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Title
Abstract
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Introduction
Arima Methodology
Materials and Methods
Data Smoothing
Discussions and Conclusions
Future Scope with Open Problems
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Applied Mathematics

Analysis of thunderstorms in Bangladesh using ARIMA model

Profile image of Anisha DasAnisha Das

2022

https://doi.org/10.22075/IJNAA.2021.21639.2284
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13 pages

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Abstract

In this paper our main goal is to study the climatology and variability of the frequency of thunderstorm days over Bangladesh region throughout the year. It has been found that the mean thunderstorm days increase significantly from March to May, i.e. during the pre-monsoon season, although the graphical devices show that there does not seem to be much deviation from the occurrences of thunderstorms each year. The mean monthly and seasonal thunderstorm days were maximum in 1993, followed by that in 1997; whereas it was a minimum in the year 1980, with an extension in its frequency in the subsequent years 1981 and 1982. The coefficient of variation of both annual and seasonal thunderstorm days is minimum over the areas of maximum frequency of mean thunderstorm days and vice-versa. The time-domain analysis confirms that the occurrence happened to be maximum in the year 1991, although each and every state did not witness thunderstorms every year. Also some other time-domain models like ...

FAQs

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AI

What are the primary findings regarding thunderstorm frequency in Bangladesh from 1980-2016?add

The study reveals significant variability in annual thunderstorm occurrences, with some years recording zero events and others substantial numbers across different regions.

How does the ARIMA model perform in forecasting thunderstorms in Bangladesh?add

The ARIMA (0, 1, 1) model is identified as the most stable and suitable model for forecasting thunderstorms, providing accurate predictions and aiding decision-making.

What statistical techniques were used to select the ARIMA model's parameters?add

Parameter selection involved analyzing autocorrelation and partial autocorrelation functions, leading to the choice of parameters p, d, and q for model effectiveness.

What is the significance of the 'white noise' criteria in model validation?add

The residual series being a white noise indicates randomness, confirming that the ARIMA model has reached optimum performance and is suitable for forecasting.

What implications do the findings have for agricultural practices in Bangladesh?add

The results suggest that forecasting capabilities can help policymakers make timely arrangements to mitigate thunderstorm-related damages to crops and infrastructure.

Figures (14)
Identification of Number of parameters to be estimated: Before estimation, for ARIMA, one needs to identify specific number and type of ARIMA parameters to be estimated. For identification of parameters, plot of the series, correlograms of auto correlation (ACF) and partial autocorrelation (PACF). An empirical time series patterns can be sufficiently approximated using one of the five basic models that can be identified based on the shape of ACF and PACF. Also, the number of parameters of each kind is almost never greater than two; it is often practical to try alternative models on the same data.
Identification of Number of parameters to be estimated: Before estimation, for ARIMA, one needs to identify specific number and type of ARIMA parameters to be estimated. For identification of parameters, plot of the series, correlograms of auto correlation (ACF) and partial autocorrelation (PACF). An empirical time series patterns can be sufficiently approximated using one of the five basic models that can be identified based on the shape of ACF and PACF. Also, the number of parameters of each kind is almost never greater than two; it is often practical to try alternative models on the same data.
Modelling process is as follows 3. Modelling Process In the first stage, the initial identification of a time series in terms of stationarity is made through checking the function of autocorrelation (ACF) and partial autocorrelation (PACF). The fact that in stationary processes the autocorrelation function decreases (as a rule, quite rapidly) is used to
Modelling process is as follows 3. Modelling Process In the first stage, the initial identification of a time series in terms of stationarity is made through checking the function of autocorrelation (ACF) and partial autocorrelation (PACF). The fact that in stationary processes the autocorrelation function decreases (as a rule, quite rapidly) is used to
Model identification involved the following steps : (1) determine the which model should be adopted, AR (p), MA (q) or ARIMA (p,d,q) and (2) determine the value of p, d and q. The above identifica- tion depends on the ACF & PACF properties. The table given below indicate the criteria of order determination. The analysis of Fig 4 & Fig 5 indicated that the ARIMA (p,d,q) model is appropriate. Now to finalize appropriate ARIMA (p,d,q) model, we need to decide how many autoregressive (p) and moving average (q) parameters are necessary to develop the effective model. To identify the number of parameters we need to use plot of series, correlograms of auto correlation (ACF) and partial autocorrelation (PACF)
Model identification involved the following steps : (1) determine the which model should be adopted, AR (p), MA (q) or ARIMA (p,d,q) and (2) determine the value of p, d and q. The above identifica- tion depends on the ACF & PACF properties. The table given below indicate the criteria of order determination. The analysis of Fig 4 & Fig 5 indicated that the ARIMA (p,d,q) model is appropriate. Now to finalize appropriate ARIMA (p,d,q) model, we need to decide how many autoregressive (p) and moving average (q) parameters are necessary to develop the effective model. To identify the number of parameters we need to use plot of series, correlograms of auto correlation (ACF) and partial autocorrelation (PACF)
Autocorrelations of Frequency of Thunderstorms in Bangladesh (1980 -2016)
Autocorrelations of Frequency of Thunderstorms in Bangladesh (1980 -2016)
As per the results listed in Table 2, it can be seen that the smooth R-square represents the estimation value of the total variation explained by the models, and the larger the value, the better the fitting degree. MAPE represents the average absolute percentage error. The smaller the value of MAPE the better model is. Also, one of the best criteria used for evaluation of model, the smaller the value of normalize BIC, the better it is. It is quite obvious that, the final model will be different wi different evaluation criterion. So considering the model fitting degree of the history data, i.e. using the MAPE and normalize BIC, we choose ARIMA (0,1,1) model. uP th
As per the results listed in Table 2, it can be seen that the smooth R-square represents the estimation value of the total variation explained by the models, and the larger the value, the better the fitting degree. MAPE represents the average absolute percentage error. The smaller the value of MAPE the better model is. Also, one of the best criteria used for evaluation of model, the smaller the value of normalize BIC, the better it is. It is quite obvious that, the final model will be different wi different evaluation criterion. So considering the model fitting degree of the history data, i.e. using the MAPE and normalize BIC, we choose ARIMA (0,1,1) model. uP th
Comparison of these models using SPSS is given below in table 2
Comparison of these models using SPSS is given below in table 2
7. Model Validation The parameters of ARIMA (0,1,1) (simple exponential smoothing) model can be evaluated by SPSS and are represented under in table 3. The model can be as follows:
7. Model Validation The parameters of ARIMA (0,1,1) (simple exponential smoothing) model can be evaluated by SPSS and are represented under in table 3. The model can be as follows:
Figure-7: Plot of observed and predicted values of thunderstorms in Bangladesh(1980-2022). Table 4: Thunderstorm forecasting in Bangladesh from 2017 to 2022
Figure-7: Plot of observed and predicted values of thunderstorms in Bangladesh(1980-2022). Table 4: Thunderstorm forecasting in Bangladesh from 2017 to 2022

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lkj lkj lkj lkj & xtZ okys Hkh"k.k rw Qkuks a ls gkus okyh {kfr ls cpko ,oa jks dFkke ds fy, bu rw Qkuks a dk igys gh irk yxkuk vkS j iw okZ uq eku fd;k tkuk vko';d gS A 1995&1999 rd ds o"kks Z a ds ebZ ,oa tw u ekg ds fnYyh ds rkieku ds ¼Vs EIk½ vk¡ dM+ ks a dks ys rs gq , ba MfDVo e'khu yfuZ x rduhd dk mi;ks x djrs gq , fupyh vkS j Åijh Lrj ij gks us okyh leL;k dks le>rs gq , Lor% Kkr djus okyh rduhd ls xtZ okys rw Qkuks a ds iw okZ uq eku djus dh rduhd dk mi;ks x djrs gq , if'peks Rrj Hkkjr es a eq [; 'kgj fnYyh es a ekulw u iw oZ _rq ds nkS jku xtZ okys rw Qkuks a dk iw okZ uq eku djus ds fy, Hkkjr es a igyh ckj ,DliVZ flLVe QkW j Fka MjLVª ke QkjdkfLVa x ¼bZ-,l-Vh-,Q-½ fodflr dh xbZ gS A blds fy, 0000 ;w-Vh-lh-ij fnYyh ds lrg ds 850] 700] 500] vkS j 300 gs-ik-Lrjks a ds ds oy rkieku ¼Vs Ei½ vk¡ dM+ ks a dh iz fof"V vko';d gS A ;s fu;e LFkkf;Ro ?kkrka dks a ,oa vU; rkih; xfr iz kpyks a ij vk/kkfjr gS ftldh x.kuk bl 'kks /k&i= es a crk, x, lkmf.Ma x ls dh xbZ gS A bl iz .kkyh ls xtZ okys rw Qkuks a ds dkj.k fnYyh es a gks us okyh tyok;fod lw puk,¡ Hkh iz kIr gq bZ gS A bZ-,l-Vh-,Q-dh oLrq fu"B rduhdks a ds lkFk rq yuk djds fnYyh es a ekulw u&iw oZ _rq ds ebZ vkS j tw u ds eghuks a es a xtZ okys rw Qku ds iw okZ uq eku ds fy, gk¡ vFkok ugha iz dkj dh xR;kRed&lk¡ f[;dh; i)fr;k¡ fodflr dh xbZ a gS A bu i)fr;ks a dks xz kfQdy fMfLØfeus 'ku iz .kkyh ,oa cgq lekJ;.k iz .kkyh rFkk blh iz dkj ds vU; vk¡ dM+ k lew gks a dk mi;ks x djrs gq , fodflr fd;k x;k gS tS ls %& fnYyh es a 1995&1999 rd ds o"kks Z a es a ebZ ,oa tw u ds eghuks a ds rkieku ¼Vs Ei½ vk¡ dM+ ks a vkS j bZ-,l-Vh-,Q-ds fodkl es a mi;ks x fd, x, leku foHko ds iw oZ lw pdks a dk mi;ks x cgq lekJ;.k iz .kkyh es a Øekxr tk¡ p iz fØ;k ds va rxZ r iz kpyks a dk egRoiw .kZ LFkku ik;k x;k gS A bl 'kks /k i= es a o"kZ 2000&2001 ds ebZ vkS j tw u ekg ds vyx&vyx vk¡ dM+ k lew gks a ls fodflr dh xbZ rhu iz .kkfy;ks a dh tk¡ p dh xbZ gS A xz kfQdy fMfLØfeus 'ku iz .kkyh] cgq lekJ;.k rduhd rFkk bZ-,l-Vh-,Q-}kjk tkjh fd, x, iw okZ uq ekuks a dks iz kpyks a ds lR;kiu ds lkFk rq yuk djus ij ns [kk x;k gS fd cgq lekJ;.k iz .kkyh ls iz kIr fd, ifj.kke xz kfQdy fMfLØfeus 'ku iz .kkyh ls iz kIr fd, x, ifj.kke ls cs grj ik, x, gS a A bZ-,l-Vh-,Q-ds mi;ks x ls iz kIr fd, ifj.kke xR;kRed LFkS frd ekW MYl ds mi;ks x ls iz kIr fd, x, ifj.kke ls cs grj ik, x, ga S A ABSTRACT. Early detection and forecasting of thunderstorms is important in safeguarding and prevention of damages resulting from violent thunderstorms. An Expert System for Thunderstorm Forecasting (ESTF) during premonsoon season over Delhi the representative location over northwest India has been developed for the first time in India by using technique of approaching the problem "bottom up" by using inductive machine learning techniques to automatically acquire the knowledge about thunderstorm forecasting from the weather development data set consisting of TEMP data of Delhi for the months of May and June for the years from 1995-1999. Only input required is the entry of 0000 UTC TEMP data of Delhi at surface, 850, 700, 500 and 300 hPa levels. The rules are based on stability indices and other thermodynamic parameters evaluated from the said sounding. The system also provides climatological information about thunderstorms over Delhi. To compare the ESTF with the objective techniques, Dynamical-statistical methods for yes or no type thunderstorm occurrence forecast over Delhi during pre-monsoon months of May and June have been developed by using graphical discrimination method and multiple regression method and by using the same development data set i.e., TEMP data of Delhi for the months of May and June for the years from 1995-1999 and by using the same potential predictors as used in development of ESTF. In multiple regression method the parameters were found to be significant by stepwise screening procedure. The three methods developed were tested with independent data sets of May and June for the years from 2000-2001. Comparison of verification parameters of the forecast issued by Graphical Discrimination method, Multiple Regression Technique and by ESTF indicates that results of multiple regression method are better than those of graphical discrimination method. The results obtained by using ESTF were better than those obtained by using dynamical statistical models.

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ASSESSING THE IMPACTS OF THUNDERSTORM AND CORRELATION WITH TEMPERATURE: A STUDY ON NORTHEASTERN BANGLADESH
Md. Yousuf Mia

Thunderstorms are particularly disruptive in Bangladesh, with lightning, gusty winds/squalls, hail of varied sizes, and frequently intense rains. Lightning and thunderstorms have frequently been recorded in past few years, producing destructive sounds and causing fatalities. The study is attempting to determine the relationship between maximum temperature and thunderstorms in Northeastern Bangladesh more specifically in Sylhet division. Thunderstorms are more common in Northeastern Bangladesh than in any other region of the country. This study is an example of analytical-based research that focuses on trend analysis, spatial analysis, and the relationship between thunderstorms and temperature. In the study region, 200 participants were chosen for a structured questionnaire to assess the effects of thunderstorms and lightning. Thunderstorms are becoming more frequent and severe in the study area on a regular basis. The correlation between maximum temperature and thunderstorm activity is highly positive in Pre-monsoon season (0.842 in Sylhet and 0.630 in Srimangal) and negative in winter season (-0.117 in Sylhet and -0.213 in Srimangal). It is found positive correlation annually in the study area (0.344 in Sylhet and 0.177 in Srimangal). The survey results suggest that the participants in the study are unaware about the causes of thunderstorms. Most individuals are affected by health issues, agricultural issues, environmental issues, social problems, infrastructural degradation, and so on. Rising thunderstorm trends may be attributed to global warming, local variables such as industrialization, degradation, forest conservation, or any other geographical changes. Keywords: Thunderstorms, Lightning, Temperature, Bangladesh, Trend analysis, Spatial analysis, Correlation

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Forecasting of thunderstorms in the pre-monsoon season at Delhi
Ajit Tyagi

Meteorological Applications, 1999

Accurate prediction of thunderstorms during the pre-monsoon season (April-June) in India is essential for human activities such as construction, aviation and agriculture. Two objective forecasting methods are developed using data from May and June for 1985-89. The developed methods are tested with independent data sets of the recent years, namely May and June for the years 1994 and 1995. The first method is based on a graphical technique. Fifteen different types of stability index are used in combinations of different pairs. It is found that Showalter index versus Totals total index and Jefferson's modified index versus George index can cluster cases of occurrence of thunderstorms mixed with a few cases of non-occurrence along a zone. The zones are demarcated and further sub-zones are created for clarity. The probability of occurrence/non-occurrence of thunderstorms in each sub-zone is then calculated. The second approach uses a multiple regression method to predict the occurrence/nonoccurrence of thunderstorms. A total of 274 potential predictors are subjected to stepwise screening and nine significant predictors are selected to formulate a multiple regression equation that gives the forecast in probabilistic terms. Out of the two methods tested, it is found that the multiple regression method gives consistently better results with developmental as well as independent data sets; it is a potential method for operational use.

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TIME SERIES ANALYSIS, MODELING AND FORECASTING OF CLIMATE VARIABLE RAINFALL: A CASE STUDY OF RAJSHAHI DISTRICT IN BANGLADESH
Md. Monimul Huq, Md. Abu Shahin

The purpose of the present study was to investigate the time series components, and to build an appropriate model to forecasttherainfall of Rajshahi district in Bangladesh using the monthly rainfall data over January, 1975 to June, 2012 collected from Bangladesh meteorological department.The statistical software R with the packages 'forecast' and 'zyp' was used for whole analysis. The descriptive statistics of rainfall showed high fluctuation from their mean, positively skewed and platykurtic curve. The time series rainfall data was decomposedinto stochastic trend, seasonal variations and random movements. The yearly rainfall data showed decreasing trend by 11.25 mm/year. The moving average smoothing of monthly rainfall intended to be decreased over May, 2007 to June, 2012. But, after first seasonal difference, the rainfall data became stationary and that wasconformed using appropriate tests. The SARIMA(0, 0, 0)(4, 1, 0) 12 model was found as best model on the basis ofdiagnostic test, stability and reliability. The forecasted values from July, 2012 to December, 2025 divulged adecreasing pattern that may be a threat to the cultivators as well as to the nature as a whole.

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