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The characteristics of daily and monthly rainfall for a decision support system

Mehari Tesfazgi Mebrhatu1, M. Tsubo2 and Sue Walker1

1Department of Soil, Crop and Climate Sciences (Agrometeorology), University of the Free State, P.O.Box 339,
Bloemfontein 9300, South Africa.
The University of Queensland, School of land and food Sciences, Brisbane, Qld 4072, Australia. E-mail:


Fitting the least squares line to the long–term annual rainfall (88 years) for Asmara gave a decreasing annual trend of 0.25mm. But the statistical analysis of the deviation from zero is not significant (p = 0.28). This means that the rainfall distribution fluctuates with time, but the annual amount did not significantly decrease over time during the last century. The Markov chain model (with threshold level of 0.8mm per day) was used to predict the length of dry spells during the rainy season (June to September). This information can be used to select the best planting date by avoiding the period of high risk of long dry periods near the beginning of the rainy season. Thus it can assist farmers in land preparation and planting strategies for different cultivars and crops.

Media Summary

Predicting the length of dry spells using the Markov chain model is helpful in a decision support system.

Key word

Dry spell, Markov chain model


Rainfall in Eritrea is characterised by a high degree of variability and it is the element of climate most influential in determining the variety and abundance of flora and fauna, land use, economic development and practically all aspects of human activity. Hence a comprehensive analysis of rainfall data is a crucial component in water management and in agricultural production. From analysis of the measured historical data it is possible to get some insight into problems related to the amount of plant available water. Thus, the main objective of this paper is to analyse the characteristics of the general trend of the annual, monthly and daily rainfall totals for a decision support system. The study site was Asmara City (15o21’N; 33o55’E), Eritrea. An 88-year (1913-2000) record of monthly rainfall and 45-year (1943-1988) record of daily rainfall were used for different analyses.

Homogeneity Testing

When analysing rainfall series of a considerable number of years one must be aware that the data collected over a long period may not reflect uniform conditions. This could be due to changes in instrumentation, sensor calibration, maintenance procedure changes, change of site, observation method, personnel and codes. Prior to performing different analyses the homogeneity of observed data with respect to non-climatic influences must therefore be assessed. A homogeneous climate time series is defined as one where variations are caused only by variation in weather and climate (Conrad & Pollak, 1950).

Most homogeneity testing techniques are primarily used in comparisons with neighbouring stations (e.g. Lavery et al., 1997; Peterson et al., 1998). It often happens, however, that the homogeneity of rainfall series of neighbouring stations is also doubtful or, as in this particular study, that there is no independent close neighbouring rainfall station which has long-term rainfall data for comparison purposes. Then use can only be made of a single rainfall series. The cumulative sum techniques (Buishand, 1977) was used for the detection and quantification of jumps to determine homogeneity in the data source was used. A first indication of departures from homogeneity due to different changes can be obtained by plotting the partial sum of the departures from the mean (Figure 1). By using the partial sum patterns together with the history of the station, the long term mean annual rainfall data was split into three sub-series, as follows: 1913-1949, 1950-1975 and 1976-2000. The main criterion for splitting into three sub-series is that each sub-series has to have a different pattern of rainfall. Estimates of the annual means, 1, 2, and 3 sub-series are 538.8, 497.4 and 537.7mm respectively.

Figure 1: Partial sum of departures from the mean of annual totals (n = 88).

Homogeneity was tested under the assumption of equal variances and normality of the annual totals. The following Snedecor’s F-statistics were done.

Ho: 1 = 2 = 3

Hi: 1 ≠ 2 ≠ 3

where: Ho = null hypothesis and Hi = alternative hypothesis

The result of the F-test is 0.65 which is not significant at the 5% significance level (critical level is 0.43). This statistical analysis gives good evidence that the station is homogeneous.

Time series analysis

The review of historical data over time provides the decision-maker with a better understanding of what has happened in the past, and how estimates of future values may be obtained. Hoshmand (1998) states that the least squares method of fitting a straight line provides the best fit.

Using the long-term annual rainfall it was shown that there has been a gradual decrease in annual rainfall for the periods 1913 to 2000. Figure 2 shows that the least squares line has an annual trend decrease of 0.25mm. But the statistical analysis of the deviation from zero is not significant, that is, p = 0.28. Thus it can be inferred that the rainfall distribution is fluctuating from time to time and the annual amount of rainfall has not significantly decreased over time during the last century.

Figure 2: Trend line fitted by least squares method for the annual rainfall totals.

Characteristics of rainy day and spell length

Determination of the number of rainfall days yielding specific amounts of rain, start of rainy season and the study of the events in general are some of the necessary steps towards an understanding of daily rainfall behaviour. It is of some importance in adapting a farming system to supplementary water resources to know how long a wet spell is likely to persist, and what probabilities are of experiencing dry spells of various duration at critical times during the growing season. In this study, a rainy day is regarded as a day with measurable rain; i.e. a day yielding 0.8mm or more (Kottagoda & Horder, 1980). A rainless day has been defined as a day yielding less than 0.8 mm. This provides a cut-off to distinguish wet and dry days.

A prolonged dry spell following the “false start” of the rains could affect seed germination and consequently lead to crop failure. Thus, a study of the start of the rainy season is very crucial for crop production.

The start of the rainy season as defined by Raman (1974), which is adapted and modified by the software INSTAT+ (INSTAT+Climatic guide, 2001), has been used in this study. That is, the first occasion with more than 20mm within a 2day period after 1st June and with no dry spell of 10 days or more within the following 30 days. This definition adds the condition of a long dry spell immediately following the start of rain in the period, which is critical for crop production. The end of the season is defined as the first date the soil profile is empty after 1st September. The earliest starting date of the rainy season is day 166 (June 14). The latest is day 218 (August 5). The mean starting date is late June (day 182) and the standard deviation is 12 days. For the end of season the earliest date is day 245 (September 1). And the latest is day 272 (September 28). The mean end of season is day 254 (September 10) and the standard deviation is about eight days.

In general, a wet spell may be defined as a run of rainy days, and a dry spell as a run of dry days. The occurrence of long dry spells during the growing season of a crop is a major agricultural hazard (Stern & Coe, 1982; Shaw, 1987). But, it is also necessary to consider that a long dry spell is needed for harvesting some crops. The maximum dry spell lengths for all months for 46 years were calculated. In comparison of the peak rainy months (JA) and the dry season (October through April) the number of dry spells fluctuates highly during the dry season. Markov chain model (Jones and Thornton, 1993; Wilks, 1999) was investigated for predicting the behaviour of dry spells for the rainy season (June to September) and the fitted model was used to estimate the risk of long dry spell lengths. The dry spell lengths for June and July were fitted and spell lengths of 8 and 10 days over periods of 30 days were calculated as shown in Figure 3. The results show that the probability of a dry spell of 8 days, within the 30 days following planting, has dropped to 0.5 by 15th June (day 167) and to 0.2 by 27th June (day 179). Supposing that in the next year, late June (day 173) is a potential sowing date, one can see the probability of a dry spell of more than 10 days within the next year 30 days is only 0.1. There is a 50 % probability of getting 10 days dry spell in day 154 but 8 days dry spell in day 167. Figure 3 also tells that June is the most likely month for moderately wet spells, and July-August for extremely wet spells. This type of result can help determine risk involved in planting strategy.

Figure 3: Modelling daily rainfall data with 8 and 10 day spell lengths for June and July.

Further by looking at the water balance some helpful ideas can be drawn. The average water balance (storage limit 100mm; evaporation 5.7mm per day (Stewart, 1994)) for the long-term record was calculated. The results indicate that, the soil profile was getting some water from the period of 6 May – 4 June, but it gets dry (empty) for quite a long time from the period of 5th June to 23rd June. Thus, without supplementing by irrigation for the dry period (5th June – 23rd June), planting on 6 May would not be recommended. In the earliest stage of crop growth the plant cover is too small to cover the soil, resulting in high soil surface evaporation. Planting on 23 June would be better because the profile is full by 8 July. At the beginning of the season, the average rainfall per day is less than the evaporation, so the resulting soil water remains near zero.


If planning of water resources development is to be successful, improved estimates of probable rainfall and its characteristics and timing are critical. Hence a comprehensive analysis of rainfall data is a crucial component in water management and in agricultural production.

Strategic management is needed by analysing the time series, start of rainy season and water balance of the long historical data for the prediction of a season to be a wet or dry. Techniques like Markov chain can be very help full for estimation of the risk of long dry spells. The information can be assist farmers in selecting drought resistant varieties, selecting best planting date by avoiding the period of high risk of long dry spell. Also the farmer will be aware of supplementary irrigation and planting strategies.


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