time-space dependent downscaling of wind stress data for ocean modellings by jun-ichi yano hiromi...
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Time-space dependent Downscaling of Wind Stress Data
For Ocean modellings
byJun-Ichi Yano
Hiromi Kobayashi Pascale Bouruet-Aubertot
Downscaling:
Downscaling:
?Principal Approach
Oceanographic Application
Downscaling:
?
Spatial scale: X x (< X )?originaloutput/
observationalscale
(e.g., atmosphere)= 50 – 200 km
requiredinformation/model-input
scale(e.g., oceans)= 5 – 10 km
Alternatively:
Temporal scale: T ?
t (< T )
Downscaling:
Principal Approach
Power Law in Tubulence (Scaling Law)
Wavelets
Downscaling
+
(Spatial-Temporal Heterogeneity)
Oceanographic Application
OceanographicContext:Wind Stress
Data:X=60km
Data:X=125km
Model:X=80km
Zonal Component(Alexandra Bozec)
Response to the 3 types of Wind StressInputsin 4 regions(rows):Depth of MixedLayer
Data:X=60km
Data:X=120km
Model:X=80km
(Alexandra Bozec)
log P(k)
log k
X x
?Extrapolation
Question:(t)?:Modificationof variability with time& space:Heterogeneity
Downscaling Principle: Fully-Nonlinear Turbulent System:Power-law Spectra :
Methods:Observational Data Analysis:
Data Set: Buoy Time Series (off coast Nice): Wind Speed:Mar 1999-Dec 2001, t=1h
x
Methods:Observational Data Analysis:
Data Set: Buoy Time Series (off coast Nice): Wind Speed:Mar 1999-Dec 2001, t=1h
Methodology: Taylor’s frozen hypothesis:k=/u: k
Seek a power law: Pt) ~(t) as a function of time (Morlet wavelet spectra)
How to estimate: =(t) ?
Spe ctre à t = 999h
(instantaneous)
Wavelet Transform of the Wind Speed Time series: 6500:6000)( jpourTSetU ijj
Power Law•Time sereis (segment)
•Wavelet Spectrum
Strategy for the Downscaling
log P()
log t T
?
Strategy for the Downscaling
log P()
log t
Tc=?
Strategy for the Downscaling
•Estimation of wavelet coefficients:
•Reconstruction of a time series
i) |<U, u,s>| ~ s(u)/2
<U, u,s> = |<U, u,s>| ei(u,s)
ii) (u,s) = ?
NB: stochastic : probability
:present work
:future work
NB: u t
Strategy for the Downscaling
log P()
log t
Tc=?
Determination of the Power Exponent:Seek a spectrum of the form : P(T) ~T
for a limited period
Mean over 2n+1 spectra, n=24Spectrum at t=15787h
Seek a spectrum of the form : P(T) ~T
for Ti < Tc:
= ?
Tc = ?
Determination of the Power Exponent:
Spectre en loi de puissanceOn cherche un spectre de la forme : P(T) ~T
pour Ti < Tc:
= ?
Tc = ?
Probability Distribution of the Exponent:t: exponent of the spectrum
Probability Density :
p(
Tot
al e
ner
gy
How to Estimate the Exponent from the
Other Conditions?: Joint-Probabilities
?
ConclusionsBuoy Data: Surface Wind-Speed time serieswith t = 1 h:Power-Law Spectra in Wavelet Space:
Most likely exponent (14% chance): Two Regimes:
2nd Regime with
Preliminary anlyses for the joint-probabilites
Future Work: Statistics for the Phase: A 1st-order Markov Model?
http://www.ipsl.jussieu.fr/CLIMSTAT/CARGESE/TALKS/JUNICHI/downscale.pptftp://ftp.lmd.jussieu.fr/pub/yano/cargese/review.ftp://ftp.lmd.jussieu.fr/pub/yano/cargese/hiromi.psftp://ftp.lmd.jussieu.fr/pub/yano/cargese/poster_bozec.ppt
Final Remark: Two Schools in Downscaling:
ClimatologicalPlanetary-Scale
SynotpicScale
Meso-Convective Scale
104 km 103 km 10 - 102 km
I. X* x
« Regionalization » (CL12, HS9, …)
II. X* x
Linear-Wave Dynamics
Nonlinear-Turbulent
How to Estimate the Exponent from the
Other Conditions?: Joint-Probabilities
Tc
How to Estimate the Exponent from the
Other Conditions?: Joint-Probabilities
Tc
Tot
al e
ner
gy
OutlineReview: what is downscaling?
scale dependence: types I & II
An explorative study for the downscaling of the wind stress over the Mediterranean Sea
approaches for the type I: linear approaches
limitations of linear approaches approaches for the type II: nonlinear
why necessary?: oceanographic context
Downscaling Type I
X* =104 km x =103 km
ClimatologicalState
SynotpicScale
determining factor « slaved »
e.g., ENSO, NAO e.g., European Rainfall
« Weakly » Nonlinear Approaches
Methodologies: Linear•Classification methods (Pattern Recognition)•Linear statistical methods: CCA, SVD
•Artificial Neural Netwrok (ANN)•Kriging but with one-to-one correspondence
(i.e., almost linear)
Linear statistical methods: CCA, SVD
Singular Vector Decomposition,SVD: x(x’)>t = lllxlx’~ ~
where <l2>x= 1, <l
2>x= 1,> > >….>0~ ~
Canonical Correlation Analysis,CCA: x(x’)>t
-1/2x(x’)>t–1/2x(x’)>t
= lllxlx’~ ~
Limitations of the Downscaling Type I (Linear Statistical Approach)
Length of data required to establish a statistically-robust result could be huge & hard to estimate (van den Dool 1994 Tellus)
(Remeady X* -> +oo, Zorita&von Stroch 1999)
Synoptic-scale is not perfectly « slaved » to a climatological state « stochasticity »
Physically-related two variables are not necessarily identified by this method (e.g., , Newman & Sardeshmakh 1995
JC)
Transfer from the Type-I Regime to Type II
increase of Nonlinearity~ Ro = U/L
Linear-WaveDynamicsTeleconnections (Hoskins&Karoly 1981 JAS)
Semi-Determinisitc
NonlinearDynamicsLocally-definedStochasitc
x
Previous Attempts for the Downscaling Type II (Synoptic Meso-Convective)
Weather generators: stochastic generation of local time series with a given climate state (Wilks, Wilby, ……)
Scaling-law based approaches: fractal, wavelets, etc. (e.g., Deidda 2000 WRS, Kuligowski
&Barros 2001 JAM, Croa&Wood 2002 JH)
Topographically-induced rains: local rainfall ~ vH.grad (h) (e.g., Sinclair 1994)
Generalization to a heterogeneous case
A Physical Basis for the Downscaling of the Fully-Nonlinear System (Type II)
log P(k)
log k
multiscalemode interactions
Linear MethodDoes not work
Data Set (Time series)
Bouée «Côte d’Azur» de Météo-France : vitesse du vent, à dt=1h, mars 1999 - décembre 2001
Correction des erreurs de chronologie de la série de mesures
Série temporelle Ui=1,M
avec M=24514, dont L=19522 termes qui seront analysés
m/s
Morlet Wavelet (continuous wavelet)
dts
ut
stffsufW
RLffonctionunedondeletteseneTransformé
ets
ut
stRsu
ondelettesdFamille
et
tMorletdeOndeletteEx
etdtt
RLmèreOndelette
su
susu
ti
)(1
)(,),)((
:)('
1)(1
)(;0,
:'
)2
exp()(
1)(:
10)(
)(:
*,
2
,,
2
2
412
2
Wavelet transform:
Théorème de reconstruction
20
2
0
2
2
)(1
),)((1
)(
)(
)(ˆ
:')(
s
dsdu
s
ut
ssufW
Ctf
RLfAlors
dC
itéadmissibildconditionlavérifiantRLSoit
NB: overcompleteness
Transformation en ondelettes de la série U
Spectre à t = 999h
2),)(()(
:
:1),)((
:
ijij
j
ij
TtUWTSi
tdatelaàUdeSpectre
MjavecTtUW
UdeondeletteseneTransformé
Time-mean
Fourier
Power Law
Methods:Observational Data Analysis:
Data Set: Buoy Time Series (off coast Nice): Wind Speed:Mar 1999-Dec 2001, t=1h
Methodology: Taylor’s frozen hypothesis:k=/u: k
Seek a power law: Pt) ~(t) as a function of time (wavelet spectra)
How to estimate: =(t) ?
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