Pr

1
Downscaling
Time-space dependent Downscaling of Wind Stress
Data For Ocean modellings
2
Downscaling
?
Principal Approach
Oceanographic Application
3
Downscaling
?
4
Downscaling
Alternatively
5
Principal Approach
6
Power Law in Tubulence (Scaling Law)
Wavelets
Downscaling
7
Oceanographic Application
8
Oceanographic Context Wind Stress
Data DX60km
Zonal Component
(Alexandra Bozec)
Data DX125km
Model DX80km
9
Response to the 3 types of Wind
Stress Inputs in 4 regions (rows) Depth of
Mixed Layer
(Alexandra Bozec)
Data DX60km
Data DX120km
Model DX80km
10
Downscaling Principle Fully-Nonlinear Turbulent
SystemPower-law Spectra
Question a a(t)? Modification of variability
with time space Heterogeneity
11
MethodsObservational Data Analysis
Data Set Buoy Time Series (off coast Nice) Wind
SpeedMar 1999-Dec 2001, Dt1h
x
12
MethodsObservational Data Analysis
Data Set Buoy Time Series (off coast Nice) Wind
SpeedMar 1999-Dec 2001, Dt1h
Seek a power law P(w,t) w-a(t) as a function
of time (Morlet wavelet spectra)
How to estimate aa(t) ?
13
Wavelet Transform of the Wind Speed Time series
14
Strategy for the Downscaling
?
log P(T)
log T
Dt
DT
15
Strategy for the Downscaling
log P(T)
log T
Dt
16
Strategy for the Downscaling

• Estimation of wavelet coefficients

ltU, Yu,sgt ltU, Yu,sgt eij(u,s)
i) ltU, Yu,sgt sa(u)/2
present work
ii) j(u,s) ?
future work
NB stochastic probability

• Reconstruction of a time series

17
Strategy for the Downscaling
log P(T)
log T
Dt
18
Determination of the Power Exponent

• Seek a spectrum of the form P(T) Ta
• for a limited period

19
Determination of the Power Exponent
Seek a spectrum of the form P(T) Ta for Ti lt
Tc
a ?
20
Spectre en loi de puissance
On cherche un spectre de la forme P(T) Ta pour
Ti lt Tc
a ?
21
Probability Distribution of the Exponent
a (t) exponent of the spectrum
Probability Density p(a)
22
How to Estimate the Exponent a from the Other
Conditions? Joint-Probabilities
?
23
Conclusions
Buoy Data Surface Wind-Speed time series with
Dt 1 h
Power-Law Spectra in Wavelet Space
Two Regimes
Most likely exponent (14 chance) a 5/3
2nd Regime with a 1
Preliminary anlyses for the joint-probabilites
Future Work Statistics for the Phase A
1st-order Markov Model?
24
http//www.ipsl.jussieu.fr/CLIMSTAT/CARGESE/TALKS/
JUNICHI/downscale.ppt ftp//ftp.lmd.jussieu.fr/pub
/yano/cargese/review. ftp//ftp.lmd.jussieu.fr/pub
/yano/cargese/hiromi.ps ftp//ftp.lmd.jussieu.fr/p
ub/yano/cargese/poster_bozec.ppt
25
Final Remark Two Schools in Downscaling
 Regionalization  (CL12, HS9, )
Linear-Wave Dynamics
Nonlinear-Turbulent
26
How to Estimate the Exponent a from the Other
Conditions? Joint-Probabilities
Tc
a
27
How to Estimate the Exponent a from the Other
Conditions? Joint-Probabilities
Total energy
Tc
28
Outline
Review
what is downscaling?
why necessary? oceanographic context
scale dependence types I II
approaches for the type I linear approaches
limitations of linear approaches
approaches for the type II nonlinear
An explorative study for the downscaling of the
wind stress over the Mediterranean Sea
29
Downscaling Type I
Methodologies Linear

• Classification methods (Pattern Recognition)
• Linear statistical methods CCA, SVD

  Weakly  Nonlinear Approaches

• Artificial Neural Netwrok (ANN)
• Kriging

but with one-to-one correspondence (i.e., almost
linear)
30
Linear statistical methods CCA, SVD
31
Limitations of the Downscaling Type I (Linear
Statistical Approach)
32
Transfer from the Type-I Regime to Type II
increase of Nonlinearity Ro U/WL
Linear-Wave Dynamics Teleconnections
(HoskinsKaroly 1981 JAS) Semi-Determinisitc
Nonlinear Dynamics Locally-defined Stochasitc
33
Previous Attempts for the Downscaling Type II
(Synoptic Meso-Convective)
34
A Physical Basis for the Downscaling of the
Fully-Nonlinear System (Type II)
multiscale mode interactions
35
Data Set (Time series)

• Bouée Côte dAzur de Météo-France vitesse du
  vent, à dt1h, mars 1999 - décembre 2001
• Correction des erreurs de chronologie de la série
  de mesures
• Série temporelle Ui1,M avec M24514, dont
  L19522 termes qui seront analysés

m/s
36
Morlet Wavelet (continuous wavelet)
Wavelet transform
37

• Théorème de reconstruction

NB overcompleteness
38
Transformation en ondelettes de la série U
Time-mean
Spectre à t 999h
39
MethodsObservational Data Analysis
Data Set Buoy Time Series (off coast Nice) Wind
SpeedMar 1999-Dec 2001, Dt1h
Seek a power law P(w,t) w-a(t) as a function
of time (wavelet spectra)
How to estimate aa(t) ?