Probability analysis of monthly rainfall on seasonal monsoon in Pakistan

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 34: (14) Published online May 13 in Wiley Online Library (wileyonlinelibrary.com) DOI: 1.12/joc.3725 analysis of monthly rainfall on seasonal monsoon in Pakistan Ishfaq Ahmad, a * Iram Mahmood, b Imran Riaz Malik, c Irshad Ahmad Arshad, a Ehtasham ul Haq a and Zahid Iqbal a a Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan b School of Chemical and Materials Engineering, National University of Sciences and Technology, Islamabad, Pakistan c Institute of Management Sciences, Peshawar, Pakistan ABSTRACT: Pakistan experiences the southwest monsoon normally from July to September every year. In this paper, we analyse the effect of monthly rainfall for the months of July, August and September on overall seasonal monsoon for the period of 19 6 across 37 different meteorological stations of Pakistan. The statistical results are based on the notion of conditional probability. We find conditional probabilities of seasonal monsoon to be in excess, deficient and normal when the monthly rainfall of July, August and September is considered to be in excess and deficient. When rainfall in the months of July and August is in excess the seasonal monsoon behaviour is also likely to be in excess and probabilities of seasonal monsoon to be deficient are zero for most of the meteorological stations. Similarly, when rainfall in the months of July and August is considered to be deficient the seasonal monsoon behaviour is also likely to be deficient and probabilities of seasonal monsoon to be in excess are zero for most of the meteorological stations. KEY WORDS conditional probability; deficient; excess; monsoon Received 5 May 12; Revised 18 January 13; Accepted 19 April Introduction Generally, the climate of Pakistan is of diverse nature throughout the country. Pakistan is located from southwest to northwest at north latitude and east latitude. Summer monsoon s season in subcontinent is of great importance for its agricultural, economic and social needs, for example, see Reeve (1996); Kothawale and Munot (1998); Parida (1999). In Pakistan monsoon contributes almost 65 75% of the total annual rainfall. Monsoon occurs normally in many parts of world such as northern Australia, Africa and South America. But these rains are especially strong in south Asian countries including Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan and Sri Lanka. In Sri Lanka Southwest monsoon season enters in late May just before it enters the Indian subcontinent. In India it enters in June and in Pakistan in early July and remains till the end of September. From July to September, most parts of the country have monsoon season (Akhlaq et al., 7). Despite of some destruction in the form of droughts and floods, monsoon season is welcomed in the country owing to its importance for agricultural and water needs in the country. Farmers depend upon * Correspondence to: I. Ahmad, Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan. Ishfaq.ahmad@iiu.edu.pk these rains to irrigate their lands, and also great deal of Pakistan s electricity is generated by water provided by these rains. Over much of Asia, the summer monsoon can be divided into cycles of rainy and dry periods, following a roughly days cycle (Lawrence and Webster, 1; Webster and Hoyos, 4; Hoyos and Webster, 7. Heavy rains in July and August caused floods in KPK (Khyber Pakhtun Khah) province, Punjab province and some areas of Sindh province of Pakistan. Furthermore, deforestation in southern Pakistan has been severe and also causes a heavy rain during the month of July and early August (Ali et al., 6). In Pakistan there are many studies which deal with rainfall data in different aspects, for example, Rasul et al. (4) carried out a diagnostic study of record heavy rain in twin cities of Pakistan, Rawalpindi and Islamabad. Klein et al. (8) investigated prospects of downscaling for seasonal precipitation prediction over Pakistan. Haroon and Rasul (9) applied the very common multivariate principal component analysis in order to identify the major modes of oscillations present in the data. Rasul et al. (9) examined the heavy monsoon precipitation over the Indus plains of south Asia using the non-hydrostatic numerical model MM5. In this paper, we have used the notion of conditional probability to see the effect of rainfall of different months, i.e. July, August and September on overall seasonal monsoon. We can perform regional analysis as well as stations-based 13 Royal Meteorological Society

2 828 I. AHMAD et al. analysis of the rainfall data. The regional analysis is sometimes important when our objective is to find the results about whole province or country. In this article we have focused on station-based analysis. As monsoon season is not homogeneous in all cities of Pakistan, we included only those stations which are most likely to experience this season. For example, see Parida (1999) and Reeve (1996). The other reason for performing station-based analysis is related to policy implication such as formation of water reservoirs in future. When we have to make some policies it is more helpful if we have information about different stations at individual level. The remaining of the paper is organized as follows: Section 2 is about data description and methodology, Section 3 presents discussion and evaluation, and Section 4 concludes the paper. 2. Data description and methodology We have used data of seasonal and monthly rainfall of 37 different meteorological stations. The data has been collected from Pakistan Meteorology Department (PMD). The meteorological stations were selected taking into account the criteria of completeness, length and homogeneity in order to cover most of the country with respect to monsoon season. The monthly rainfall (mm) as well as monsoon seasonal rainfall, which is the total of monthly rainfall of July, August, and September, are not symmetric. In case of symmetric data we can use usual mean, standard deviation or coefficient of variation for descriptive information to measure central tendency and variation in the data. The rainfall data having lack of symmetry and the use of arithmetic mean and usual standard deviation to define classes is not appropriate, as they are highly influenced by extreme observations. Generally, there are two approaches to deal with rainfall data. The first approach uses percentiles or quartiles, and the second approach deals with the rainfall data using a statistical model Parida (1999) and Reeve (1996), Stern and Coe (1984), Hosking et al. (1985), Hosking and Wallis (1997). In this paper, we use the first approach to deal with our monthly and seasonal rainfall data. First of all, we sorted the monthly and seasonal monsoon data, and derived the first and third quartiles for each of them. If the rainfall of any month i.e July, August and September or season i.e total of these three months in millimetre was less than or equal to first quartile, we counted the specific month or season, a deficient month or deficient season in the given station corresponding to a particular year in the given period 19 to 6. If the given rainfall was greater than or equal to third quartile, we counted the specific month or season, a excess month or excess season in the given station corresponding to a particular year in the given period 19 to 6 and if the rainfall is between first and third quartiles then we say the given month or season a normal month or a normal season in the given station corresponding to a particular year in the given period 19 to 6. In this way, we can find the probabilities of being excess, deficient and normal for the months of July, August, September and monsoon season as well for any meteorological station in the given period. To check the individual effect of each month s rainfall or joint effect of two months rainfall on seasonal rainfall, we calculated the conditional probabilities of seasonal rainfall to be in excess, deficient and normal when monthly rainfall is in excess and deficient. These conditional probabilities can be calculated for individual months and also for more than 1 month. The mathematical formula of conditional probability for two events A and B is P ( A / B ) = P (A B) /P (B) where event A is considered to be as the seasonal rainfall and event B is considered to be as monthly rainfall. For example, to see the effect of July s rainfall to be in excess on seasonal rainfall, first, for the month of July, we should calculate the probabilities for those number of years, which are in excess in the month of July in a given station or in other words calculate the probabilities of being excess for the month of July in a given station corresponding to different years in the given period Then we should find the probabilities of being excess and deficient for seasonal rainfall. These are the simple probabilities telling about the percentage of number of years to be in excess and deficient in the monthly and seasonal data. To find the conditional probabilities, i.e. probabilities of seasonal monsoon to be in excess, deficient and normal when monthly rainfall is considered to be in excess, we should find the probabilities of those number of years which are in excess, in monsoon season and as well as in the month of July. The probabilities of these common number of years should be calculated. These common probabilities should be divided by the probabilities of number of years to be in excess only for the month of July. In this way we can get the conditional probabilities of monsoon season to be in excess when July s rainfall is in excess for the given period. Similarly, we can find the conditional probabilities for monsoon season to be deficient and normal when July s rainfall is in excess for the given period. For the months of August and September we can also perform similar probability analysis. These results are given in Table 1(a) for the months of July, August and September for different meteorological stations from 19 to 6. Similarly, we can find conditional probabilities for seasonal monsoon to be in excess, deficient or normal when monthly rainfall is considered to be deficient. These results are given in Table 1(b) for the months of July, August and September. Further, we have also found the joint effect of July and August on overall seasonal rainfall to be in excess, deficient and normal. These results have been given in Table 2. The same results of Tables 1 and 2 have also been presented in Figures Royal Meteorological Society Int. J. Climatol. 34: (14)

3 PROBABILITY ANALYSIS MONTHLY RAINFALL SEASONAL MONSOON IN PAKISTAN 829 Table 1. Conditional probabilities (%) of seasonal monsoon to be in excess, deficient and normal when monthly rainfall is considered to be in excess. (b) Conditional probabilities (%) of seasonal monsoon to be in excess, deficient and normal when monthly rainfall is considered to be deficient. a b July August September July August September Excess Deficient Normal Excess Deficient Normal Excess Deficient Normal Excess Deficient Normal Excess Deficient Normal Excess Deficient Normal Hyderabad Jacobabad Karachi Padidan Quetta Rohri Zhob Draosh Islamabad Kakul Kotli Lahore Multan Peshwar Resalpur Sialkot Badin Chor Nawabshah Punkgur Sibbi Astor Bahawalpur Bunji Chilas D. I. Khan Fas Abad Garhi Dupatta Gilgat Khanpur Kohaat Mianwali Muree Muzabad Parachinar Sargodha Sakardu Royal Meteorological Society Int. J. Climatol. 34: (14)

4 83 I. AHMAD et al. Table 2. Conditional probabilities (%) of seasonal monsoon to be in excess, deficient and normal when July and August both (a) are in (a) excess (b) deficient. (a) July and August (both are in excess) (b) July and August (both are in deficient) Excess Deficient Normal Excess Deficient Normal Hyderabad 1 Jacobabad 1 1 Karachi 1 Padidan Quetta Rohri Zhob 1 1 Draosh 1 Islamabad 1 1 Kakul Kotli 1 1 Lahore 1 1 Multan 1 1 Peshwar 1 1 Resalpur Sialkot 1 1 Badin 1 1 Chor 1 1 Dalbandin Jiwani Nawab Shah 1 Nokundi Punkgur Sibbi 1 1 Astor 1 1 Bahawalpur 1 1 Bunji Chilas 1 1 D. I. Khan 1 1 Fas Abad Gari Dupatta 1 1 Gilgat 5 5 Khanpur 1 Kohaat Mianwali 1 1 Muree 1 1 Muzabad 1 1 Parachinar 1 1 Sargodha 1 1 Sakardu Excess Normal Conditional Probabilities (%) of Seasonal Monsoon to be in Excess, Deficient and Normal when Rainfall in the month of July is in Excess Figure 1. Conditional probabilities of seasonal monsoon to be in excess, deficient and normal when rainfall in the month of July is in excess. 13 Royal Meteorological Society Int. J. Climatol. 34: (14)

5 PROBABILITY ANALYSIS MONTHLY RAINFALL SEASONAL MONSOON IN PAKISTAN 831 Probabilities Conditional Probabilities (%) of Seasonal Monsoon to be in Excess, Deficient and Normal when Rainfall in the month of August is in Excess Excess Deficient Normal Figure 2. Conditional probabilities of seasonal monsoon to be in excess, deficient and normal when rainfall in the month of August is in excess Conditional Probabilities (%) of Seasonal Monsoon to be in Excess, Deficient and Normal when Rainfall in the month of September is in Excess EXCESS DEFICIENT NORMAL GARI DUPATTA Figure 3. Conditional probabilities of seasonal monsoon to be in excess, deficient and normal when rainfall in the month of September is in excess Excess Deficient Normal Conditional Probabilities (%) of Seasonal Monsoon to be in Excess, Deficient and Normal when Rainfall in the month of July is Deficient Figure 4. Conditional probabilities of seasonal monsoon to be in excess, deficient and normal when rainfall in the month of July is deficient. 13 Royal Meteorological Society Int. J. Climatol. 34: (14)

6 832 I. AHMAD et al Conditional Probabilities (%) of Seasonal Monsoon to be in Excess, Deficient and Normal when rainfall in the month of August is Deficient Excess Deficient Normal Figure 5. Conditional probabilities of seasonal monsoon to be in excess, deficient and normal when rainfall in the month of August is deficient Conditional probabilities (%) of seasonal monsoon to be in Excess, Defiecient and Normal when Rainfall in the month of September is deficient DEFICIENT EXCESS NORMAL GARI DUPATTA Figure 6. Conditional probabilities of seasonal monsoon to be in excess, deficient and normal when rainfall in the month of September is deficient. 1 1 Excess Normal Conditional Probabilities (%) of Seasonal Monsoon to be in Excess and Deficient when rainfall in the both months (July and August collectively) is in Excess Figure 7. Conditional probabilities of seasonal monsoon to be in excess and deficient when rainfall in the both months (July and August collectively) is in excess. 13 Royal Meteorological Society Int. J. Climatol. 34: (14)

7 PROBABILITY ANALYSIS MONTHLY RAINFALL SEASONAL MONSOON IN PAKISTAN Deficient Conditional Probabilities (%) of Seasonal Monsoon to be in Excess and Deficient when rainfall in the both months (July and August collectively) is Defecient Normal Figure 8. Conditional probabilities of seasonal monsoon to be in excess and deficient when rainfall in the both months (July and August collectively) is deficient. 3. Discussion and evaluation From Table 1(a) we see that there are 29 meteorological stations with 5 7% probability of being excess when July s rainfall is in excess out of 37 meteorological stations for the given period. There are six stations which have more than 7% this conditional probability, indicating that these stations may be more affected in the month of July and we need precautionary measures in these areas in forthcoming years. Further, two stations have less than 5% probability of seasonal rainfall to be in excess when rainfall in the month of July will be in excess. There is no meteorological station which has greater than probability for the seasonal monsoon to be deficient when July s rainfall is in excess. It implies that when rainfall in the month of July is going to be in excess there is no way that the monsoon season for the given period will be deficient. There are only two possibilities either the seasonal monsoon will be normal or in excess. For August similar behaviour has been observed, with 28 stations having probabilities 5 7% of seasonal monsoon to be in excess, 3 stations have this probability less than 5%, 6 stations have this probability greater than 7%, when rainfall in the month of August is in excess, indicating a threat of moderate and high level respectively. The conditional probability of seasonal monsoon to be deficient when August is in excess is greater than zero for three stations, i.e. 8%, for Lahore, Kotli and Kakul. For September this behaviour is little bit different, with 24 stations having probabilities between 5 and 7%, 13 stations with less than 5% probability, of being excess when rainfall in the month of September is in excess. The numbers of stations with conditional probabilities less than 5% are more as compared with the months July and August. There is no station with this conditional probability greater than 7% for the month of September. The effect of rainfall in September of being excess on seasonal monsoon to be deficient also varies with this conditional probability from 8 to 25%. A total of 14 stations with the highest probability 25% of seasonal monsoon of being deficient for Multan. For any station if monthly rainfall is high especially for July and August then seasonal monsoon s probability to be in excess will be high, the remaining probability will be shifted either for seasonal monsoon to be normal or deficient. For the months of July and August, the probability of seasonal monsoon to be deficient is for most of the stations when rainfall in these months is in excess, so seasonal monsoon is likely to be in excess or normal. Another interesting point to be noted is that when rainfall in the month of July is in excess the probability of seasonal monsoon to be normal is less than 5% except for two stations. For the month of August, there are only three stations with greater than 5% probability of seasonal monsoon to be normal and for September there are 11 stations with probability greater than 5%. To address the question what will be the effect on seasonal monsoon if monthly rainfall in the month of July, August and September is in deficient, we can calculate the corresponding conditional probabilities, given in Table 1(b). First, we see for the month of July, the conditional probability (%) of seasonal rainfall to be in excess is non-zero for 21 stations, with maximum probability for Zhob which is 25% and minimum 3% for Nawab Shah. The highest probability of seasonal monsoon for Astor to be deficient when July s rainfall considered to be deficient is 86%. A seasonal monsoon to be normal is less than 5% for most of the stations. Similar behaviour can be observed for August. For September the results are bit different. When rainfall in the month of September is considered to be deficient the probabilities of seasonal monsoon to be deficient are smaller and of being excess are greater as compared with July and August. In Table 2, we can also see the joint effect of July and August on seasonal monsoon to be in excess, deficient or normal when their joint rainfall is in excess and deficient. When both months are in excess the seasonal monsoon to be in excess is very high, i.e. almost 1% for most of the stations and the corresponding 13 Royal Meteorological Society Int. J. Climatol. 34: (14)

8 834 I. AHMAD et al. probabilities of seasonal monsoons to be deficient and normal are zero. Similarly, when these two months have deficient rainfall, the probabilities of seasonal monsoon to be deficient are 1% for most of the stations and the corresponding probabilities of seasonal monsoon to be normal and in excess are for these stations. It implies that July and August are the months which cause for heavy seasonal monsoon. 4. Conclusion We can find the effect of monthly rainfall on seasonal monsoon for the period 19 6 across 37 meteorological stations of Pakistan. The contribution of different months to make seasonal monsoon to be in excess or deficient varies from station to station and also from month to month. When rainfall in July and August is in excess, the probability of seasonal monsoon to be in excess is 1% in most of the stations and the probability of seasonal monsoon to be deficient is. If the probability of seasonal monsoon to be excess is not 1% in some stations, the remaining probability will be shifted to the probability of seasonal monsoon to be normal. When September rainfall is considered to be in excess, the probability of seasonal monsoon to be in excess is less than July and August, but the probability of seasonal monsoon to be normal is higher than July and August in most of the stations. Similar behaviour has been noticed on the seasonal monsoon to be deficient when rainfall in July and August is considered to be deficient. Overall, July and August have significant effect on seasonal monsoon. For policy implications, we should take defensive measures prior to these months in those areas where this kind of conditional probabilities are high in order to avoid any destruction in the form of floods and droughts. Ali Y, Shahbaz B, Suleri A. 6. Analysis of myths and realities of deforestation in northwest Pakistan: implications for forestry extension. International Journal of Agriculture and Biology 8: Haroon MA, Rasul G. 9. Principal component analysis of summer rainfall and outgoing long-wave radiation over Pakistan. Pakistan Journal of Meteorology 5(1): Hosking JRM, Wallis JR, Wood EF Estimation of the generalized extreme-value distribution by the method of probability weighted moments. Technometrics 27: Hosking JRM, Wallis JR Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge University Press: Cambridge, UK. Hoyos CD, Webster PJ. 7. The role of intraseasonal variability in the nature of Asian monsoon precipitation. Journal of Climatology : DOI: /JCLI Klein TAMG, Peterson TC, Quadir DA, Dorji S, Zou X, Tang H, Santhosh K, Joshi UR, Jaswal AK, Kolli RK, Sikder A, Deshpande NR, Revadekar JV, Yeleuova K, Vandasheva S, Faleyeva M, Gomboluudev P, Budhathoki KP, Karori MA, Zhang P. 8. Downscaling NCC CGCM output for seasonal precipitation prediction over Islamabad-Pakistan. Pakistan Journal of Meteorology 4(8): Kothawale DR, Munot A Probabilities of excess and deficient southwest monsoon rainfall over different meteorological subdivisions of India. Proceedings of the Indian Academic of Sciences (Earth and Planetary Sciences) 17: Lawrence DM, Webster PJ. 1. Inter annual variations of the intraseasonal oscillation in the South Asian summer monsoon region. Journal of Climatology 14: DOI: /15-442(1)14<291: VOTIO>2..CO; 2 Parida BP Modeling of Indian summer monsoon rainfall using a four-parameter Kappa distribution. International Journal of Climatology 19: Stern RD, Coe R A model fitting analysis of daily rainfall data. Journal of the Royal Statistical Society 147: Rasul G, Chaudhry QZ, Mahmood A. 9. Numerical simulation of heavy rainfall case in South Asia. Pakistan Journal of Meteorology 6(11): Rasul G, Chaudhry QZ, Sixiong Z, Qingcun Z. 4. A diagnostic study of record heavy rain twin cities Islamabad- Rawalpindi. Advances in atmospheric Sciences 21(6): Reeve DE Short contribution, estimation of extreme Indian monsoons rainfall. International Journal of Climatology 16: Webster PJ, Hoyos CD. 4. Prediction of monsoon rainfall and river discharge on 15 3 day time scales. Bulletin of the American Meteorological Society 85(11): DOI: /BAMS References Akhlaq J, Naeem S, Anzar AJ. 7. Weather in Pakistan: monsoon season (July-September 6). Pakistan Journal of Meteorology 7: Royal Meteorological Society Int. J. Climatol. 34: (14)

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