The rainfall analysis with daily resolution in Algeria is a subject of great interest. This type of analysis is justified by the existence of severe environmental hazards in the Mediterranean, such as floods and soil instability resulting from the high percentages of annual total precipitation falling in a limited number of very rainy days. Thus, the area presents long periods of drought (Martin-Vide, 1994) and irregular temporal rainfall distribution in large areas of the western Mediterranean (Cortesi et al., 2012).

The interest is not only focused on climate but also on the effect of heavy rainfalls on other areas of the environment and society. However, the importance of daily precipitation has not been sufficiently studied. Only a few papers on the statistical structure of precipitation with daily resolution have been published. For example, studies of the Mediterranean basin (De Luis et al., 1996, 1997; Martin-Vide, 2004; Sánchez Lorenzo and Martin-Vide, 2006; Benhamrouche and Martin-Vide, 2011, 2012; Cortesi et al., 2012; Coscarelli and Caloiero, 2012) concluded that 25 % of the rainiest days represent at least 75 % of the annual total, and the highest values of the concentration index (CI) (over 0.66) are found on the eastern façade of peninsular Spain (from Barcelona to Almería). The results of similar studies in Iran (Alijani et al., 2008) and China (Zhang et al., 2009) indicated that the CI values detected in China were higher than in Iran (0.74–0.80 and 0.58–0.73, respectively).

High CI values have been obtained in southeastern peninsular Spain and the geographical proximity to our study area invites us to focus on the spatiotemporal daily rainfall distribution of 42 meteorological stations evenly distributed over the entire Algerian territory. Statistical analysis was performed to determine the relative impact of different classes of daily precipitation and an assessment of accumulated rainfall.

The study of CI in Algeria is important due to its geographical position between the Mediterranean zone and the hot Sahara. The main objective of the article is to analyze the spatial distribution of the concentration of the daily precipitation in Algeria. The specific objectives are (1) to calculate the values of the CI, (2) map the CI values and (3) correlate the CI values with the values of other precipitation variables.

Regardless of the variable or index analyzed, there is a need to study spatial precipitation patterns in Algeria to provide a better understanding of this phenomenon. These studies are relatively complex because of (1) the latitudinal position of Algeria between the Tropic of Cancer and the mid latitudes, which produces several climate zones, and (2) the considerable variety of altitudes, orientations and sloped reliefs.

Algeria, situated in northern Africa (between latitudes 19∘ and somewhat over 37∘ N and longitudes 9∘ W and 12∘ E), is the largest country on the continent, occupying an area of 2 381 740 km2 (Fig. 1). Algeria is bordered by the Mediterranean Sea to the north, Tunisia and Libya the east, Mauritania, Niger and Mali to the south, and Morocco and Western Sahara toward the west. The Saharan region (center and south of the country), accounting for 80 % of the territory, is almost completely uninhabited.

Algeria's climatic regions and landscapes can be divided into three zones distributed parallel to each other along the country's N–S axis. Coastal Algeria has a Mediterranean climate with mild, rainy winters and hot, dry summers. Mean temperatures in January are above 10 ∘C and slightly higher than 27 ∘C in July. Average annual rainfall for Algeria is 83 mm, but most of the northern area receives over 400 mm total annual precipitation, with some areas receiving more than 1270 mm according to the National Meteorological Office (ONM). The highest ranges of the Tell Atlas, which runs parallel to the coast, are 2290 m above sea level. The uneven terrain is interrupted by small plains, particularly along the coast. To the south of the Tell Atlas lie High Plateaus, characterized by a dry steppe climate with cooler winters and slightly hotter summers. Rainfall averages 250 to 500 mm annually, concentrated in winter and spring. The southernmost range of the Atlas mountains is the Saharan Atlas, which borders on the desert. Though generally low, the Saharan Atlas reaches a height of over 2320 m. It presents a very dry climate that is varied as a result of its elevation. Finally, much of the country is occupied by the Sahara desert, one of the world's most desolate areas, which has a tropical hot climate. Average summer temperatures are above 35 ∘C and frequently rise as high as 43 ∘C or over. Temperatures vary radically from day to night. Total precipitation is very low or almost zero; for example, in the extreme southeast of the country (Illizi, Bordj Badji Moukhtar, and Adrar), amounts lower than 20 mm are recorded. In the Hoggar mountains to the south lies Mount Tahat, Algeria's highest point, rising to 3000 m.

We obtained daily rainfall data for 42 Algerian weather stations from the ONM. The stations' recording periods varied in duration, but many data are available from 1970 to 2008. We therefore selected stations that provide daily rainfall data presenting relatively uniform coverage throughout the country. The quality of the data series has been verified by the ONM. The station with less recorded data over the whole period has over 93 % of the total data. Station characteristics are shown in Table 2 and their spatial distribution is mapped in Fig. 4.

The methodology applied in this study, proposed by Martin-Vide (2004) and including the definition of daily precipitation concentration and index, will be illustrated by an example (Table 1). Data from the Chlef station was available for the period from 1970 to 2008. These meteorological stations do not show high daily precipitation values and, therefore, their frequency distribution can be presented in a moderate-length table.

In the first column of Table 1, class limits are presented in ascending order and the second column shows their midpoints or centre of class. In the third column (Ni) the number of recorded precipitation days in each class, or absolute frequency, is listed. For example, in 39 years, 819 rainy days were recorded with variant amounts from 0.1 to 0.9 mm, and 407 rainy days represented amounts ranging from 1.0 to 1.9 mm. The rainiest day is between 99.9 and 100.9 mm. Overall, there were 2753 rainy days. The fourth column represents cumulative frequencies of rainy days (∑ Ni), which are obtained by adding the absolute frequencies of all classes (the last value of this column is the same as the total number of precipitation days). The fifth column is the total precipitation for each Pi class and is obtained by multiplying the corresponding Ni value (midpoint). The total accumulated rainfall (∑ Pi), in the sixth column, is obtained by progressively adding up the values of the previous column; the value of the last class is the total precipitation of 13 958.5 mm recorded in the study period (1970–2008). The last two columns can be interpreted as follows: almost one-third of rainy days (29.75 %), with 0.9 mm or less, represent only 2.93 % of the total accumulated rainfall.

These results give the graphic representation shown in Fig. 2: the cumulative percentage of rainy days (next-to-last column of Table 1), ∑ Ni (%) or X is plotted against the cumulative percentage of rainfall amounts (last column), ∑ Pi (%) or Y. Note that the resulting polygonal line is markedly exponential in the statistics and is called concentration curve or Lorenz.

However, we can refine Lorenz or concentration curves of the Chlef meteorological station by replacing polygons by exponential curves (Jolliffe and Hope, 1996). The work of Riehl (1949), Olascoaga (1950) and Martin-Vide (2004) showed that such functions are of the kind Y=aXebx, with a and b as constants.

Parameters a and b of Eq. (1) were determined by the least squares method, given by Eqs. (2) and (3): ln⁡a=∑x12∑ln⁡y1+∑x1∑x1ln⁡x1-∑x12∑ln⁡x1-∑x1∑x1ln⁡y1N∑x12-(∑x1)2 b=N∑x1∑ln⁡y1+∑x1∑ln⁡x1-N∑x1ln⁡x1-∑x1∑ln⁡y1N∑x12-(∑x1)2, where N is the number of classes.

After determining the two constants a and b, the definite integral of the exponential curve between 0 and 100 shows the area S under the curve (the abscissa and the ordinate 100), which is given by the formula s=abebxx-1b0100. Based on S, the area S′ compressed by the exponential curve, the equidistribution line and X = 100 is the difference between 5000 and the value of S (Fig. 3). S′=5000-S Calculation of the CI given by the following formula from Martin-Vide (2004): CI=S′/5000. Note that the CI value is a fraction of S′ and the lower surface of the triangle is bounded by the equidistribution line.

In the case of the Chlef station, the application of Eqs. (2), (3) and (6) gives the following results: a= 0.036, b= 0.033 and CI = 0.59. CI > 0.61 is high, 0.55 < CI < 0.61 is moderate and CI < 0.55 is low. The calculations were performed using software developed using Delphi (see Supplement 1 and 2).

Spatial interpolation methods, particularly the kriging technique, yield better results than other techniques, since kriging produces the standard error for the estimated values. Among all the kriging methods, ordinary kriging is used in this study. Statistical software was used for kriging application while mapping of the results was done using ArcGIS 10.1. The correlation methods used for each pair of variables – (CI, P), (CI, CV) and (CI, N) – are the Pearson's correlation coefficient, Spearman's rho and Kendall's tau-b.

The exponential curves of a given type in Eq. (1) were calculated for 42 meteorological stations in Algeria for the period from 1970 to 2008 (Table 3 and Fig. 5). Extreme values are CI = 0.57 in M'sila (mid-northeast Algerian territory), an area influenced simultaneously by the Saharan climate and the Mediterranean climate, and CI = 0.70 in Biskra (mid-eastern Algeria) with characteristics of marked rainfall by the Saharan climate. Despite the minimal distance between the two stations, a significant difference is observed with a variation coefficient of 13 % from the surface exponentially compressed by the two stations and the equidistribution line. This means that the daily rainfall patterns are quite different.

Through the exponential concentration curves, the rainfall percentage contributed 25 % of the rainiest days, i.e., those with larger amounts were calculated. The results are presented in Table 3. Extreme rainfall values can be found in Tindouf, with 79 %, and M'sila, with 66 % (Table 3).

Note that in the first case, as in other stations (Illizi Assekrem and Bordj Badji Mokhtar) in southern Algeria, the fourth part of rainy days represent 75 % of total rainfall. This leads to a marked uncertainty in terms of annual rainfall considering the low number of rainy days per year obtained.

Any anomaly in atmospheric general circulation can greatly increase or reduce the total annual precipitation.

The daily rainfall concentration in the region of Biskra and in the southwestern part of the country is high, with concentration index values close to 0.70. This reflects the fact that very few rainy days are bringing a high percentage of annual precipitation.

The occurrence or not of such large quantities every day can change the character (dry or wet) of any month, season or year. This leads to considerable uncertainty in the average rainfall contributions, which in turn leads to environmental and social impacts.

Thus, it was concluded that in Algeria, the essential features of climate in different regions are characterized by narrow climatic zones close to the coast, under the combined influence of the sea. The relief of the soil, the latitude and the diversity of climates in Algeria lead to a very different rainfall distribution.

The CI values obtained at 42 meteorological stations across Algeria range from 0.70 (Biskra) to 0.57 (M'sila). Tracing isohyets are also largely determined by the topography of the surface. Northern, western and central regions are areas where rainfall is regular compared to eastern regions, while the southern region shows the most aggressive rainfall.