Statistical modeling of turbulent wind velocity at canopy top: application to forest wind damage

(1)

HAL Id: hal-02738612

https://hal.inrae.fr/hal-02738612

Submitted on 2 Jun 2020

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Statistical modeling of turbulent wind velocity at canopy top: application to forest wind damage

Sylvain Dupont

To cite this version:

Sylvain Dupont. Statistical modeling of turbulent wind velocity at canopy top: application to forest wind damage. Mathematical Modelling of Wind Damage Risk to Forests, Oct 2015, Arcachon, France.

�hal-02738612�

(2)

S TATISTICAL MODELING OF TURBULENT WIND VELOCITY AT CANOPY TOP :

APPLICATION TO FOREST WIND DAMAGE

S ^YLVAIN D ^UPONT

UMR ISPA

A L I M E N T A T I O N A G R I C U L T U R E

E N V I R O N N E M E N T

(3)

2

Recent findings

Dupont et al., Agric. For. Meteorol. (2015)

‒ damage propagation involves two stages

‒ 1^st stage: randomness nature of damages, damages induced by sweeps

‒ 2^nd stage: wind increases inside damaged areas

‒ storm duration plays a major role for predicting the final level of damage

‒ tree dynamics has to be considered in evaluating the critical bending moment

► Give clues to develop a new generation of mechanistic wind risk model

(4)

A new generation of wind risk model

‒ use a probabilistic approach

‒ account for the gustiness of the flow

‒ account for damage propagation

‒ account for windstorm duration and its intensity variation (ideally measured at a nearby meteorological station)

‒ allow to easily compare damage prediction between different stands or different storms as well as to investigate the impact of silvicultural practices

(5)

4 PAI,h

ds

₁

d₁(s,t) d3(s,t)

s

3 A wind-tree model to predict the probability of wind damage

► Tree: flexible cantilever beams, perfectly clamped in the ground (Pivato et al. 2014)

► Wind: statistical modeling of wind velocity time series at canopy top

Proposition

(6)

Wind time series from U

_h

, h and PAI

 1^st step: autocorrelated Gaussian time series m_i:

 2^nd step: transformation from Gaussian to real PDF

m_i => normalized u_i* ( =[u_i-U_hδ_i1]/σ_i) F_i: CDF of u_i*

(1^st way: correlation between velocity components done through F_i)

=

^∗

+

σ_i=e_iU_h

 3^rd step: denormalization

2

^nd

way: inv. Fourier transform

‒ Energy spectra of m_i (S_i)

‒ Correlation between u and w done through phase dependence (S_uw)

1

^st

way: stochastic approach

‒ Integral scale of turbulence (Λ_i)

‒ No correlation between u and w at this stage

(7)

6

Main hypothesis

Unknown variables of the model:

β_N: “extinction coefficient” of the mean wind velocity within the canopy Λ_i: integral scale of turbulence for the wind velocity u_i (1^st way)

S_i, S_uw: analytical wind spectra and cospectrum (2^nd way) e_i: ratio between u_i standard deviations and U_h

F_i: CDF of the wind velocity u_i*

Hypothesis: Above variables are independent of the wind intensity and canopy morphology Supporting reasons:

‒ β_N usually around 0.30 (Harman & Finnigan 2007)

‒ Constancy of Λ_i over a large range of canopies (Kaimal & Finnigan 1994)

‒ Observations and simulations showed small variabilities of normalized wind statistics at canopy top (e.g., Raupach et al. 1996, Dupont & Brunet 2008)

Limits:

‒ Hypothesis only valid at canopy top (inflection point position)

‒ Hypothesis not valid over very sparse canopies

► Following this hypothesis, β_N, Λ_i, e_iand F_i deduced from LES over a Maritime pine forest

(8)

Illustration of simulated time series of wind speed and tree motion

Velocity of damage propagation:

Deduced from the number of damaging periods

Hypothesis:

Impact of damaged areas on the wind neglected

Limits:

 Only valid for short or weak windstorm

But allows comparison of stand vulnerability following stand morphology

(9)

8

Wind model evaluation: method

Two different canopy species:

‒ 3 Mature Maritime pine forests, h = 22 m and PAI=1.25, 2.50, 5.00

‒ Walnut orchard, h = 10 m and PAI=2.50 Evaluation against measurements:

‒ Maritime pine forest (PAI=2.50): Le Bray experiment (Dupont et al. 2011, 2012)

‒ Walnut orchard: CHATS experiment (Patton et al. 2011) Evaluation against LES:

‒ Maritime pine forest (PAI=1.25, 2.50, 5.00)

(10)

Wind model evaluation: probability density functions

u*

v*

w*

(11)

10

Wind model evaluation: wind spectra

u* v*

w*

f h/U_h fS v/ v2

10^-2 10^-1 10⁰ 10¹ 10² 10^-3

10^-2

10^-1 ⁺¹

-2/3

f h/U_h fS w/ w2

10^-2 10^-1 10⁰ 10¹ 10² 10^-3

10^-2 10^-1

+1 -2/3

obs (pine) LES (pine) obs (walnut) stat. model (1^stway) stat. model (2^ndway)

f h/U_h fS u/ u2

10^-2 10^-1 10⁰ 10¹ 10² 10^-3

10^-2 10^-1

+1 -2/3

f h/U_h fS uw/( u w)

10^-2 10^-1 10⁰ 10¹ 10² -0.3

-0.2 -0.1 0

Cospectra uw

(12)

Wind model evaluation: summary

‒ The wind model retrieves the main characteristics of canopy-top turbulence

‒ Results obtained by only describing the canopy from its cumulative PAI and its height

‒ The main hypothesis on the weak dependence of canopy-top normalized wind statistics on wind intensity and canopy morphology is well verified

(13)

12

Impact of storm intensity on damage propagation (Maritime pine)

U

_h

(ms

^-1

) v

prop1

(% d a m a g e d tr e e s /m in )

0 1 2 3 4 5 6

0 1 2 3

DU2015

Wind-tree model from U_crit & W_crit

(14)

f h/U

_h

f S

u

/ 

u2

, f S

dx

/ 

dx2

10^-2 10^-1 10⁰ 10¹ 10² 10³ 10⁴ 10⁵ 10^-3

10^-2 10^-1

wind

tree motion (U_h= 0.50 ms^-1) tree motion (U_h= 1.50 ms^-1) tree motion (U_h= 6.50 ms^-1)

 With increasing wind speed, the tree natural vibration frequency moves upward along the inertial subrange region of the wind spectrum

Impact of storm intensity on wind and tree motion spectra (Maritime pine)

(15)

14 u(ms-1 )

-1 -0.5 0 0.5 1

0 10

20 ^Uh

(a)

v(ms-1 )

-1 -0.5 0 0.5 1

-10 0 10

(b)

w(ms-1 )

-1 -0.5 0 0.5 1

-10 -5 0 5

(c)

Time (h) d x(m)

-1 -0.5 0 0.5 1

0 2 4

(d)

-1 -0.5 0 0.5 1

0 10

20 ^Uh

-1 -0.5 0 0.5 1

-10 -5 0 5

Time (h)

-1 -0.5 0 0.5 1

0 2 4

-1 -0.5 0 0.5 1

-10 0 10

High windstorm Low windstorm

Damage prediction on a Maritime pine stand

(16)

Number of storm

50 100 150

0 10 20 30

Meancumulative damageprob.(%)

Number of storm

50 100 150

60 80 100

Low windstorm High windstorm

Damage prediction on a Maritime pine stand

► Without considering the 2^nd damage stage

► 2^nd damage stage starts when damaged areas reach 10% of the stand (Dupont et al. 2015) v_prop2= 4.30 U_h-42.71 (% of damaged trees/min)

10%

72%

Time (h)

Damageprob.(%)

-0.4 -0.2 0 0.2 0.4

0 50 100

Time (h)

Damageprob.(%)

-0.4 -0.2 0 0.2 0.4

0 50 100

10%

72%

(17)

16

Number of storm

50 100 150

0 10 20 30

Number of storm

50 100 150

60 80 100

Low windstorm High windstorm

Damage prediction on a Maritime pine stand

► Without considering the 2^nd damage stage

► 2^nd damage stage starts when damaged areas reach 10% of the stand (Dupont et al. 2015) v_prop2= 4.30 U_h-42.71 (% of damaged trees/min)

Time (h)

Damageprob.(%)

-0.4 -0.2 0 0.2 0.4

0 50 100

Time (h)

Damageprob.(%)

-0.4 -0.2 0 0.2 0.4

0 50

100 considering the second propagation damage stage

10%

72%

100%

(18)

Conclusion

Simple wind-tree model:

► allowing to easily compare damage prediction between different stands or different storms as well as to investigate the impact of silvicultural practices

► answering to several weaknesses of existing wind risk models

More works need to be done to reach a complete wind risk model:

(1) stand heterogeneities: not considered in the present model and poorly accounted for in existing wind risk models (Dupont et al. 2015, Can. J. For. Res.)

(2) accentuation of damage propagation when damaged areas become significant enough to modify the wind flow

(3) tree failure due to tree uprooting, not yet considered in the tree swaying model (4) evaluation of the model against reported damage after windstorms

(19)

18

T HANKS FOR YOUR ATTENTION

Financial support from the Agence Nationale de la Recherche (ANR): FORWIND and TWIST projects

Statistical modeling of turbulent wind velocity at canopy top: application to forest wind damage

S TATISTICAL MODELING OF TURBULENT WIND VELOCITY AT CANOPY TOP :

APPLICATION TO FOREST WIND DAMAGE

S YLVAIN D UPONT

Recent findings

A new generation of wind risk model

Proposition

Wind time series from U

, h and PAI

=

+

2

way: inv. Fourier transform

1

way: stochastic approach

Main hypothesis

Illustration of simulated time series of wind speed and tree motion

Wind model evaluation: method

Wind model evaluation: probability density functions

u*

v*

w*

Wind model evaluation: wind spectra

u* v*

w*

Cospectra uw

Wind model evaluation: summary

Impact of storm intensity on damage propagation (Maritime pine)

U

(ms

) v

(% d a m a g e d tr e e s /m in )

0 1 2 3 4 5 6

0 1 2 3

f h/U

f S

/ 

, f S

/ 

Impact of storm intensity on wind and tree motion spectra (Maritime pine)

Damage prediction on a Maritime pine stand

Damage prediction on a Maritime pine stand

Damage prediction on a Maritime pine stand

Conclusion

T HANKS FOR YOUR ATTENTION

S ^YLVAIN D ^UPONT