The start of the rains is defined as the first occurrence of a specified amount of rain within two successive days. The probability distribution of the date of the start of the rains is derived from the rainfall models of Stem (1980a). The probabilities of occurrence of dry spells are used to define an earliest practical starting date. Results are presented for eleven stations on a N-S transect in West Africa. The variation in starting date with latitude is described. Advantages of the model approach over conventional analyses are discussed.
S U M M A R YSimple methods are described for the analysis of daily rainfall measurements. The distinctive feature is that each year provides one number for any event or characteristic of interest. The resulting observations are then analysed, assuming that they are a simple random sample from a single distribution. An estimate of the probability of an event can be made directly from its relative frequency of occurrence, or alternatively a distribution (such as the normal) can be fitted. The methods are applied to agronomic questions on dry spells, the start, end and length of the growing season, and the distribution of amounts of rainfall through the year. Examples are given from Nigeria and India.Rainfall governs crop yields in the seasonally arid tropics and determines the choice of crops that can be grown. For an agriculturalist, the important questions on rainfall are concerned with the start, end and length of the rainy season, the distribution of rainfall amounts through the year, and the risk of dry spells. A great deal of research has been devoted to these topics, but little of it has been based on daily data, which is perhaps understandable considering the large arrays of numbers which must be manipulated. The analysis of rainfall amounts on a daily basis appears complex because there is a reasonable probability of a day being dry, even within the rainy season, and the analysis seems easier when rainfall is totalled over five, seven or ten days. This aspect, plus the fact that plant water requirements over periods of about ten days can usually be met by water stored in the soil, has resulted in many agroclimatic analyses being based on data grouped over several days. However, much agronomically useful information is lost by summation into totals, notably that on dry spells and the beginning and end of the rains.In this and a subsequent paper (Stern et al., 1982) we describe methods which use daily rainfall data. We aim to show that the use of daily data to define rainfall events gives several advantages over grouped data. This paper is about simple, direct methods and their advantages and limitations. We start with observations on the conventional analysis of rainfall amounts, and then use daily data to estimate the risk of dry spells, and the frequency distributions of the dates of the start, end and length of the rains. Examples are given for three places within the seasonally arid tropics (Table 1) and daily observations for one year at Kano are used to illustrate the analyses (Table 2).
Two rainfall series for the Sahel region of West Africa have been updated to 1983. Annual and monthly series are presented and analysed. Relatively dry conditions have persisted in this region since 1968 due mainly to a decline in rainfall during August, the wettest month. Drought has probably been less severe in this region during the late rather than the early 1970s because of better rainfall early in the season. It is suggested that agricultural planning should be based on rainfall records for the last twenty years.
A probabilistic model of daily rainfall can be used to derive results of potential value to agriculture. A simple example shows how this model works, but more realistic models are also fitted, using standard statistical computer packages, and examples of the results are presented graphically. The modelling approach is compared and contrasted with direct methods of analysing daily rainfall.Some limitations of the direct method of analysing rainfall observations were discussed in the conclusions of a companion paper (Stern et al., 1982). These limitations, due to inefficient use of the data, are quite severe and provide an incentive to develop an alternative approach to the analysis. The raw data for both approaches consist of daily rainfall measurements. In the direct approach we first specify the event or characteristic in which we are interested, such as the date when the rains start for a given definition, or the ten-day total rainfall for the first decade in May. We then find the appropriate date or value for each year of the record, and these numbers are summarized to give the required results.In the alternative approach, described here, the annual pattern of rainfall is first summarized to give estimates of the chance of rain falling on any day of the year, and of the distribution of rainfall amounts on rainy days. The summary, or model, may be of some interest in its own right, but here it is mainly to be seen as a stepping-stone to results of practical value. The probability of any event of interest can be calculated from the model. The methods are illustrated with the data from Sholapur (India) and Kano (Nigeria) used in the direct analysis (Stern et al., 1982), where long records enable the results from the two approaches to be compared. We have tried to outline the methods without assuming any specialized knowledge of the statistical techniques involved.Recent advances in statistical methods have dramatically improved the range of techniques available for analysing data that are not from normal distributions. These new techniques, which are used here, parallel those used in the analysis of variance and regression for normally distributed data. This development is of considerable importance, since daily rainfall data are clearly not normally distributed. The wide availability of computer packages associated
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