Location, geography, and climatic condition of the study area
The study area, Dinajpur district, is in Bangladesh's northwestern hydrological zone. The study area's location is between 25010' and 26004' north latitudes and 88023' and 89?23' east longitudes. Usually, the climate of Dinajpur District is warm and temperate. The district experiences a wet, hot, and humid tropical climate. According to the Köppen Climate classification, the environment of Dinajpur is humid subtropical. It has a remarkable monsoon period. The annual average temperature is 250C (77?F). The summer receives more rainfall than the winter, and the average rainfall reported herein is 1728 mm.
Criteria for the determination of arrival dates of monsoon in Dinajpur
Bangladesh Meteorological Department fixes 1 June as the monsoon arrival date for Bangladesh (Ahasan et al., 2010). However, it is not feasible to clarify the exact date of monsoon arrival date (Das 1986). Ahmed and Karmakar (1993) provided some criteria for identifying the monsoon onset date in Bangladesh. According to their study, two variables- rainfall amount and wind vector- are considered to determine monsoon rainfall's arrival date in Bangladesh. For getting a brief idea of the arrival dates, the daily rainfall (April, May) and wind vector (May) of Dinajpur in 2000 are elucidated in Figure 2. The following criteria are followed to identify the monsoon arrival date of the Dinajpur district from previous studies. the first day of three or more consecutive days having 5 mm or more rainfall along with the southerly or southeasterly winds for the rest of the season.
Criteria for the determination of withdrawal dates of monsoon in Dinajpur
Ahmed and Karmakar (1993) mentioned that the monsoon's withdrawal starts in the reverse direction to the arrival. Moreover, detecting the withdrawal date is more complicated than the arrival date in Bangladesh. However, they provided some criteria for identifying the withdrawal dates of monsoon rainfall. For getting a brief idea of the withdrawal dates, the daily rainfall (September, October) and wind vector (September) of Dinajpur in 2000 are elucidated in Figure 3. The following criteria are followed to identify the monsoon withdrawal date in the Dinajpur district: the last day of three or more consecutive days having 5 mm or more rainfall along with the north-westerly or northerly wind for the rest of the time.
Data collection and analysis
Daily rainfall (mm) and wind speed (knots) data of 30 years (1986 to 2015) have been collected from Bangladesh Meteorological Department (BMD) station in Dinajpur. Correction for missing data was done in exceptional cases. To determine the arrival and withdrawal dates, the monsoon onsets calculate considering the first date of Julian pentad (Lau and Yang 1997). Thirty numbers of arrival and withdrawal dates were obtained by analyzing the initial data by following the criteria set by Ahmed and Karmakar (1993). In 1987, 2000, and 2003 the arrival dates were obtained before May. In this circumstance, the dates were not considered, though they fulfill the criteria. Only the dates with arrival after 1 May were accepted. The wind directions are considered the standards likewise because it is a natural phenomenon. The trend of arrival and withdrawal of monsoon rainfall was observed by plotting the data in graphs. Then the shifting of monsoon rainfall has been calculated by considering 1986 as the baseline. Furthermore, in order to perform a detailed probabilistic analysis of monsoon rainfall, the earliest and latest arrival dates for the future of 1 year out of 4, 10, and 25 years were taken into consideration. Such approaches were also applied in the case of probabilistic withdrawal dates. For establishing the probabilistic arrival and withdrawal dates, the data must be distributed normally. The data were tested for normal distribution using Statistical Package for the Social Sciences (SPSS) software. In addition, to estimate the probabilistic arrival and withdrawal dates of monsoon rainfall, the mean rainfall (X), standard deviation (σ), and the number of observation (n) dates were computed. By applying the Z-score formula, probabilistic dates of arrival and withdrawal of the monsoon of Dinajpur district over expected time-scales obtained. However, to find out the probabilistic arrival and withdrawal dates of the monsoon, the following equation has been used. Xp = X + Zσ. Here, Xp is the probabilistic estimated date of arrival or withdrawal of monsoon rainfall. This method is used in this study to obtain the probabilistic dates of the arrival and withdrawal of the monsoon over three different time-scales. (i) Arrival or withdrawal date in 1 year out of 4 years that gives frequent event. It can be expressed as Xp = X ± 0.67σ. (ii) Arrival or withdrawal date in 1 year out of 10 years that gives a less frequent event. It can be expressed as Xp = X ± 1.28σ. (iii) Arrival or withdrawal date in 1 year out of 25 years that gives a least frequent event. It can be expressed as Xp = X ± 1.75σ. The value of Z is obtained from the Z score percentile table. In this study, the data were analyzed primarily with Microsoft Excel and IBM SPSS Statistics. In addition, Python modules NumPy (Walt et al., 2011), Pandas (McKinney, 2010), and Matplotlib (Hunter, 2007) along with Excel were applied to visualize the resultant data in this study.