Forecasting of Humidity of Some Selected Stations from the Northern Part of Bangladesh: An Application of SARIMA Model

Corresponding Author: Md. Moyazzem Hossain Department of Statistics, Jahangirnagar University, Savar, Dhaka-1342, Bangladesh Email: mmhmm.justat@gmail.com Abstract: Community risk from natural hazards and climate change depends largely on physical and climatic settings of an area, socioeconomic condition of a community and the magnitude, duration and consecutiveness of the hazard or change itself. Impacts of climate change can be characterized by increasing temperatures, rainfall, humidity changes and climate related extreme events such as floods, cyclone, droughts, sea level rise, salinity and soil erosion etc. Humidity affects crops through evaporation, transpiration and condensation. Crop agriculture is highly influenced by climatic change and majority of population is dependent on agricultural crop in Bangladesh. Any unfavorable change in future climate could have a devastating impact on agriculture and the economy of the country. It is needed to know the socio-economic settings of the rural community, their agricultural practices, anticipated changes in climatic parameters and the link between the climatic variables and crop growth and productivity. Time Series analysis and forecasting has become a major tools in different applications in meteorological phenomena, such as rainfall, humidity, temperature, draught etc. and environmental management fields. Among the most effective approaches for analyzing time series data is the Autoregressive Integrated Moving Average (ARIMA) model introduced by Box and Jenkins. In this study, we used Box-Jenkins methodology to build seasonal ARIMA model for monthly Humidity data taken from Bogra, Dinajpur, Rajshahi and Rangpur stations over the period January, 2001 to October, 2014. In this study, ARIMA (2,0,2)(2,1,2)12, ARIMA (0,1,2)(1,1,1)12, ARIMA (1,0,2)(2,1,1)12 and ARIMA (1,0,2)(2,1,2)12 model respectively are found to be suitable models for Dinajpur, Rajshahi, Bogra and Rangpur stations respectively and these models are used to forecasting the monthly humidity for the upcoming two years to help decision makers to establish priorities in terms of water demand management.


Introduction
Climate may be defined as a complex of meteorological conditions, which exists in any given area. Climate of a place plays important role in water resources management, crop management, operations of dams and generation of hydroelectricity planning of location of industrial sites, defense planning, tourism and transport, air pollution studies and in fact almost all spheres of human activity. Bangladesh occupies an area of 144,430 sq. kilometers between latitudes 20°35'N and 26°75'N longitudes 88°3'E and 92°75' E. Climatology deals with the spatial distribution of average values of climatic elements, e.g., temperature, rainfall, pressure and winds, humidity, evapotranspiration and evaporation etc. and their relation to man's activities. Community risk from natural hazards and climate change depends largely on physical and climatic settings of an area, socioeconomic condition of a community and the magnitude, duration and consecutiveness of the hazard or change itself. Assessment of such risk must require credible information on existing climate and its trend and the future climate and its variability. The information on future climate and its variability is usually obtained from general circulation and regional climate model projection. However, the information on existing climate and its trend is derived either from the analysis of the observed historical data or from the community perception and experience (Mondal et al., 2012). Bangladesh is confronted with a big challenge to mitigate the significant impact of climate change. Due to the climate change, Bangladesh has already experienced average maximum temperature rising, minimum temperature decreasing, rainfall, relative humidity and cloud coverage decreasing resulting frequent and severe floods, tropical cyclone, extensive river bank erosion and drought. Impacts of climate change can be characterized by increasing temperatures, rainfall, humidity changes and climate related extreme events such as floods, cyclone, droughts, sea level rise, salinity and soil erosion etc (Asaduzzaman et al., 2010;Yu et al., 2010).
Humidity is the amount of Water vapor in the air and relative humidity considers the ratio of the actual vapor pressure of the air to the saturated vapor pressure which is usually expressed in percentage. Atmospheric water vapor is a complex meteorological element. It is a fundamental component in the climate system as the most significant greenhouse gas and a key driver of many atmospheric processes. Water vapor and its transport around the atmosphere is a fundamental component of the hydrological cycle. The vapor plays a key role in determining the dynamic and radioactive properties of the climate system. Atmospheric water vapor accounts for only about 1/10,000th of the total amount of water in the global hydrological cycle. Nevertheless, atmospheric water vapor is one of the most important factors in determining Earth's weather and climate, because of its role as a greenhouse gas and because of the large amounts of energy involved as water changes between the gaseous (vapor) phase and liquid and solid phases. Humidity is very important as an environmental condition which influences the growth of the plants, health, pollution etc. For example, plants also respond to changes in humidity. Humidity affects crops through evaporation, transpiration and condensation. Crop agriculture is highly influenced by climatic change and majority of population is dependent on agricultural crop in Bangladesh. Crop agriculture is the mainstay of Bangladesh and will continue to be so in the foreseeable future. About 60.1% of the area is presently under agriculture and the sector contributes about 22% to the GNP. Any unfavorable change in future climate could have a devastating impact on agriculture and the economy of the country. It is needed to know the socioeconomic settings of the rural community, their agricultural practices, anticipated changes in climatic parameters and the link between the climatic variables and crop growth and productivity. The cropping practices again vary according to geographical locationsthe practices are different in haors, coasts, central floodplains and uplands. Field level information is necessary to identify the vulnerability of different crops in different locations at different times (Mondal et al., 2012). High humidity in tropics, particularly during the rainy season is likely to affect the plant growth by reducing the transpiration cooling of the plant. The lowering of the yield with the increase in maximum and minimum daily relative humidness may be related to this effect. This hypothesis is further supported by the fact that low humidity is one of the important agrometeorological environmental factors for maximum rice production (De Datta and Zarate, 1970).
Bangladesh is predominantly an agricultural country. The cultivation mainly depends on natural calamities like rainfall, humidity and temperature. But in-depth statistical analysis did not carry out yet on humidity and its relationship with other atmospheric components like temperature and rainfall. Humidity is one of the most valuable components of air, which is very important for tree plantation as the atmospheric moisture levels do significantly influence on plant growth and development. The prediction of atmospheric parameters is essential for climate monitoring, drought detection, severe weather prediction, agriculture and production, planning in energy and industry, communication, pollution dispersal etc. Accurate prediction of Humidity is a difficult task due to the dynamic nature of the atmosphere. It is very much essential to know the nature of changes of Humidity. Purposively we select four stations for this study from the northern part of Bangladesh namely Dinajpur, Rajshahi, Rangpur and Bogra stations over the period January, 2001-October, 2014. Box-Jenkin's Methoology is used to identify the appropriate ARIMA model for the humidity of the selected stations and the selected model is used to forecast the humidity of the selected stations. The necessary secondary data have been taken from the website of "Bangladesh Agricultural Research Council (BARC)". This analysis has completely done by statistical programming based open source Software named as R with the version 3.1.2.

Literature Review
Bangladesh is predominantly an agricultural country. Since the irrigation system in Bangladesh has not yet been implemented vigorously, the cultivation mainly depends on natural calamities like rainfall, humidity and temperature. But in-depth statistical analysis did not carry out yet on humidity and its relationship with other atmospheric components like temperature and rainfall. Humidity is one of the most valuable components of air, which is very important for tree plantation as the atmospheric moisture levels do significantly influence on plant growth and development (Tibbitts, 1979). Islam (2014) carried out a study to find Trends, periodicities and frequency distribution of the annual average humidity by using the standard statistical techniques. He considered the annual average humidity of 30 meteorological stations of Bangladesh over the period . He has done the test of normality of the frequency distribution of the annual average humidity using the method suggested by Geary (1935Geary ( , 1936. He found that the frequency distribution of most of the stations of Bangladesh follow normal distribution. Positive trends are shown for the data of Dinajpur, Rajshahi, Mymensingh, Ishurdi, Jessore, Madaripur, Satkhira, Hatiya, Sitakunda, Teknaf and Patuakhali, while Dhaka the capital of Bangladesh has negative trend. The periodigram analyses of the annual average humidity of most of the stations show a significant cycle of range 8 to 12 years. Abu-Taleb et al. (2007) examines the recent changes in annual and seasonal relative humidity variations in Jordan. Their analysis indicates an increasing trend in relative humidity at different stations. Their analysis also shows a significant increasing trend at Amman Airport Meteorological (AAM) station with a rate of increase 0.13% per year. These increasing trends are statistically significant during summer and autumn seasons. Finally, they found that a major change point in the annual relative humidity occurred in 1979 at AAM station. Syeda (2012) investigates the trend and variability pattern for decadal, annual and seasonal (three crop seasons) Average Relative Humidity (ARH) of six divisional stations in Bangladesh: Dhaka, Rajshahi, Khulna, Barisal, Sylhet and Chittagong. She examined the rates of Linear Trend (LT) for minimum, maximum and range humidity. To forecast the monthly ARH for 2009-2012 she used the univariate Box-Jenkin's Autoregressive Integrated Moving Average (ARIMA) modelling technique. The findings of her research were as follows: The rates of LT for annual ARH were found negative for Dhaka and Chittagong but positive for others. The rates were found negative for all the Coefficient of Variations (CVs). The rate for annual minimum humidity was positive for Dhaka but negative for others. The rates for annual maximum and range humidity were negative for Dhaka and Chittagong but positive for others. The rates for seasonal ARH were negative for Dhaka while positive for Rajshahi and Barisal in all the three seasons. It was negative for Kharif season, whereas positive for Prekharif and Rabi seasons for Khulna and Sylhet. It was negative for Kharif and Prekharif seasons, as the same time as positive for Rabi season for Chittagong. Chowdhury and Hossain (2011) were carried out a study during 2005-08 to find the effect of weather prevalence of seedling diseases of jackfruit in different areas of Bangladesh and develop an environment friendly disease management practice. They found that Occurrence of seedling diseases was significantly influenced by temperature, rainfall and relative humidity. Keka et al. (2013) found the characteristics of different climatic parameters and the recent climatic trends in Bangladesh by using the surface climatological data at 30 stations for the period of 34 years from 1971 to 2004. Mondal et al. (2013), shown that the relative humidity at Khulna has increasing trends of 2.3, 1.3 and 0.3% per decade in the winter, post-monsoon and pre-monsoon seasons, respectively.

Methods and Materials
Seasonal ARIMA Box and Jenkins (1976) suggested the use of Seasonal Autoregressive (SAR) and Seasonal Moving Average (SMA) terms for monthly or quarterly data with systematic seasonal movements. The Box-Jenkins approach for modeling and forecasting has the advantage in analyze the seasonal time series data. In this case the seasonal components are included and the model is called seasonal ARIMA model or SARIMA model. A seasonal ARIMA model is classified as: In the Seasonal ARIMA model the lowercase for non-seasonal part meanwhile the uppercase for seasonal part can be written in form of:

Results
Four stations namely Bogra, Dinajpur, Rajshahi and Rangpur district were considered in this study from the northern part of Bangladesh. The first step of time series analysis is to make the time series plot of the data. Such a plot gives preliminary idea about the nature of the time series. Time series plot can also be used to find the Seasonality, Cyclical variation, trend or irregular pattern of the series.
From Fig. 1a-d it appeared that the series is stationary; that is, mean is constant as time increases and we do not take any additional difference. In this study Augmented-Dickey-Fuller (ADF) unit root test was used to check whether the data series is stationary or not.   Table 1 revealed that the seasonal variation is present in humidity of Bogra, Dinajpur, Rajshahi and Rangpur district. Thus it is necessary to take a seasonal difference. However, it is clear that first seasonal differenced data series shows stable variance for all stations which implies that the data becomes stationary for all stations considered in this study. The seasonally differenced data are shown in Fig. 2. Figure 2a shows that there are significant spikes in the PACF at lags 12 and 24, but nothing at seasonal lags in the ACF. This may suggest a seasonal AR (2) model. In the non-seasonal lags, there are three significant spikes in the PACF suggesting a possible AR (3) model. The pattern in the ACF is not indicative of any simple model. Consequently, this initial analysis suggests that the possible model for these data is an ARIMA (3,0,0)(2,1,0) 12 . Figure 2b shows that there is a significant spike on PACF at lag 12, 24 and 36. This may be suggestive of a seasonal AR (3) term. In the nonseasonal lags, there are three significant spikes in the PACF suggesting a possible AR (3) term. This initial analysis suggests that a possible model for these data is an ARIMA (3,0,0)(3,1,0) 12 . Again, from Fig. 2c it is clear that there are significant spikes at lag12, 24 and 36 but nothing at seasonal lags in the ACF. This may be suggestive of a seasonal AR (3) term. In the nonseasonal lags, there are one significant spikes in the PACF suggesting a possible AR (1) term. Consequently, this initial analysis suggests that a possible model for these data is an ARIMA (1,0,0)(3,1,0) 12 . Furthermore, Fig. 2d shows that there are significant spikes at lag 12, 24 and 36 but nothing at seasonal lags in the ACF. This may be suggestive of a seasonal AR (3) term. In the nonseasonal lags, there are three significant spikes in the PACF suggesting a possible AR (3) term. Consequently, this initial analysis suggests that a possible model for these data is an ARIMA (3,0,0)(3,0,1) 12 .
The graphical comparison of the original series and the forecasted series is shown in Fig. 4. It is apparent that the forecasted series (blue-color) fluctuate from the original series (pink-color) with a very small amount of variation. So the forecasted series is really better representation of the original humidity of Bogra, Dinajpur, Rajshahi and Rangpur district.

Conclusion
The prediction of atmospheric parameters is essential for climate monitoring, drought detection, severe weather prediction, agriculture and production, planning in energy and industry, communication, pollution dispersal etc. Accurate prediction of Humidity is a difficult task due to the dynamic nature of the atmosphere. It is very much essential to know the nature of changes of Humidity. In this study, ARIMA (2,0,2)(2,1,2) 12 , ARIMA (0,1,2)(1,1,1) 12 , ARIMA (1,0,2)(2,1,1) 12 and ARIMA (1,0,2)(2,1,2) 12 model respectively are found to be suitable models for Dinajpur, Rajshahi, Bogra and Rangpur stations respectively and these models are used to forecasting the monthly humidity for the upcoming two years to help decision makers to establish priorities in terms of water demand management.