Spatial and Temporal Distribution of Rainfall Breaks in Senegal

This study analyzes the spatio-temporal distribution of daily rainfall data from 13 stations in the country of Senegal located in the North-West of Africa. These data, covering the period 1950-2010, are extracted from the database of the Regional Study Center for the Improvement of Drought Adaptation (CERAAS). They allow to calculate, in each station, dry episodes and their sequences and the results reveal a latitudinal variability of class 1 breaks (1 - 3 days) with the highest values recorded in the south. Unlike the class 2 episodes (greater or equal than 15 days), the latitudinal gradient is less pronounced but they are more frequent in the north. For most of the regions studied, a break in the trend towards an increase in dry sequences can be noted, most often at the beginning of the 1970s, which coincides with the start of the great drought of the 1970s decade. For all sites, the frequency of dry episodes of class 1 (1 - 3 days) exceeds 70%. The frequency of class 2 of dry episodes (greater or equal than 15 days) decreased from 30% in 1951-1970 to 18% in 1991-2010 in the region of Thiès; from 25% in 1951-1970 to 20% in 1991-2010 in Louga; from 22% in 1951-1970 to 18% in 1991-2010 in Tamba; 23% in 1951-1970 to 15% in 1991-2010 in Ziguinchor; 25%


Introduction
Senegal is currently facing a very strong degradation of its agricultural production capacity. With a population of about 16.209.125 habitants in 2019, it will have to feed about 19.390.727 habitants in the horizon of 2025 according to the Senegalese National Agency of Statistics and Demography (ANSD). According to an essentially extensive agriculture and a strong climate variability characterizing the area, the food supply of these populations represents an even more difficult challenge to overcome. The increasing frequency of extreme events such as floods, prolonged rainy breaks, droughts (International Panel on Climate Change; IPCC, 2019), but also the delay in the start and the short duration of the rainy season will increase the vulnerability of agricultural production systems.
To decrease consequences of this vulnerability on local populations, the Senegalese scientific community must double its efforts to improve the understanding and prediction of climate variability and change in the country. It is in this context that some projects at the level of the Sahelian sub-region have emerged, such as AMMA (Multidisciplinary Analysis of the African Monsoon) (Redelsperger et al., 2006;Lebel et al., 2010), ESCAPE (Environmental and Social Changes in Africa: Past, present and future) (Sultan et al., 2011), CORDEX (Coordinated Regional Downscalling Experiments, http://wcrp.ipsl.jussieu.fr), etc. The originality of these projects lies in the scope of the field measurement campaigns, their multidisciplinary and multilateral character in order to better identify the mechanisms and complexity of the monsoon system at different time and space scales and in consequence improve our knowledge.
In Senegal, there are hardly studies that have focused on updating the state of the art on the spatio-temporal distribution of rainy breaks, i.e. characterizing the temporal and multisite distribution of rainy days in this region of the Sahel.
However, this is crucial given the increased spatio-temporal variability of rainfall in this region of the Sahel but also the uncertainty of climate projections, especially those of rainfall. Nevertheless, some authors have described breaks in rainfall at the sub-regional level (Garcia & Martin-Vide, 1993;Sané et al., 2008) and in East Africa (Segele & Lamb, 2005). Salack et al. (2012) showed that extreme breaks were more frequent at the beginning and end of the season. They showed that breaks longer than 15 days (May-June-July) and 8 -14 days (August-September) are of low frequency of occurrence and correlated with annual rainfall deficits. However, since the drought of the 1970s in West Africa, these extreme breaks have become more and more frequent even in mid-season (Bichet & Diedhiou, 2018;Porkka et al., 2021). Sivakumar (1992)  May, when the accumulated rainfall on at least three consecutive days is 20 mm and no dry period within the following 30 days exceeds 7 days. However, in a context of climate change these sowing dates are highly variable and the growing seasons have become shorter and shorter especially in Senegal. Sané et al. (2008), to characterize the rainy season through rainfall breaks, used only two stations in southern Senegal (Kolda and Vélingara). However, these two stations are located in a humid zone (>800 mm/year) whereas the agro-climatic risks associated with rainfall breaks are more important in arid and semi-arid regions of the Sahel as shown by Barron et al. (2003). Fodé & Adamou (1996) studied dry sequence analysis in Niger by trying to fit empirical (observed) dry sequence distributions using MARKOV chain models. It appeared that the second-order MARKOV chain gives a better fit to the empirical probability distribution of occurrence of dry sequences, the higher the frequency of rainfall and the length of the dataset is limited to the last rainy day of the season, the better the match. In the Sahel, the control of rainfall distribution and variability, which is also an indirect way of characterizing the distribution and variability of rainfall breaks, remains a challenge for the scientific community as well as for the populations and all development actors. Indeed, in its sixth Assessment Report, the Intergovernmental Panel on Climate Change (IPCC, 2016), considers that climate projections in the 21st century remain subject to uncertainties. One of the main causes of these uncertainties is the lack of a perfect mastery of the physical processes and mechanisms that drive rainfall variability in West Africa. At the level of the population of the region, adaptation to rainfall variability is a vital issue. In addition, the population of the region lives mainly from rain-fed agriculture or extensive livestock depending not only on seasonal rainfall accumulation but also on intra-seasonal rainfall variability. The recurrent droughts and the decline in agricultural productivity over the last two decades in West Africa highlight the need to better understand the duration of dry periods and especially their frequency. In Senegal, agriculture is defined as a driving sector of the economy in the program Plan Sénégal Émergent (PSE) which serves as a reference framework for public policies over the period 2014-2035. The program Programme d'Accélération de la Cadence de l'Agriculture Sénégalaise (PRACAS) represent the agricultural component of the PSE program. The agricultural sub-sector is characterized in 2016 by a counter-performance of certain agricultural varieties such as millet, groundnuts and maize in connection with the rainfall deficit (ANSD, 2019). It is an essentially extensive agriculture subject to many constraints, among which we can cite the following: -the lack of rice fields with water control mechanisms; -climate variability and change; -insufficient certified seed; -soils that are generally shallow, with surface crusting that promotes runoff, low water retention capacity and low organic matter content. They are subject to strong water and wind erosion in the Sahelian zone and are showing signs of exhaustion. This work aims to contribute to the improvement of our understanding of the spatial and temporal distribution of rainfall breaks in Senegal. It seeks to detect rainfall breaks for each selected station in the country of Senegal but also to characterize them in terms of frequency, classification and duration. Moreover, their relationships with rainfall variability before and after the drought of the 1970s in the Sahel are examined.

Study Area
Senegal is located at the extreme west of West Africa between latitudes 12˚30N -16˚30N and longitudes 11˚30W -17˚30W and covers about 197.000 km 2 . The topography of the country is free of steep terrain. Only a small part of the relief, on the south-eastern border with Guinea, is relatively high with altitudes greater than 200 m above the sea level. Trees and shrubby steppe dominate the north, wooded savannah predominates in the center of the country while dense savannah and forest are increasingly found towards the south (Moron et al., 2006).
Apart from large and mesoscale factors, local atmospheric circulation is particularly influenced by the proximity to the North Atlantic Ocean.
In Senegal, cumulative rainfall follows a north-south gradient and southern areas receive rainfall at the beginning and end of the monsoon due to its north-south migration. The rainy season lasts longer in the southern than in has an average cumulative rainfall of more than 800 mm. It has a fairly secure agricultural system that uses long-cycle millet varieties, sorghum, maize, cotton and rice.

Data
In the framework of this work, it was necessary to gather rainfall data from sever-

Methodology
The main agro-climatic parameters are the start date, the length of the season and eventually the end of the season. Their knowledge is essential in several areas such as fishing, livestock and especially agriculture where breaks of more than 20 days seriously threaten the fields and the grass that serves as food for livestock.

Start and End Dates of the Season
There are several criteria for determining the start date, but the one used to determine these parameters is that of Sivakumar (1992) because of its simplicity of implementation and is the most widely used in the Sahelian zone.
-The start date of the season according to Sivakumar (1992) corresponds to the date X on which a quantity of 20 mm of rain has been collected in three (3) consecutive days after the first of May without a dry period of more than 7 days within the following 30 days.
-The end date of season Y is the day when, after 1 September, there are no more rains for two decades (20 days).
-The length of the season is obtained simply by taking the difference between Y-X. American Journal of Climate Change

Dry Sequences
Notion of drought: Drought is defined as a lack of water availability in relation to a situation considered normal for a given period and a given region (Benzerti & Habaieb, 2001). There are four types of droughts according to areas of application: -Meteorological drought: reduction, poor distribution, or absence of rainfall in a given region over a given period of time (Wilhite & Glantz, 1985).
-Agronomic drought: a situation where soil moisture and water reserves become insufficient to meet crop needs in a given area (Wilhite & Glantz, 1985).
-Hydrological drought: the deviation of surface and groundwater supply from a normal supply over a given period of time (Wilhite & Glantz, 1985).
Depending on the context of this work, meteorological drought is more appropriate for our study. Given that drought is a decrease in water availability for a particular time and over a particular region, the notion of drought is relative (Benzerti & Habaieb, 2001). It is on the basis of this assertion that our study focused on the persistence of drought on an annual scale. The most plausible definition of a rainfall pause is a day without any rainfall record, but meteorologists have set a threshold of 0.1 mm/day to characterize a rainy day. In order to take into account the errors due to the measurements of the instruments and those rainfall measuring in the stations, a threshold of 1 mm/day was chosen in our study. Any day with a rainfall value below this threshold is considered as a dry day and a day with a value above this threshold is considered as a rainy day.
Thus, two or more consecutive days without rainfall are called dry sequences or dry pockets. Given the fact that there is no official indicator of drought, we have made a representation of the annual rainfall of the different stations, simultaneously with a graph that will represent the average annual rainfall of the whole series and of each site. This allowed us to illustrate the dry years which are the years whose value of the rainfall sum of the whole year is below the curve of the average, and logically the wet years those which will be above.
Under the climate of Senegal, the rainy season (June to October) in our case is characterized by dry and rainy sequences. The numbers of dry sequences during the rainy season and their interannual variability is of capital interest not only to farmers but also to all other rain-dependent domains. The occurrence of dry episodes at certain key phases of the rainy season has adverse consequences on crop development, which may prevent the plant from completing its full vegetative cycle. Knowledge of the variability of dry events in the rainy season in Senegal is of vital importance especially for the prevention of famines and food crises. Our analysis covers the entire period from 1950 to 2010. The breaks have been classified according to their duration. In fact, the majority of the rainy breaks between 1 and 3 days are in class 1, those between 4 and 6 days in class 2, those between 7 and 9 days in class 3 and finally those over 9 days in class 4. This period was marked by a great irregularity of episodes of dry days.
B. Ndiaye et al.

Interannual Variability of Dry Sequences from 1950 to 2010
The

Decadal Variability of the Different Classes of Dry Episodes
Decadal analysis of dry episodes in the Dakar region shows that the decade 1951-1960 whose numbers remain well below average in almost all years ( Figure  23) is the decade with the highest number of dry episodes in class 1, followed by the decades 1961-1970, 2001-2010, 1981-1990, 1971-1980 and lastly 1991-2000. For the class 2, it is always the decade 1951-1960 that comes first (with the exception of the years 1953, 1958 and 1960, all the numbers in the other years are above the average for each year). This decade is followed by the decades 1971-1980, 1961-1970 and 1981-1990 (which have very similar numbers) and finally comes the decade 2001-2010. For class 3 it is again the first decade (1951)(1952)(1953)(1954)(1955)(1956)(1957)(1958)(1959)(1960) that records the highest number of students, followed by 1981-1990, 1971-1980, 2001-2010, 1961-1970 and 1991-2000. Beyond class 3 the decadal variability is very irregular (Figure 23). In Ziguinchor, the decadal analysis shows that the decade 1951-1960 records the largest number (about 300) of dry episodes of class 1 followed by the decades 1981-1990; 1961-1970; 2001-2010; 1971-1980 and 1991-1990 (whose numbers for this class are very similar). Then there is a rapid decrease (for all decades) in the number of dry episodes from class 1 to class 2, with the 1971-1980 decade coming first for class 2, followed by the decades 1981-1990; 2001-2010; 1991-2000 and 1951-1960    class 3 followed by the decades 1991-2000; 1971-1980; 1981-1990; 2001-2010 and 1961-1970, but beyond this class there is no significant variation between decades ( Figure 24). American Journal of Climate Change In the Thiès region, it is the decade 1951-1960 that shows, according to class 1, the largest number of dry episodes followed by 1961-1970; 1981-1990; 1991-2000; 2001-2010 and 1971-1980 periods (whose annual numbers are below average except for a few small years). The last two decades (1991-2000; 2001-2010) and the decade 1971-1980 have numbers very close to the dry episodes of class2 but also have the largest numbers for breaks in this class, whose first decade has the smallest numbers. For the class 3 breaks, the 1971-1980 period has the smallest number. For other decades, the difference in their numbers is not significant enough and beyond that there is little decadal variability ( Figure   25).
In the Diourbel region, the decadal variability of dry episodes shows that the period 1951-1960 is the most important for dry episodes of class 1, followed by the periods 1961-1970; 2001-2010; 1971-1980; 1981-1990 and 1991-2000   has the largest number of breaks, followed by the decades 1971-19801991-20001981-1990and lastly 1951-1960. The decade 1971-1980 has the smallest number of breaks for class 3 and for the same class the decade 1981-1990 has the highest number of episodes followed by 2010-2010; 1961-1970; 1951-1960 and 1991-2000. It can be noted that beyond this class the decadal variability is very low ( Figure   26).
In the Kaffrine region, it is the first decade of 1951-1960 that records the greatest number of rainfall breaks in class1 (over the whole decade the annual numbers are below average). For class1, the 1951-1960 decade is followed by the decades 1961-1970, 2001-2010, 1981-1990, 1971-1980 and 1991-2000 and for class 2 it is the decades 1961-1970, 1971-1980, 1981-1990, 1991-2000    As for the Kaolack region, the period 1951-1960 shows the highest values in class 1, followed by 2001-2010; 1981-1990; 1971-1980 and finally 1991-2000. For the class 2, all decades record similar values except for the decade 1971-1980, which shows the lowest number of breaks for this class. One can note that, it is this same class that records the highest number of 10 -12 day class episodes ( Figure 28).
In the Kedougou region, class 1 is the highest in terms of numbers during the decade 1961-1970, followed by 1951-1960, 2001-2010, and the other decades (1971-1980, 1981-1990 and 1991-2000) have the lowest numbers with very similar values. For class 2, with the exception of the decade 1991-2000, which is higher, all classes show more or less little different. It can be noted that from class 3 onwards the variability is very low (Figure 29).  In the Tamba region, it is always the first decade of the period  that shows high values for the class1, then come the decades 1961-1970; 1981-1990; 1971-1980; 2001-2010 and finally 1991-2000. For class 2, it is the period 1971-1980 that records the greatest values, followed successively by the decades 1981-1990; 2001-2010; 1991-2000 and the two decades 1961-1970; 1951-1960  In the region of Louga, the decade 1951-1960 which has the greatest number of dry episodes of the class 1, followed by the decades 1961-197; 1981-1990; 2001-2010; 1991-2000 and finally 1971-1980. It is always the period 1950-1960 which shows higher values in terms of class 1 and class 2, followed by the periods 1991-2000; 2001-2010; 1961-1970; 1971-1980 and 1981-1990. For the class 3, the two decades (2001-2010 and 1961-1970) show similar values followed by the decades 1951-19601971-19801981-1990and 1991-2000).
In the Saint-Louis region, apart from the first two decades (1951-1960 and 1961-1970) 1951-1960; 1991-2000; 2001-2010; 1981-1990 and finally 1971-1980. In contrast to the other stations, this region has a fairly high variability for the other classes of dry episodes (Figure 32).

Correlation
A correlation coefficient (R) calculates the extent to which two variables tend to change together. The coefficient describes the importance and direction of the   relationship. In our study two methods (Pearson and Spearman) were used to calculate the correlation coefficients between the average length of breaks and maximum breaks on the one hand and between the annual rainfall and the annual total number of dry spells on the other hand. Indeed, Pearson's correlation evaluates the linear relationship between two continuous variables. A relationship is said to be linear when a change in one of the variables is associated with a proportional change in the other variable. Spearman's correlation evaluates the monotonic relationship between two continuous or ordinal variables. In a monotonic relationship, the variables tend to change together, but not necessarily at a constant rate. The p-value coefficient (p) has also been determined to see if the correlation between the variables is significant by comparing the value of p to the significance level. In general, a significance level (rated alpha or α) of 0.05 gives good results. A value of 0.05 in α indicates that the risk of concluding that a correlation exists when in reality there is no correlation is 5%. The value of p indicates whether the correlation coefficient is significantly different from 0 (a null coefficient indicates that there is no linear relationship).
Value of p ≤ α: the correlation is statistically significant if the value of p is less than or equal to your significance level, you can conclude that the correlation is different from 0.
Value of p > α: the correlation is not statistically significant if the value of p is greater than your significance level, you cannot conclude that the correlation is different from 0.
For the correlation between the mean duration of breaks and maximum breaks, both methods (Pearson and Spearman) show a strong linear but also monotonous relationship between the two series in all the regions studied. This is well confirmed by the p-values which are, at all times, lower than 0.05. The correlation between the mean duration of breaks and the maximum breaks is also well confirmed by the p-values which are, at all times, lower than 0.05 (Table 1) Table 2).
The monthly evolution of dry episodes presents different situations according to classes of selected episodes. Indeed, the evolution of dry sequences of class 1 (1 -3 days), which are the most important, increase until the middle of the rainy P-value 5 × 10 −14 4 × 10 −10 4 × 10 −14 2 × 10 −9 10 −8 10 −12 9 × 10 −10 3 × 10 −11 7 × 10 −11 2 × 10 −12  For all the regions studied, the dry episodes of this class reach their maximum in August (Table 3) Louga and Saint-Louis. These developments reflect the importance of convective systems, which provide most of the rainfall in the Sahel in general, and whose activity is most intense in August-September (Sagna et al., 2016).

Conclusion and Perspectives
We have used timeseries of precipitation data for many stations of Senegal to study the spatio-temporal variability of rainfall breaks. These data, extracted from the CERAAS database, cover the period 1950-2010 and represent an enough long series to allow such study. To do this, we have defined the rainfall breaks in terms of days regrouped in classes, going from class 1 to class 4 for rainfall breaks of 1 -3 days; 4 -6 days; 7 -9 days and those greater than 9 days respectively.
Our results show that in the southern regions of Senegal (Zigunchor; Tamba; Kedougou; Kolda; Vélingara) class 1 is much more frequent. This is mainly due to the fact that ITCZ is present almost throughout the rainy season. Class 4 shows practically very low values, which means breaks longer than 9 days are in-American Journal of Climate Change frequent. For the Center (Diourbel, Kaolack, Fatick), we note all the classes but with a slight predominance of class 2 and class 3. In addition, we note that in this area, class 2 is more frequent in June. As for the North region (Saint-Louis), classes 3 and 4 are much more frequent. This spatial variability of rainfall breaks is clearly associated with the rainfall gradient between the North and the South.
The temporal evolution of the numbers of each class intrinsically follows the evolution of the ITCZ.
This study on the spatio-temporal distribution of rainfall breaks is a step forward in understanding the installation and development of the rainy season in Senegal. The results show that the number of dry days of the class 1 (1 -3 days) decreases from south to north as opposed to maximum breaks which increase from south to north. The practical interest of having a calendar of the rainfall break intensification phases is that it can serve as a basis for long-term planning of activities sensitive to intra-seasonal rainfall variability. In the agriculture sector, break periods can be seen as periods when the risk of the dreaded dry sequence occurrence at critical crop phases (maize flowering, sorghum ripening) is higher. The results of our study offer interesting research perspectives to be developed in the near future. These are organized around the following main axes: -Extend the study until 2018 to take into account the recent variations in rainfall breaks.
-To make medium-term forecasts of the occurrence of breaks and to make projections.
-Evaluate the impact of dry episodes on aggressive vector densities via their consequences on the water height of larval sites.
-The demonstration of possible correlations between dry episodes and the recrudescence of dangerous meteorological phenomena for several domains would be of great practical use for the planning of the activities of companies in charge of the management of the safety of air navigation and air carriers, but also for agriculture.