Download Investigation and Prediction of Time Series of Temperature and

Investigation and Prediction of Time Series of
Temperature and Rainfall Variation in North-Eastern
Region of Bangladesh
By
Ahmad Hasan Nury
Advisor:
Prof. Dr. rer. nat. Manfred Koch, Kassel University
Dr. Md. Jahir Bin Alam, SUST, Bangladesh
Department of Geohydraulics and Engineering Hydrology, University of Kassel
1
Introduction:
 Climate change is one of the biggest environmental threats to food production, water
availability, forest biodiversity and livelihoods. It is widely believed that developing countries
such as Bangladesh will be impacted more severely than developed countries (e.g. UK and
USA).
 According to F.HoVerhoog (1987) to estimate the impact of climatic change on the
morphology of river basins, firstly estimation of the impact of climate change on precipitation
and temperature variation analysis are necessary.
 In this study, it is considered the region for the analysis where huge amount of rainfall occur
in every year, which is Sylhet and Moulvibazar district. Every year there is great loss in rice
production in this zone due to flood.
2
Scope of the study:
 Time series graph

•
•
•
Statistical analysis:
Mean
Standard deviation
Mann-Kendall trend test
 Rainfall frequency analysis
 Short term prediction:
• ARIMA (p d q) model
3
Study Area:
 Sylhet division, the northeastern administrative division of Bangladesh, located at 24053’ latitude and 91052’
longitudes.
 The climate of Sylhet division is tropical monsoon with a predominantly hot and humid summer and a
relatively cold winter.
 Change in global climate rise of sea level may alter the productions in this area.
Figure: Study Area
4
Data Collection:
Table: Monthly Rainfall data (Source: Bangladesh Water Development Board)
District
Area (km2)
Station ID
Sylhet
3490.40
CL129
Time
CL 228
Maulvibazar
2799.39
CL 104
1981 to 2010
CL126
(29 years)
CL 229
Table: Monthly Temperature data (Source : Bangladesh Meteorological
Department)
District
Area (km2)
Type of data
Sylhet
3490.40
Maximum
Time
Temperature (0C)
Minimum
Maulvibazar
(Srimongal)
2799.39
Temperature (0C)
1977 to 2011
Maximum
(34 years)
Temperature (0C)
Minimum
Temperature (0C)
5
Data Analysis:
y = 0.0001x + 12.65
30
50
40
Temperature 30
20
(0C)
10
0
y = 0.0001x + 29.365
Temperature 20
(0C)
10
Jul-09
Jan-07
Jul-04
Jul-99
Jan-02
Jan-97
Jul-94
Jul-89
Jan-92
Jan-87
Jul-84
Jul-79
Jan-82
Jan-77
Jul-79
Jan-82
Jul-84
Jan-87
Jul-89
Jan-92
Jul-94
Jan-97
Jul-99
Jan-02
Jul-04
Jan-07
Jul-09
Jan-77
0
Month
Month
Figure 1: Variation of monthly maximum temperature of sylhet.
Figure 2: Variation of monthly minimum temperature of sylhet.
y = 0.0001x + 11.257
30
y = 7E-05x + 31.408
50
40
Temperature 30
20
(0C)
10
0
Temperature 20
(0C)
10
Jan-77
Jul-79
Jan-82
Jul-84
Jan-87
Jul-89
Jan-92
Jul-94
Jan-97
Jul-99
Jan-02
Jul-04
Jan-07
Jul-09
Jul-09
Jan-07
Jul-04
Jan-02
Jul-99
Jan-97
Jul-94
Jul-89
Jan-92
Jan-87
Jul-84
Jan-82
Jul-79
Jan-77
0
Month
Month
Figure 3: Variation of monthly maximum temperature of Moulvibazar.
Figure 4: Variation of monthly minimum temperature of Moulvibazar.
6
y = 0.0033x + 254.73
2000
y = -0.0171x + 872.51
3000
2500
Rainfall 2000
1500
(mm) 1000
500
0
1500
Rainfall
1000
(mm)
500
Month
Sep-07
Jan-08
Jan-05
Jan-02
Jan-99
Jan-96
Jan-93
Jan-90
Jan-87
Jan-84
Jan-81
Jan-08
Jan-05
Jan-02
Jan-99
Jan-96
0
Jan-93
0
Jan-90
1000
Rainfall
(mm) 500
Jan-87
y = -0.0012x + 260.33
1500
1000
Rainfall
(mm) 500
Jan-84
May-04
Figure 6: Variation of monthly Rainfall of sylhet station CL228.
y = -0.0065x + 500.43
Jan-81
Jan-01
Month
Figure 5: Variation of monthly Rainfall of sylhet station CL129.
1500
Sep-97
Jan-91
Month
May-94
Sep-87
May-84
Jan-81
Sep-07
May-04
Jan-01
Sep-97
May-94
Jan-91
Sep-87
May-84
Jan-81
0
Month
Figure 8: Variation of monthly Rainfall of Moulvibazar station CL126.
Figure 7: Variation of monthly Rainfall of Moulvibazar station CL104.
Jul-08
Jan-06
Jul-03
Jul-98
Jan-96
Jul-93
Jan-91
Jul-88
Jan-86
Jul-83
Jan-81
Jan-01
y = -0.0031x + 340.09
1200
1000
800
Rainfall
600
(mm)
400
200
0
Month
Figure 9: Variation of monthly Rainfall of Moulvibazar station CL229.
7
Mean and Standard deviation of monthly maximum and minimum temperature:
Table 2: Mean temperature of monthly maximum temperature of sylhet station with their standard deviation for last 35 years (from 1977 to 2011)
Month
January
February
March
April
May
June
July
August
September
October
November
Decenber
Mean (0C)
28.72
31.14
34.56
35.15
35.51
35.43
35.49
35.69
35.35
34.49
32.41
29.34
Standard deviation (0C)
2.736
2.713
2.709
2.710
2.711
2.713
2.715
2.719
2.727
2.726
2.727
2.727
Table 3: Mean temperature of monthly minimum temperature of sylhet station with their standard deviation for last 35 years (from 1977 to 2011)
Month
January
February
March
April
May
June
July
August
September
October
November
Decenber
Mean (0C)
9.50
11.07
14.34
17.46
19.33
21.53
23.11
23.57
22.39
19.47
15.35
11.39
Standard deviation (0C)
4.954
4.932
4.913
4.914
4.916
4.921
4.928
4.927
4.932
4.928
4.927
4.934
8
Table 4: Mean temperature of monthly maximum temperature of Moulvibazar station with their standard deviation for last 35 years (from 1977 to 2011)
Month
January
February
March
April
May
June
July
August
September
October
November
Decenber
Mean (0C)
28.77
31.28
35.23
35.74
35.79
35.32
35.31
35.43
35.10
34.31
32.13
29.71
Standard deviation (0C)
2.784
2.785
2.790
2.787
2.800
2.802
2.803
2.800
2.806
2.805
2.805
2.807
Table 5: Mean temperature of monthly minimum temperature of Moulvibazar station with their standard deviation for last 35 years (from 1977 to 2011)
Month
January
February
March
April
May
June
July
August
September
October
November
Decenber
Mean (0C)
6.68
7.90
11.41
16.69
18.85
20.94
22.75
22.64
22.17
17.87
12.51
8.96
Standard deviation (0C)
6.235
6.221
6.204
6.202
6.204
6.213
6.222
6.226
6.226
6.217
6.218
6.231
9
Mean and Standard deviation of monthly rainfall:
Table 6: Mean rainfall of every month of Sylhet station CL129 with their standard deviation for last 30 years (from 1981 to 2010)
Month
January
February
March
April
May
June
July
August
September
October
November
Decenber
Mean (mm)
8.16
29.79
85.70
279.27
464.86
647.97
653.01
491.24
394.54
168.88
24.99
9.79
Standard deviation (mm)
142.83
142.92
142.80
142.58
142.64
142.12
141.99
135.59
134.59
134.58
134.60
134.52
Table 7: Mean rainfall of every month of Sylhet station CL228 with their standard deviation for last 30 years (from 1981 to 2010)
Month
January
February
March
April
May
June
July
August
September
October
November
Decenber
Mean (mm)
14.45
50.81
199.10
444.78
626.46
857.80
764.95
705.67
531.22
227.57
29.60
9.98
Standard deviation (mm)
161.88
162.18
161.75
162.66
163.64
167.79
167.78
167.92
168.67
168.57
168.57
168.45
10
Table 8: Mean rainfall of every month of Moulvibazar station CL104with their standard deviation for last 30 years (from 1981 to 2010)
Month
January
February
March
April
May
June
July
August
September
October
November
Decenber
Mean (mm)
8.40
37.32
136.21
362.01
520.97
584.60
551.61
455.56
377.49
188.75
32.06
12.59
Standard deviation (mm)
176.57
176.64
176.46
176.53
176.60
176.40
176.34
176.11
175.97
175.99
176.34
176.22
Table 9: Mean rainfall of every month of Moulvibazar station CL126 with their standard deviation for last 30 years (from 1981 to 2010)
Month
January
February
March
April
May
June
July
August
September
October
November
Decenber
Mean (mm)
6.99
37.34
98.20
243.57
487.09
469.64
375.78
353.61
301.02
178.34
33.85
13.01
Standard deviation (mm)
118.48
118.55
118.57
118.55
118.93
118.84
118.84
118.48
118.23
118.18
118.20
118.21
Month
January
February
March
April
May
June
July
August
September
October
November
Decenber
Mean (mm)
13.97
36.69
118.714
285.49
445.85
504.23
451.709
359.89
326.50
159.89
41.32
18.52
Standard deviation (mm)
122.51
122.44
122.58
122.61
122.26
122.19
122.92
123.11
122.99
123.13
123.16
123.159
Table 10: Mean rainfall of every month of Moulvibazar station CL229with their standard deviation for last 30 years (from 1981 to 2010)
11
Mann-Kendall trend test:
• H0: There is no trend in the series
• Ha: There is a trend in the series
•It can be used for nonnormal data such as seasonal data
Table 11: MK Statistics and their corresponding p-Value at 5 % significance level for Temperature
Station
Monthly maximum
temperature of Sylhet
Monthly minimum
temperature of Sylhet
Monthly maximum
temperature of Moulvibazar
Monthly minimum
temperature of Moulvibazar
Test statistic
0.135
p-Value
0.0001
0.120
0.0008
0.116
0.001
0.128
0.0005
Table 12: MK Statistics and their corresponding p-Value at 5 % significance level for Rainfall
Station
Sylhet station CL129
Sylhet station CL228
Moulvibazar station CL104
Moulvibazar station CL126
Moulvibazar station CL229
Test statistic
-0.112
0.075
-0.102
-0.109
-0.061
p-Value
0.003
0.022
0.009
0.007
0.034
12
Annual maximum Rainfall frequency:
400
y = 70.363ln(x) + 109.74
R² = 0.932
300
Rainfall (mm) 200
100
0
1
10
100
Return period, T (year)
Figure 10: Rainfall frequency curve for Sylhet CL129
y = 75.18ln(x) + 81.808
R² = 0.8097
500
400
300
Rainfall (mm)
200
100
0
1
10
100
Return period,T (year)
Figure 11: Rainfall frequency curve for Sylhet CL228
13
y = 55.003ln(x) + 119.74
R² = 0.9043
400
300
Rainfall (mm) 200
100
0
1
10
100
Return period,T (year)
Figure 12: Rainfall frequency curve for Moulvibazar CL104
y = 82.078ln(x) + 85.433
R² = 0.7701
600
500
400
Rainfall (mm) 300
200
100
0
1
10
100
Return period,T (year)
Figure 13: Rainfall frequency curve for Moulvibazar CL126
y = 72.783ln(x) + 96.194
R² = 0.864
500
400
300
Rainfall (mm)
200
100
0
1
10
100
Return period,T (year)
Figure 14: Rainfall frequency curve for Moulvibazar CL229
14
ARIMA (p,d,q) model:
•p order of autoregressive terms
•d order of integrated term (non-seasonal differences; linear, quadratic,
etc.)
•q order of moving average (forecast errors)
 If seasonality in time series than ARIMA will be (p,d,q)(P,D,Q)12
1
0.8
0.6
0.6
Autocorrelation
0.4
0.2
0
-0.2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
-0.4
Partial autocorrelation
1
0.8
0.4
0.2
0
-0.2
-0.4
-0.6
-0.6
-0.8
-0.8
-1
Lag
Figure 15: Autocorrelation plot of time series
of monthly maximum temperature of Sylhet
station.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
-1
Lag
Figure 16: Partial autocorrelation plot of time
series of monthly maximum temperature of
Sylhet station.
The order of d and D have been selected as 1
15
Figure 17: Autocorrelation plot of differenced ( d and D = 1) time series of monthly maximum temperature of Sylhet station.
Figure 18: Partial autocorrelation plot of differenced ( d and D = 1) time series of monthly maximum temperature of Sylhet station.
• The order of p and P have been selected as 1
• The order of q and Q have been selected as 1
16
Figure: ACF and PACF plot of residuals for the monthly maximum temperature of
Sylhet Station.
17
The selected ARIMA model of Monthly maximum temperature of Sylhet
station is (1 1 1)(1 1 1)12
Table 13: Parameter estimation for ARIMA (1 1 1) (1 1 1)12 model of monthly maximum temperature of sylhet
Coefficients
Estimate
Ɵ1AR
Ɵ1MA
Ɵ1SAR
Ɵ1SMA
0.123
0.972
0.140
0.896
Standar
d
error
0.042
0.076
0.048
0.069
Log
likelihood
AIC
AICc
BIC
1201.633
1211.303
1211.920
1228.486
 Data of temperature station for the period from 1977 to 2009 has been used for the calibration and from
2010 to 2011 has been used for the verification of the prediction.
 Data of rainfall station for the period from 1981 to 2008 has been used for the calibration and from 2009 to
2010 has been used for the verification of the prediction.
18
PBIAS = 0.18%
predicted min
temperature
Oct-11
Jul-11
Apr-11
Jan-11
Oct-10
Jul-10
Oct-11
Jul-11
Apr-11
Jan-11
Oct-10
Jul-10
Apr-10
Jan-10
Predicted Max
Tempereture
Observed min.
Temperature
Apr-10
Observed Max
Temperature
PBIAS = - 0.33%
30
25
20
Temperature
15
( 0C)
10
5
0
Jan-10
40
35
30
25
Temperature
20
( 0C)
15
10
5
0
Month
Month
Figure 19: Comparison graph of Observed vs. Predicted values of the Monthly
Maximum Temperature data of Sylhet Station.
Figure 20: Comparison graph of Observed vs. Predicted values of the Monthly
Minimum Temperature data of Sylhet Station.
PBIAS = 0.43%
PBIAS = - 0.53%
30
40
25
Observed min.
Temperature
5
predicted min
temperature
Oct-11
Jul-11
Apr-11
Jan-11
Oct-10
0
Jul-10
Oct-11
Jul-11
20
Temperature
15
( 0C)
10
Apr-10
Month
Apr-11
Jan-11
Oct-10
Predicted Max
Tempereture
Jul-10
0
Apr-10
Observed Max
Temperature
Jan-10
Temperature
20
( 0C)
10
Jan-10
30
Month
Figure 21: Comparison graph of Observed vs. Predicted values of the Figure 22: Comparison graph of Observed vs. Predicted values of the
Monthly Maximum Temperature data of Moulvibazar Station.
Monthly Minimum Temperature data of Moulvibazar Station.
19
Oct-10
Jul-10
Apr-10
Jan-10
Oct-09
predicted rainfall (mm)
Jul-09
Oct-10
Jul-10
Apr-10
Jan-10
Oct-09
Jul-09
Apr-09
Jan-09
predicted rainfall
(mm)
Observed rainfall (mm)
Apr-09
Observed rainfall
(mm)
PBIAS = - 1.07%
1600
1400
1200
1000
Rainfall
800
(mm) 600
400
200
0
Jan-09
PBIAS = 4.5%
700
600
500
Rainfall 400
(mm) 300
200
100
0
Month
Month
Figure 23: Comparison graph of Observed vs. Predicted values of the Figure 24: Comparison graph of Observed vs. Predicted values of the
Rainfall data of Sylhet Station CL129.
Rainfall data of Sylhet Station CL228.
PBIAS = - 3.62%
600
1000
500
800
400
Rainfall 600
(mm) 400
Month
Oct-10
Jul-10
Apr-10
Jan-10
Oct-10
Jul-10
Apr-10
Jan-10
Oct-09
Jul-09
Apr-09
Jan-09
0
predicted rainfall (mm)
0
Oct-09
predicted rainfall
(mm)
Jul-09
100
Observed rainfall (mm)
200
Apr-09
Observed rainfall
(mm)
Jan-09
Rainfall
300
(mm)
200
PBIAS = - 6.56%
Month
Figure 25: Comparison graph of Observed vs. Predicted values of the Figure 26: Comparison graph of Observed vs. Predicted values of the
Rainfall data of Moulvibazar Station CL104.
Rainfall data of Moulvibazar Station CL126.
20
PBIAS = - 1.89%
600
500
400
Rainfall
300
(mm)
200
Observed rainfall (mm)
100
predicted rainfall (mm)
Oct-10
Jul-10
Apr-10
Jan-10
Oct-09
Jul-09
Apr-09
Jan-09
0
Month
Figure 27: Comparison graph of Observed vs. Predicted values of the
Rainfall data of Moulvibazar Station CL229.
21
Conclusion:
 The upward trend line and positive Mann-Kendall test statistics of time series of temperature (for the
period between 1977 and 2011) indicates that both the monthly maximum and minimum temperature
is increasing with time.
 The downward trend line and negative Mann-Kendall test statistics of time series of rainfall (for the
period between 1981 and 2010) indicates that monthly rainfall is decreasing with time except Sylhet
station CL228 (almost upward trend line).
 Mean temperature with their standard deviation indicates the variation of temperature in year to year
is not very high.
 Mean rainfall with their standard deviation indicates the variation of rainfall in year to year is high.
 A best fitted curve has been drawn between return period and annual maximum rainfall for each
rainfall station to see the frequency of it.
 The fitness of ARIMA model for the temperature and rainfall is well. The temperature and rainfall
time series fitted to ARIMA model for the selected stations can be used for estimating missing
temperature and rainfall values, forecasting and investigating short term temperature and rainfall
change.
22
References:
•F.HoVerhoog, the Influence of Climate Change and Climatic Variability on the Hydrologic Regime and Water Resources (Proceedings
of the Vancouver Symposium, August 1987) IAHSPubl.no.168, 1987
•Ministry of Environment and Forests, Government of the People's Republic of Bangladesh(2008), Bangladesh Climate Change Strategy
and Action Plan
•CEGIS & ADB (2009), Inception Report on Field Based Research on the Impacts of Climate Change on Bangladesh Rivers
•IWM (2005), Hydrological Impact Study of Tipaimukh Dam Project of India on Bangladesh
•UNFCC (2007), Climate Change: Impacts, Vulnerabilities and Adaptation In Developing Countries.
•Sarwar G. M. (2005), Impacts of Sea Level Rise on the Coastal Zone of Bangladesh, M.Sc. Thesis, Lund University International
Masters Program in Environmental Science, Lund University, Sweden.
•Subramanya K, (2005), Engineering Hydrology, Tata McGraw-Hill Publishing Company Limited, New Delhi, India.
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Thank You
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