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SARIMA Model-Based Maximum Temperature Forecasting in Bangladesh: A Data-Driven Evaluation from 1981 to 2024

Received: 31 August 2024     Accepted: 20 September 2024     Published: 18 October 2024
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Abstract

Bangladesh is a tropical nation where there are notable seasonal temperature changes. The Seasonal Autoregressive Integrated Moving Average (SARIMA) model is used in this study to forecast Bangladesh's maximum temperature from 2023 to 2042. The objective is to assess how rising temperatures can affect public health, energy consumption, and agriculture. Autocorrelation and partial autocorrelation analysis will be used to improve the model. Analysis was done using historical maximum temperature data spanning from 1981 to 2022. Forecasts were produced using the SARIMA model, whose parameters were chosen in accordance with plots of the autocorrelation function (ACF) and partial autocorrelation function (PACF). The model SARIMA (1,1,2)(0,0,1) is selected based on AIC. In order to account for forecast uncertainty, forecasts were created for the years 2023–2042. 95% prediction ranges were then calculated. Bangladesh's maximum temperatures are predicted by the SARIMA model to rise gradually, from roughly 33.75°C in 2023 to 34.17°C in 2042. With some degree of uncertainty, the 95% prediction intervals show a steady increasing trend between 33.53°C and 34.51°C. The anticipated increase in the highest temperatures has major consequences for Bangladesh. These results highlight how crucial it is to create adaptation plans and laws in order to lessen the effects of warming temperatures and increase resilience.

Published in American Journal of Biological and Environmental Statistics (Volume 10, Issue 4)
DOI 10.11648/j.ajbes.20241004.11
Page(s) 96-104
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

SARIMA Model, Maximum Temperature Forecast, Climate Change, Bangladesh, Temperature Trends

1. Introduction
One of the biggest environmental issues of our time is climate change, having a huge impact on economies, ecosystems, and populations all over the world. One of the most obvious effects of climate change is rising temperatures, which have a significant impact on a number of industries, including public health, energy, and agriculture.
Bangladesh, a heavily populated nation in South Asia's low-lying delta region, is one of the countries most affected by climatic instability and extreme weather occurrences. It is known for being vulnerable to cyclones, flooding, and rising temperatures, that is facing greater threats to infrastructure, public health, agriculture, and general socioeconomic stability. Rising temperatures have been reported in South Asia, particularly in Bangladesh, in recent years, owing to a combination of human activity and variability in nature . In spite of this, exact and realistic temperature forecasting becomes essential for developing plans for effective climate adaptation and mitigation.
Forecasting maximum temperatures is very important since it has a direct impact on many different areas, such as public health, energy consumption, agriculture, and water resource management. For example, prolonged periods of high heat can cause crop failures, raise the energy needed for cooling, and increase the number of heat-related illnesses.
To estimate and anticipate temperature fluctuations, many statistical and machine learning techniques have been used over the years. The capacity of the Seasonal Autoregressive Integrated Moving Average (SARIMA) model to extract the seasonal and trend components included in time series data has made it stand out among the others. According to research by Hyndman and Athanasopoulos (2018), the model is a good option for predicting weather patterns because of its ability to handle seasonal data well . The SARIMA model was used to forecast maximum temperatures in a number of Indian cities, proving its effectiveness in capturing both short- and long-term trends. According to the study's findings, SARIMA models are especially helpful in areas like the Indian subcontinent that have prominent seasonal climate patterns. For example, Ghosh and Mujumdar (2006) emphasized the usefulness of the model in monsoonal climate regions by modeling precipitation patterns in India using SARIMA .
Although SARIMA models have been widely used in many different climate zones, there are still few thorough studies assessing their effectiveness in Bangladesh. SARIMA was used in a study by Rahman et al. (2017) to forecast temperature in Dhaka city, showcasing the model's capacity to account for seasonal fluctuations . Nevertheless, the depth of this study was limited because it only looked at one city and had a brief forecast horizon. Islam et al. (2014) conducted a noteworthy investigation that used time series analysis to analyze temperature patterns in Bangladesh; nevertheless, the study did not concentrate on long-term forecasts . Again In another study the selected SARIMA models give two-year predicted monthly maximum and minimum temperatures that can help decision makers to establish priorities for preparing themselves against forthcoming weather fluctuations . A notable gap in the literature is the absence of long-term, national studies employing SARIMA, especially considering the significance of precise temperature forecasting for Bangladesh's climate adaption plans. The research has importance as it has the potential to improve Bangladesh's temperature forecasts' predictive accuracy. This would in turn promote evidence-based decision-making concerning resource management and climate adaption. In order to close these gaps, a thorough assessment of the SARIMA model for predicting Bangladesh's maximum temperatures between 1981 and 2041 is being carried out in this work. The project seeks to give a more accurate and region-specific forecast by utilizing a large dataset and concentrating on long-term trends. This will add to the body of knowledge on climate modeling in Bangladesh and inform climate resilience measures.
2. Materials and Methods
2.1. Data Source
Data on maximum temperatures collected from the Bangladesh Meteorological Department are used in the study from year 1981 to 2022, a period of 42 years. The dataset has extensive geographical and temporal coverage, encompassing several meteorological stations located throughout Bangladesh.
2.2. Methods
Time series data having seasonal components can be handled using the Seasonal Autoregressive Integrated Moving Average (SARIMA) model, which is why it was chosen.
An expansion of the ARIMA (Autoregressive Integrated Moving Average) model that takes into account seasonality in addition to the non-seasonal components is called SARIMA (Seasonal Auto-Regressive Integrated Moving Average). While SARIMA models are especially made to handle data with seasonal trends, ARIMA models are commonly utilized for time series analysis and forecasting.
Natural phenomena such as temperature, rainfall etc. was strong components corresponding to seasons. Hence, the natural variability of many physical, biological and economic processes tends to match with seasonal fluctuations .
SARIMA Model is represented as
ARIMA p,d,qP,D,Qn
Where,
p=Number of non-seasonal AR terms;
d=Number of non-seasonal differences;
q=Number of non-seasonal MA terms;
P= Number of seasonal AR terms;
D= Number of seasonal differences;
Q= Number of seasonal MA terms;
n= number of periods per season.
2.3. Materials
Statistical software tools sigmaXL and OriginPro was used to develop the SARIMA model.
3. Results
Our data, which is the highest temperature recorded at meteorological stations throughout Bangladesh between 1981 and 2022, must first be checked for non-stationarity before fitting a suitable model can be applied. The ARIMA model summary and statistics from Tables 1 and 2 show that the SARIMA(1,1,2)(0,0,1) model is suitable for this study, and that Model selection and validation are carried out using statistical metrics like the Akaike Information Criterion (AIC).
Table 1. SARIMA Model summary.

ARIMA Model Summary

AR Order (p)

1

I Order (d)

1

MA Order (q)

2

SAR Order (P)

0

SI Order (D)

0

SMA Order (Q)

1

Seasonal Frequency

4

Include Constant

1

No. of Predictors

0

Model Selection Criterion

AIC

Box-Cox Transformation

Rounded Lambda

Lambda

0

Threshold

0

Table 2. ARIMA model statistics.

ARIMA Model Statistics

No. of Observations

42

DF

36

StDev

0.003302916

Variance

1.09093E-05

Log-Likelihood

172.4809266

AICc

-330.491265

AIC

-332.9618533

BIC

-322.6804209

Tables 3 and 4 indicates forecast accuracy and parameter estimations. These tables shows that aside from other pertinent statistical metrics, MAPE and RMSE are used to assess the model's performance.
Table 3. Forecast Accuracy.

Metric

In-Sample (Estimation) One-Step-Ahead Forecast

N

41

RMSE

0.112134686

MAE

0.07812542

MAPE

0.2323724

MASE

0.556754964

Table 4. Parameter estimation.

Term

Coefficient

SE Coefficient

T

P

AR_1

-0.320499718

0.322653049

0.993326

0.3272

MA_1

0.116379184

0.289675857

0.401757

0.6902

MA_2

0.865069025

0.279552583

3.094477

0.0038

SMA_1

0.798604076

0.282023659

2.831692

0.0075

Const: Trend

0.000511282

3.27672E-05

15.60347

0.0000

As seen in Figure 1 through Figure 5 given below, the SARIMA model accurately depicts the historical temperature trends with few residual errors. The seasonal and non-seasonal components of the SARIMA model were determined using Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots. The model's proper representation of the underlying temperature trends is ensured by the lag values selected in accordance with the guidance provided by the ACF and PACF displays.
Figure 1. Autocorrelation Function (ACF) Plot Significance Limit Alpha = 0.05.
Figure 2. Partial Autocorrelation Function (PACF) Plot Significance Limit Alpha = 0.05.
Figure 3. Autocorrelation Function (ACF) Plot – Residuals Significance Limit Alpha = 0.05.
Figure 4. Partial Autocorrelation Function (PACF) Plot –Residuals Significance Limit Alpha = 0.05.
Figure 5. Residuals vs Data Order for: Maximum Temperature.
Table 5 and Figure 6 displays Forecast table of anticipated maximum temperatures over the next 20 years and forecasting chart accordingly.
Table 5. Forecast table.

Period

One-Step-Ahead Forecast

Lower 95.0% PI

Upper 95.0% PI

2023

33.75065484

33.52627455

33.97653683

2024

33.74756774

33.49020739

34.0069058

2025

33.47343764

33.21564916

33.73322682

2026

33.94965421

33.68771756

34.21362752

2027

34.00628604

33.68759764

34.32798927

2028

33.89133434

33.55939269

34.22655928

2029

33.95104819

33.61700358

34.28841213

2030

33.95481525

33.62060258

34.29235023

2031

33.97653931

33.64209075

34.31431274

2032

33.99251747

33.65791141

34.33044998

2033

34.01034992

33.67556693

34.34846113

2034

34.02759951

33.6926463

34.36588264

2035

34.04504775

33.70992211

34.38350503

2036

34.06244404

33.72714657

34.40107486

2037

34.07986875

33.74439915

34.41867342

2038

34.09729611

33.76165435

34.43627466

2039

34.11473439

33.77892037

34.45388692

2040

34.13218095

33.79619458

34.47150754

2041

34.14963663

33.81347782

34.48913738

2042

34.16710117

33.83076984

34.50677617

Figure 6. ARIMA Time Series Forecasting Chart 95.0% Prediction Intervals.
Figure 7. Average temperature of annual time series data.
Figure 7 indicates the average temperature of annual time series data which is given below,
4. Discussion
The results of the analysis show that, from 1981 to 2022, Bangladesh's maximum temperatures showed a distinct and significant increasing trend. The effects of climate change on Bangladesh's climatic system are highlighted by the average increase of 1°C per decade, which is consistent with larger regional and global warming patterns. The seasonal and long-term trends in the historical temperature data were effectively captured by the SARIMA model, which was created through thorough statistical research. The model is a reliable instrument for temperature forecasting, as shown by its strong validation metrics (e.g., MAPE, RMSE, and AIC) and low residuals.. Over the next 20 years, the SARIMA model predicts that maximum temperatures will continue to rise. In comparison to the baseline period of 1981–2022, a rise of around 1°C is predicted in the average maximum temperature by 2041. The results of the one-step-ahead forecast show that the maximum temperature in Bangla-desh would continue to rise from 2023 to 2042. The highest temperature expected in 2023 is roughly 33.75°C, and by 2042, it will have risen gradually to 34.17°C. A range of uncertainty is shown by the 95% prediction intervals, with 33.53°C as the lower bound and 33.98°C as the upper bound of the forecast for 2023. This range changes by 2042, with the lower bound being 33.83°C and the top bound being 34.51°C. These forecasts align with the patterns in global warming shown in comparable South Asian research, which show a continuous rise in local temperatures brought on by rising greenhouse gas emissions . According to these forecasts, temperatures will climb steadily, which is consistent with the region's overall observations of global warming trends. Bangladesh's agriculture is expected to be significantly impacted by the predicted temperature increase, especially for crops that are susceptible to heat stress. Rice yields can be significantly reduced by even small temperature rises during critical growth periods . The progressive increase from 33.75°C in 2023 to 34.17°C in 2042 indicates that peak energy demand during the summer months may increase over time. This growing demand would put further strain on Bang-ladesh's energy infrastructure, demanding investments in energy efficiency and renewable energy development. The predicted temperatures also highlight the significance of incorporating climate projections into long-term energy planning to guarantee that the country can meet its future energy demands responsibly. Rising temperatures can cause a noticeable spike in electricity consumption as homes and businesses use air conditioning and cooling systems more frequently . Furthermore, there could be an increase in the frequency and severity of heatwaves, which would increase the risks to public health. Research has indicated that elevated temperatures are linked to a higher frequency of heat-related ailments, including dehydration, heatstroke, and cardiovascular events. This is particularly true for susceptible groups like the elderly and those with pre-existing medical conditions .
Although the forecast produced by the SARIMA model is dependable, it is crucial to take into account the inherent uncertainties in long-term climate projections. As a result of errors in the model and the underlying data, the prediction intervals show a range of potential outcomes. Variations from the predicted temperatures could be caused by a number of factors, including changes in greenhouse gas emissions worldwide, changes in the local environment, and unforeseen meteorological phenomena. Furthermore, any non-linearities in climate responses—which can intensify as temperatures rise—are not taken into consid-eration by the model. More intricate models or ensemble methods could be useful in future research to capture a greater variety of possible circumstances. Moreover, abrupt changes in temperature patterns brought on by intricate climatic interactions may not be properly captured by the linear structure of the SARIMA model .
Future research should examine the socioeconomic effects of rising temperatures, with a focus on Bangladesh's vulnerable people. To lessen the effects of rising temperatures, research into adaptive solutions is also necessary in the fields of energy, agriculture, and public health. Furthermore, combining regional climate models with SARIMA projections may offer a more thorough comprehension of the geographical variety of temperature variations throughout the nation. To improve the accuracy of future climate estimates, more research might concentrate on the interactions between rising temperatures and other climatic factors, such as humidity and precipitation .
5. Conclusions
The maximum temperatures predicted by the SARIMA model for Bangladesh between 2023 and 2042 show a consistent trend, with important ramifications for public health, energy, and agriculture. After refining the model with historical temperature data from 1981 to 2022 and ACF and PACF plots, the SARIMA projections showed a steady and progressive increase in maximum temperatures, from roughly 33.75°C in 2023 to 34.17°C by 2042. The findings of this study suggest that Bangladesh would continue to face serious issues as a result of climate change. The results emphasize the necessity of proactive mitigation and adaptation plans to deal with the problems caused by climate change. In order to provide a more thorough knowledge of climate consequences, future study could build on these findings by including additional climate variables, such as humidity and precipitation. In addition, including non-linear models may result in longer-term climate forecasts with higher accuracy. In order to maintain Bangladesh's socioeconomic stability and environmental sustainability, it will be essential to incorporate accurate climate forecasts into national planning as the country experiences continuous temperature rises. Also, policymakers must include these estimates into national climate programs.
Abbreviations

SARIMA

Seasonal Autoregressive Integrated Moving Average

ARIMA

Autoregressive Integrated Moving Average

AIC

Akaike Information Criterion

ACF

Autocorrelation Function

PACF

Partial Autocorrelation Function

Author Contributions
Nur Hosain Md. Ariful Azim: Conceptualization, Project administration, Supervision
Sofi Mahmud Parvez: Data curation, Formal Analysis, Investigation, Resources, Visualization
Mumtahin Taharima: Methodology, Writing – original draft
Md. Sabbir Ahmed Rudman: Data curation, Resources, Writing – review & editing
Funding
None.
Data Availability Statement
We obtained the Annual Maximum Discharge data (m^3/s) for the 23 between 2000 and 2022 years that were recorded for the SW266 Kanairghat station on the Meghna River in Sylhet district. Not applicable.
Conflicts of Interest
The authors declare no conflicts of interest.
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Cite This Article
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    Azim, N. H. M. A., Parvez, S. M., Taharima, M., Rudman, M. S. A. (2024). SARIMA Model-Based Maximum Temperature Forecasting in Bangladesh: A Data-Driven Evaluation from 1981 to 2024. American Journal of Biological and Environmental Statistics, 10(4), 96-104. https://doi.org/10.11648/j.ajbes.20241004.11

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    Azim, N. H. M. A.; Parvez, S. M.; Taharima, M.; Rudman, M. S. A. SARIMA Model-Based Maximum Temperature Forecasting in Bangladesh: A Data-Driven Evaluation from 1981 to 2024. Am. J. Biol. Environ. Stat. 2024, 10(4), 96-104. doi: 10.11648/j.ajbes.20241004.11

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    AMA Style

    Azim NHMA, Parvez SM, Taharima M, Rudman MSA. SARIMA Model-Based Maximum Temperature Forecasting in Bangladesh: A Data-Driven Evaluation from 1981 to 2024. Am J Biol Environ Stat. 2024;10(4):96-104. doi: 10.11648/j.ajbes.20241004.11

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  • @article{10.11648/j.ajbes.20241004.11,
      author = {Nur Hosain Md. Ariful Azim and Sofi Mahmud Parvez and Mumtahin Taharima and Md. Sabbir Ahmed Rudman},
      title = {SARIMA Model-Based Maximum Temperature Forecasting in Bangladesh: A Data-Driven Evaluation from 1981 to 2024
    },
      journal = {American Journal of Biological and Environmental Statistics},
      volume = {10},
      number = {4},
      pages = {96-104},
      doi = {10.11648/j.ajbes.20241004.11},
      url = {https://doi.org/10.11648/j.ajbes.20241004.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajbes.20241004.11},
      abstract = {Bangladesh is a tropical nation where there are notable seasonal temperature changes. The Seasonal Autoregressive Integrated Moving Average (SARIMA) model is used in this study to forecast Bangladesh's maximum temperature from 2023 to 2042. The objective is to assess how rising temperatures can affect public health, energy consumption, and agriculture. Autocorrelation and partial autocorrelation analysis will be used to improve the model. Analysis was done using historical maximum temperature data spanning from 1981 to 2022. Forecasts were produced using the SARIMA model, whose parameters were chosen in accordance with plots of the autocorrelation function (ACF) and partial autocorrelation function (PACF). The model SARIMA (1,1,2)(0,0,1) is selected based on AIC. In order to account for forecast uncertainty, forecasts were created for the years 2023–2042. 95% prediction ranges were then calculated. Bangladesh's maximum temperatures are predicted by the SARIMA model to rise gradually, from roughly 33.75°C in 2023 to 34.17°C in 2042. With some degree of uncertainty, the 95% prediction intervals show a steady increasing trend between 33.53°C and 34.51°C. The anticipated increase in the highest temperatures has major consequences for Bangladesh. These results highlight how crucial it is to create adaptation plans and laws in order to lessen the effects of warming temperatures and increase resilience.
    },
     year = {2024}
    }
    

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    T1  - SARIMA Model-Based Maximum Temperature Forecasting in Bangladesh: A Data-Driven Evaluation from 1981 to 2024
    
    AU  - Nur Hosain Md. Ariful Azim
    AU  - Sofi Mahmud Parvez
    AU  - Mumtahin Taharima
    AU  - Md. Sabbir Ahmed Rudman
    Y1  - 2024/10/18
    PY  - 2024
    N1  - https://doi.org/10.11648/j.ajbes.20241004.11
    DO  - 10.11648/j.ajbes.20241004.11
    T2  - American Journal of Biological and Environmental Statistics
    JF  - American Journal of Biological and Environmental Statistics
    JO  - American Journal of Biological and Environmental Statistics
    SP  - 96
    EP  - 104
    PB  - Science Publishing Group
    SN  - 2471-979X
    UR  - https://doi.org/10.11648/j.ajbes.20241004.11
    AB  - Bangladesh is a tropical nation where there are notable seasonal temperature changes. The Seasonal Autoregressive Integrated Moving Average (SARIMA) model is used in this study to forecast Bangladesh's maximum temperature from 2023 to 2042. The objective is to assess how rising temperatures can affect public health, energy consumption, and agriculture. Autocorrelation and partial autocorrelation analysis will be used to improve the model. Analysis was done using historical maximum temperature data spanning from 1981 to 2022. Forecasts were produced using the SARIMA model, whose parameters were chosen in accordance with plots of the autocorrelation function (ACF) and partial autocorrelation function (PACF). The model SARIMA (1,1,2)(0,0,1) is selected based on AIC. In order to account for forecast uncertainty, forecasts were created for the years 2023–2042. 95% prediction ranges were then calculated. Bangladesh's maximum temperatures are predicted by the SARIMA model to rise gradually, from roughly 33.75°C in 2023 to 34.17°C in 2042. With some degree of uncertainty, the 95% prediction intervals show a steady increasing trend between 33.53°C and 34.51°C. The anticipated increase in the highest temperatures has major consequences for Bangladesh. These results highlight how crucial it is to create adaptation plans and laws in order to lessen the effects of warming temperatures and increase resilience.
    
    VL  - 10
    IS  - 4
    ER  - 

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Author Information
  • Department of Electrical and Electronic Engineering, Southeast University, Dhaka, Bangladesh

    Biography: Nur Hosain Md. Ariful Azim was born in Rangpur, Bangladesh in1976. He completed B.Sc. and M.Sc. in Mathematics from the University of Dhaka. After that He completed M. Phil. and Ph. D in Mathematics from Bangladesh University of Engineering and Technology. NHM. A. Azim has wide experience in teaching and administrative in both Business and Science schools. In 2001, he joined International Islamic University Chittagong (Bangladesh) as a lecturer in the Department of Business Administration. In 2005, he joined Southeast University (Bangladesh) as an Assistant Professor in Southeast Business School (SBS) and promoted as an Associate Professor in Mathematics in 2014. He has joined in the Department of Electrical and Electronics Engineering of Southeast University in 2018 and working there till the date. His research interest mostly on computational fluid dynamics and heat transfer. Besides, he has keen interest on standard statistical analysis and numerical modelling. The author is a life member of BMS and BSPUA and also connected with several charitable organizations.

  • Department of Electrical and Electronic Engineering, Southeast University, Dhaka, Bangladesh

    Biography: Sofi Mahmud Parvez was born Cumilla, Bangladesh in 1997. He received B.Sc. (Hons) degree in Applied Mathematics from Noakhali Science and Technology University, Noakhali-Bangladesh in2019. He achieved the MS degree in Applied Mathematics from the same University in 2020. Currently, Sofi Mahmud Parvez is working as a lecturer in the department of Electrical and Electronic Engineering of Southeast University, Dhaka, Bangladesh. His research interest in Bio-Mathematics, especially mathematical modelling on epidemiology, ecology and demography.

  • Department of Applied Mathematics, Noakhali Science and Technology University, Noakhali, Bangladesh

    Biography: Mumtahin Taharima was born in Feni, Bangladesh in 1999. She received B.Sc. (Hons) degree in Applied Mathematics from Noakhali Science and Technology, Noakhali, Bangladesh in 2024. She is currently pursuing her master’s degree in Applied mathematics from same University. Her research interest is in Data analysis especially explaining and forecasting different problems through various time series model. She is now looking for more opportunities to conduct research in the same field and advance her career.

  • Bangladesh Meteorology Department, Dhaka, Bangladesh

    Biography: Md. Sabbir Ahmed Rudman was born Brahmanbaria I hold a Bachelor of Science in Environmental Science from Noakhali Science and Technology University and a Master of Science in Meteorology from the University of Dhaka in 2019 and 2022 respectively.