Assessment of Climate Variability for Coconut and Other Crops: A Statistical Approach

Public opinion in Sri Lanka has been seriously concerned about the possible impact of climate change on different sectors, and in particular for the agricultural sector. Annual and weekly climate data were analyzed to provide useful information to farmers, planners and scientists to assess the suitability of different types of crops. The statistical methodology of the analysis is illustrated using daily rainfall and air temperature from 1951 to 2001 for Hambantota, a major coconut growing district in Sri Lanka. The increase in maximum air temperature and decrease in the amount of rainfall per effective rainy day (> 5mm) are the significant features of the climate variability in the Hambantota area. The warming rate for maximum air temperature was significantly higher (p<0.005) than that for minimum, mean and diurnal temperature, irrespective of time scales. The annual rate of increase of maximum temperature after 1995 is 0.026C. The intensity of rainfall per effective rainy day (> 5mm) decreased significantly (p<0.005). Distribution of weekly rainfall during January to September is uncertain. The probability of weekly rainfall greater than 20 mm does not exceed 50% in any week during this period. Long-term weekly rainfall was greater than 30 mm only during mid October to early December, but the probability of weekly rainfall greater than 30 mm exceeds 50% only during the first three weeks of November. The probability of occurrence of dry spells of duration greater than 60 days in a year is around 70%, but the time of occurrence of such dry spell is not consistent among years. These findings suggest that the expected future climate would not be suitable for coconut cultivation, if growers do not apply the recommended practices to face long dry spells. Also the increasing temperature could impact to dominate plant pest during dry periods.


Introduction
Climate in a narrow sense is usually defined as the "average weather", or more rigorously, climate is the long term variability of weather parameters. The variability can be described using statistical parameters such as the mean and variance of climate variables. The climate at a given location or a region is determined by the net variability of precipitation, surface air temperature, relative humidity, sunshine duration, wind velocity and numerous other parameters (Peiris, et al, 2000). It is one of the most important limiting factors for agricultural crop production. The climate of Sri Lanka is predominantly governed by the seasonally varying monsoon system and the associated air masses that are part of the planetary wind regime over South Asia (Domroes, 1974) and thus there is a high variability in climate between different districts in Sri Lanka.
Hambantota is a rapidly urbanizing area occupying a land area of 100 km 2 and is situated in the southeast of Sri Lanka between the latitudes 6.07 º N to 6.54 º N and the longitudes 80.64 º E to 81.68 º E with an altitude of 16 m. The Hambantota area belongs to the low country high dry (DL5) region of Sri Lanka and the 75% expectancy of annual rainfall is 1000 mm. The economy of Hambantota depends mainly on rain fed crops and it has the greatest coconut extent of about 20000 hectares which is equivalent to 5% of the total coconut extent in Sri Lanka. In addition to coconut, rice and short term crops are grown in this area, which was one of the districts worst affected by the Tsunami of 2004. Variability in precipitation and temperature would strongly affect agricultural crops through their influences on internal plant processes and external factors such as soil water availability and pest and diseases incidence. Past analyses of rainfall in Hambantota, based on annual or monsoon seasons did not produce sufficient information on climate variability for farmers to plan their activities; Malmgren, et al., 2003). There have also been claims that the onset of monsoon rains has changed in various locations in Sri Lanka (Peiris, et al. 2000). Thus there is a need to assess the suitability of crops from time to time.
The objective of this study was therefore to demonstrate a methodology for statistical analysis of the weekly rainfall and temperature data in the Hambantota area to elucidate the past climate variability and to make inferences regarding future climate variability in the area for the purpose of planning agricultural activities.

Climate data
Daily data on rainfall (RF), maximum air temperature (TMAX) and minimum air temperature (TMIN) in Hambantota (6.12 º N, 81.13 º E, 16.0m) during the period from 1951 to 2001 were acquired from the climate database of the Biometry Division of the Coconut Research Institute. Data were quality controlled and some missing daily rainfall values were estimated using exponential smoothing techniques (Malmgren et al., 2003).

Statistical analysis
Data were analyzed using SAS and Minitab statistical packages. Linear trend analysis was carried out on both yearly and weekly data for four temperature and three rainfall indices namely (i) maximum TMAX, (ii) minimum TMIN, (iii) mean TMEA = (TMAX + TMIN)/2), (iv) diurnal temperature TDIF = (TMAX -TMIN), (v) total RF, (vi) rainfall intensity (RFI) and (vii) effective rainfall intensity (RFEI). Rainfall intensity (RFI) and effective rainfall intensity (RFEI) were defined as the amount of rainfall per rainy day (>0 mm) and per effective rainy day (>5 mm). The effective rainfall is generally subjective thing depend on the crop, however it this study it was taken as 5 mm as coconut is concern.
The average water requirement of adult coconut palm is 50 liters per day (Mahindapala and Pinto, 1991). Considering that the radius of the root system is approximately 2.1m and the depth is 1m, the height of requirement of water was calculated as 5mm, excluding a circle of 0.30m radius for the area of root ball. Thus, an effective rainy day for coconut can be considered as 5 mm per day.
To obtain weekly data, a year was divided into 52 weeks (Appendix A). In leap years rainfall on 29 th February was added to the 9 th week and converted to a 7 day total. The autocorrelation function and single spectrum density function were derived to detect any seasonal or cyclic pattern of the yearly series (Chatfield and Collins, 1980). The non-parametric statistics u(t) and u'(t) of Mann-Kendall rank correlation test (Turkes, et al, 2002) were used to detect any possible significant periods of trend or change points in the RF, TMAX, TMIN, TMEA and TDIF times series. When the value of either u(t) or u'(t) is significant at the 5% level, it can be decided whether one or other trend is increasing (u(t) > 0 ; u'(t)>0) or decreasing (u(t) <0 ; u'(t)< 0.
The length of the three longest dry spells in each year during 1951 to 2001 was computed using an SAS program. The empirical cumulative density functions for dry spells were derived to compute probabilities for the occurrence of dry spells for different lengths under normality assumption. The normality was confirmed using Anderson-Darling statistics (Chatfield and Collins, 1980).

Annual climate variability
The plot of autocorrelation for all annual series confirmed that there is no cyclic pattern in the series of TMAX, TMIN, TMEA, TDIF or RF. Basic statistics of four temperature and three rainfall indices were used to describe annual climate variability (Table 1).
Annual rainfall during the 51 year period varied from 603 mm to 1825 mm with a mean of 1021 mm. Annual variability of rainfall intensity (cv=26%) is higher than that of total rainfall (cv=25%). Variability of TDIF is significantly higher compared to other temperature indices. Figure 1(a) clearly indicates a significant increasing trend for TMAX (R 2 = 0.51; p < 0.001) at the rate of 0.02 º C/year. About 50% of annual variability is explained by the linear model. Figure 2(a) indicates that the significant warming trend of TMAX commenced in 1978. There were no periodic changes during the period 1951 to 2001. After 1978, the increasing rate of TMAX was 0.0260 º C/year as compared to 0.0082 º C/year prior to 1978.

Minimum temperature -TMIN
TMIN showed a significant increasing trend and the warming rate was 0.007 º C/year ( Figure  1.b). According to Figure 2(c) u(t) exceeds the critical value during the period from 1966 to 1975 and again after 1995. The analysis also indicates that significant rates of increase and decreases commenced during 1966 and 1995 respectively. The annual rate of increase after 1995 was 0.0204 º C/year as against 0.0042 º C/year prior to 1995. The u'(t) shows no systematic trend or interaction between u(t) and u'(t). No significant strong linear relationship was found between TMAX and TMIN (r=0.658).

Mean temperature -TMEA
Mean temperature also showed a significant increasing trend (p < 0.001), but the rate of increase (0.0135 º C/year) was less than that of TMAX. The highest TMEA, 28.4 º C,   was recorded in 1998. There are no periodic changes for TMEA in Figure 2(b). Based on the pattern for u(t) (Figure 2.b) it can be confirmed that a significant change in the increasing mean temperature trend occurred in 1983. The warming rate after 1983 was 0.0225 º C/year compared to 0.0064 º C/year prior to 1983.

Diurnal temperature -TDIF
TDIF varied from 5.38 º C (1961) to 6.84 º C (2001). Figure 1(d) shows that the significant increment rate (p< 0.001) of TDIF was 0.0128 º C/year. Both u(t) and u'(t) intersect at 1971 (Figure 2.d) confirming that the significant change of TDIF has started during 1971, but the significant increasing trend can be seen clearly only after 1980. The increment rate of TDIF after and prior to 1980 was 0.0142 º C/year and 0.0119 º C/year respectively.
The comparison of indices for increasing rates of temperature before and after the corresponding significant turning point is given in Table 2.
Based on the results in Table 2, it can be confirmed that warming rates after 1995 are significantly higher for all four temperature indices. In fact 1990-2000 has been identified as the warmest decade on record (IPCC, 2001).

Rainfall -RF
Annual rainfall shows a decreasing linear trend (Figure 3.a), but it is not significant at 5% level. The plot of u(t) and u'(t) for annual rainfall (Figure 3.b) varies within the limiting points and the two curves intersect in 1976. It confirms that there is no turning point to demonstrate significant rainfall change during 1951 to 2001. Thus, analysis of total annual rainfall is less important for climate variability in Hambantota.

Rainfall intensity
Trend analysis showed that rainfall intensity (RFI) and effective rainfall intensity (RFEI) ( Figure 4) have significantly decreased with time. The rainfall intensity decreased much faster than effective rainfall intensity. During the period from 1951 to 2001 rainfall intensity has dropped from about 25 mm/day to about 8 mm/day. Corresponding rates for effective rainfall intensity were 10 mm/day and 5 mm/day.

Dry spells
Mean and coefficient of variation (CV) for the three longest dry spells and the sum of the three dry spells are shown in Table 3.
The length of the longest dry spell had the greatest variability. Based on the empirical cumulative density function shown in Figure 5 the probability of the length of the dry spell in a year being more than 60 days was 31%. It implies that at least a dry spell of 60 days would occur once in three years. Figure 5 indicates that the probability of the length of the dry spell in a year being more than 65 days was 25%. The probability of at least three dry spells of more than 30 days in a year was 40%. The plot of the longest dry spell in a year also showed an increasing trend though it is not statistically significant. The periods of dry spells varied between the years indicating that a specific period can not be recommended for the occurrence of dry spells for all years.

Weekly climate variability Weekly TMAX
The temporal variability of long term weekly TMAX is shown in Figure 6(a). It indicates that the weekly TMAX has varied with a maximum of 31.4 º C (±0.09) during the 13 th week (26 Mar -02 Apr) and a minimum of 29.6 º C (±0.11) during the 52 nd week (24 -31 Dec). The temperature during the period from 9 th week to 21 st week (26 February to 29 May) is generally higher (> 31 º C) than other weeks. Similarly, after the 48 th week (30 th November) temperature is lower than in all previous weeks. Weekly TMAX rapidly increased The estimated parameters (b) of the linear trend model (y = a + b*t) fitted for each temperature index on a weekly basis is shown in Appendix B. All weeks, except the 32 nd week showed warming trends. Out of 52 weeks, 44 (85%) showed a significant increasing trend (p < 0.05). The rate of increase is significantly higher during the 7 th to 8 th week (12 Feb -25 Feb) and the 29 th to 30 th week (19 Jul -01 Aug). Of these four weeks, the lowest rate of increase was observed during the 7 th week (12-18 February). As described above 5 mm of rainfall per day was considered as effective rainfall. Thus a 'rainy week' is defined as a week of which exceeds rainfall more than 35mm) (0.0322 º C/year, p<0.01). Further, the period from the 9 th week (26 Feb -04 Mar) to the 24 th week (13-19 Jun) also showed a high warming rate with a mean of 0.0222 º C/year. The 52 nd week (24-31 December) also showed a warming rate of 0.02 º C/year, but the mean TMAX during that week was below 29 º C.

Weekly TMIN
The pattern of temporal variability of weekly TMIN (Figure 6.b) is not as complex as that of TMAX. Weekly TMIN increased from 22.8 o C (±0.14) during the 6 th week (5-11 Feb) to 25.7 o C (±0.09) in the 21 st week (30 May -5 Jun) as depicted in Figure 6(b). The TMIN during the period the 15 th to the 22 nd week [dates] is higher (> 25 o C) than in other weeks. The temperature during the 1 st to the 9 th week is lower (< 23.5 o C) than that of other weeks. During the period from the 6 th to the 19 th week (05 Feb -15 May) the weekly TMIN rapidly increased with time and thereafter decreased gradually. As for TMAX, all weeks except the 23 rd and 26 th weeks showed warming trends. However, only ten weeks in the year 26 Mar -17 Apr (13-15th week), 25 Apr -08 May (17-18 th week), 09 Nov -29 Nov (45-47 th week) and 21 -31 Dec (51-52 week) showed a significant increasing trend (p < 0.05) for TMIN as shown in Appendix B. A significantly increasing trend for TMAX was also seen during the above weeks. The highest increment rate for TMIN was 0.0173 o C/year during the 13 th and 17 th weeks (26 March -01 May). The rate of increase was higher for TMAX than for TMIN for all weeks and in most of the cases rate of increase for TMAX was more than double that of TMIN (Appendix B).

Weekly TMEA
The mean temperature increased from the 6 th to the 20 th week (05 Feb -22 May) and thereafter TMEA decreased with time ( Figure  6.c). The TMEA varied with a maximum of 28.3 o C (±0.08) (19 th week, 9-16 May) and a minimum of 26.3 o C (±0.07) (3 rd week, 15-21 January) during the year. The trends in weekly TMEA significantly increased during the 1 st to the 18 th week (01 Jan -08 May), the 21 st to the 23 rd week (30 May-12 June), and the 28 th to the 30 th week (12 July -01 Aug) and in almost all weeks after 12 th October. The highest rate of increase was observed in the 30 th week (26 July-01 Aug) when it was 0.0232 o C/year. Figure 6(d) indicates that the temporal variation of the weekly TDIF increased from the 1 st to the 12 th week (01 Jan to 25 Mar). The mean diurnal temperature during the 5 th to the 12 th week (29 Feb -25 Mar) was above 7ºC. During these weeks diurnal temperature was significantly increased with time. TDIF was lowest during the 21 st and 22 nd weeks (23 May to 05 Jun) and when it was around 5 0 C.

Weekly RF
The long-term weekly rainfall is shown in Appendix C. It is reasonable to assume that at least 35 mm of rainfall per week is required if coconut is to be grown successfully in any area (Mahindapala and Pinto, 1991). Appendix C shows that weekly rainfall exceeds 35 mm (5mm per day) only during the period from the 42nd to the 48th week (19 Oct -06 Dec). Analysis also showed that there is no significant increasing or decreasing trend in weekly rainfall.
Rainfall data described above using arithmetic means provide a general idea of the weekly rainfall variability. In order to develop suitable strategies for agricultural planning and implementation, it is important to have some estimates of the amount of rainfall on a weekly basis. For this purpose, the probability of receiving weekly rainfall greater than a specific amount (e.g. 0, 10, 20, 30, 35 mm) was computed (Appendix C) without assuming any distribution. These threshold values were chosen to enable the user to decide upon appropriate amounts of rainfall considered as sufficient for various field operations related to agriculture. The probability of rainfall on a given week being at least 35 mm exceeds 50% only during the 44th to 46 th weeks (02 Nov -22 Nov). Similarly, the probability of rainfall on a given week being at least 30 mm exceeds 50% only during the 44 th to 47 th weeks (02 Nov -28 Nov]. These results confirm that in Hambantota, a reliable rainy spell can be expected only during the 44 th -to 47 th weeks (02 Nov -28 Nov).

Discussion
All annual temperature indicators (TMAX, TMIN, TMEA and TDIF) in Hambantota showed significant increasing trends (p < 0.01) during the period 1951-2001. The warming rate for TMAX (0.02 º C/year) is significantly higher than that for TMIN (0.0071 º C/year), TMEA (0.0135 º C/year) and TDIF (0.0128 º C/year). However, according to the global warming scenario the rate of TMIN is higher than that of TMAX. Thus it can be hypothesized that local effects in Hambantota area are different from the global effects. The scientific reason for this different trend has to be investigated, but the low altitude and proximity to the ocean may contribute to the observed trend in temperature at Hambantota. Similar trends have been observed in parts of other coconut growing

indices (mean ±SE) for (a) TMAX (b) TMIN, (c) TMEA and (d) TDIF
areas (Peiris, unpublished). The warming rate of TMAX is almost equal to the rate of global warming predicted by the global circulation model. As the rate of increase of TDIF is lower than that of minimum temperature, increase of warmer periods with warming during day and night could be expected in Hambantota in the future.
The increasing temperature could lead to an increased demand for water by plants. This would be a serious problem for both the agriculture and livestock industries in Hambantota. The increase of temperature in Hambantota may also be due to increased greenhouse gas concentrations in the atmosphere due to rapid urbanizing programs in the district.
Annual rainfall showed a significant negative correlation (p < 0.05) with maximum air temperature. Thus reduction in the annual rainfall could be expected, though it may not be statistically significant. Decrease of both rainfall intensity and effective rainfall intensity would have serious impacts on agricultural and livestock production in Hambantota. The rate of decline of the amount of effective rain is much higher than that for rainy days. Thus, less rainfall as well as lower intensity of rainfall could be expected in the future, in the Hambantota area.
The probability of dry spells of greater than 60 days in a year is 30%. The probability of at least three dry spells of duration greater than 30 days in a year is 41% indicating three to four months of dry, warm weather within a year, which can occur about twice every five years. This pattern of dry spells would negatively impact on coconut as an inflorescence is produced every month. Thus the expected future climate in Hambantota will not be suitable for high coconut production. Tree crops like cashew and mango would be ideal for the Hambantota area.
Weekly rainfall showed the highest negative significant correlation with the corresponding weekly maximum air temperature. High maximum and minimum temperatures increase water demand and adversely affect planting seed material, establishment of seedlings; reduction of canopy cover and the final yield of any crop. In fact, most of the weeks, rainfall is below 25 mm and only the period between the 44th and 47th weeks have a probability greater than 50% of receiving a weekly rainfall exceeding 30 mm. This analysis suggests that the amount of rainfall in Hambantota is not sufficient to store rainwater in tanks for agricultural purposes. Use of ground water, where available, would be the only water source for both annual and perennial crops in the Hambantota area.
The highest maximum temperature (>31 o C) is shown generally during the 11 th -18 th weeks (12 Mar -08 May) in each year. The highest diurnal temperature period also falls during the same period. The probability of weekly rainfall being greater than 25 mm during this period is about 10% confirming that adequate rainfall in the Hambantota area can hardly be expected during the first inter-monsoon. Therefore, this period is not suitable for planting any short term crop. Rice is one of the major crops in Hambantota. During the period from mid September (38 th week) to end of December (52 nd week), the maximum temperature is below the average and the probability of weekly rainfall being greater than 35 mm is 50%. Hence, early September is suitable for land preparation. The second inter-monsoon rains in Hambantota district commence during the 42 nd week (19-25 October) and weekly rainfall is above 35 mm up to the 48 th week (30 Nov -06 Dec) with the rains continuing up to the 51 st or 52 nd week (20 th -31 st December). Paddy planted during early September receives heavy rains during November (44th -45th weeks) and the harvest can be obtained at the end of December or January in the dry season.
In this paper a more robust method was illustrated in to analyse various climate indicator using long-term rainfall and temperature data in a given location to derive more beneficial inferences to planners, scientists and farmers. The analysis is valid irrespective of crop. Thus more specific information can be obtained if the same techniques are applied to analyse long-term water deficits data for a particular crop or identify relationships between climate and crop yield.
An alternative approaches to study the relationship between coconut and rainfall have been discussed by some authors (Peiris et al 2008, Peiris andThattil, 1998).

Conclusion
In the Hambantota area of Sri Lanka, the local effects may have a stronger influence than global effects in determining long term climate variability. All annual temperature indices (maximum temperature, minimum temperature, mean temperature and diurnal temperature) and weekly maximum temperature showed significant increasing trends. Rates of increase are higher since 1995. The amount of rainfall per rainy day (> 0 mm) and that per effective rainy day (> 5 mm) declined significantly over the period between 1951 and 2001. Rainfall and maximum temperature showed a significant negative relationship. The probability of occurrence of a dry spell of more than 60 days duration is 30%. However, the time of the year during which a longer dry spell could occur is not consistent between years. The rate of increase of weekly maximum air temperature is higher than that of weekly minimum air temperature in all weeks in a year. Alternative methods to obtain water such as exploration of ground water are necessary, if agriculture is to be promoted in the Hambantota area in the future. The results derived from this study provide important information on climate variability in Hambantota which have policy implications. These results could also be considered during implementation of crop insurance programs to protect farmers. Similar analysis of weekly rainfall of long-term data is recommended to understand the expected climate variability in any other areas. Peiris, T. S. G., Hansen, J. W and Lareef, Zubair (2008). Use of seasonal climate information to predict coconut production in Sri Lanka.