Influence of Teleconnections on the Precipitation

Precipitation plays vital role in the economy of agricultural country like Pakistan. Baluchistan being the largest province of Pakistan in term of land is facing reoccurring droughts as well as flashflood due unprecedent torrential precipitation pattern.


Introduction
Atmospheric linkage like climate indices strongly control the precipitation and droughts around the world. All around the globe, these climate indices/teleconnections are influencing far-flung as well as nearby regions predominantly through large scale, Qausi stationary atmospheric Rossby waves, consequent of which some regions receive more rainfall or are hotter than the prevailing global scale changes (IPCC.2014). Climate variations are mainly due to large scale ocean circulations, atmospheric circulations, moisture transportation, wind speed, wind direction and heat fluxes etc. Large scale ocean circulations are studied under the influence of teleconnections (Wallace and Gutzler 1981), which reflects our climate pattern (Lucas et al. 2011;Vermeer and Rahmstorf, 2009). Analysis of teleconnections its impact and influence can help apprehend climate and precipitation pattern (Krichak et al. 2014). Pakistan, Indian and China have experienced erratic flash flooding in past few decades due to unprecedented torrential precipitation, (Viterbo et  This study is eminent for Pakistan because it is ranked 8th most affected country from 1998 to 2017 by Climate Risk Index (GCRI 2019), having the death toll of 512 people, with total the loss of US$ 3.8 Billion and the total 145 number of events that struck Pakistan in ten years 1998-2017 (GCRI 2019). Pakistan was also ranked as the third most affected country in 2012 by the impact of climate change (Kreft and Eckstein 2013). According to United Nations Development Program me (UNDP) and the Pakistan Council of Research in Water Resources (PCRWR) reports that by 2025 Pakistan will be water scare country from water stressed country if it does not take serious measure and steps now, the situation gets worsen in Baluchistanthe study area in particular due to the fact that water is even now scarce in the area and precipitation which is the main source of water is decreasing. Baluchistan also suffers from devastating, sporadical, catastrophic flash flood due to unprecedented precipitation. Additionally, the contemporary significance of the region is far more than ever before due to China-Pakistan Economic Corridor (CPEC) stretching throughout the province and due to Gawadar port. Moreover, this study would be useful for policy makers to comprehend the latest situation in view of climate change and make policies accordingly (IPCC, 2013).
Teleconnections indices are employed to study climate variability on monthly, seasonal, as well as large time periods. Arctic Oscillation ( Iqbal and Athar. (2017) uses Pearson's correlation to determine the influence of climatic indices, namely NAO, AO, AMO, IOD, PDO, QBO and ENSO on precipitation with 80% and above significance level for the positive and negative phases of the indices separately. It was found out that IOD has a positive correlation for its positive phase, the Positive (Negative) phase of AO shows the correlation and PDO shows positive correlation and ENSO exhibits correlation in Baluchistan monthly.
In this study nonparametric Mann Kendall test is used to assess the monthly precipitation trend. The variation in trend in the presence of climate indices is determined by using Partial Mann Kendall, which is the best one step method that do the adjustment for the covariate and trend detection at the same time.

Study Area
The Province of Baluchistan is selected as the study area for this research. It is the largest province of Pakistan with an area of 347,190 square kilometers which is nearly 44 % of Pakistan's totals land area and forms the southwestern part of the country as shown in Figure-1

Precipitation Data
Monthly Precipitation data in millimeters, for this research was acquired from Pakistan Meteorological department (PMD). Thirteen stations throughout Baluchistan were carefully chosen based on accuracy, completeness and availability of data for the selected study period of 41 years. Thirteen stations all over Baluchistan are shown in Figure-1. The Study period constitute of forty-one (41) years from 1977-2017 for the designated 13 different stations in Baluchistan, namely Barakhan, Dalbandin, Jiwani, Kalat, Khuzdar, Lasbella, Nokkundi, Ormara, Pasni, Punjgur, Quetta, Sibbi and Zhob. Data collected from PMD was on the monthly basis in (mm/month) for each of the weather stations, which were averaged to convert them to annual precipitation data for analysis.
The average rainfall monthly and annually within the study period from 1997-2017 over each of the 13 different stations in Baluchistan is tabulated below in Table-1.

METHODOLOGY
In the monthly time series precipitation data at each of 13 stations trends are examined using Mann Kendall Tests. The reasons for adopting the Mann Kendall test is that it is strong and insensitive to the data with gaps and best for the data that is not normally distributed, The association between precipitation and climate indices is determined by Pearson's correlation test; whereas the influence of climate indices (influencing variables) on Trends in precipitation is examined by the Partial Mann Kendall test. The tests are performed on individual stations for monthly time series data.

Mann Kendall for Trend Detection
Mann The MK test is a procedure based on ranks and is not sensitive to sudden breaks in the uneven data. The nonparametric MK test is one of the strong methods of identifying monotonic trends in precipitation data where the data is skewed and/or where data is either consistently increasing or decreasing in a time series whereas MK test is not suitable when there are recurring trends.
In Where, i and j are the rank of observation of the xi and xj of the time series. The variance associated with Sx is given as Where g is the groups of tied rank and t is ties in the group. For a sample size of n>10 or larger, the MK statistics Zmk is computed by Positive Zmk values show increasing trends, while negative Zmk values reflect decreasing trends. If | Zmk | is greater than Z 1-α/2 for the chosen value of significance level, (α) then the trends are considered significant or when p-value is smaller than the significance level (α), the null hypothesis (Ho) of no trend is rejected in favor of alternative the hypothesis (Ha) and the trend is considered as a significant trend in the time series. Z 1-α/2 and p-value are obtained from the standard normal distribution table.

Pearson's Correlation for Finding Linear Associations
Based on the method of covariance, Pearson's correlation is one of the best methods that measure the strength of linear association between the two variables. It provides the information about the magnitude and direction of the association. The direction can be positive or negative, and the magnitude ranges between +1, a perfect positive correlation and -1, a perfect negative correlation. A value of zero indicates that there is no linear correlation. It should be kept in mind that existence of significant correlation is not causation for the variables. The significance of the correlation is determined by the student t-test. The t-test establishes whether there is an evidence of significant correlation is present between the variables or not. The t-test is given by Where, r and n are the correlation coefficient and number of observations in the data series respectively. For precipitation and climatic index being the two variables, Correlation is considered significant for the desired value of significance level (α) having n-2 degree of freedom if |t| is greater than the critical t1-α/2 or if p-value is smaller than the significance level (α). The null hypothesis of no correlation is rejected in favor of the alternative hypothesis that there is a significant correlation between the precipitation and climatic indices. The t1-α/2 and p-value are obtained from the student t-distribution table.

Partial Mann Kendall for Examining the Influence of Climatic Indices on Precipitation Trends
The PMK is one of the best one step procedures that do the adjustment for covariates (influencing variables) and trend testing simultaneously. In PMK, the effect of explanatory variables is studied on the response variable and the influence is calculated using the conditional mean and the conditional variance of the response variable. As given by Libiseller and Grimvall (2002), the test statistic for response variable y, with its covariate x being the explanatory variable is given by Where, Sy is the Mann Kendall statistics of response variable, Sx is the Mann Kendall statistics of explanatory variable, ρˆ denotes the conditional correlation between the MK statistics Sx and Sy. The PMK statistic is normally distributed with mean 0 and standard deviation 1. The details can be seen in Libiseller and Grimvall, 2002, studies.

Results and Discussions
Increasing or decreasing Trends were observed, when the uni-variate Mann Kendall test was run on the precipitation time series data. The effect of Climatic Indices as relevant covariates (influencing variables) was considered to assess the trends in precipitation by applying Partial Mann Kendall.

Trends in Precipitations
Monotonic Trends in precipitation from 1977 to 2017 at 13 stations of Baluchistan is found through Mann Kendall tests monthly at individual stations. Table-2 shows that out of 15 statistically significant trends, 10 were decreasing trends whereas 5 were increasing trends, which clearly shows that decreasing trend is dominating in most of the stations in Baluchistan which explained the decreasing rainfall prevailing in Baluchistan during the last couple of decades. Kalat, Lasbella, Nokkundi and Pasni showed no statistically significant trend in precipitation at 5% significance level. Barakhan showed decreasing trend in the month of January and November, Dalbandin, Jiwani and Khuzdar showed decreasing trends in December, Ormara showed decreasing trends in May, Panjgur showed decreasing trends in July and December, Quetta and Zhob showed decreasing trends in January. Barakhan showed the increasing trend in the month of June, Ormara showed increasing trends in May and October, Quetta showed increasing trends in June and September whereas Sibbi showed increasing trends in June.

Linear Association of Climatic Indices with Precipitation
Pearson correlation is performed between the climate indices and GPCP gridded precipitation to check the association between the two variables. For a 41-year time series data, a correlation value of 0.316 (-0.316) or higher (lower) is considered significant for a two-tailed test at 5% significance level.

Association of NAO with Precipitation
The correlation contour map of Baluchistan (period 1977 to 2017 and months January to December) between NAO and GPCP for months from January to December in the Baluchistan. The correlation coefficient ranges from -0.4 to 0.4. The correlation map in Table-3 shows that NAO has a significant negative correlation with October GPCP precipitation.

Association of AO with Precipitation
The correlation contour map of Baluchistan (period 1977 to 2017 and months January to December) between AO and GPCP Precipitation for months from January to December in the Baluchistan prepared from the NCPP. The correlation coefficient

Association of PDO with Precipitation
The correlation contour map of Baluchistan (period 1977 to 2017 and months January to December) between PDO and GPCP precipitation is attached below. The correlation coefficient ranges from -0.6 to 0.5. The correlation map in Table-7 shows that PDO has a negative significant correlation with January, February, August, September and December GPCP precipitation and the positive significant correlation with October GPCP precipitation

Association of QBO with Precipitation
The correlation contour map of Baluchistan (period 1977 to 2017 and months January to December) between QBO and GPCP precipitation is attached below. The correlation coefficient ranges from -0.5 to 0.5. The correlation map in Table-8 shows that QBO has a negative significant correlation in May and September GPCP precipitation and positive significant correlation with October, November, and December GPCP precipitation

Association of ENSO-MEI with Precipitation
The correlation contour map of Baluchistan (period 1977 to 2017 and months January to December) between ENSO-MEI and GPCP precipitation is attached below. The correlation coefficient ranges from -0.5 to 0.5. The correlation map in Table-9 shows that ENSO-MEI has a negative significant correlation with August GPCP precipitation and the positive significant correlation in October and November GPCP precipitation.   Where * is the significant positive correlation and (*) is the significant negative correlation at 5% significance.

Influence of Climatic and Atmospheric Indices on Precipitation Trends
Several studies emphasize ENSO and NAO has affected the weather of Pakistan regionally and locally. Yadav

Climatic Indices on Monthly Precipitation at Individual Stations
PMK test was run on the monthly precipitation time series being the response variable and the climatic indices being explanatory variables including NAO, AO, AMO, IOD, PDO, QBO and ENSO-MEI. The statistically significant trend in the presence of the relevant influencing variables is tabulated in the Table-11 to Table-16.

a) Influence of NAO on Precipitation
The PMK test shows that NAO has insignificant influence on precipitation of February, March, April, and August in Baluchistan. It shows that NAO has weak influence on precipitation of January, May, September, November, and December over some stations in Baluchistan. It also shows that NAO has weak to moderate (+ve) influence on June and moderate (-ve) influence on precipitation of July whereas NAO has strong (-ve) influence on October precipitation over Panjgur station in Baluchistan. The p-values of PMK at 5% significance level along with Statistics and the influence of NAO are shown in the Table-11 below.

b) Influence of AO on Precipitation
The PMK test shows that AO has insignificant influence on precipitation of February, March, April, August, and October in Baluchistan. It shows that AO has weak influence on precipitation of January, May, June, November, and December over some stations in Baluchistan. It also shows that AO has moderate (-ve) influence on precipitation of July but moderate (+ve) influence on precipitation of September over some stations in Baluchistan. The p-values of PMK at 5% significance level along with Statistics and the influence of AO are shown in the Table-12 below.

d) Influence of IOD on Precipitation
The PMK test shows that IOD has insignificant influence on precipitation of February, March, April, August and October in Baluchistan. It shows that IOD has weak influence on precipitation of January, June, July and December over some stations in Baluchistan. It also shows that IOD has moderate (-ve) influence on precipitation of May, moderate to strong (-ve) influence on precipitation of November and weak to moderate (-ve) influence on precipitation over some stations in Baluchistan whereas NAO has strong (+ve) influence on September precipitation over the Quetta station in Baluchistan. The p-values of PMK at 5% significance level along with Statistics and the influence of IOD is shown in the Table-13 below.

Summarized Results of Climatic Indices on Monthly Precipitation at Individual Stations
The Table-17 shows that NAO, AO, IOD, PDO, and ENSO-MEI mostly has weak influence on precipitation in Baluchistan except they have moderate to strong effect in some months. NAO has moderate influence in June and July but strong influence in October, AO has moderate influence in July and September, IOD has a moderate effect in May, November and December, but has a strong effect in September and November, PDO has a moderate effect in May, July and September, QBO has weak influence all year whereas ENSO has a moderate effect in December but has a strong effect in November.

Conclusions
The results of linear correlation are in line with the partial Mann Kendall in some instances and different in others because of the nonlinear nature of the precipitation which is indicative of that the Partial Mann Kendall is most suitable method to determine the influence in precipitation rather than the linear correlation. Alternatively, the correlation shall be performed on the positive (negative) phases of the explanatory variable (climate indices) separately with the corresponding year precipitation time series.
Baluchistan receives its greater portion of the Precipitation in winter and spring months. Decreasing Trends in precipitation are observed in the winter and Spring Months of November, December January and May, when the time series data is analyzed from 1977 to 2017 through Mann Kendall Test, which confirms that the Baluchistan is receiving lesser precipitation since the past few decades. It is also observed ENSO-MEI and IOD has strong to moderate influence on the precipitation Trends in these months while NAO, AO, PDO and QBO has weak influence on precipitation when tested with Partial Mann Kendall test using precipitation as the response variable and climatic indices as explanatory variables. This confirms the findings in the previous study with respect to ENSO and NAO that in recent years ENSO is affecting the climate more than AO/NAO and the latter is losing control in determining the variability in climate in the winter months on North Western Indian precipitation which is adjacent to Pakistan. Decreasing trends are observed in the months of October when continental air prevails, and NAO has a strong influence on precipitation in this month. Increasing Trends are observed in the months of June and September whereas decreasing trends are observed in the month of July in the areas close to Punjab and Sindh, but in these Monsoon months the amount of rainfall is lesser which would affect the overall rainfall in Baluchistan to a lesser extent. It is observed that NAO, AO and PDO have strong to a moderate influence on precipitation in these months whereas ENSO-MEI, IOD and QBO has a weak influence on precipitation.
The study also shows that QBO and AMO do not directly influenced precipitation in the Baluchistan, but the linear combination of AMO with NAO/AO, QBO with IOD (EQUINOO/DMI) and ENSO may have noticeable influence on the winter and Monsoon rainfalls. Similarly, the linear combination of PDO with IDO (EQUINOO/DMI) and ENSO may also be studied.