Trend and change point detection of seasonal rainfall for effective crop planning over southern transition zone of Karnataka, India **

The significance of the trends was tested by Mann-Kendall test for annual and seasonal rainfall. Among the 14 taluks, only Hassan taluk shows a significant positive trend in annual rainfall while eight taluks have shown non-significant positive trend and remaining five taluks have shown non-significant negative trend. The annual rainfall for the entire zone have shown non-significant positive trend. For the SWM season, Alur taluk shows a significant negative trend and eight taluks have shown non-significant positive trend. However, five taluks and whole zone showed a non-significant negative trend. Southwest monsoon and annual rainfall in Bhadravathi taluk was increased in 2007 (571.9 mm to 785.1 mm and 857.6 mm to 1090.9 mm, respectively) and in Shivamogga, the change in annual rainfall was decreased during 1983 (1497.5 mm to 944.0 mm) and 2011 (944.0 mm to 796.6 mm). The northeast monsoon rainfall was increased during 1992 (134.3 mm to 441.1 mm) and it was decreased during 1994 (441.1 mm to 162.0 mm) in Shikaripura taluk. Similarly, in Hunsur taluk, the SW Monsoon rainfall has increased (701.8 mm to 1010.2 mm) during 1991 and it was decreased during 2001 (1010.2 mm to 723.3 mm), in Periyapatna and Honnali taluk, Northeast monsoon rainfall has decreased during 2012 and 2011, respectively.

mining communities have been interested in detecting fluctuations in time-series data (Basseville and Nikiforov, 1993). The change-point analysis is emerged as a commanding new means for assessing the change occurrence and for detecting slight changes missed by control charts. Furthermore, it provides confidence levels and intervals to better explain the changes observed. A change-point analysis is not a substitute for control charting when collecting online data. However, since a change-point analysis can offer additional information, these two approaches can be used in tandem. Changepoint analysis is desirable to control charting while analyzing historical data, particularly while dealing with large data sets. This method is more efficient with better characterization of changes and also manages the overall error rate. It is also easier to use, robust to outliers and found more versatile.
Control charts have traditionally been used to detect changes. Change-point analysis differs from control charting in terms that, control charts can be updated after each data point is collected, while changepoint analysis can only be done after all the data has been collected. Control charts are superior at identifying isolated abnormal points and detecting major changes rapidly, while change-point analysis can detect subtle changes that control charts frequently miss. These two approaches may be used in conjunction for the analysis (Patakamuri et al., 2020). A change-point analysis has the benefit of controlling change-wise error rate. Thus, each change identified is may be factual and the point-wise error rate will be shown in control charts.
When there are thousands of data points, even in the absence of change, a large number of them will surpass the control limits. Thus, change-point analysis offers many advantages over others. In view of above, this study has attempted to examine seasonal as well as annual rainfall trends and shifts in order to better understand the recent changes in rainfall patterns in the region.

Site description and data collection
The Southern transition zone covers 14 taluks of 5 districts, spread over Mysuru, Shivamogga, Hassan, Davanagere and Chikkmagalore districts, is a narrow strip of land stretching from Shikaripura taluk

Mann -Kendall (M-K) test for trend analysis
Non-parametric test given by Mann, 1945 andMckee et al., 1993 has been extensively employed to determine the importance of monotonic trend in meteorological time series.

Change point detection
In historical climate data series, the change point detection method is an excellent means for detecting climatic eroticism. Recognizing a change point in a climate series is critical as this affects the hydrological cycle processes. Cumulative sum charts (CUSUM) and bootstrapping can be used together to identify changes over several iterations. The change point analyzer is a Microsoft Excel add-in program that detects change points in a dataset (Taylor, 2000). Using MSE and CUSUM maps, this analyzer is a valuable method for determining the exact year when a transition or shift occurs. The confidence levels and level of change reflect the massive change point in the entire dataset. If the data series does not shift, the values will usually oscillate between the horizontal axis. The building of the CUSUM chart is the first step in the analysis. CUSUM charts are made for data by computing and plotting a cumulative sum. Let, X1, X2…, X 14 represent the 14 data points. From this, the cumulative sums S0, S1…, S14 are calculated. The cumulative sums are computed as follows: 2. Start the cumulative sum at zero by setting S0 = 0.
3. Calculate the other cumulative sums by adding the difference between current value and the average to the previous sum, i.e., S i = S i-1 +(X i -for i = 1, 2…….14. The sums of the variations between the values and their average are the total sums. All differences sum to zero, hence that the cumulative sum will always at zero (S14 =0). However, defining a CUSUM chart need some experience. Over the period, if the values appear to be higher than the overall average, then the majority of values added to the total will be positive and increase gradually. A CUSUM chart section with an upward slope shows a time when the values are generally higher than overall average. Section with downward slope, on the other hand denotes a span of time in which the values appear to be lower than overall average. A sudden shift in the average is showed by a sudden shift in the direction of the CUSUM. The average did not change during periods when the CUSUM chart followed a pretty straight path.
The analysis detects different changes that occurred during the study period, with a confidence level associated with each change showing how optimistic the analysis is that the change occurred.
After choosing an estimator for the extent of the change, the bootstrap can be studied. A single bootstrap is accomplished by: The concept of bootstrapping is that, bootstrap samples reflect random reordering of data, simulating the behavior of CUSUM if there is no change. You can predict how much S diff will change if there is no change caused by running a large sets of bootstrap samples. Later compare this value to the S diff value determined from the original order data to see whether it is consistent without change.

Rainfall statistics of the zone
The mean annual rainfall of Southern transition zone is 927.3±172.1 mm with a coefficient of variation of 18.6 per cent. The taluk-wise information is furnished in

Trend analysis
Daily values of precipitation and rainy days have been converted into seasonal (Southwest monsoon and Northeast monsoon) and annual amounts. Linear trend was worked out and the significance of the trends was tested by Mann-Kendall test for annual rainfall (Table 2). Among the 14 taluks only Hassan taluk shows significant positive trend in annual rainfall and eight taluks (Tarikere, Channagiri, Honnali, Arkalgudu, Holenarsipura, H. D. Kote, Hunsur and Bhadravathi) have shown non-significant positive trend, remaining five taluks (Alur, Belur, Periyapatna, Shikaripura and Shimoga) have non-significant negative trend in annual rainfall. Similarly, Annual rainfall for the entire zone has shown non significant positive trend. Sevak et al. (2018) analyzed the long term rainfall of Sardarkrushinagar  and observed significant increase in annual rainfall at 13.9 mm/year over its normal rate of 704.1 mm. The study also showed decadal change in rainfall trend by In case of number of annual rainy days, five taluks (Honnali, Holenarsipura, H. D. Kote, Hunsur and Bhadravathi) and zone as a whole have shown significant positive trend. Whereas, Tarikere, Channagiri, Arkalgudu, Belur, Hassan and Periyapatna showed non-significant positive trend and in remaining taluks (Alur, Shikaripura and Shivamogga) non-significant negative trend was observed for annual rainy days.
For the SW Monsoon rainy season, Alur taluk shows a significant negative trend and eight taluks (Tarikere, Channagiri, Arkalgudu, Hassan, Holenarsipura, H.D. Kote, Bhadravathi and Shivamogga) have shown non-significant positive trend. However, in five taluks (Honnali, Belur, Hunsur, Periyapatna and Shikaripura) and zone as a whole, Non-significant negative trend was observed. For the NEM season, 12 out of 14 taluks and zone as a whole have shown non-significant negative trend and the remaining two taluks (Hassan and Periyapatna) were shown non-significant positive trend in NEM rainfall.
In seasonal rainy days during SWM season, a significant positive trend was noticed in three taluks (Honnali, Hunsur and Bhadravathi) and only Alur taluk shows a significant negative trend. Seven taluks (Tarikere, Channagiri, Arkalgudu, Hassan, Holenarsipura, H. D. Kote and Periyapatna) and zone as a whole showed a non-significant positive trend. Whereas, non-significant negative trend was observed in Belur, Shikaripura and Shivamogga. During NEM season, all the taluks and zone as a whole noticed non-significant positive trend in rainy days.

Change point detection
For the monthly rainfall of the Southern transition zone, the change point occurs in May month during 2018 with the confidence level of 99 per cent. Before the existence of change, the mean monthly rainfall is about 82.6 mm and after change, it was 209.2 mm. Similarly, the rainfall occurrence also changed during October and North east monsoon season (NEM) during 2012 with the confidence level of 94 and 97 per cent, respectively. The rainfall before change was 147.8 and 210.6 mm and after change it was 79.6 and 119.1 mm respectively in the southern transition zone. This clearly indicates the climate change in terms of shifts in the occurrence of rainfall. Hence, the May rainfall dependency may be used exclusively for land preparation rather than as a sowing opportunity (Table 3).
Taluk wise change point detection was estimated to know the rainfall pattern of southern transition zone (Table 3). In the Shivamogga district, the number of occurrences of change in rainfall distribution was higher in all three taluks. In Shikaripura, the April rainfall increased after the change point during 2003 (35.7 to 75.4 mm) and decreased during 2014 (75.4 to 18.0 mm). Similarly, in May and August the occurrence of rainfall was increased in Bhadravathi during 2013 and 2007 (53.6 to 131.0 and 167.4 to 223.8 mm, respectively) and Shivamogga (60.1 to 123.8 mm) during 2013 for May month. The decrease in rainfall was noticed after the change point in Bhadravathi (331.7 to 99.2 mm) and Shivamogga (452.6 to 107.0 mm) during 1981 in September month. In October month, all three taluks (2012 for Bhadravathi and Shikaripura and 2006 for Shivamogga taluk) and December month in Shikaripura also shown decreasing rainfall pattern. Seasonal and annual rainfall is concerned, in Bhadravathi southwest monsoon and annual rainfall was increased in 2007 (571.9 to 785.1 and 857.6 to 1090.9 mm, respectively) and in Shivamogga, the change in annual rainfall was decreased during 1983 (1497.5 to 944.0 mm) and 2011 (944.0 to 796.6 mm). The northeast monsoon rainfall was increased during 1992 (134.3 to 441.1 mm) and it was decreased during 1994 (441.1 to 162.0 mm) in Shikaripura taluk. The increase in rainfall occurrence is always beneficial during summer months (April and May) for land preparation to sow the kharif crops. September and October months rainfall is crucial for crops to attain the flowering and maturity stage; reducing rainfall causes immature grains or declining yield. The sowing dates adjustment or selection of suitable short duration variety/hybrid can escape shortfall of moisture during the maturity stage. It is advisable to go for sowing of single crop due to reduced post-monsoon rainfall in the district's significant parts. Waghaye et al. (2018) analyzed the change point of annual rainfall of 23 stations of Andra Pradesh by using the MWP and CD test. The results reveals that quite variable change was found across the years but most probable change was noticed during 1953 as noticed over 5 stations.
In Hassan district, summer rainfall did not show any change in all the taluks except Holenarsipura. However, Holenarsipura noticed a decrease in rainfall during 1982 (242.3 to 87.2 mm) and an increase during 2018 (87.2 to 228.2 mm) in the May month. A decrease in July rainfall during 2000 (492.5 to 197.7 mm) and increase (197.7 mm to 396.3 mm) was observed during 2005 in Alur taluk. Seasonal and monthly change in rainfall occurrence was higher in recent years, particularly Southwest, Northeast monsoon season, August, September and October months in all the taluks of Hassan district. This indicates that climate change negatively affects crop production due to irregular rainfall distribution even though there was a slight increase in annual rainfall in recent years. In Mysore district, the change of normal rainfall distribution was higher in Hunsur taluk. The increase and decrease of occurrence of rainfall change was noticed in June (1991 and 1993), South west monsoon season (1991 and 2001) and annual (1991 and 2001) and reduction of rainfall was observed in recent years. Similarly, in Periyapatna decease in rainfall was observed in September (1997), October (2015) and Northeast monsoon season (2012) it shows that shift in monthly rainfall distribution without affecting total annual rainfall. Summer rainfall is beneficial for land preparation for the sowing of kharif crops. The slight increase (60.0 to 100.0 mm) in April rainfall was recorded in H. D. Kote taluk.
The increase in rainfall was noticed in May month during 2013 and 2002 for Channagiri (56.9 to 113.2 mm) and Honnali (38.7 to 92.0 mm) taluks. In recent years in Honnali taluk, there was a decrease in October and Northeast monsoon rainfall that indicates go for sowing of short duration cultivars or adjust sowing time for normal crop production. In Tarikere taluk, the rainfall change occurred in October month during 2004. The normal monthly rainfall was 155.1 mm before the existence of change and it was 100.1 mm after the existence of change. Khapalova et al. (2013) applied the statistical methods for change point analysis of annual precipitation for northern, southern and tropical latitudes by using past 100 years data. According to the findings, there has been a significant shift in precipitation from southern to northern latitudes since 1944. However, no change was noticed in the data of tropical latitudes. They concluded that, shift in data from southern to northern latitudes could not be due to gauge change which was introduced around 1950.

CONCLUSIONS
The results indicate that the annual rainfall had shown a rising trend, whereas the seasonal rainfall trend decreased. Still, it didn't negatively affect the total rainy days, both the seasons and annual. The variation in monthly rainfall during the Kharif season is the main cause of rainfall shift due to climate change. It often has adverse effects on crop production due to the irregular distribution of seasonal rainfall even there was a slight increase in annual rainfall in recent years. As a result, analysing the trend of a data set will assist water resource managers in reducing the impact of vulnerable disasters and to recommend changes in the cropping patterns.