Application of Standard Precipitation Index (SPI) to Assess Rainfall variability in a Major Agricultural Area in Dry Zone of Sri Lanka

Agriculture in the dry zone of Sri Lanka is highly constrained by the inadequacy of irrigation water. The small village tanks located in these areas help farmers to cultivate their lands during dry periods by storing rainwater. However, the rainfall variability has made a considerable threat to functioning of these tanks and in providing expected benefits to the farmers. The objective of this study was to assess the climatic variability using 30-year (1989 to 2018) daily rainfall data from six rain gauging locations (Anuradhapura, Mahagalkadawala, Hingurakgoda, MahaIlluppallama, Girithale and Diyabeduma) in a small tank dominated area in the Dry Zone. Standard Precipitation Index (SPI) was calculated to assess the temporal variability of dry and wet extremes. Mann Kendal Trend Test (MK test) was used to analyze the trend of SPI and Sen’s Slope Estimator to assess the magnitude of the trend. The results of Anuradhapura, Diyabeduma and Mahagalkadawala show significantly increasing trend of SPI 12/ annual rainfall. According to the SPI, there were increasing trends in First Inter Monsoon in Anuradhapura and MahaIlluppallama, which have resulted an increasing rainfall trend in Yala season. Additionally, there was an increasing trend in Second Inter-Monsoon in Anuradhapura. These changes highlight that there are extreme rainfall events occurring in some seasons without making a significant impact in the annual rainfall pattern of the area.


INTRODUCTION
Water is a main constraint for agriculture in the Dry Zone of Sri Lanka due to temporal variability of rainfall. Sri Lanka's climate is divided into four rainfall seasons: First inter-monsoon (FIM) (March-April), Southwest monsoon (SWM) (May-September), Second inter-monsoon (SIM) (October-November) and Northeast monsoon (NEM) (December-February). Maha, the major cultivation season falls from September to February, which overlaps with SIM and NEM. Yala, the minor cultivation season falls from March to August which is during FIM and SWM periods (Chithranayana and Punyawardena, 2014).
Climate variability brings adverse weather conditions such as droughts and floods (Trenberth, 2008), and high intensity rainfall. Accordingly, the rainfall variability can result in number of adverse impacts such as landslides (Melchiorre andFrattini, 2012, Rathnayake andHerath, 2005), destruction of infrastructure, agricultural lands and ecosystems (Smith, 2011, Vogel et al., 2019, Eriyagama et al., 2010. Several studies have revealed the climatic variability experienced during recent past in Sri Lanka (Wickramagamage, 2016, Jayawardena et al., 2018, Hemachandra et al., 2020. Village tanks/ cascade systems have been constructed in Dry Zone of Sri Lanka to harvest rainwater. So that the collected water can be utilized for irrigation and other uses during dry periods (Madduma Bandara, 1985;Jayatilaka et al., 2003;Panabokke et al., 2001;Dharmasena, 2010). Therefore, small tanks/ cascade systems can be affected by climatic variability (Chandrasiri et al., 2020). Droughts affect the small tanks by depleting soil moisture, drying up vegetation (crops, natural fauna), increasing wild animal problems, etc. (Dharmasena, 2010). Heavy rains and floods also can damage the crops and the livelihood of people. Hence it is necessary to have an understanding of the pattern of rainfall variability for planning and management of farming under small tanks in order to minimize crop failures.
The objective of this study was to assess the variability of SPI and its trends from 1989 to 2018 in six rain gauging locations situated in an area dominated by small tanks and Tank Cascade Systems in North Central Dry Zone of Sri Lanka.

Description of data
Daily rainfall data of thirty-year period (1989 -2018) were collected from six rain gauging locations namely, Anuradhapura, Mahagalkadawala, Hingurakgoda, Maha Illuppallama, Girithale and Diyabeduma. These gauging stations are located in close proximity to numerous small village tanks and a number of important small tank cascade systems including Rathmale, Divulwewa, Athabendiwewa, Mahakanmulla, Thirappane, Ulagalla, Thoruwewa, Horivila-Palugaswewa and Ethabendiwewa in the North Central dry zone of Sri Lanka. Selection of the rain gauging stations was mostly influenced by the availability of data for the recent thirty year period and having only few missing rainfall data values. The rainfall data were collected from the Department of Meteorology, Natural Resources Management Centre of the Department of Agriculture and the Department of Irrigation, Sri Lanka. Figure 1 depicts the rain gauging locations and some important small tanks/ cascades present in the area.

Analysis of Standard Precipitation Index
The daily rainfall data were examined for missing rainfall values and other inconsistencies. The missing values of each station were filled with the values of the closest rain gauging station as it was considered as the most suitable option with the available data. The consistency of rainfall values at each station was assessed using mass curves and found to be consistent. It requires at least 30-year historical rainfall data to develop SPI (WMO, 2012). The SPI values can be interpreted as the number of standard deviations by which the observed value deviates from the long-term mean. Accordingly, the SPI is computed by dividing the difference between the normalized seasonal precipitation and its longterm seasonal mean by the standard deviation (Equation 1).
where, Xi is i th observation of the seasonal precipitation at a particular rain gauge station, Xm the long-term seasonal mean of that particular rain gauge station and σ is its standard deviation (Bhuiyan et al., 2006). The categorization of the moisture based on SPI value is presented in   (Bordi et al., 2004). In this study, SPI related to three-time scales; 3month SPI (SPI 3), 6-month SPI (SPI 6) and 12month SPI (SPI 12) were developed.
SPI 12 was developed to assess the long-term precipitation patterns. Accordingly, SPI 12 for month of September (SPI 12 September) was taken for the analysis representing the annual rainfall variation of the hydrological years. "Water year/ Hydrological year" is defined as the 12-month period from October 1 for any given year through September 30 of the following year (Dodge et al., 1998).
SPI 12 is a cumulative result of the shorter periods. Therefore, SPI 3 and SPI 6 were developed to assess the seasonal rainfall variations (main rainfall seasons and cultivation seasons).
SPI 3 for month of February (SPI 3 February) indicating the NEM, SPI 3 for month of May (SPI 3 May) indicating the FIM, SPI 3 for month of August (SPI 3 August) indicating SWM and SPI 3 for month of November (SPI 3 November) indicating SIM were developed.
According to WMO (2012) the 6-month SPI indicates seasonal to medium-term trends in precipitation and it is very effective in showing the precipitation over distinct seasons. Therefore, SPI 6 was developed to assess the droughts and wet extremes related to major cultivation seasons of Yala and Maha. Accordingly, SPI 6 was developed for months of February and August (SPI 6 February and SPI 6 August) to indicate the influences of the rainfall for two major cultivation seasons of Yala and Maha.

Autocorrelation test
Since the null hypothesis in the Mann-Kendall test is that the data are independent and randomly ordered, the existence of positive autocorrelation in the data increases the probability of detecting trends when actually non-exist, and vice versa (Hamed and Rao, 1998, Mondal et al., 2012, Yue and Wang 2004. Therefore, the serial autocorrelation was tested in the monthly rainfall data as well as the derived SPI 3,6 and 12 values to observe the presence of any serial dependency of rainfall data during 1989 to 2018 period prior to apply Mann Kendall test.

Mann Kendal Trend Test (MK test)
The null hypothesis (H0) was identified as there is no trend in the data points in the record and the alternative hypothesis (H1) was that there is an increasing or decreasing monotonic trend. Depending on the Z value, null hypothesis was accepted or rejected.
The MK test statistic S was calculated using Equation 2 and Equation 3 where xj and xk are the annual values in years j and k, j > k, respectively.
However, when n ≥ 8, the statistic S is approximately normally distributed with the mean (Mondal et al., 2012). Hence the variance statistic is given as in Equation 4.
Here q is the number of tied groups and tp is the number of data values in the p th group. The values of S and VAR(S) are used to compute the test statistic Z as Equation 5.
Accordingly, Z test was used to assess the trend of SPI as this analysis provides 29 data points (from the hydrological year of 1989/1990 to 2017/2018).

Sen's Slope Estimator
Sen's method is used to estimate the true slope of an existing trend (as change per unit time) where it is assumed to be linear (Equation 6).
where Q is the slope and B is a constant.
For obtaining Q, slopes of all the data value pairs were calculated. The estimation of slope of N pairs of data is expressed as Equation 7.
where, J > k and xj and xk are data values at times j and k respectively. Hence, Q was estimated by the Sen's non-parametric method where the trend was assumed as linear using MAKESENS application. Hence, Sen's estimator for a linear trend calculated with the equation 8 by MAKESENS .

Autocorrelation analysis
According to the results of autocorrelation test, either the monthly rainfall data in individual locations or derived SPI 3, 6 and 12 are not autocorrelated. Therefore, the MK trend test and Sen's slope estimator was directly applied to assess the trend of SPI. Figure 2 presents the occurrence of drought and wet events according to the derived "SPI 12
The SPI 12 looks at the annual rainfall variability considering the hydrological year.  The short term or the seasonal variabilities of rainfall can cause more impacts on the functioning of small tanks/ tank cascade systems than the longterm variabilities such as SPI 12 and SPI 24. Therefore, SPI 3 and SPI 6 analyses present the short term and seasonal variabilities of rainfall.

Variability of SPI 3 during 1989-2018 years
SPI 3 provides a comparison of the precipitation over a specific 3-month period with the precipitation totals from the same 3-month period for all the years included in the historical record. Therefore, SPI 3 reflects short and medium-term moisture conditions and provides a seasonal estimation of precipitation. It is highly suitable for primary agricultural regions (WMO, 2012).

SPI 3 February
SPI 3 February in this analysis compares precipitation total of December, January and February in a particular year with the precipitation totals of the same period (December, January and February) in past thirty-years (1989 -2018) in a particular location. Since the NEM rains also occur during December to February (Domroes and Ranatunge, 1992), SPI 3 February presents the changes of NEM rains.
According to MK test and Sen's Slope Estimate, none of the rain gauging locations showed significant trends in SPI 3 February. Hence it indicates that there is no significant trend in NEM rains for this area (Data are not presented).

SPI 3 May
SPI 3 May compares precipitation total of March, April and May in a particular year with the precipitation totals of the same period (March, April and May) in past thirty-years (1989 -2018) in a particular location. Hence it includes the FIM which occurs during the months of March and April. In fact, it shows that there is an increasing trend in the FIM rains in these areas. However, there is no trend of rainfall in Mahagalkadawala, Diyabeduma, Giritale and Higurakgoda during FIM.
Since dry zone of Sri Lanka is receiving highly intensive rains during inter monsoonal periods (Abeysekera et al., 2015), the increments of SPI 3 could be due to increase of high intensive rains.

SPI 3 August
SPI 3 August compares the precipitation total of June, July and August in a particular year with precipitation totals of the same period (June, July and August) in past thirty-years (1989 -2018) in a particular location. It represents the SWM season.
However, according to, MK test and Sen's Slope Estimate, there was no trend of SPI 3 August in all the rain gauging locations (Data are not presented).

SPI 3 November
SPI 3 November in this analysis compares precipitation totals of September, October and November in a particular year with the precipitation totals of the same period (September, October and November) in past thirty-years (1989 -2018) of a particular location. Hence it represents the SIM period of October and November.

Variability of SPI 6 February and August
SPI 6 provides a comparison of the precipitation over a specific 6-month period with the precipitation totals from the same 6-month period for all the years included in the historical record. SPI 6 February compares the precipitation total for the September to February period in a particular year with precipitations for that same period (September to February) in past thirty-years (1989 -2018)  Even though most of the rain gauging locations show random increasing trends of seasonal or annual rainfalls (SPI3/ SPI 6/ SPI 12) a continuous increasing or decreasing trend was not observed except in Anuradhapura. Hence it is obvious that the increasing trends of SPI at different locations at different time periods were due to extreme rainfall events. Abeysekera et al. (2015) also revealed about an increasing trend of extreme rainfall events during 1990 -2014 period in dry zone of Sri Lanka Hence the untimely rainfall can adversely affect to the sustainability of village tanks/ cascade systems interrupting human activities, crop production, hydrologic relations including eco system functions. Since small village tanks play a vital role in livelihood of the people in this area, it is important to consider sustainable management of these tanks and cascade systems to cope up with the changing climatic conditions. Hence it is understood that future studies should be focused on shifting of the rainfall seasons and defining the cultivation seasons accordingly as an adaptation strategy.

CONCLUSIONS
The variability of rainfall is evident in this area according to the SPI analysis which shows alternative dry and wet periods. Rain gauging locations of Anuradhapura, Diyabeduma and Mahagalkadawala shows an increasing trend of annual rainfall. In seasonal rainfall, there are no trends in the main two monsoons (either NEM or SWM) in any of the rain gauging location. However, increasing trends were observed in FIM in Anuradhapura and Maha Illuppalama which had resulted in an increasing rainfall trend in Yala season. Therefore, it can be considered as a positive impact for agriculture since water scarcity is a major obstacle for farming in Yala season. Additionally there was an increasing trend of SIM in Anuradhapura. There were no trends of SPI 3 and SPI 6 Hingurakgoda, Diyabeduma and Mahagalkadawala and there may be random extreme rainfall events which have made the increasing trend only for the annual rainfall. Hence it can be concluded that there can be an increment of random extreme heavy rainfalls in this area in the future.