CO2 Data Analysis
Filter : Wavelet vs. EMD
EMD as Filter
N
x( t )   c j ,
Once we have the EMD expansion :
j 1
we candefine the filters as fellows :
N
Low Pass Filter :
xL( t )   c j ;
j L
H
High Pass Filter :
Band Pass Filter :
xH ( t )   c j ;
j 1
xB ( t ) 
M
cj

j B
.
MAUNA LOA
CO
2
DAILY DATA ( blue: obs;
CO2
red: with interp)
380
360
340
320
1000
2000
3000
4000
5000
6000
7000
8000
9000 10000 11000
ENLARGEMENT OF A SECTION
370
365
360
355
350
7100
7200
7300
7400
7500
7600
7700
7800
7900
8000
WAVELET DECOMP.
CO2 High, Low Components and NONAC using WPD
25
20
15
10
5
0
1975
1980
1985
1990
time (year)
1995
2000
2005
WAVELET NANAC
CLIMAC (bule), NONAC (mean: blk)
4
3
2
1
0
-1
-2
-3
-4
-4
-2
0
2
4
6
8
10
EEMD DECOMP.
CO2 High, Low Components and Nonlinear Non-stationary Annual Cycle (NONAC)
25
20
15
10
5
0
1975
1980
1985
1990
time (year)
1995
2000
2005
WAVELET DECOMP.
CO2 High, Low Components and NONAC using WPD
25
20
15
10
5
0
1975
1980
1985
1990
time (year)
1995
2000
2005
STATISTICS
CLIMAC (bule), NONAC (mean: blk)
4
3
2
1
0
-1
-2
-3
-4
-4
-2
0
2
4
6
8
10
ENVELOPE OF NANAC
NONAC Envelope (blue), SST (red) and HEAT CONTENT (green) components
3
2
1
0
-1
-2
-3
1975
1980
1985
1990
1995
2000
2005
Observations
• Decomposition with a priori basis produces
components with wave form similar to the
basis adopted.
• Decomposition with adaptive basis produces
components with wave form retaining the
physical properties of the underlying
processes.
• Adaptive basis could be used as filters that
would preserve the intrinsic properties of the
data.