A novel method to quantifyatmospheric stability…

Presenter: Lasse Svenningsen

Or… what can you do with only standard measurements?

Presenter: Lasse Svenningsen

Outline

• A question!

• Intro, Motivation & Hypothesis

• Some MOST Theory

• Method & Demo

• Validation main assumption

• Conclusions

[References and eq. numbers refer to windEU 2018 paper]https://iopscience.iop.org/article/10.1088/1742-6596/1102/1/012009/pdf

Which measurements do you typically have from a mast?

A) Just wind speed / TI (cups)

B) + Temp. diff / dual temp.

C) + 3D-Sonic

First a question!

Which measurements do you typically have from a mast?

(my guess ☺)

A) Just wind speed / TI (cups) [~85%]

B) + Temp. diff / dual temp. [<10%]

C) + 3D-Sonic [<5%]

First a question!

Stability – what is it?

• Static stability

– Temp. lapse rate compared to adiabatic lapse rate (~1°/100m)

– Only static effects on buoyancy forces (wind speed≈0)

– Measures: Δθ/Δz

Intro

Stability – what is it?

• Static stability

– Temp. lapse rate compared to adiabatic lapse rate (~1°/100m)

– Only static effects on buoyancy forces (wind speed≈0)

– Measures: Δθ/Δz (Stable: Δθ/Δz>0 / Unstable: Δθ/Δz<0)

Intro

Stability – what is it?

• Static stability

– Temp. lapse rate compared to adiabatic lapse rate (~1°/100m)

– Only static effects on buoyancy forces (wind speed≈0)

– Measures: Δθ/Δz (Stable: Δθ/Δz>0 / Unstable: Δθ/Δz<0)

• Dynamic stability

– The dynamic effect of wind speed is accounted for

– Wind shear => turbulent mixing and fluxes of heat and momentum

– Measures: Ri, L

Intro

Stability – how is it quantified and measured?

• Recommended methods:

– Monin-Obukhov length (L)

– Richardson number (Ri)

Intro

Stability – how is it quantified and measured?

• Recommended methods:

– Monin-Obukhov length (L)

– Richardson number (Ri)

Intro

Stability – how is it quantified and measured?

• L – The Monin-Obukhov length

– Below L: shear-effects dominate TI, Above L: buoyancy-effects dominate TI

– Required measurements: 3D sonics (𝜃𝑣′𝑤′ and 𝑢′𝑤′ ~ 𝐻 and 𝑢∗)

– Very sensitive to 𝑢∗ => very local, 𝑢∗3 depends strongly on roughness and terrain

Intro

L =𝜌𝐶𝑝𝜃𝑢∗

3

𝜅𝑔𝐻

Stability – how is it quantified and measured?

• L – The Monin-Obukhov length

– Below L: shear-effects dominate TI, Above L: buoyancy-effects dominate TI

– Required measurements: 3D sonics (𝜃𝑣′𝑤′ and 𝑢′𝑤′ ~ 𝐻 and 𝑢∗)

– Very sensitive to 𝑢∗ => very local, 𝑢∗3 depends strongly on roughness and terrain

– Is this point estimate optimal choice e.g. to drive input to a CFD model?

Or do we actually need a more ‘regional’ value?

Intro

L =𝜌𝐶𝑝𝜃𝑢∗

3

𝜅𝑔𝐻

Stability – how is it quantified and measured?

• Ri - Richardson number (gradient)

– Ri is the ratio of ‘buoyant TI-generation/consumption’ to ‘shear TI-generation’

– Required measurements: temperature diff. and wind speed difference (issue for du/dz→0)

– Directly related to z/L via similarity theory:

Unstable (Ri<0): z/L ≡ 𝜑𝑚2

𝜑ℎ≈ Ri

Stable (Ri>0): z/L ≡ 𝜑𝑚2

𝜑ℎ≈ Ri/(1-5Ri) (alternative expressions published)

Intro

Ri =𝑔 ൗ∆𝜃

∆𝑧

𝜃 ൗ∆𝑢∆𝑧

2

Stability – how is it quantified and measured?

The problem:

• Recommended methods require measurements not installed on standard masts

• What can we do with only a standard mast setup?

Motivation

Stability – what are the (well known) effects?

• Turbulence (*): 𝑇𝐼

𝑇𝐼𝑁Vs

𝑧

𝐿

• Shear (o): 𝛼

𝛼𝑁Vs

𝑧

𝐿

Motivation

Stability – what are the (well known) effects?

• Turbulence (*): 𝑇𝐼

𝑇𝐼𝑁Vs

𝑧

𝐿

• Shear (o): 𝛼

𝛼𝑁Vs

𝑧

𝐿

Motivation

Can we quantify MOL from shear and turbulence?

• Previous studies:

– Iterative profile methods (e.g. Holtslag et al., 2012)

– Stability classification from shear only (e.g. Wharton & Lundquist, 2012)

– M. Kelly (2014) mentions possible equation: Τ𝛼 𝑇𝐼 − 1 ≅ Τ𝑧 𝐿

• This study:

– Quantify shear and TI deviations from their neutral value (u→∞)

– Must be handled versus direction due to terrain and roughness effects v

– Can we infer L from these deviations?

Hypothesis

Can we quantify MOL from shear and turbulence?

• Previous studies:

– Iterative profile methods (e.g. Holtslag et al., 2012)

– Stability classification from shear only (e.g. Wharton & Lundquist, 2012)

– M. Kelly (2014) mentions possible equation: Τ𝛼 𝑇𝐼 − 1 ≅ Τ𝑧 𝐿

• This study:

– Quantify shear and TI deviations from their neutral value (u→∞)

– Must be handled versus direction due to terrain and roughness effects v

– Can we infer L from these deviations?

Hypothesis

MO Similarity Theory for shear and TI

Theory

MO Similarity Theory for shear

• Wind profile:

• Shear exponent:

φ𝑚𝑧

𝐿is the universal similarity function for shear

Ψ𝑚𝑧

𝐿is an integral of φ𝑚

𝑧

𝐿.

Theory

𝑢 𝑧 =𝑢∗𝜅

ln𝑧

𝑧0−Ψ𝑚

𝑧

𝐿

𝛼 ≡ൗ𝑑𝑢𝑑𝑧Τ𝑢 𝑧

=𝑢∗𝑢 ⋅ 𝜅

φ𝑚

𝑧

𝐿

MO Similarity Theory for TI

• Turbulence:

– Does not fully follow MOST, as it does not fully scale with z

– For unstable conditions it scales with zi (ABL height), but with low sensitivity

𝜑1?

𝐿is a quasi-universal similarity function for turbulence

Theory

𝜎𝑢 = 𝑢∗𝜑1𝑧

𝐿(stable)

𝜎𝑢 = 𝑢∗𝜑1𝑧𝑖

𝐿(unstable)

Universal functions for shear and TI

• Some published expressions for the similarity functions:

• Typical constants: a=1.7-2.3, … (see paper)

• Neutral limits: let L → ±∞

• Problem(?): “a” not consistent across published stable-unstable

Theory

u-function Neutral limit Stable Unstable

Shear: 𝛗𝒎 1 1 + 𝑏𝑧𝐿

[8–10] 1 − 𝑏𝑧𝐿

𝑐[8–10]

TI: 𝛗𝟏 a 𝑎 + 𝑏 𝑧

𝐿

𝑐[11,12] 𝑎 1 − 𝑏𝑧𝑖

𝐿

𝑐[10,13]

MO Similarity Theory for shear and TI

• Revisit of MOST expected shear and TI

deviations versus roughness and z/L:

• Notice the alignment across roughnesses

• And how the lines converge to {-1,-1}

• Why?....

Theory

MO Similarity Theory for shear and TI

• Revisit of MOST expected shear and TI

deviations versus roughness and z/L:

• Notice the alignment across roughnesses

• And how the lines converge to {-1,-1}

• Why?....

• The ratio is independent

of roughness

Theory

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1

MO Similarity Theory for shear and TI

• Plot of versus all roughnesses!

Theory

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1𝑧

𝐿

MO Similarity Theory for shear and TI

• Plot of versus all roughnesses!

• A “universal” relationship only a function

of ratios of universal functions:

Theory

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1𝑧

𝐿

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1

=φ𝑚

φ𝑚,𝑁

𝜑1𝜑1,𝑁

−1

MO Similarity Theory for shear and TI

• Plot of versus all roughnesses!

• A “universal” relationship only a function

of ratios of universal functions:

• Constants like “a” in cancel out

Theory

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1𝑧

𝐿

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1

=φ𝑚

φ𝑚,𝑁

𝜑1𝜑1,𝑁

−1

𝜑1

MO Similarity Theory for shear and TI

• Approximations to versus :

Theory

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1 𝑧

𝐿

MO Similarity Theory for shear and TI

• Approximations to versus :

Theory

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1 𝑧

𝐿

Stable: 𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1> 1,

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1≅ 4.1

𝑧

𝐿+ 1

Unstable: 𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1< 1,

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1≅ −0.15 ln

−𝑧

𝐿+ 0.4

Steps of the proposed method

Method & Demo

Steps of the proposed method

1. Estimate neutral limits of shear and TI versus direction

2. Estimate normalized deviations of shear and TI

3. Apply smoothing kernel to enhance stability signal

4. Estimate , MOL and make validation plot

Method & Demo

𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏

Steps of the proposed method

1. Estimate neutral limits of shear and TI versus direction(Example Cabauw, dir=220°±10°)

Method & Demo

Steps of the proposed method

2. Estimate normalized deviations of shear and TI

3. Apply smoothing kernel to enhance stability signal

Method & Demo

Steps of the proposed method

2. Estimate normalized deviations of shear and TI

3. Apply smoothing kernel to enhance stability signal

Method & Demo

Steps of the proposed method

4. Estimate , MOL and make validation plot– Make deviation plot as validation

– Overlaid constant MOL iso-lines

– Strongly resembles theoretical pattern (u>5m/s)

Method & Demo

𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏

Steps of the proposed method

4. Estimate , MOL and make validation plot– Make deviation plot as validation

– Overlaid constant MOL iso-lines

– Strongly resembles theoretical pattern (u>5m/s)

Method & Demo

𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏

Steps of the proposed method

4. Estimate , MOL and make validation plot– Make deviation plot as validation

– Overlaid constant MOL iso-lines

– Strongly resembles theoretical pattern (u>5m/s)

Method & Demo

𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏

Validation of main assumption

• Is there a ‘universal’ relation ship between and ??

• Validation requires concurrent measurements of L and

Three masts:

– Høvsøre

– Ryningsnäs

– NREL-M5

Validation of theory

𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏𝒛

𝑳

𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏

Validation of main assumption

• Is there a ‘universal’ relation ship between and ??

• Validation requires concurrent measurements of L and

Høvsøre (DK west coast): Ryningsnäs (Swedish forest): NREL-M5 (Rockies foothills):

Validation of theory

𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏𝒛

𝑳

𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏

Validation of main assumption

• Is there a ‘universal’ relation ship between and ??

• Validation requires concurrent measurements of L and

Høvsøre (DK west coast): Ryningsnäs (Swedish forest): NREL-M5 (Rockies foothills):

Validation of theory

𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏𝒛

𝑳

𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏

TI from sonic

A new method to quantify stability has been presented:

• z/L can be estimated from just shear and turbulence

Conclusions

A new method to quantify stability has been presented:

• z/L can be estimated from just shear and turbulence

• Key assumption seems to hold acceptably for the 3 test masts

Conclusions

A new method to quantify stability has been presented:

• z/L can be estimated from just shear and turbulence

• Key assumption seems to hold acceptably for the 3 test masts

• Unstable conditions is the difficult part: low z/L-sensitivity & high scatter

Conclusions

A new method to quantify stability has been presented:

• z/L can be estimated from just shear and turbulence

• Key assumption seems to hold acceptably for the 3 test masts

• Unstable conditions is the difficult part: low z/L-sensitivity & high scatter

Conclusions

A new method to quantify stability has been presented:

• z/L can be estimated from just shear and turbulence

• Key assumption seems to hold acceptably for the 3 test masts

• Unstable conditions is the difficult part: low z/L-sensitivity & high scatter

• Further validation cases are needed:

– Test effect of TI sensor type, sonic vs cup

– Test in complex terrain

– Test across multiple heights

= More 3D sonic validation data is needed!

Conclusions