterns could be found” (Finnigan et al. 2020) and could allow retrieving universality offered by MOST: slope angle, anisotropy

Summary

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Babić, K., Rotach, M. W., & Klaić, Z. B. (2016). Evaluation of local similarity theory in the wintertime nocturnal boundary layer over heterogeneous surface. https://doi.org/10.1016/j.agrformet.2016.07.002

Babić, N., Večenaj, Ž., & De Wekker, S. F. J. (2016). Flux–variance similarity in complex terrain and its sensitivity to different methods of treating non-stationarity. https://doi.org/10.1007/s10546-015-0110-0

Banerjee, S., Krahl, R., Durst, F., & Zenger, C. (2007). Presentation of anisotropy properties of turbulence, invariants versus eigenvalue approaches. https://doi.org/10.1080/14685240701506896

de Franceschi, M., Zardi, D., Tagliazucca, M., & Tampieri, F. (2009). Analysis of second-order moments in surface layer turbulence in an Alpine valley. https://doi.org/10.1002/qj.506

Finnigan, J., et al. 2020: Boundary-Layer Flow Over Complex Topography, https://doi.org/10.1007/s10546-020-00564-3

Hang, C., Oldroyd, H. J., Giometto, M. G., Pardyjak, E. R., & Parlange, M. B. (2021). A Local Similarity Function for Katabatic Flows Derived From Field Observations Over Steep- and Shallow-Angled Slopes. https://doi.org/10.1029/2021GL095479

Kral, S. T., Sjöblom, A., & Nygård, T. (2014). Observations of summer turbulent surface fluxes in a High Arctic fjord. https://doi.org/10.1002/qj.2167

Nadeau, D. F., Pardyjak, E. R., Higgins, C. W., & Parlange, M. B. (2013). Similarity Scaling Over a Steep Alpine Slope. https://doi.org/10.1007/s10546-012-9787-5

Oldroyd, H. J., Pardyjak, E. R., Higgins, C. W., & Parlange, M. B. (2016). Buoyant turbulent kinetic energy production in steep-slope katabatic flow. https://doi.org/10.1007/s10546-016-0184-3

Rotach, M. W., & Zardi, D. (2007). On the boundary-layer structure over highly complex terrain: Key findings from MAP. https://doi.org/10.1002/qj.71

Sfyri, E., Rotach, M. W., Stiperski, I., Bosveld, F. C., Lehner, M., & Obleitner, F. (2018). Scalar-Flux Similarity in the Layer Near the Surface Over Mountainous Terrain. https://doi.org/10.1007/s10546-018-0365-3

Stiperski, I., Calaf, M. (2018): Dependence of near-surface similarity scaling on the anisotropy of atmospheric turbulence. https://doi.org/10.1002/qj.3224

Stiperski, I., Calaf, M., & Rotach, M. W. (2019). Scaling, Anisotropy, and Complexity in Near-Surface Atmospheric Turbulence. https://doi.org/10.1029/2018JD029383

Stiperski, I., Chamecki, M., & Calaf, M. (2021). Anisotropy of Unstably Stratified Near-Surface Turbulence. https://doi.org/10.1007/s10546-021-00634-0

Stiperski, I., Calaf, M., 2023: Generalizing Monin-Obukhov similarity theory (1954) for complex atmospheric turbulence. https://doi.org/10.1103/PhysRevLett.130.124001

References