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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

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





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

Intro





– 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


• 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


• 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


• 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


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

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]


• 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


• 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


• Plot of versus all roughnesses!

Theory

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1𝑧

𝐿



• 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



• 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


• Approximations to versus :

Theory

𝛼

𝛼𝑁

𝑇𝐼

𝑇𝐼𝑁

−1 𝑧

𝐿


• 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


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


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

Method & Demo


2. Estimate normalized deviations of shear and TI

3. Apply smoothing kernel to enhance stability signal

Method & Demo


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




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


𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏𝒛

𝑳

𝜶

𝜶𝑵

𝑻𝑰

𝑻𝑰𝑵

−𝟏




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


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



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

Conclusions




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

Conclusions




• 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

accuracy of load assessments based on modelled … › sites › winddenmark.dk › files...–m....

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