Detection of climate trends from local time series using a Monte

Detection of climate trends from local time series using a Monte

Calculation of climate trends
functions from local time series
Dieter F. Ihrig, FH Suedwestfalen, Iserlohn, Germany
• Introduction and motivation
• Calculate a trend function by filtering of time series
• Results for temperature time series
• Robustness and precision of the method
• Results for other data
• Conclusion
Regensburg16
Prof. Dr. Dieter F. Ihrig
1
Calculate a trend function by filtering of time series
10
1
45
9,5
40
9
9
8,5
8,5
8
8
35
0,5
25
7,5
20
7
7
6,5
6,5
15
6
5,5
6
Time Series
Average (330±20) y
Average (345±20) y
Average (369±20) y
5
250
290
310
330
350
370
390
5
250
0
270
290
310
330
350
370
390
Year
Year
Regensburg16
5
5,5
0
270
10
Time Series
Number of Averaged Points
Prof. Dr. Dieter F. Ihrig
2
W eighting
7,5
Tem perature
30
W e igh tin g
T e m p e ra tu re
9,5
10
High Pass
Calculate a trend function by filtering of time series
Transformation
Spectra
Filtering
Low Pass
Time Series
Apodization
Trend Line
Unprocessed
Apodization
Transformation
Apodization
Transformation
Variation of Filter Parameter
Residua
Monte-Carlo-Optimization
Regensburg16
Prof. Dr. Dieter F. Ihrig
3
Global Mean 1880 – 2015
1
1,00
0,80
0,60
0,40
0,20
0,00
-0,201880 1900 1920 1940 1960 1980 2000 2020
-0,40
-0,60
-0,80
January
February
March
April
May
June
July
August
September
October
November
0,8
Temperature Anomalies in K
Temperature Anomalies in K
1,20
0,6
0,4
0
-0,2
-0,4
-0,6
1880
Temperature Anomalies in K
0,60
0,40
0,20
0,00
1880 1900 1920 1940 1960 1980 2000 2020
-0,20
-0,40
-0,60
Year
Regensburg16
1900
1920
1940
1960
Years
1980
2000
2020
Temperature Increase
Global Mean Trend
0,80
1K
0,2
Year
1,00
High Frequency
Trend
Time Series
January
February
March
April
May
June
July
August
September
October
November
December
2015 minus 1880
1,2
1
0,8
0,6
0,4
0,2
0
February
April
June
August
October December
January
March
May
July
September November
Prof. Dr. Dieter F. Ihrig
4
Zonal Mean 1880 – 2015
Temperature Increase
Temperature Anomalies in K
Time Series
2,50
2,00
1,50
1,00
0,50
0,00
-0,501880 1900 1920 1940 1960 1980 2000 2020
-1,00
-1,50
-2,00
2015 minus 1880
Global Mean
24N-90N
24S-24N
90S-24S
64N-90N
44N-64N
24N-44N
EQU-24N
24S-EQU
44S-24S
64S-44S
3,5
3
2,5
2
1,5
1
0,5
0
64S-44S 24S-EQU 24N-44N 64N-90N
24S-24N
Global
90S-64S 44S-24S EQU-24N 44N-64N
90S-24S 24N-90N
Zone
Year
Temperature Increase
Zonal Mean Trend
Temperature Anomalies in K
2,50
2,00
1,50
1,00
0,50
0,00
1880 1900 1920 1940 1960 1980 2000 2020
-0,50
-1,00
-1,50
Year
Regensburg16
Global Mean
24N-90N
24S-24N
90S-24S
64N-90N
44N-64N
24N-44N
EQU-24N
24S-EQU
44S-24S
64S-44S
2015 minus 1880
3,5
3
2,5
2
1,5
1
0,5
-90
-70
-50
-30
0
-10
10
30
50
70
90
Latitude
Prof. Dr. Dieter F. Ihrig
5
Vardo 70,4N 31,1E 1880 – 2015
4
Time Series
Temperature in °C
10
5
0
1880 1900 1920 1940 1960 1980 2000 2020
-5
-10
-15
January
February
March
April
May
June
July
August
September
October
November
December
Annual Mean
3
Temperature in °C
15
1
0
1880
-1
Temperature in °C
6
4
2
0
-21880 1900 1920 1940 1960 1980 2000 2020
-4
-6
-8
Year
Regensburg16
1900
1920
1940
1960
1980
2000
2020
-2
Years
Temperature Increase
2015 minus 1880
Monthly Trends
8
2,6 K
2
Year
12
10
High Frequency
Trend
Time Series
January
February
March
April
May
June
July
August
September
October
November
December
6
5
4
3
2
1
0
February
April
June
August
October December
January
March
May
July
September November
Prof. Dr. Dieter F. Ihrig
6
Stations Temperature Increase 1880 – 2015
Los Angeles California 33,7N 118,3W
Phoenix Sky H 33,4N 112,0W
6
5
5
4
2,2 K
4
3
3
1,43 K
2
2
1
1
0
0
February
April
June
August
October December
January
March
May
July
September November
February
April
June
August
October December
January
March
May
July
September
November
-1
Shreveport Re 32,5N 93,8W
St Louis Lamb 38,8N 90,4W
2
4
3
1
2
0
February
April
June
August
October December
January
March
May
July
September
November
-1
-2
-3
-4
Regensburg16
1
0
February
April
June
August
October December
-1 January
March
May
July
September November
-0,04 K
-2
-3
0,82 K
-4
Prof. Dr. Dieter F. Ihrig
7
Stations Temperature Increase 1880 – 2015
3,5
Zonal Mean
Polynomisch (Zonal
Mean)
Stations
Stations
Zonal Mean
Mean
Zonal
Ocean
Continental
3
2,5
2
1,5
1
0,5
0
-90
-70
-50
-30
-10
10
30
50
70
90
-0,5
Latitude
Regensburg16
Prof. Dr. Dieter F. Ihrig
8
Robustness and precision of the method
Difference between given and calculated trend
Simulated Time Series
10
0,06
9,5
0,04
9
0,02
8
0
diffe r e nce in K
temperature in oC
8,5
7,5
7
0
50
100
6
200
250
300
350
0,025
-0,02
Spalte
Spalte
Spalte
Spalte
Spalte
-0,04
Spalte H
Spalte I
Spalte E
6,5
150
0,02
F
K
P
U
Z
0,015
0,01
0,005
0
-0,06
-0,005
0
50
100
150
200
250
300
350
-0,01
5,5
-0,015
-0,08
-0,02
5
-0,025
0
50
100
150
200
250
300
350
-0,1
year
ye ar
Difference betw een given and calculated trend functions
Simulated Time Series (exponential increase)
10
0,18
9,5
0,16
0,08
0,06
0,04
9
0,02
0,14
0
-0,02 0
0,12
8
50
100
150
200
250
300
350
-0,04
-0,06
difference in K
temperature in oC
8,5
7,5
7
6,5
-0,08
run 1
run 2
0,08
run 3
0,06
Spalte H
Spalte I
Spalte E
6
0,1
run 4
0,04
run 5
0,02
5,5
5
0
50
100
150
200
250
300
350
0
0
year
Regensburg16
50
100
150
200
250
300
350
year
Prof. Dr. Dieter F. Ihrig
9
Robustness and precision of the method
Comparison: Trend of Annual Mean vs.
Mean of Monthly Trends
Annual Trend vs. Mean of Monthly Trends
Te m perature in °C
Nantes 47,2N 1,6W
13,0
12,8
12,6
12,4
12,2
12,0
11,8
11,6
11,4
11,2
11,0
1880
Standard Deviation of 25 Stations: 0,27 K
Confidence Limit: 0,077 K
3,5
1900
1920
1940
1960
1980
2000
2020
3
Ye ar
Annual Mean
Mean Trend
2,5
Annual Trend vs. Mean of Monthly Trends
2
Godthab Nuuk 64,2N 51,8W
0,0
-0,5
1,5
Te m perature in °C
-1,0
-1,5
1
-2,0
-2,5
0,5
-3,0
-3,5
-4,0
1880
0
1900
1920
1940
1960
1980
2000
2020
-90
-70
-50
-30
-10
10
30
50
70
90
Year
Annual Mean
-0,5
Mean Trend
Latitude
Regensburg16
Prof. Dr. Dieter F. Ihrig
10
Precipitation
Regensburg16
Prof. Dr. Dieter F. Ihrig
11
Conclusion and Outlook
• The Process calculates trend functions as new time series
(Standard Deviation: 0,27 K; Confidence Limit: 0,077 K)
• 400 time series were processed
• Recently the most successful solution of the border problem is
the use of regression lines. (In future: higher order or irrational functions? )
• But it’s necessary to optimize the field length processed by
calculation of regression lines using a Monte-Carlo-process.
• The algorithm cannot decide whether the calculated trend is
man-made!
• There is a significant tendency of higher temperature
(Up to 3.2 K at higher latitudes)
I thank you for your attention!
Regensburg16
Prof. Dr. Dieter F. Ihrig
12