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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
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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.
Introduction:
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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
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Study Area:
Sylhet division, the northeastern administrative division of Bangladesh, located at 24 053’ 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
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Data Collection:
District Area (km2) Station ID TimeSylhet 3490.40 CL129
1981 to 2010(29 years)
CL 228Maulvibazar 2799.39 CL 104
CL126CL 229
District Area (km2) Type of data TimeSylhet 3490.40 Maximum
Temperature (0C) 1977 to 2011(34 years)
Minimum Temperature (0C)
Maulvibazar (Srimongal)
2799.39 Maximum Temperature (0C)Minimum Temperature (0C)
Table: Monthly Rainfall data (Source: Bangladesh Water Development Board)
Table: Monthly Temperature data (Source : Bangladesh Meteorological Department)
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Jan-77
Jul-79Jan
-82Jul-8
4Jan
-87Jul-8
9Jan
-92Jul-9
4Jan
-97Jul-9
9Jan
-02Jul-0
4Jan
-07Jul-0
90
1020304050
f(x) = 0.000122989082941342 x + 29.3652542128739
Month
Temperature (0C)
Jan-77
Jul-79Jan
-82Jul-8
4Jan
-87Jul-8
9Jan
-92Jul-9
4Jan
-97Jul-9
9Jan
-02Jul-0
4Jan
-07Jul-0
90
10
20
30
f(x) = 0.000136483085416826 x + 12.6501660488277
Month
Temperature (0C)
Figure 1: Variation of monthly maximum temperature of sylhet. Figure 2: Variation of monthly minimum temperature of sylhet.
Jan-77
Jul-79Jan
-82Jul-8
4Jan
-87Jul-8
9Jan
-92Jul-9
4Jan
-97Jul-9
9Jan
-02Jul-0
4Jan
-07Jul-0
90
1020304050
f(x) = 6.57309827028196E-05 x + 31.4083679683943
Month
Temperature (0C)
Figure 3: Variation of monthly maximum temperature of Moulvibazar.
Jan-77
Jul-79Jan
-82Jul-8
4Jan
-87Jul-8
9Jan
-92Jul-9
4Jan
-97Jul-9
9Jan
-02Jul-0
4Jan
-07Jul-0
905
1015202530
f(x) = 0.00013112446456781 x + 11.2574278667069
Month
Temperature (0C)
Figure 4: Variation of monthly minimum temperature of Moulvibazar.
Data Analysis:
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Jan-81
Mar-84
May-87
Jul-90
Sep-93
Nov-96Jan
-00
Mar-03
May-06
Jul-09
0500
10001500200025003000
f(x) = − 0.0171470680721389 x + 872.514662230674
Month
Rainfall (mm)
Jan-81
Mar-84
May-87
Jul-90
Sep-93
Nov-96Jan
-00
Mar-03
May-06
Jul-09
0
400
800
1200
1600
f(x) = 0.00334206828455125 x + 254.727585407721
Month
Rainfall (mm)
Figure 5: Variation of monthly Rainfall of sylhet station CL129. Figure 6: Variation of monthly Rainfall of sylhet station CL228.
Jan-81
Oct-83
Jul-86
Apr-89Jan
-92
Oct-94
Jul-97
Apr-00Jan
-03
Oct-05
Jul-08
0
400
800
1200
f(x) = − 0.00650528321579975 x + 500.433671088937
Month
Rainfall (mm)
Figure 7: Variation of monthly Rainfall of Moulvibazar station CL104.
Jan-81
Oct-83
Jul-86
Apr-89Jan
-92
Oct-94
Jul-97
Apr-00Jan
-03
Oct-05
Jul-08
0
400
800
1200
f(x) = − 0.00124939701280888 x + 260.326525346117
Month
Rainfall (mm)
Figure 8: Variation of monthly Rainfall of Moulvibazar station CL126.
Jan-81
May-83
Sep-85
Jan-88
May-90
Sep-92
Jan-95
May-97
Sep-99
Jan-02
May-04
Sep-06
Jan-09
0200400600800
10001200
f(x) = − 0.00313452195668542 x + 340.093583200547
Month
Rainfall (mm)
Figure 9: Variation of monthly Rainfall of Moulvibazar station CL229.
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Month Mean (0C) Standard deviation (0C)January 28.72 2.736February 31.14 2.713
March 34.56 2.709April 35.15 2.710May 35.51 2.711June 35.43 2.713July 35.49 2.715
August 35.69 2.719September 35.35 2.727
October 34.49 2.726November 32.41 2.727Decenber 29.34 2.727
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 Mean (0C) Standard deviation (0C)January 9.50 4.954February 11.07 4.932
March 14.34 4.913April 17.46 4.914May 19.33 4.916June 21.53 4.921July 23.11 4.928
August 23.57 4.927September 22.39 4.932
October 19.47 4.928November 15.35 4.927Decenber 11.39 4.934
Table 3: Mean temperature of monthly minimum temperature of sylhet station with their standard deviation for last 35 years (from 1977 to 2011)
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Month Mean (0C) Standard deviation (0C)January 28.77 2.784February 31.28 2.785
March 35.23 2.790April 35.74 2.787May 35.79 2.800June 35.32 2.802July 35.31 2.803
August 35.43 2.800September 35.10 2.806
October 34.31 2.805November 32.13 2.805Decenber 29.71 2.807
Table 4: Mean temperature of monthly maximum temperature of Moulvibazar station with their standard deviation for last 35 years (from 1977 to 2011)
Month Mean (0C) Standard deviation (0C)January 6.68 6.235February 7.90 6.221
March 11.41 6.204April 16.69 6.202May 18.85 6.204June 20.94 6.213July 22.75 6.222
August 22.64 6.226September 22.17 6.226
October 17.87 6.217November 12.51 6.218Decenber 8.96 6.231
Table 5: Mean temperature of monthly minimum temperature of Moulvibazar station with their standard deviation for last 35 years (from 1977 to 2011)
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Month Mean (mm) Standard deviation (mm)January 8.16 142.83February 29.79 142.92
March 85.70 142.80April 279.27 142.58May 464.86 142.64June 647.97 142.12July 653.01 141.99
August 491.24 135.59September 394.54 134.59
October 168.88 134.58November 24.99 134.60Decenber 9.79 134.52
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 Mean (mm) Standard deviation (mm)January 14.45 161.88February 50.81 162.18
March 199.10 161.75April 444.78 162.66May 626.46 163.64June 857.80 167.79July 764.95 167.78
August 705.67 167.92September 531.22 168.67
October 227.57 168.57November 29.60 168.57Decenber 9.98 168.45
Table 7: Mean rainfall of every month of Sylhet station CL228 with their standard deviation for last 30 years (from 1981 to 2010)
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Month Mean (mm) Standard deviation (mm)January 6.99 118.48February 37.34 118.55
March 98.20 118.57April 243.57 118.55May 487.09 118.93June 469.64 118.84July 375.78 118.84
August 353.61 118.48September 301.02 118.23
October 178.34 118.18November 33.85 118.20Decenber 13.01 118.21
Table 9: Mean rainfall of every month of Moulvibazar station CL126 with their standard deviation for last 30 years (from 1981 to 2010)
Month Mean (mm) Standard deviation (mm)January 13.97 122.51February 36.69 122.44
March 118.714 122.58April 285.49 122.61May 445.85 122.26June 504.23 122.19July 451.709 122.92
August 359.89 123.11September 326.50 122.99
October 159.89 123.13November 41.32 123.16Decenber 18.52 123.159
Table 10: Mean rainfall of every month of Moulvibazar station CL229with their standard deviation for last 30 years (from 1981 to 2010)
Month Mean (mm) Standard deviation (mm)January 8.40 176.57February 37.32 176.64
March 136.21 176.46April 362.01 176.53May 520.97 176.60June 584.60 176.40July 551.61 176.34
August 455.56 176.11September 377.49 175.97
October 188.75 175.99November 32.06 176.34Decenber 12.59 176.22
Table 8: Mean rainfall of every month of Moulvibazar station CL104with their standard deviation for last 30 years (from 1981 to 2010)
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Station Test statistic p-ValueMonthly maximum
temperature of Sylhet0.135 0.0001
Monthly minimum temperature of Sylhet
0.120 0.0008
Monthly maximum temperature of Moulvibazar
0.116 0.001
Monthly minimum temperature of Moulvibazar
0.128 0.0005
Table 11: MK Statistics and their corresponding p-Value at 5 % significance level for Temperature
Station Test statistic p-ValueSylhet station CL129 -0.112 0.003Sylhet station CL228 0.075 0.022
Moulvibazar station CL104 -0.102 0.009Moulvibazar station CL126 -0.109 0.007Moulvibazar station CL229 -0.061 0.034
Table 12: MK Statistics and their corresponding p-Value at 5 % significance level for Rainfall
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
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1 10 1000
50100150200250300350
f(x) = 70.3627605160942 ln(x) + 109.744750037028R² = 0.931969684220051
Return period, T (year)
Rainfall (mm)
Figure 10: Rainfall frequency curve for Sylhet CL129
1 10 1000
50100150200250300350400450500
f(x) = 75.1798180506854 ln(x) + 81.8075283460772R² = 0.809670163832024
Return period,T (year)
Rainfall (mm)
Figure 11: Rainfall frequency curve for Sylhet CL228
Annual maximum Rainfall frequency:
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1 10 1000
100
200
300
400
f(x) = 55.0033545312087 ln(x) + 119.743923424323R² = 0.904315417400048
Return period,T (year)
Rainfall (mm)
Figure 12: Rainfall frequency curve for Moulvibazar CL104
1 10 1000
100200300400500600
f(x) = 82.0783685849745 ln(x) + 85.43263387097R² = 0.770072306417606
Return period,T (year)
Rainfall (mm)
Figure 13: Rainfall frequency curve for Moulvibazar CL126
1 10 1000
100200300400500
f(x) = 72.7833989819325 ln(x) + 96.1937613790595R² = 0.864025587886463
Return period,T (year)
Rainfall (mm)
Figure 14: Rainfall frequency curve for Moulvibazar CL229
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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)
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
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Lag
Aut
ocor
rela
tion
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
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Lag
Parti
al a
utoc
orre
latio
nFigure 15: Autocorrelation plot of time series of monthly maximum temperature of Sylhet station.
Figure 16: Partial autocorrelation plot of time series of monthly maximum temperature of Sylhet station.
If seasonality in time series than ARIMA will be (p,d,q)(P,D,Q)12
The order of d and D have been selected as 1
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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 q and Q have been selected as 1
• The order of p and P have been selected as 1
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Figure: ACF and PACF plot of residuals for the monthly maximum temperature of Sylhet Station.
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The selected ARIMA model of Monthly maximum temperature of Sylhet station is (1 1 1)(1 1 1)12
Coefficients Estimate Standard
error
Log likelihood
AIC AICc BIC
Ɵ1AR 0.123 0.042 1201.633 1211.303 1211.920 1228.486
Ɵ1MA 0.972 0.076
Ɵ1SAR 0.140 0.048
Ɵ1SMA 0.896 0.069
Table 13: Parameter estimation for ARIMA (1 1 1) (1 1 1)12 model of monthly maximum temperature of sylhet
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.
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Jan-10
Apr-10Jul-1
0
Oct-10Jan
-11
Apr-11Jul-1
1
Oct-11
05
10152025303540
Observed Max TemperaturePredicted Max Tempereture
Month
Temperature( 0C)
Figure 19: Comparison graph of Observed vs. Predicted values of the Monthly Maximum Temperature data of Sylhet Station.
Jan-10
Apr-10Jul-1
0
Oct-10
Jan-11
Apr-11Jul-1
1
Oct-11
05
1015202530
Observed min. Temperaturepredicted min temperature
Month
Temperature( 0C)
PBIAS = 0.18%
Figure 20: Comparison graph of Observed vs. Predicted values of the Monthly Minimum Temperature data of Sylhet Station.
PBIAS = - 0.33%
Jan-10
Apr-10Jul-1
0
Oct-10
Jan-11
Apr-11Jul-1
1
Oct-11
05
10152025303540
Observed Max TemperaturePredicted Max Tempereture
Month
Temperature( 0C)
PBIAS = 0.43%
Jan-10
Apr-10Jul-1
0
Oct-10
Jan-11
Apr-11Jul-1
1
Oct-11
0
5
10
15
20
25
30
Observed min. Temperaturepredicted min temperature
Month
Temperature( 0C)
Figure 21: Comparison graph of Observed vs. Predicted values of the Monthly Maximum Temperature data of Moulvibazar Station.
Figure 22: Comparison graph of Observed vs. Predicted values of the Monthly Minimum Temperature data of Moulvibazar Station.
PBIAS = - 0.53%
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Jan-09
May-09
Sep-09
Jan-10
May-10
Sep-10
0100200300400500600700
Observed rainfall (mm)predicted rainfall (mm)
Month
Rainfall(mm)
PBIAS = 4.5%
Figure 23: Comparison graph of Observed vs. Predicted values of the Rainfall data of Sylhet Station CL129.
Jan-09
Apr-09Jul-0
9
Oct-09
Jan-10
Apr-10Jul-1
0
Oct-10
0200400600800
1000120014001600
Observed rainfall (mm)predicted rainfall (mm)
Month
Rainfall(mm)
PBIAS = - 1.07%
Figure 24: Comparison graph of Observed vs. Predicted values of the Rainfall data of Sylhet Station CL228.
Jan-09
May-09
Sep-09
Jan-10
May-10
Sep-10
0100200300400500600
Observed rainfall (mm)predicted rainfall (mm)
Month
Rainfall(mm)
Figure 25: Comparison graph of Observed vs. Predicted values of the Rainfall data of Moulvibazar Station CL104.
PBIAS = - 3.62%
Jan-09
Apr-09
Jul-09
Oct-09
Jan-10
Apr-10
Jul-10
Oct-10
0100200300400500600700800900
Observed rainfall (mm)predicted rainfall (mm)
Month
Rainfall(mm)
Figure 26: Comparison graph of Observed vs. Predicted values of the Rainfall data of Moulvibazar Station CL126.
PBIAS = - 6.56%
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Jan-09
Apr-09
Jul-09
Oct-09
Jan-10
Apr-10
Jul-10
Oct-10
0
100
200
300
400
500
600
Observed rainfall (mm)predicted rainfall (mm)
Month
Rainfall(mm)
Figure 27: Comparison graph of Observed vs. Predicted values of the Rainfall data of Moulvibazar Station CL229.
PBIAS = - 1.89%
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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.
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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