REPORT ON SOWING PERIOD AND FLOODING RISKS IN DOUALA, CAMEROON BY GERVAIS DIDIER YONTCHANG Cameroon Meteorological Department PROJECT WORK FOR PART FULFILMENT OF THE e-siac COURSE (STATISTICS IN APPLIED CLIMATOLOGY APRIL AUGUST 2010) MAINTAINED BY THE MET. OFFICE COLLEGE AND THE SSC WITH SUPPORT FROM THE UK MET. OFFICE AND WMO. August 2010 1
TABLE OF CONTENTS REPORT ON SOWING PERIOD AND FLOODING RISKS IN DOUALA, CAMEROON... 1 TABLE OF CONTENTS... 2 A. BACKGROUND:... 3 1). Extreme climate events increasingly important for Cameroon... 3 2) Location and climate of Douala, Cameroon in Africa... 3 B. OBJECTIVES:... 4 i. Assessment of the annual distribution of sowing dates... 4 ii. Assessment of the flooding risks during the rainfall peak period... 4 iii. To quantify the risk of having floods with crop failure... 4 iv. Towards development of a possible cautious strategy... 4 C. METHODOLOGY:... 5 1. Find the dates when sowing are possible using the suitable definitions... 5 2. Assessment of the risk of flooding with crop failure... 5 3. Boxplots for visual comparison, descriptive statistics as dates and Comment on the summaries.... 5 4. Some conclusions for the client (Ministry of agriculture) based on these summaries and risks calculations.... 5 D. DATA AND DEFINITIONS USED:... 6 1. Daily rainfall data for the period of 1950 to 2006 collected at the Douala international Airport... 6 2. DATA reformatted using SSC-Stat tool before it could be imported from EXCEL to INSTAT... 6 E. RESULTS:... 1) - Find the dates when sowing and flooding is possible using suitable definitions:... 7 2. Assessment of the risk of flooding with crop failure:... 8 3. RISK OF FLOODING WITH CROP FAILURE... 9 4. Text boxes showing the chance (proportion) of experiencing floods and crop failure during the month of August:... 13 5. Boxplots for visual comparison, descriptive statistics as dates and Comment on the summaries:... 16 F. IMPLICATIONS:... 21 1. The sowing strategy definition that I would recommend to a farmer... 21 2. The advantages... 21 3. The disadvantages... 21 G.APPENDICES:... 22 Appendix A: References and sources documentation... 22 Appendix: Daily data for Douala, Cameroon 1950-2006... 27 Day numbers in the year... 29 2
BACKGROUND: 1). Extreme climate events increasingly important for Cameroon Climate extremes such as droughts and floods have increased in frequency and severity in Africa over the past 30 years (Nicholson, 1987). The probability of extreme climate events is becoming increasingly important for Cameroon because of the inherent vulnerability of its agricultural system and even the associated risk of the potential spread of plant, animal as well as human diseases (malaria, typhoid, cholera, etc.) that are highly linked to climate variability and climate change. 2) Location and climate of Douala, Cameroon in Africa Cameroon lies within latitudes 1 45 N to 13 N and Longitude 8 25 E to 16 28 E. It is situated on the west coast of Africa, running north to south from Sahara desert to the Atlantic Ocean. The country is bounded on the north by Lake Chad; on the east by Chad and the Central African Republic; on the south by the Republic of the Congo, Gabon, and Equatorial Guinea; and on the west by the Bight of Biafra (an arm of the Atlantic Ocean) and Nigeria (Figure 1). The country is shaped like an elongated triangle, and forms a bridge between West Africa and Central Africa. Cameroon has a total area of 475,442 km 2. Yaoundé is the capital, and Douala is the largest city. The major industries (petroleum refineries, fishing industries, international air transports and others) are located in this region. Douala city is situated at the junction of the southern coastal plain region with dense equatorial rain forests and the west area of high forested mountains of volcanic origin, where lies Mount Cameroon Mountain (4095m), the highest peak in western Africa and an active volcano. One of the country s most fertile soils is found in this region. July and August are seen to be the peak of the rainy season, with a lowest total of 207.4mm in July 2003 and one year (August1966) with over 1240mm. The rains are usually from January to December, though December, January and February are occasionally dry. The mean maximum relative humidity occurs here due to its proximity to Atlantic Ocean (exposure to the warm Guinean Gulf s currents). Here, the type and intensity of the weather is determined by the meridional variations in the depth of the monsoon layer (moisture). The southwest (SW) monsoon flow at lower levels, source of humidity to a large extent determined by the large scale atmospheric circulation and 3
sea-air interaction over much of the tropical Atlantic sector.(lamb,1983). Douala Cameroon (about 4ºN) is well usually marked by a zone with deep active and convective clouds, thunderstorms and squall lines (SW winds) and heavy precipitations. The African Waves are often associated with Squall lines that form, develop and dissipate within the waves. Figure 1: Location of Douala, Cameroon in Africa B. OBJECTIVES: The main objective of the study is to investigate the sowing period variability and flooding risks in the city of Douala. These will be achieved by addressing the following specific objectives: i. Assessment of the annual distribution of sowing dates; ii. iii. iv. Assessment of the flooding risks during the rainfall peak period; To quantify the risk of having floods with crop failure for each week in the month of August, where 100mm of rain or more in a day has caused flooding and crop destruction. Again we compute the number of years in the time series when at exactly one day in the week in question has registered 100mm or more of rain. If the event was observed at least once, then we define that a week experiences a crop failure. Week 1 is from day number 212 to day number 218; Week 2 is from day number 219 to day number 225; Week 3 is from day number 226 to day number 232; Week 4 is from day number 233 to day number 239. Towards development of a possible cautious strategy. 4
C. METHODOLOGY: The methods used to achieve the objectives mentioned above are the following: All these results describe the rainfall data for Douala, Cameroon and were computed (plots, graphs, tables, figures, risks or variability calculations) using Instat+ v3.36 and Excel packages. To define the events of interest (start of the season, dry spell) the climatic>>events menu options from INSTAT were used. Then the sowing dates were extracted and analyzed based on the below definitions. 1. Find the dates when sowing are possible using the suitable definitions: a)- First date from 1 st March getting more than 40mm in 1,2,3 or 4 days; b)- First date from 1 st April getting more than 40mm in 1,2 or 3 days; c) First date from 1 st May getting more than 40mm in 1 or 2 days; d) First date from 1 st June getting more than 40mm in 1 day 2. Assessment of the risk of flooding with crop failure e) Fist occasion after 1 st August with more than 100mm totalled over 2 consecutive days and no dry spell of 3 days or more in the next 30 days. If the event was observed at least once we define that a year experiences a flood in low-land areas. f) First occasion after 1 st August with more than 100mm totalled exactly over one day. If the event was observed at least once we define that a year experiences a general flood with crop failure. g) The average rainfall total for August will be compared with the average totals for the other months to get a general idea as to how wet the month is. Then the month will then be broken down in 4 weeks as specified above, where the average total for each week will be looked at and the highest rainfall totals will be highlighted. After this, a count of the number of days with at least 100mm in exactly 1 day will be looked at for each week, then find the average number of times per week each of these occurred over the past 57 years. This will give the probability of the event of flooding, and therefore the level of risk for encountering crop failure in either week 1, 2, 3 or 4 will be estimated. 3. Boxplots for visual comparison, descriptive statistics as dates and Comment on the summaries. 4. Some conclusions for the client (Ministry of agriculture) based on these summaries and risks calculations. 5
D. DATA AND DEFINITIONS USED: 1. Daily rainfall data for the period of 1950 to 2006 collected at the Douala international Airport Daily rainfall data for the period of 1950 to 2006 collected at the Douala international Airport which was provided by the Cameroon meteorological service. The accumulated number of years of daily data is 57, because almost all the data was available. A rainy day in this instance is considered to be a day with at least 0.85mm of rainfall. The data described are the daily rainfall values from 1950 to 2006. The mean annual total rainfall over this period was 3895mm with an average of about 220 rainy days. The highest annual total was 5327.6mm in 1956; the lowest total recorded was 2595.9mm in 1984. The daily rainfall data was originally provided in EXCEL format by the Meteorological office. It was then examined to ensure its quality. A thorough inspection was done in an effort to clean the data from any erroneous values whenever necessary. There where very few missing data and no negative values. The measurement units millimeters were consistently used throughout the dataset. The data had to be reformatted. 2. DATA reformatted using SSC-Stat tool before it could be imported from EXCEL to INSTAT DATA was reformatted using SSC-Stat tool before it could be imported from EXCEL to INSTAT where supplementary checks were conducted to ensure adequate coding for nonleap years and proper calendar year settings. The coding used fro non leap years was 9988 represented as ***. 6
E. RESULTS: These results describe the rainfall data for Douala, Cameroon. This section gives all the results (plots, graphs, tables, figures, risks or variability calculations, using Instat+ v3.36). It is also the space for analysis of the events. To define the events of interest (start of the season, dry spell) the climatic>>events menu options from INSTAT were used. Then the sowing dates were extracted and analyzed based on the given definitions. 1) - Find the dates when sowing and flooding is possible using suitable definitions: Table 1: Sowing & flooding dates YEAR 1st Mar 1st Apr 1st May 1st Jun 1st Aug floods 1st Mar 1st Apr 1st May 1st Jun 1st Aug flood s 1950 5-Mar 3-Apr 24-May 3-Jun 22-Aug 10-Sep 65 94 145 155 235 254 1951 23-Apr 23-Apr 4-May 8-Jun 1-Aug 1-Sep 114 114 125 160 214 245 1952 11-Mar 14-Apr 4-May 1-Jun 14-Aug 14-Aug 71 105 125 153 227 227 1953 24-Mar 29-Apr 1-May 7-Jun 21-Aug 18-Sep 84 120 122 159 234 262 1954 5-Mar 13-Apr 12-May 7-Jun 4-Sep 12-Sep 65 104 133 159 248 256 1955 1-Mar 8-Apr 2-May 14-Jun 9-Aug 28-Aug 61 99 123 166 222 241 1956 10-Mar 8-Apr 20-May 2-Jun 11-Aug 11-Aug 70 99 141 154 224 224 1957 3-Mar 1-Apr 18-May 9-Jun 1-Aug 5-Aug 63 92 139 161 214 218 1958 19-Mar 12-Apr 11-May 17-Jun 7-Aug 14-Sep 79 103 132 169 220 258 1959 16-Mar 4-Apr 2-May 7-Jun 2-Aug 2-Aug 76 95 123 159 215 215 1960 7-Mar 17-Apr 9-May 19-Jun 5-Aug 5-Aug 67 108 130 171 218 218 1961 23-Mar 1-Apr 29-May 29-Jun 11-Aug 13-Aug 83 92 150 181 224 226 1962 14-Mar 14-Apr 4-May 7-Jun 1-Aug 11-Aug 74 105 125 159 214 224 1963 5-Apr 5-Apr 7-May 4-Jun 14-Aug 14-Aug 96 96 128 156 227 227 1964 8-Mar 7-Apr 3-May 4-Jun 14-Aug 14-Aug 68 98 124 156 227 227 1965 11-Mar 8-Apr 6-May 9-Jun 2-Aug 15-Aug 71 99 127 161 215 228 1966 7-Mar 1-Apr 5-Jun 5-Jun 4-Aug 23-Aug 67 92 157 157 217 236 1967 12-Apr 12-Apr 11-May 16-Jun 16-Aug 24-Aug 103 103 132 168 229 237 1968 6-Mar 19-Apr 5-May 9-Jun 30-Aug 21-Sep 66 110 126 161 243 265 1969 3-Mar 3-Apr 9-May 22-Jun 11-Aug 2-Sep 63 94 130 174 224 246 1970 18-Mar 12-Apr 16-May 25-Jun 1-Aug 3-Sep 78 103 137 177 214 247 1971 18-Mar 4-Apr 20-May 13-Jun 2-Aug 2-Sep 78 95 141 165 215 215 1972 29-Mar 17-Apr 2-Jun 2-Jun 10-Aug 10-Aug 89 108 154 154 223 223 1973 18-Mar 4-Apr 30-May 1-Jun 6-Aug 1-Sep 78 95 151 153 219 245 1974 12-Mar 23-Apr 8-May 29-Jun 4-Aug 14-Aug 72 114 129 181 217 227 1975 8-Mar 18-Apr 8-May 7-Jun 17-Aug 29-Sep 68 109 129 159 230 273 1976 2-Apr 2-Apr 7-May 5-Jun 1-Aug - 93 93 128 157 214 0 1977 29-Mar 5-Apr 28-May 12-Jun 12-Aug 12-Aug 89 96 149 164 225 225 1978 5-Apr 5-Apr 11-May 1-Jun 3-Aug 19-Aug 96 96 132 153 216 232 1979 3-Mar 19-Apr 1-May 1-Jun 2-Aug 27-Sep 63 110 122 153 215 271 1980 17-Mar ** 11-May 2-Jun 5-Sep 6-Sep 77 *** 132 154 249 250 1981 18-Mar 1-Apr 3-May 8-Jun 1-Aug 22-Aug 78 92 124 160 214 235 1982 10-Mar 9-Apr 2-May 28-Jun 21-Aug 12-Sep 70 100 123 180 234 256 1983 28-Mar 1-Apr 9-May 22-Jun 2-Aug - 88 92 130 174 215 0 1984 10-Mar 4-Apr 17-May 21-Jun 8-Aug 8-Aug 70 95 138 173 221 221 1985 15-Mar 1-Apr 2-May 13-Jun 5-Aug 30-Aug 75 92 123 165 218 243 1986 29-Mar 2-Apr 3-May 4-Jun 11-Aug 3-Nov 89 93 124 156 224 308 1987 7-Mar 4-Apr 28-May 26-Jun 17-Aug 17-Aug 67 95 149 178 230 230 1988 8-Mar 21-Apr 20-May 17-Jun 24-Aug 24-Aug 68 112 141 169 237 237 1989 20-Mar 16-Apr 4-May 12-Jun 12-Aug 12-Aug 80 107 125 164 225 225 1990 24-Apr 24-Apr 3-May 2-Jun 9-Aug 25-Aug 115 115 124 154 222 238 1991 8-Apr 8-Apr 1-May 21-Jun 5-Aug - 99 99 122 173 218 0 7
Rainfall ( mm ) 1992 8-Mar 14-Apr 6-May 13-Jun 5-Oct 5-Oct 68 105 127 165 279 279 1993 9-Mar 13-Apr 14-May 3-Jun 4-Aug 30-Aug 69 104 135 155 217 243 1994 23-Mar 3-Apr 2-May 22-Jun 9-Aug 9-Aug 83 94 123 174 222 222 1995 17-Mar 15-Apr 8-May 5-Jun 3-Aug 3-Aug 77 106 129 157 216 216 1996 1-Mar 11-Apr 27-May 1-Jun 18-Aug - 61 102 148 153 231 0 1997 25-Mar 6-Apr 1-May 16-Jun 1-Aug - 85 97 122 168 214 0 1998 6-Apr 6-Apr 2-May 15-Jun 13-Aug 13-Aug 97 97 123 167 226 226 1999 28-Mar 3-Apr 7-May 18-Jun 3-Aug 3-Sep 88 94 128 170 216 247 2000 22-Mar 3-Apr 5-Jun 5-Jun 3-Aug 16-Aug 82 94 157 157 216 229 2001 1-Mar 2-Apr ** 3-Jun 20-Sep 23-Sep 61 93 *** 155 264 267 2002 1-Mar 1-Apr 1-May 15-Jun 15-Aug 15-Aug 61 92 122 167 228 228 2003 29-Mar 9-Apr 24-May 7-Jun 5-Aug 5-Aug 89 100 145 159 218 218 2004 25-Mar 4-Apr 3-May 9-Jun 0-Jan - 85 95 124 161 0 0 2005 11-Mar 21-Apr 4-May 5-Jun 6-Aug 14-Sep 71 112 125 157 219 258 2006 15-Mar 1-Apr 4-May 14-Jun 1-Aug 17-Aug 75 92 125 166 214 230 Earliest 1-Mar 1-Apr 1-May 1-Jun 1-Aug 1 st -Aug 61 92 122 153 214 214 Latest 24-Apr 29-Apr 5-Jun 29-Jun 5-Oct 3-Nov 115 120 157 181 279 308 2. Assessment of the risk of flooding with crop failure: Graph of the Average monthly rainfall for years 1950-2006 at Douala International Airport 1400 1200 1000 800 600 Average minimum monthly rainfall Average monthly rainfall Average maximum monthly rainfall 400 200 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Graph (i): Average monthly rainfall for years 1950-2006 (Douala) According to graph (i) (see also table1, page 25 of appendix), August is the wettest month of the year with an average of 739.5 mm over 57 year period. 8
Graph (ii): Total rainfall in August for years 1950-2006 (Douala Airport) Graph (ii) shows the yearly totals of rainfall for the month of August throughout the years. The year with the highest totals was 1966 with 1240 mm and the year with the lowest total was 1954 with a mere 248.3 mm of rainfall. 3. RISK OF FLOODING WITH CROP FAILURE Table 3: showing the yearly totals of rainfall within the month of August Year Week 1 Week 2 Week 3 Week 4 1950 244,4 81,1 135,7 231,3 1951 240,8 132,1 82,9 117,5 1952 92,7 94,4 292,4 188,9 1953 125 115,9 121 399 1954 58,9 40,6 31,5 77,1 1955 121,1 271,8 130,9 125,2 1956 154,4 252 273,4 37,8 1957 318,8 206,8 185,7 271,5 1958 161,7 243,7 127,7 134,6 1959 320,6 262,4 195,7 220,8 1960 211,5 508,5 292 77,5 1961 23,4 270,3 334,9 197,9 1962 363,9 217,5 168,4 152,2 1963 227,2 117,5 209 145,6 1964 38,3 32,3 740 52,2 1965 286,5 155,1 317,6 210,3 1966 301,5 229,2 290,5 444,4 9
1967 97,3 175,8 198,8 369,9 1968 26,4 126,9 65,5 58,2 1969 95,5 144,8 189,8 193,9 1970 187,7 170,4 198,4 140 1971 452,2 211,7 138,7 239,2 1972 160,9 296,5 167,9 66,4 1973 187,4 232 109,4 137,6 1974 170,2 67,7 497,9 140,3 1975 70,3 82,7 134,6 211,3 1976 139 162,3 74 110,8 1977 92,5 257,8 26,1 416 1978 219,2 143,6 268,2 189,8 1979 189,6 97,6 126,7 92,1 1980 136,4 91,7 82,3 106,7 1981 242,9 132,3 219,2 285,3 1982 156,8 73,7 96,8 267,3 1983 152,8 84,4 60,4 104,5 1984 117,8 177,6 94,9 50,9 1985 164,8 125,4 83 201,7 1986 100 194,1 42,6 133 1987 50,4 90,3 310,9 323,5 1988 84 95 59,9 259,3 1989 136,7 213,9 352,4 200,3 1990 205,9 226,2 127,3 211,8 1991 305,4 131,6 206,6 199,1 1992 129,1 49,9 59,2 72,8 1993 225,5 149,9 133,7 174,8 1994 129 240,3 248,1 117,6 1995 188,3 105,3 171,6 126,1 1996 102,4 58,6 272,4 64,3 1997 340,6 124,1 195 37,1 1998 94,4 47 209,8 170,3 1999 227,4 42,3 61,4 110 2000 205,7 72,4 265 291,2 2001 143 151,5 83,6 55,1 2002 253,8 189,5 252,2 159,1 2003 175,1 161,8 281,3 165 2004 1,5 55,1 57,1 43,9 2005 179,5 134,7 125,8 200,6 2006 348,9 21,2 288,1 161,6 Total 9977 8640,8 10565,9 9742,2 10
Graph (iii): Yearly totals rainfall in August for week 1, 2, 3 & 4 Table (3) and graph (iii) show that week 2 and 4 are those with the least amount of rainfall while week 3 and 1 are the wettest. Assessment of the weekly risk of flooding with crop failure: To quantify the risk of experiencing a flood for each week in the month of August, when 100mm or more rain in exactly one day has occurred. We compute the number of years in the time series when at least one day in the week in question has registered 100mm or more of rain. If the event was observed at least once, then we define that a week experienced a flood. TABLE 4: Showing the frequency of having 100 mm or more rainfall in a day (possible flooding with crop failure) for weeks 1, 2, 3 & 4 for the month of August over the years. Year WEEK-1 WEEK-2 WEEK-3 WEEK-4 1950 0 0 0 0 1951 0 0 0 0 1952 0 0 1 0 1953 0 0 0 0 1954 0 0 0 0 1955 0 0 0 0 1956 0 1 0 0 1957 1 0 0 1 1958 0 0 0 0 1959 1 1 1 0 1960 1 2 1 0 1961 0 0 1 0 1962 2 1 0 1 1963 1 0 1 0 1964 0 0 3 0 1965 0 0 1 1 1966 0 0 0 1 11
1967 0 0 0 1 1968 0 0 0 0 1969 0 0 0 0 1970 0 0 0 0 1971 3 0 0 0 1972 0 2 0 0 1973 0 0 0 0 1974 0 0 3 0 1975 0 0 0 0 1976 0 0 0 0 1977 0 1 0 1 1978 0 0 1 0 1979 0 0 0 0 1980 0 0 0 0 1981 1 0 0 1 1982 0 0 0 0 1983 0 0 0 0 1984 0 1 0 0 1985 0 0 0 0 1986 0 0 0 0 1987 0 0 1 0 1988 0 0 0 1 1989 0 1 2 1 1990 0 0 0 1 1991 1 0 0 0 1992 0 0 0 0 1993 0 0 0 0 1994 0 1 0 0 1995 1 0 0 0 1996 0 0 0 0 1997 1 0 0 0 1998 0 0 1 0 1999 0 0 0 0 2000 0 0 1 1 2001 0 0 0 0 2002 1 0 1 0 2003 1 0 1 0 2004 0 0 0 0 2005 0 0 0 0 2006 0 0 1 0 Total nonzero 12 9 16 11 The frequency of possible crop failure shown in table (iv) indicate that over the past 57 years, there were 12 years when 100 mm or more fell in week 1, compared with 9 years in week 2, 16 years in week 3 and 11 years in week 4. 12
4. Text boxes showing the chance (proportion) of experiencing floods and crop failure during the month of August: Simple Models - Normal Distribution, One Sample TINt 'Flooding' Normal model, one sample Column Flooding Sample size 57 Minimum 0 Maximum 308 Range 308 Mean 214 Std. deviation 76.272 Standard error of mean = 10.103 with 56 d.f. 95% confidence interval for mean 193.76 to 234.24 From our sample of 57 years, the true mean date of the start of threatening flooding ( from 1 st August, 100mm or more of rain/ 1day) is estimated to be day 214(1.August) and is highly likely to be between day 193 (11.July) and day 234 (21.August). I am 95% confident that the margin error is ± 20 days (about 3 weeks). WEEK 1 CHANCE OF CROP FAILURE One proportion - binomial model BINomial;stats 57 12;SIMple;EXAct Binomial model, single sample Sample size 57 Successes 12 Proportion 0.211 Approx s.e. of proportion = 0.054 Exact results: 95% confidence interval for prop. 0.114 to 0.339 Simple normal approximation: 95% confidence interval for prop. 0.105 to 0.316 The 95% confidence interval for the true risk of flooding with crop failure for the first week in August is from 11.4% to 33.9%. Estimated value (proportion) = 0.211 (21.1%) s.e. = 0.054 (5.4%) The risk of crop failure during week 1 of August is (12/57): 21.05% or about 21% with a return period of (1/0.2105 = 4.75) about 5 years. I am 95% confident that the estimate of 21.1% is within ± 11.25% of the true risk of flooding with crop failure for the first week.. 13
WEEK 2 CHANCE OF CROP FAILURE One proportion - binomial model BINomial;stats 57 9;SIMple;EXAct Binomial model, single sample Sample size 57 Successes 9 Proportion 0.158 Approx s.e. of proportion = 0.048 Exact results: 95% confidence interval for prop. 0.075 to 0.279 Simple normal approximation: 95% confidence interval for prop. 0.063 to 0.253 The 95% confidence interval for the true risk of flooding with crop failure for the second week in August is from 7.5% to 27.9%. Estimated value (proportion) = 0.158 (15.8%) s.e. = 0.048 (4.8%) The risk of crop failure during week 2 of August is (9/57 = 0.1579): 15.79% or about 16% with a return period of (1/0.1579 = 6.333) about 6.5 years. I am 95% confident that the estimate of 15.8% is within ± 10.2% of the true risk of flooding with crop failure for the second week. WEEK 3 CHANCE OF CROP FAILURE One proportion - binomial model BINomial;stats 57 16;SIMple;EXAct Binomial model, single sample Sample size 57 Successes 16 Proportion 0.281 Approx s.e. of proportion = 0.060 Exact results: 95% confidence interval for prop. 0.170 to 0.415 Simple normal approximation: 95% confidence interval for prop. 0.164 to 0.397 The 95% confidence interval for the true risk of flooding with crop failure for the third week in August is from 17% to 41.5%. Estimated value (proportion) = 0.281 (28.1%) s.e. = 0.06 (6%) 14
The risk of crop failure during week 3 of August is (16/57 = 0.2807): 28.07% or about 28% with a return period of (1/0.2807 = 3.56) about 3.5 years. I am 95% confident that the estimate of 28.1% is within ± 12.25% of the true risk of flooding with crop failure for the third week. WEEK 4 CHANCE OF CROP FAILURE One proportion - binomial model BINomial;stats 57 11;SIMple;EXAct Binomial model, single sample Sample size 57 Successes 11 Proportion 0.193 Approx s.e. of proportion = 0.052 Exact results: 95% confidence interval for prop. 0.100 to 0.319 Simple normal approximation: 95% confidence interval for prop. 0.091 to 0.295 The 95% confidence interval for the true risk of flooding with crop failure for the fourth week in August is from 10% to 31.9%. Estimated value (proportion) = 0.193 (19.3%) s.e. = 0.052 (5.2%) The risk of crop failure during week 4 of August is (11/57 = 0.193): 19.3% or about 19% with a return period of (1/0.193 = 5.2) about 5 years. I am 95% confident that the estimate of 19.3% is within ±10.95% of the true risk of flooding with crop failure for the fourth week..5. Boxplots for visual comparison, descriptive statistics as dates and Comment on the summaries: 15
Boxplots for visual comparison: Graph (iv): Boxplots showing the distribution of sowing and flooding dates ( day numbers) for the given definitions: From the above boxplots, it is obvious that the bold (1 st Mar) distribution presents a median date of sowing almost on day 76 (16.March). As a matter of fact ( boxplot stdr1lo, based on definition e ) the median occurrence of flooding in low lands is on day 221 (8.August). Boxplot of flooding with crop failure based on definition f shows that from 1 st August,100mm or more rainfall in exactly one day is highly likely to be between day 214 (1.August) and day 280 (6-October). From 6 years out of 57 years, the general risk of having this event is 10.53%, which is a 9.5 years return period. 16
Graph (v): Boxplots showing the distribution of rainfall in August for week 1, 2, 3 & 4 Graph (v) shows that week 3 and 1 have more variations in the rainfall totals for the week. Comparing week 3 and 1, it shows that week 3 has more variation than week 1 with almost the same amount of outliers. Descriptive statistics as dates: Conditions Table 5: Statistics summaries of sowing and flooding day numbers missin g count Mean SDE Min 5% 25% 40% Media n 60% 75% 95% Maximum 1 st Mar 0 57 77.86 13 61 61 68 71 76 78 86.5 104.1 115 1 st Apr 1 56 100.2 7.38 92 92 94 95.8 98.5 100.4 105 114.2 120 1 st May 1 56 132.1 10.2 122 122 124 125.8 128.5 130.4 138.8 154.5 157 1 st Jun 0 57 162.9 8.12 153 153 156 159 161 164.8 168.5 180.1 181 1 st Aug 0 57 220.5 32.2 214 214 215.5 218 221 224 227.5 250.5 279 flooding 0 57 214 76.27 0 0 222.5 227 230 237 247 273.6 308 17
Table 6: Statistics summaries of sowing and flooding dates Conditions Minimum 25% Median 75% Maximum 1stMar(bold) 1.Mar 8.Mar 16.Mar 26.Mar 24.Apr 1 st Apr 1.Apr 3.Apr 7.Apr 14.Apr 29.Apr 1 st May 1.May 3.May 7.May 18.May 5.Jun 1 st Jun(latest) 1.Jun 4.Jun 9.Jun 16.Jun 29.Jun 1 st Aug(lowlands) 1.Aug 2.Aug 8.Aug 14.Aug 5.Oct 1 st Aug(flooding) 1.Aug 9.Aug 17.Aug 3.Sep 3.Nov Table 7: summaries of flooding risk with crop failure for each week in August August Week 1 Week 2 Week 3 Week 4 RETURN PERIODS ( of flooding with crop failure) 5 years 6.5 years 3.5 years 5 years Comment on the summaries: Graph (v) shows that week 3 and 1 have more variations in the rainfall totals for the week. Comparing week 3 and 1, it shows that week 3 has more variation than week 1 with almost the same amount of outliers. What is the distribution of sowing dates? In Douala, farmers always sowed before the start of the peak of rainfall when the soil is saturated, especially in August. So, the maximum or latest sowing date is the same for both farmers: day 214 (1.August). Earliest sowing date for bold farmer is day 61 (1 March) opposed to day 153 (1.June) for latest farmer. How wider is the season of the bold farmer compared to that of a latest farmer? 18
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Difference in the length of growing season as experienced by bold and latest farmers Bold farmers Latest farmers Year Day_number Date Day_number Date Difference 1950 65 5-Mar 155 3-Jun 90 1951 114 23-Apr 160 8-Jun 46 1952 71 11-Mar 153 1-Jun 82 1953 84 24-Mar 159 7-Jun 75 1954 65 5-Mar 159 7-Jun 94 1955 61 1-Mar 166 14-Jun 105 1956 70 10-Mar 154 2-Jun 84 1957 63 3-Mar 161 9-Jun 98 1958 79 19-Mar 169 17-Jun 90 1959 76 16-Mar 159 7-Jun 83 1960 67 7-Mar 171 19-Jun 104 1961 83 23-Mar 181 29-Jun 98 1962 74 14-Mar 159 7-Jun 85 1963 96 5-Apr 156 4-Jun 60 1964 68 8-Mar 156 4-Jun 88 1965 71 11-Mar 161 9-Jun 90 1966 67 7-Mar 157 5-Jun 90 1967 103 12-Apr 168 16-Jun 65 1968 66 6-Mar 161 9-Jun 95 1969 63 3-Mar 174 22-Jun 111 1970 78 18-Mar 177 25-Jun 99 1971 78 18-Mar 165 13-Jun 87 1972 89 29-Mar 154 2-Jun 65 1973 78 18-Mar 153 1-Jun 75 1974 72 12-Mar 181 29-Jun 109 1975 68 8-Mar 159 7-Jun 91 1976 93 2-Apr 157 5-Jun 64 1977 89 29-Mar 164 12-Jun 75 1978 96 5-Apr 153 1-Jun 57 1979 63 3-Mar 153 1-Jun 90 1980 77 17-Mar 154 2-Jun 77 1981 78 18-Mar 160 8-Jun 82 1982 70 10-Mar 180 28-Jun 110 1983 88 28-Mar 174 22-Jun 86 1984 70 10-Mar 173 21-Jun 103 1985 75 15-Mar 165 13-Jun 90 1986 89 29-Mar 156 4-Jun 67 1987 67 7-Mar 178 26-Jun 111 1988 68 8-Mar 169 17-Jun 101 1989 80 20-Mar 164 12-Jun 84 1990 115 24-Apr 154 2-Jun 39 1991 99 8-Apr 173 21-Jun 74 1992 68 8-Mar 165 13-Jun 97 1993 69 9-Mar 155 3-Jun 86 1994 83 23-Mar 174 22-Jun 91 1995 77 17-Mar 157 5-Jun 80 1996 61 1-Mar 153 1-Jun 92 1997 85 25-Mar 168 16-Jun 83 1998 97 6-Apr 167 15-Jun 70 1999 88 28-Mar 170 18-Jun 82 2000 82 22-Mar 157 5-Jun 75 20
2001 61 1-Mar 155 3-Jun 94 2002 61 1-Mar 167 15-Jun 106 2003 89 29-Mar 159 7-Jun 70 2004 85 25-Mar 161 9-Jun 76 2005 71 11-Mar 157 5-Jun 86 2006 75 15-Mar 166 14-Jun 91 Minimum Mean Range Std.deviation Maximum 57 years 39 days 85.053 days 72 days 15.461 days 111 days 5.5weeks 12weeks = 3months 10weeks 2weeks 16weeks = 4 months How often will the bold farmer have a longer growing season than the latest farmer? This question is answered by quantifying how often the season was longer for a bold farmer than for a latest farmer (conditional on differences being greater than zero). It will be found that the bold farmer who sows earlier in the season will always have the benefit of a longer season, which is a full 100% of the time. Talking about the length of the growing season, when we subtract starting date (as day number) of the latest farmer from that of the bold farmer we get 57 non-zero values, indicating that the former experienced a longer growing season every single year. On average his season was 85 days longer, at last 39 days longer and at most 111days longer, with a standard deviation of about 15.5 days. How far is the sowing season of the bold farmer compared to the occurrence of the flooding period? The maximum or latest sowing date for bold farmer is day 115 (24.April). Earliest flooding occurrence date is day 214 (1.August) according to our given definition. So, the bold strategy is at least 99 days (almost 3 months) before the first flooding strike which is almost 2.5 weeks (19 days) more variable, and completely off after 3 rd November (day 308). 21
F. IMPLICATIONS: Some conclusions for the client (Ministry of agriculture) based on these summaries and risks calculations. At last, we could say the highest true risk of experiencing flood with crop failure is observed once every 3.5 years during the third week of August. There is little difference between weeks 1 and 4 with a chance of flooding with crop disruption every 5 years. The smallest risk is observed in week 2 with a 6.5 years return period. 1. The sowing strategy definition that I would recommend to a farmer The sowing strategy definition that I would recommend to a farmer is the bold method. 2. The advantages The advantages could be: The greatest (range =54 days) and variable (s.d. =13 days) spread of sowing dates. The possibility to harvest more than one type of crops within this long sowing period. The possibility of choosing the accurate crop to match the expected season length, with higher yield. A crop growing during a shorter season (3 months) can be sow, with (57/57) 100 % risk or zero risk not to meet a long dry spell. As the threshold rainfall for sowing is high (40 mm), chance of crop failure is low even if there is long dry spell later. Hence, by sowing earlier, the risk of early crop failure due to flood could be greatly reduced even in low lands because after three months, the growing stage enables more plants maturity to face flooding events and the farmer can gain in confidence in the whole system of recommendations. 3. The disadvantages The disadvantages could be: Even with a better seasonal forecast, there still be at least once every three (3) years a chance of crop destruction in Douala, during the peak period (July, August, and September) of rainfall when the soil is saturated, especially in August. The flooding event in low land areas has a range of 65 days (about 2 months). There is highest interannual variability i.e. spread in flooding dates with a variability of 32 days (about 4.5 weeks mainly within the month of August). So maximum awareness must be taken around day 221(8.August) and also the farmer needs to keep himself in state of preparedness for this period so as to take action of the 1 st occasion to protect or to secure the crop). That is why I strongly recommend to the farmers dwelling in Douala and surrounding: Please! Sow earlier!. 22
G.APPENDICES: Appendix A: References and sources documentation Instat Climatic Guide Chapters 4-7 Roger Stern, Derk Rijks, Ian Dale, Joan Knock ed. January 2006 Confidence and significance: Key Concepts of Inferential Statistics, the University of Reading Statistical Services Centre, February 2006 Climatic e-books (www.reading.ac.uk/ssc ) CAST for SADC ( www.ssc.rdg.ac.uk/sadc-training-pack/) Appendix: Daily data for Douala, Cameroon 1950-2006 Fig. 1.a Time series plot of annual rainfall totals and number of rainy days at Douala, Cameroon, from 1950 to 2006. The dotted horizontal lines show one and two standard deviations above and below the mean. 23
PLOT OF ANNUAL NUMBER OF RAINY DAYS IN DOUALA;CAMEROON(1950-2006) 250 240 230 220 210 200 190 1950 1960 1970 1980 Year 1990 2000 2010 The individual daily values or rainfall for every year, together with monthly summaries, are given in the Appendix. Fig. 2. Daily rainfall values for 1950 and 1951. 1950 1951 24
Figure 2 shows the pattern of rainfall through the year for two years. Notice the false start to the season in each year, where a few early days of rainfall are followed by a long spell of dry days. Fig. 3. Summary values of monthly rainfall. 1950-2006 PLOT OF THE SUMMARY STATISTICS AGAINST THE MONTHS IN DOUALA; CAMEROON gfedcb 1200 gfedcb gfedcb gfedcb 1000 gfedcb gfedcb X76 X77 X78 X79 X80 X81 800 600 400 200 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec MONTHS 25
Table1: Summary values of monthly rainfall Column Min. 25% Mean Median 75% Max. Jan 0 8.3 42.95 28.2 64.35 183.5 Feb 2.3 33.15 65.52 55 100.4 216.2 Mar 21.1 127.2 181 174.9 228.4 425.7 Apr 122.6 194.7 238.2 228.1 271.8 434.6 May 133 216 286 297 345.8 433.1 Jun 174.5 322.3 441.1 404.4 540.4 1002 Jul 207.4 555.6 695.7 689.1 867.1 1208 Aug 248.3 556.9 739.5 733.4 884.3 1240 Sep 273.9 472.7 623.1 613.3 773.6 1026 Oct 196.3 334.7 408.4 410.2 456.2 635.5 Nov 0 94.45 132.4 120.1 165.7 305.2 Dec 0 11.15 40.85 25.8 59.15 168.3 Figure 3, Table 1 and 2 show some summary values for the monthly totals. July and August are seen to be the peak of the rainy season, with a lowest total of 207.4mm in July 2003 and one year (August1966) with over 1240mm. The rains are usually from January to December, though December, January and February are occasionally dry. Table 2: minimum, mean and maximum monthly rainfall summaries MONTH MINIMUM MEAN MAXIMUM January 0 42.95 183.5 February 2.3 65.52 216.2 March 21.1 181 425.7 April 122.6 238.2 434.6 May 133 286 433.1 June 174.5 441.1 1002 July 207.4 695.7 1208 August 248.3 739.5 1240 September 273.9 623.1 1026 October 196.3 408.4 635.5 November 0 132.4 305.2 December 0 40.85 168.3 26
Table 2: Monthly rainfall totals in each year (1950-2006). Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1950 135 123 426 270 141 510 1003 743 606 346 168 56 1951 7 47 71 188 345 639 571 689 979 379 164 25 1952 74 22 191 316 420 502 954 707 777 453 130 46 1953 90 119 216 132 325 862 689 802 733 361 148 19 1954 23 142 181 340 330 711 813 248 763 493 210 69 1955 39 47 225 272 297 317 547 838 460 404 151 4 1956 182 185 273 283 263 415 1154 836 770 560 284 124 1957 184 48 220 248 359 505 750 997 657 421 112 31 1958 29 55 179 271 193 555 684 693 797 455 227 79 1959 105 37 273 195 353 493 739 1091 636 602 120 120 1960 74 43 167 193 298 371 675 1232 870 338 46 32 1961 63 5 284 271 299 298 757 947 568 308 149 8 1962 30 106 244 333 346 564 913 819 553 417 298 39 1963 20 73 58 216 331 328 869 566 475 263 99 119 1964 6 35 307 261 234 648 889 1117 805 337 176 57 1965 51 111 212 199 263 786 327 992 826 502 95 73 1966 41 39 302 349 182 407 666 1240 639 346 168 168 1967 0 107 141 201 310 1002 682 952 613 421 146 40 1968 79 67 146 190 335 556 499 498 517 239 121 28 1969 37 50 217 196 251 592 776 641 918 437 134 134 1970 27 115 142 175 216 556 881 680 854 535 113 14 1971 42 38 211 211 348 393 980 1081 616 545 93 38 1972 44 26 94 123 198 362 636 616 672 539 77 6 1973 90 103 125 304 168 310 761 668 418 315 88 100 1974 12 53 160 155 215 223 650 1025 619 382 74 8 1975 15 59 184 270 191 478 743 571 752 604 223 26 1976 36 216 119 159 346 352 845 548 347 333 155 62 1977 11 13 147 280 330 380 873 785 462 196 46 32 1978 2 79 77 226 276 441 474 904 859 526 140 15 1979 9 120 218 228 339 619 778 530 393 368 187 0 1980 66 153 237 222 412 361 564 506 1026 433 106 22 1981 0 50 139 203 225 432 1208 847 891 458 110 1 1982 120 48 115 249 381 329 646 641 806 481 29 12 1983 0 4 131 156 158 245 534 490 520 385 102 73 1984 32 32 129 294 298 175 280 534 313 452 54 2 1985 118 20 313 342 247 267 403 755 536 282 216 2 1986 7 68 179 195 324 451 936 537 598 520 305 1 1987 40 19 109 168 258 177 417 851 569 453 83 15 1988 28 36 175 266 214 393 865 588 408 444 98 124 1989 0 2 89 233 187 296 332 861 621 372 115 5 1990 43 90 53 213 230 442 656 829 540 436 209 96 1991 1 64 117 348 166 203 1091 733 398 321 34 3 1992 8 5 242 198 268 404 665 370 558 438 161 0 1993 2 61 149 260 433 304 593 897 289 348 232 50 1994 0 34 170 435 373 264 742 761 676 394 0 34 1995 7 9 165 186 380 388 610 635 715 484 156 25 1996 32 154 247 307 406 356 326 514 477 323 7 12 1997 13 4 233 250 291 378 963 637 274 410 117 17 1998 28 8 21 206 216 328 468 534 706 276 47 23 1999 86 79 76 231 275 437 814 472 470 636 120 11 2000 28 4 229 216 133 436 789 871 386 322 117 20 2001 8 71 155 255 406 753 752 524 602 304 205 46 2002 3 104 214 291 316 708 618 961 591 427 125 8 2003 153 85 106 183 190 526 207 948 339 307 104 15 2004 27 98 129 255 294 269 353 275 459 446 150 89 2005 20 62 228 170 395 393 303 670 786 322 87 14 2006 24 89 359 195 324 250 943 853 1009 385 117 39 27
Appendix: Daily data for Douala, Cameroon 1950-2006 Daily data for: Yr1950 Mon Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec --------------------------------------------------------------------------- Day. --------------------------------------------------------------------- 1 -- 32.6 -- 20.3 10.2 2.6 71.0 65.6 -- 0.1 0.1 1.6 2 -- 72.0 0.1 -- 0.9 1.7 28.0 28.0 11.0 32.0 3.8 -- 3 -- -- 8.0 63.0 0.1 109.6 7.8 54.4 45.6 23.5 -- -- 4 -- -- -- 1.5 -- 4.2 4.1 2.6 59.5 10.4 16.9 -- 5 0.4 -- 36.2 1.7 3.0 -- 32.1 6.6 2.4 0.8 0.2 -- 6 -- -- -- 4.0 -- 1.0 7.7 14.4 32.5 4.4 -- -- 7 -- -- 127.8 -- 1.0 11.7 52.7 0.3 9.0 7.6 -- -- 8 -- 0.7 7.2 27.9 0.1 -- 17.7 -- 1.2 1.8 4.1 -- 9 -- -- -- 2.6 -- 1.7 22.8 -- 2.0 -- -- -- 10 -- -- 3.3 -- 0.6 8.9 56.8 7.7 104.0 1.1 14.3 -- 11 -- -- -- -- -- 3.7 21.3 44.0 4.6 1.5 11.5 -- 12 -- -- 0.2 -- 1.3 14.3 215.0 14.7 15.6 10.1 -- -- 13 2.3 -- 4.0 -- -- 10.5 14.4 9.1 11.6 -- -- -- 14 56.0 -- -- -- 0.8 10.5 -- 43.3 17.7 0.2 13.5 -- 15 9.7 -- -- 0.3 4.9 9.0 -- 11.2 10.7 29.9 16.1 -- 16 -- -- 7.0 1.3 -- -- 39.8 0.2 12.5 34.0 0.3 -- 17 -- -- 21.6 -- 0.7 2.8 17.5 48.5 23.7 3.9 3.9 -- 18 -- -- -- -- 0.2 17.8 4.3 23.4 1.1 34.5 5.8 -- 19 -- -- 0.7 -- 11.6 7.9 48.6 -- 10.7 4.3 0.5 1.2 20 -- -- 101.2 5.7 0.5 -- 4.8 3.8 0.2 1.1 -- 13.9 21 -- -- 5.5 3.7 4.1 9.4 0.3 37.8 4.6 26.8 -- 0.7 22 -- -- -- 38.4 9.1 11.5 1.7 81.4 16.5 18.2 0.7 -- 23 -- -- 0.2 -- 7.3 -- 1.8 22.0 0.2 22.0 -- -- 24 -- -- -- 11.5 49.6 87.1 18.3 48.1 49.8 0.4 -- -- 25 2.9 4.1 62.5 12.3 0.9 0.1 14.4 9.5 126.2 -- -- -- 26 27.7 -- 37.8 47.1 8.2 -- 43.9 28.7 6.3 28.4 -- 1.6 27 -- 10.8 -- -- 7.9 58.9 108.9 68.0 11.8 2.0 0.2 -- 28 -- 2.5 -- 25.4 -- 115.0 49.1 8.5 7.5 46.2 -- 18.9 29 -- -- 2.6 0.5 8.2 10.5 5.2 5.5 0.6 75.8 -- 30 35.5 0.7 0.6 0.2 2.3 55.2 55.3 1.7 -- 0.2 -- 31 -- 1.7 17.0 32.0 1.1 -- 18.4 28
Daily data for: Yr1951 Mon Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec --------------------------------------------------------------------------- Day. --------------------------------------------------------------------- 1 -- -- -- -- 3.1 0.7 1.8 34.9 102.2 3.5 6.7 -- 2 -- 0.1 0.2 -- 5.2 0.8 1.1 14.4 42.0 2.9 -- -- 3 -- -- -- -- 2.6 22.6 19.8 85.1 -- 2.1 111.9 -- 4 -- 32.7 -- -- 80.9 16.0 8.4 6.9 0.1 28.1 1.6 -- 5 5.1 -- 0.6 6.3 -- 14.7 36.0 8.6 7.5 2.5 9.3 -- 6 1.2 0.3 -- -- 18.6 0.8 17.4 31.8 9.6 3.4 8.2 -- 7 -- 13.7 12.1 3.8 -- 1.8 25.4 27.8 22.5 9.2 1.6 -- 8 -- -- -- 1.1 0.3 53.6 7.9 25.6 21.7 13.1 -- -- 9 -- -- -- -- 0.4 29.0 3.4 6.9 32.3 11.8 0.8 -- 10 -- -- -- 1.4 -- 9.2 31.6 16.2 65.3 1.5 3.4 -- 11 -- -- -- -- -- 2.0 1.1 23.0 97.1 0.9 0.1 -- 12 -- -- 1.3 10.3 3.3 11.5 3.3 0.8 65.5 28.0 -- -- 13 -- 0.3 -- -- -- 6.4 5.3 6.0 76.4 1.4 0.1 -- 14 -- -- 9.3 -- 4.5 -- -- 57.1 12.5 11.3 0.4 -- 15 -- -- -- 10.5 -- 0.6 2.0 16.9 18.5 19.2 2.4 -- 16 -- -- -- -- 2.4 6.0 9.4 -- 7.7 -- -- -- 17 -- -- -- 0.6 2.0 4.6 26.2 0.1 -- 73.9 3.3 -- 18 -- -- 16.0 -- 4.4 7.7 1.0 -- 20.0 44.9 10.3 -- 19 -- -- 10.1 11.0 12.0 0.6 27.3 2.8 15.2 9.1 -- -- 20 -- -- -- -- 9.0 -- 23.8 5.4 3.0 0.2 -- -- 21 -- -- -- -- 19.2 4.9 -- 15.2 26.2 16.8 -- 24.8 22 -- -- -- -- 3.7 192.7 77.7 16.5 74.7 0.5 3.1 -- 23 -- -- -- 51.0 21.0 217.3 1.8 11.7 44.9 35.0 -- -- 24 -- -- 1.3 -- 1.7 10.7 1.9 2.0 -- -- -- -- 25 -- -- 7.1 70.7 70.6 -- 63.7 24.9 12.6 -- -- -- 26 -- -- -- -- 0.8 -- 40.5 41.8 40.0 3.8 -- -- 27 -- -- 1.4 -- 68.9 -- 6.0 9.4 18.1 14.9 -- -- 28 -- -- -- -- -- -- 6.0 66.5 31.7 35.3 -- -- 29 -- -- 4.1 -- -- 30.1 33.4 47.6 5.6 -- -- 30 -- -- 16.8 1.4 24.9 17.8 95.0 64.1 0.3 0.3 -- 31 1.0 11.6 9.5 73.1 1.8 -- -- 29
Day numbers in the year Month: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec -------------------------------------------------------------------------------- Day ---------------------------------------------------------------------------- 1 1 32 61 92 122 153 183 214 245 275 306 336 2 2 33 62 93 123 154 184 215 246 276 307 337 3 3 34 63 94 124 155 185 216 247 277 308 338 4 4 35 64 95 125 156 186 217 248 278 309 339 5 5 36 65 96 126 157 187 218 249 279 310 340 6 6 37 66 97 127 158 188 219 250 280 311 341 7 7 38 67 98 128 159 189 220 251 281 312 342 8 8 39 68 99 129 160 190 221 252 282 313 343 9 9 40 69 100 130 161 191 222 253 283 314 344 10 10 41 70 101 131 162 192 223 254 284 315 345 11 11 42 71 102 132 163 193 224 255 285 316 346 12 12 43 72 103 133 164 194 225 256 286 317 347 13 13 44 73 104 134 165 195 226 257 287 318 348 14 14 45 74 105 135 166 196 227 258 288 319 349 15 15 46 75 106 136 167 197 228 259 289 320 350 16 16 47 76 107 137 168 198 229 260 290 321 351 17 17 48 77 108 138 169 199 230 261 291 322 352 18 18 49 78 109 139 170 200 231 262 292 323 353 19 19 50 79 110 140 171 201 232 263 293 324 354 20 20 51 80 111 141 172 202 233 264 294 325 355 21 21 52 81 112 142 173 203 234 265 295 326 356 22 22 53 82 113 143 174 204 235 266 296 327 357 23 23 54 83 114 144 175 205 236 267 297 328 358 24 24 55 84 115 145 176 206 237 268 298 329 359 25 25 56 85 116 146 177 207 238 269 299 330 360 26 26 57 86 117 147 178 208 239 270 300 331 361 27 27 58 87 118 148 179 209 240 271 301 332 362 28 28 59 88 119 149 180 210 241 272 302 333 363 29 29 60 89 120 150 181 211 242 273 303 334 364 30 30 -- 90 121 151 182 212 243 274 304 335 365 31 31 -- 91 -- 152 -- 213 244 -- 305 -- 366 First 1 32 61 92 122 153 183 214 245 275 306 336 Last 31 60 91 121 152 182 213 244 274 305 335 366 30