Agence Nationale de la Météorologie du Sénégal
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1 Using INSTAT software with daily rainfall data to estimate best sowing dates for farmers in Saint Louis of Senegal By Elarion Sambou Agence Nationale de la Météorologie du Sénégal (A.N.A.M.S.) BP 8257, Dakar, SENEGAL A report submitted to Statistical Services Centre, University of Reading, UK, in partial fulfilment for the completion of the on-line course in Statistics in Applied Climatology (e-siac) Date November, 2009
2 P a g e 2 Content Page number 1 BACKGROUND 3 2 OBJECTIVES 4 3 METHODOLOGY Examining the data Describing and summarising the data Defining events (start of the season, sowing dates, dry spells, water balance) Describing events Making inferences (risk, determination, confidence limits) 8 4 DATA 9 5 RESULTS AND CONCLUSIONS Data description and summaries (statistics) Annual and monthly summaries of precipitation The growing season Risk determination and confidence limits (inferences) 16 6 RECOMMENDATIONS 19 7 APPENDICES Appendix A References and sources documentation Appendix B - Station metadata Appendix C - Calendar year display Appendix D - Display of daily dataset for Saint Louis of Senegal 22
3 P a g e 3 1 Background Water constitutes a very important requirement to the growing of agricultural products. For farmers in the 50 s, in Senegal, this was not much of a preoccupation because the rainfall season was known to be long enough and provided sufficient quantities of rainwater needed for the agricultural speculations being produced. In the southern part of the country, the rainy season would normally starts from May/June and usually ended in mid-october, with amounts of rainfall totalling up to 1300 mm/year (sometimes more). Whereas in the northern part, the start of the rains is delayed to June/July, ending in September, with annual amounts up to 300 mm/year (sometimes less) Those happy days seem to be long gone with today s farmers. In Saint Louis of Senegal (see map below on Fig. 1), where this study is taking place, discussions with farmers tend to reveal the common belief that the rainfall season is getting shorter, less regularly distributed (in time and in space), with decreasing amounts from year to year. Inter-annual and intra-annual rainfall variability has become a deep preoccupation and most farmers are now being easily convinced that climate change is not just a hypothetical future event, but is really taking place within their localities. Some farmers are turning towards climate services from the Meteorological office and are asking for recommendations to guide them in the choices of appropriate speculations and the best sowing time. They want to know what risks there may be in sowing too early. For the northern part of Senegal, where the Region of Saint Louis is located, sowing early means beginning of July. Fig. 1 Geographical location of Saint Louis
4 P a g e 4 2 Objectives The objective in this study is to try and give an answer to the following questions: For a bold farmer, willing to sow early in the rainy season, i.e. beginning of July, what could be the distribution of sowing dates, and what is the risk of early crop failure due to long dry spells (15 days without rain after the first rain)? What is the length of the growing season for a cautious farmer compared to that of a bold farmer? Can we quantify the reduction of risk when a farmer has to re-sow with a 'cautious' strategy being implemented? How often (i.e. in what proportion of years) will a bold farmer have a longer growing season than a cautious farmer? 3 Methodology In this section, we will describe and explain how this study work was conducted and which functions in which tools (mainly Instat) were used. The resulting figures and tables will then be commented and analysed in the subsequent sections. 3.1 Examining the data The daily rainfall data for Saint Louis was provided in EXCEL format (Fig. 2) by the Senegalese Meteorological Agency. It has been examined to ensure its quality. A detailed inspection and regular cross checking policy was implemented in order to clean the data from any erroneous values whenever necessary. In fact, the dataset was free of missing data or negative values. Use of measurement units was also appropriate as can be noticed from the displayed tables in Appendix D. Fig. 2 Worksheet display of provided dataset in Excel and Instat format The data was then imported from EXCEL to INSTAT (Fig. 3), where supplementary checks were conducted to ensure adequate coding for non-leap years and adequate calendar year settings (in this case, 1 st of January, using the Climate Display daily menu, Appendix C).
5 P a g e 5 Fig. 3 Import from Excel to Instat, using the «EXCEL» button ( )on the Instat tools bar When importing the data from Excel to Instat, adequate coding has to be defined for missing values (see dialogue box in front) : 9999 for missing data, 8888 for trace precipitation and 9988 for non-leap year coding. 3.2 Describing and summarising the data Statistical description and summary of the data will be obtained using the summary dialogue. From the Instat main menu, we use Statistics Summary Describe, to calculate different statistics (mean, median, Range, standard deviation, etc.). We will also look at various representations of the data, such as plots, box-plots, time series plots, tables, etc. This will be done using Climatic Summary or Graphics Plot / Boxplot. An example of these dialogues is shown on fig.4 Fig.4 Describing and summarising the data
6 P a g e Defining events (start of the season, sowing dates, dry spells, water balance) To define the events of interest (start of season, dry spell, water balance, etc.) we use Climatic Events menu options from INSTAT and fill in the dialogue as shown on fig. 5. We then extract and analyse the sowing dates based on the following definitions commonly agreed upon with the farmers: (i) First date from 1 st July getting more than 15mm in 1or 2 days. (ii) (iii) (iv) (v) First date from 1 st July getting at least 15mm in 1 or 2 days, with the condition that there is no 15 day dry spell or longer within the next 30 days. First date from 1 st August getting at least 10mm in 1 or 2 days. First date from 1 st August getting more than 10mm in 1 or 2 days, with the condition that there is no 15 day dry spell or longer, within the next 30 days. A combined definition of (i), (ii) and (iii), i.e. the earliest date each year, arising from the three preceding definitions. A dry spell being defined (in agreement with the farmers) as a period of 15 consecutive nonrainy days 1, we will estimate the risk of having to re-sow in case of a dry spell event. The end of the growing season will be determined using the Instat concept of water balance, i.e. the first date the soil profile is empty after a given date (cf. Instat Climatic Guide, chapter 4, by Roger Stern, Derk Rijks, Ian Dale, Joan Knock, January 2006). In fact, from our knowledge of the climate realities in the Saint Louis area, the end of the season would normally occur during the month of October, sometimes early November, after the last significant rain 2 has occurred and water balance is close to zero. Fig. 5 Example of event definition: the start of the rainy season 1 In this definition, a non-rainy day will be considered as one with less than 0.85 mm of rain. 2 Here, a significant rain is taken to be at least 5mm over one day.
7 P a g e 7 Calculating the events with the given definitions, there was no start date for the sowing season for the year To avoid getting aberrant values in the subsequent calculations a * code was introduced to indicate the value for 1977 as missing (Fig. 6) Fig. 6 using a * code for no start date in 1977 To determine the length of the season, we must calculate the difference between the end and the start of the season. The end of the season is obtained using the Instat concept of water balance. The water balance values are calculated for each year using Climatic Events Water balance dialogue as shown on Fig.7. Finally, we determine the end season as the first date after 1 st October when the water balance profile is zero. Fig.7. Determining the end of the growing season 3.4 Describing events Description of the calculated start of the rains, lengths of the season, etc. is obtained using the Describe dialogue mentioned in the preceding sections. Resulting statistics, such as means, ranges, standard errors, etc. will be looked over in the subsequent sections as already stated earlier.
8 P a g e Making inferences (risk, determination, confidence limits) Using the Simple Models - Normal Distribution, One Sample and the One proportion - binomial model, will allow us to calculate the standard error of the risk of re-sowing as well as confidence limits for the true risk (with the Simple normal (symmetrical) method). To do that, we select from the Instat main menu Statistics Simple Models Fig. 8. Use of the Models - Normal Distribution, One Sample and the One proportion - binomial model
9 P a g e 9 4 Data Daily rainfall data observed at Saint Louis weather station from 1971 to 2000 will be used. It is common practice that the observed data be checked for possible errors before it is sent to the main Meteorological Agency headquarters, in Dakar. There, it will be manually crosschecked and finally key-entered into computers for future use in research, climate information services, etc. During the key-entering process, more rigorous quality controls are performed before it can be provided to the public. Consequently, this data can be considered to be of good quality despite possible minor errors. 5 Results and Conclusions Results from the Methodology section are analysed here to support a few conclusions in relation to the stated objectives in this study. 5.1 Data description and summaries (statistics) Annual and monthly summaries of precipitation Fig. 9 Serie s plot of the total annual rainfall Fig. 10 Serie s plot of the number of rainy days in the year Fig. 9, 10 and 11 give the annual series plot both for rainfall totals, number of rainy days and annual rainfall summary, respectively (1971 to 2000). From these graphics, there does not seem to appear evidence of climate change. The year to year variation seems to be contained within 2 standard deviations (green light dotted lines on fig. 9) of the mean. A maximum value (over 300mm) is noticed around 1975, whereas a minimum value (over 50mm) is observed in A minimum of less than 5 days and a maximum of more than 35 days (fig.10) are also observed in 1995 and 1996, respectively.
10 rainfall in mm Using Instat software with daily rainfall data to estimate best sowing dates for farmers in Saint Louis of Senegal P a g e 10 Fig. 11 Descriptive Statistics of the total rainfall DES X34;STE;MED;LQU;UQU;IQU;MDE;PER No. of observations 30 Minimum 59.1 Maximum Range Mean Std. deviation Median Lower Quartile Upper Quartile Quartile Deviation Std. Error of Mean Mean Deviation th percentile th percentile th percentile Column 20% 50% 80% Total annual rainfall The probability of total rainfall being at least mm is 20%, which correspond to a 5 year return period. The s.e. of the mean is 15.8mm. From the monthly summary (fig. 12 and table 1 below), we can first notice that maximum rainfall occur during the August / September period. The rainy season starts around June / July and ends around October / November. Some precipitation occur in the December- February period, with a maximum of 33mm in December and a second maximum of 21mm in January.. These precipitation events are usually not related to the rainy season. Fig. 12 Monthly rainfall summary Plot of the monthly rainfall summaries Saint Louis of Senegal ( ) Legend gfedcb gfedcb Min gfedcb Max gfedcb gfedcb p25 gfedcb Mean Median p Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months
11 P a g e 11 Table 1 Table of Monthly rainfall summary Column Mean Min. Max. Median 25% 75% X51 X52 X53 X54 X55 X56 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec The growing season Fig. 13 shows the year to year variation of the sowing dates according to the five definitions, whereas fig. 14 gives a box-plot representation of the same information. Table 2 presents summary values for the sowing dates. From those graphical presentations, we can see that, of the five definitions, def_1c (most cautious strategy) has the longest spread (74 days). def_1b has the same spread but was calculated with a missing value. The combined definition (earl_sta), which was defined as the earliest of the other definitions, has a range of 61 days with a standard deviation of 15 days. It s mean sowing date is 211 (29 July) compared to 214 for def_1c, 223 (most cautious) for def_2c (second most cautious) and 227 (most bold strategy).
12 P a g e 12 Fig. 13. Sowing dates for the five definitions The 20% point, i.e., the 5 year return period value is (10 July) for the earl_sta (earliest starting date) definition, compared to 217 (4 August) for def_2b, 214 (1 st August) for def_2c and 196 for def_1c. For the 50% point (2 year return period), the corresponding values are for def_1c, for def_2c for def_2b and for earl_sta. If we look at the 80% point, we can realize that the 1.25 year return period value is (21 August) for def_1c, which means that in 1 out of 5 years sowing would not have been done until after 21 August. The corresponding values for the other definitions are 25, 18, 24 and 11 August for def_1b, def_2c, def_2b and earl_sta respectively. Fig. 15 and 16 and table 3 are related to the length of the seasons with respect the four definitions. There, we can notice that SLwrt1c 3 has the longest spread (91days), followed by SLwrtES 4 (78 days). Again looking at the box-plot representations (Figs. 14 and 15), we can notice that def_1c and the combined definition (earl_sta) look fairly symmetrical. 3 SLwrt1c: season length with respect to definition 1c 4 SLwrtES: season length with respect to the combined definition (earliest start date)
13 P a g e 13 Fig. 14. Sowing dates box-plot representation Table 2 Column Statistics for the sowing dates STA X57-X62;MEA;MIN;MAX;MED;SDE;PER 20;PER 50;PER 80 Column Mean Min. Max. Median SDE 20% 50% 80% Spread def_1c def_ (1) def_2c def_2b earl_sta August August August August July st July st July st August st August st July Sept Sept August Sept August July August August August July July July st August August July July August August August July August August August August August In other words, we could say that, by comparison of the sowing dates for the different definitions and on the basis of the preceding summary statistics, the two best choices for the farmers would be definition 1 (def_1c) and the one combining the all other definitions (earl_sta).
14 P a g e 14 Fig. 15. Length of the growing season box-plot representation Table 3 Column Statistics for the length of the seasons STA X63-X66;MEA;MIN;MAX;MED;SDE;PER 20;PER 50;PER 80 Column Mean Min. Max. Median SDE 20% 50% 80% Spread SLwrt1c SLwrt2c SLwrt2b SLwrtES Column 1b_1c Column 2b_2c Column 1c_ES No. of observations 30 No. not missing 29 Minimum 0 Maximum 41 Range 41 Mean 6 Std. deviation 13 Count <= 0 24 % of data <= 0 83 No. of observations 30 Minimum 0 Maximum 43 Range 43 Mean 5 Std. deviation 11 Count <= 0 25 % of data <= 0 83 No. of observations 30 Minimum 0 Maximum 43 Range 43 Mean 3 Std. deviation 10 Count <= 0 26 % of data <= 0 87 To calculate the risk associated with a bold policy strategy, we have to compare season lengths related to cautious policy against the season length related to bold policy. To do this, we subtract SLwrt1c from SLwrt1b, i.e., the season length for a farmer sowing early in July, minus the season length of a farmer sowing on the same period with the additional condition that no dry spells occurs. The result is saved is saved into column 1b_1c. The same procedure has been used to obtain columns 2b_2c and 1c_ES. Then we run the Column Statistics function of Instat to obtain different statistics (sample size, count of values equal to zero) to be used with the One proportion - binomial model function, in the risk calculation and confidence limits determination (section 5.2).
15 P a g e 15 Fig. 16 Descriptive Statistics the different season lengths Column SLwrt2b No. of observations 30 Minimum 19 Maximum 89 Range 70 Mean 55 Std. deviation 18 Median 53 Lower Quartile 42 Upper Quartile 63 Quartile Deviation 11 Std. Error of Mean 3 10th percentile 33 20th percentile 40 50th percentile 53 80th percentile 73 90th percentile 83 Column SLwrt2c No. of observations 30 Minimum 32 Maximum 96 Range 64 Mean 59 Std. deviation 16 Median 60 Lower Quartile 46 Upper Quartile 63 Quartile Deviation 9 Std. Error of Mean 3 10th percentile 40 20th percentile 45 50th percentile 60 80th percentile 75 90th percentile 88 Column SLwrtES No. of observations 30 Minimum 32 Maximum 110 Range 78 Mean 71 Std. deviation 18 Median 74 Lower Quartile 62 Upper Quartile 84 Quartile Deviation 11 Std. Error of Mean 3 10th percentile 41 20th percentile 54 50th percentile 74 80th percentile 87 90th percentile 93 Column SLwrt1c No. of observations 30 Minimum 19 Maximum 110 Range 91 Mean 68 Std. deviation 22 Median 71 Lower Quartile 51 Upper Quartile 84 Quartile Deviation 16 Std. Error of Mean 4 10th percentile 33 20th percentile 46 50th percentile 71 80th percentile 87 90th percentile Percent Probability Plot of SLwrt2b 20 Percent Probability Plot of SLwrt1c Season length in days Percent Probability Plot of SLwrt2c 40 Percent Probability Plot of SLwrtES Season length in days Length of season in days Season length in days
16 P a g e Risk determination and confidence limits (inferences) Using the Simple Models - Normal Distribution, One Sample, we obtain the following results: 1b_1c One proportion - binomial model Binomial model, single sample Sample size 29 Successes 24 Proportion Approx s.e. of proportion = Simple normal approximation: 95% confidence interval for prop to We can use Instat Interactive command function to calculate the error margin ( :?( )/2) = ) and the return periods: for the approximated standard error :?1/0.070 = for the lower limit :?1/0.690 = for the upper limit :?1/0.965 = b_2c One proportion - binomial model Binomial model, single sample Sample size 30 Successes 25 Proportion Approx s.e. of proportion = Exact results: 95% confidence interval for prop to Simple normal approximation: 95% confidence interval for prop to Error margin (:?( )/2)) = c_ES One proportion - binomial model Binomial model, single sample Sample size 30 Successes 26 Proportion Approx s.e. of proportion = Exact results: 95% confidence interval for prop to Simple normal approximation: 95% confidence interval for prop to Error margin (:?( )/2)) = In the preceding calculations, we have considered count of cases where the difference is equal to zero. For example, column 1b_1c statistics gives 24 years out of 29 (1 missing value) where the difference is zero. This is to say that in those cases, the two strategies (cautious and bold) led to the same starting day, which equally means that in 5 years out of 29, the sowing date was different due to the difference in strategy, with a mean difference of 6 days and a standard deviation of 13 days. Using the Binomial model, single sample, we get:
17 P a g e 17 Sample size 29 Successes 5 Proportion (17%) Approx s.e. of proportion = Exact results: 95% confidence interval for prop to Simple normal approximation: 95% confidence interval for prop to From Instat interactive command (:?( )/2), the error margin can be approximated by and the mean difference, expressed as 6 days ± The proportion of successes is 0.172, so there is a 17% risk of crop failure due to dry spells occurrence. Using the same procedure for column 1c_ES, which compares the farmer sowing early in July (cautious) to a bold farmer but implementing a cautious policy, we can determine that the risk is now reduced to 13%. Looking back at table 2 (Column Statistics for sowing dates) and table 3 (column statistics for the length of the seasons), and using the One proportion - binomial model, we can calculate the return periods at different probability points for each definition and express the true mean values of each population with an estimate error, which leads to the following : 1. For definition 1c (1 st July with at least 15mm of rainfall in 2 days, i.e., cautious farmer): Sample size 30 Mean Std. deviation Standard error of mean = with 29 d.f. 95% confidence interval for mean to From the Instat Interactive command d :?( )/2 = For definition 1b (1 st July with at least 15mm of rainfall in 2 days, no dry dry spell exceeding 15 days bold) Sample size 29 (1 missing value) Mean Std. deviation Standard error of mean = with 28 d.f. 95% confidence interval for mean to From the Instat Interactive command d?( )/2 = For definition 2c (1 st August with at least 10mm of rainfall in 2 days, second cautious) Sample size 30 Mean Std. deviation Standard error of mean = with 29 d.f. 95% confidence interval for mean to From the Instat Interactive command d?( )/2 = 3.26
18 P a g e For definition 2b (1 st August with at least 10mm of rainfall in 2 days, no dry dry spell exceeding 15 days second bold) Sample size 30 Mean Std. deviation Standard error of mean = with 29 d.f. 95% confidence interval for mean to From the Instat Interactive command d?( )/2 = For definition earl_sta (earliest date of the preceding definitions) Sample size 30 Mean Std. deviation Standard error of mean = with 29 d.f. 95% confidence interval for mean to From the Instat Interactive command d?( )/2 = 5.7 The same types of calculations as above can be done with the lengths of season associated with each definition. All those values are recapitulated into table 4. Table 4 Recapitulating table for sowing dates and season lengths Column Sowing dates for Saint Louis of Senegal Mean SDE 20% (5 year return) 50% (2 year return) 80% (1.25 year return) def_1c ± def_ (1) ± def_2c ± def_2b ± earl_sta ± Column SLwrt1c SLwrt2c SLwrt2b SLwrtES Lengths of growing season for Saint Louis of Senegal Mean SDE 20% (5 year return) 50% (2 year return) 80% (1.25 year return) ± ± ± ±
19 P a g e 19 6 Recommendations This study has allowed us to determine sowing dates and, consequently, growing season lengths based on the different definitions that we agreed upon with the farmers. We have been able to compare different risk and advantages (longer spread) as related to different strategies. In so far as the growing season length is concerned, a cautious strategy consisting in early sowing (early July) should be recommended in order to take advantage of the long spread (91 days for def_1c). Agricultural speculations requiring up to 90 days could be experimented without any risk of rainwater shortage. The second longest growing season length (78 days) is obtained with and bold strategy yet implementing a cautious policy. This is given by the earl_sta definition in our study. The season length is shorter compared to def_1c, but the risk of crop failure due to dry spells is reduced as we have seen in the study.
20 P a g e 20 7 Appendices 7.1 Appendix A References and sources documentation Instat Climatic Guide, chapter 4, Roger Stern, Derk Rijks, Ian Dale, Joan Knock, ed.january 2006 Exploring daily rainfall data to investigate evidence of climate change in southern Zambia and its implication for farmers in the area, Parin Kurji, Durton Nanja and Roger Stern 7.2 Appendix B - Station metadata Mean Sea Level Pressure Name of Station : Saint Louis Aéro Type : Synoptic Latitude : 16 03' Longitude : 16 27' Altitude : 4m above sea level Start Date :1957 Available Period (computerised): Mean Temperatures Extreme Temperatures Mean Humidity Annual Rainfall Mean ( ) Min Max Min Max Min Max Min Max Solar radiation
21 P a g e Appendix C - Calendar year display Mon Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Day
22 P a g e Appendix D - Display of daily dataset for Saint Louis of Senegal Daily data for: y1971 Mon Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Day Total (Overall: 177.0) Maximum (Overall: 31.0) Number greater than 0 (Overall: 18)
23 P a g e 23 Daily data for: y1972 Mon Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Day Total (Overall: 152.1) Maximum (Overall: 47.8) Number greater than 0 (Overall: 12)
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