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a) Bergen:Sep temperature
15
o
Temperature ( C)
14
13
12
11
10
9
8
1860
1880
1900
1920
1940
1960
1980
2000
time
b) Bergen:Sep temperature distribution (1861−1997)
30
Frequency
25
20
15
10
5
0
5
6
7
8
9
10
11
Temperature (oC)
12
13
14
15
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0.4
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0.35
Frequency
0.3
0.25
0.2
0.15
0.1
0.05
0
5
6
7
8
9
10
11
Temperature range (oC)
12
13
14
15
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Probability of achiving less than 3 heads if a coin is flipped 100 times
0.08
N
x
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0.07
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0.06
Pr (%)
0.05
0.04
0.03
0.02
0.01
0
0
10
20
30
40
50
60
70
80
90
100
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a) Daily Oslo precipitation
60
Precipitation (mm)
50
40
30
20
10
0
1964
1973
1984
time
1993
b) Oslo precipitation distribution: α =0.11696, β =13.9255 (moments estimator)
0.4
Frequency
0.3
0.2
0.1
0
0
2
4
6
8
10
12
Precipitation (mm)
14
16
18
20
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ûü
a) Bergen:Sep temperature
14
o
Temperature ( C)
16
12
10
8
1860
1880
1900
1920
1940
1960
1980
2000
time
b) Bergen September temperature >12.5oC: µ =0.60435 years−1
0.8
Frequency
0.6
0.4
0.2
0
0
5
10
15
20
25
30
Number of events per 10 years
35
40
45
50
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a) Daily Oslo precipitation
60
Precipitation (mm)
50
40
30
20
10
0
time
−1
b) Oslo daily precipitation >30mm : µ =0.89521 days
0.5
Frequency
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
Number of events per 365 days
7
8
9
10
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15
10
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0
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1860
1880
1900
1920
1940
1960
1980
2000
time
b) Bergen:Sep temperature distribution (1861−1997)
50
µ =11.32 µ =11.34
Frequency
o
Original
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+
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q(0.5) =11.30 q(0.5) =11.30
30
s =1.17 s =2.62
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10
0
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Temperature (oC)
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20
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a) Yearly maximum daily mean precipitation in Oslo
Max precip (mm)
80
60
40
20
0
1880
1889
1900
1910
1920
time
1930
1940
1950
1960
c) cdf for Gummel distribution: β =7.2984, ξ =27.9243
b) Oslo maximum daily precipitation : β =7.2984, ξ =27.9243
1
p(rr
max
0.1
< 60mm) =0.9859
0.9
p(rrmax > 60mm) = [1−p(rrmax < 60mm)] =0.0141
p(rrmax > 60mm) =0.0141
0.7
Cumulative probability
Frequency
0.08
0.8
0.06
0.04
0.6
0.5
0.4
0.3
0.02
0
0.2
0.1
0
10
20
30
40
Max precip (mm)
50
60
70
rr(10) =46mm, rr(50) =58mm, rr(100) =63mm.
0
0
10
20
30
40
Max precip (mm)
50
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a) BERGEN and OSLO Sep rainfall
700
yvz|{~}_Jt CH
Precipitation (mm)
(
Bergen: rr
Oslo: rr
600
500
400
300
200
100
0
1880
1900
1920
1940
Time
1960
1980
2000
b) BERGEN and OSLO Sep rainfall distribution
µ =245.82 µ =77.42
14
B
O
s2B =14051.98 s2O
12
aB =−0.11 aO =73.90
=1903.65
t =1.50
Frequency
10
8
6
Bergen: n
obs
Oslo: nobs
Bergen: n
exp
Oslo: n
4
2
exp
0
−200
1O]J
0
200
400
600
Precipitation (mm)
800
1000
1200
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60
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50
Expected and observed occurences
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Oslo: nexp
40
30
20
10
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400
600
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800
1000
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CorrTest: similar trend
CorrTest: AR(n), detrended
3
3
x
1
x
2
x (dt)
1
x (dt)
1
x
1
x
2
Data
Data
2
2
0
2
1
0
−1
−1
−2
−2
0
5
10
15
20
0
25
5
10
2
1.5
Counts
Counts
2
1.5
1
−0.6
−0.4
−0.2
0
0.2
Correlation range
CDF
0.4
0.6
0.8
25
1
0
−1
1
0.8
0.6
0.4
N
0.2
0
−0.8
−0.6
−0.4
−0.2
0
Correlation
0.2
0.4
0.6
Accumulated counts
−0.8
−0.8
−0.4
−0.2
0
0.2
Correlation range
CDF
0.4
−0.8
−0.6
−0.4
−0.2
0
Correlation
0.2
0.4
x
1
x2
Data
1
0
−1
−2
0
5
10
15
20
25
Time
MC r−distribution
2
Counts
1.5
1
0.5
O
0
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
Correlation range
CDF
0.4
0.6
0.8
1
1
0.5
0
−0.8
−0.6
−0.4
−0.2
0
Correlation
0.2
0.4
0.6
0.8
1
0.5
CorrTest: AR(n), random trend
2
0.6
1
0
0.8
−0.6
3
Accumulated counts
Accumulated counts
M
20
0.5
0.5
0
−1
15
Time
MC r−distribution
Time
MC r−distribution
0.8
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0.6
0.8
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Correlation between slp and Sep Bergen temperature, lag=0
1
80
0.8
60
0.6
40
0.4
Latitude (oN)
20
0.2
0
0
−0.2
−20
−0.4
−40
−0.6
−60
−0.8
−80
−1
−150
−100
10% of area with r > rcrit (0.30)
−50
0
o
Longitude ( N)
50
100
150
(de−trended)
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Probability of achiving greater than 5% significant cases
0.8
Pr(X=x) = NCx px ( 1 − p )N−x
ÙÚ×ÛÝÜÞDßàKáâãäßå[ãÌæNáÇçèËé§áèêèëçbìí
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P(5%)=9.52%, N=20
0.7
0.6
Pr
0.5
0.4
0.3
0.2
0.1
0
Binomial PDF
critical level
scaled CDF
0
5
10
15
20
cases with significant results (%)
25
30
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−0.01
−0.02
−0.03
1940
1950
1960
1970
1980
1990
2000
(de−trended)
õ
Leading EOF, var=76%
0.03
03
0.
80
0.03
0.0
4
02
0.
3
0.0
0.02
0.03
0.02
0.01
0.
4
3
40
0.0
02
60
0.0
0.01
0.01
20
0.00
0
0
0.0
0.
100
−0.01
−0.01
−0.01
−40
−60
70
60
−0.01
01
−0.
−150
50
40
30
−0.02
−0.02
ö
80
1
−0.0
−0.01
−0.01
−0.01
−80
Variance
Error bars
cumulative variance
90
%
−20
Variance described by the EOFs (%)
00
0.00
0.00
20
−100
−50
0
50
100
150
10
(de−trended)
eof__ncep_z500.nc
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0
0
5
10
15
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100
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2nd EOF
3rd EOF
1st wave
2nd wave
3rd wave
80
60
40
o
Latitude ( N)
20
0
−20
−40
−60
−80
−100
−1
−0.8
æ¤çgèéêë{ì.íïîð2ñ
−0.6
−0.4
−0.2
0
0.2
Tempareature anomaly
0.6
0.8
1
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90
1
Latitude (oN)
80
0.5
70
60
0
50
−0.5
40
30
−1
−80
−60
−40
−20
0
20
o
Longitude ( N)
40
60
80
T
b) Correlation based on X=UWV
90
1
Latitude (oN)
80
0.5
70
60
0
50
−0.5
40
30
−1
−80
−60
−40
−20
0
20
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40
60
80
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Theoretical red noise
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0
Power density
10
−1
10
−2
10
0
1
2
3
4
5
Time scale (years)
6
7
8
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