Variability and Trend of Annual Maximum Daily Rainfall in Northern Algeria

The daily rainfall dataset of 35 weather stations covering the north of Algeria was studied for a period up to 43 years, recorded after 1970s. The variability and trends in annual maximum daily rainfall (AMDR) time series and their contributions in annual rainfall (AR) were investigated. The analysis of the series was based on statistical characteristics, Burn’s seasonality procedure, Mann-Kendall test, and linear regression technique. The contribution of the AMDR to AR analysis was subjected to both the Buishand test and the double mass curve technique. The AMDR characteristics reveal a strong temporal irregularity and have a wide frequency of occurrence in the months of November and December while the maximum intensity occurred in October. The observed phenomenon was so irregular that there was no dominant season and the occurrence of extreme event can arrive at any time of the year. The AMDR trends showed that only six of 35 stations have significant trend. For other stations, no clear trend was highlighted. This result was confirmed by the linear regression procedure. On the contrary, the contribution of AMDR in annual totals exhibited a significant increasing trend for 57% of the sites studied with a growth rate of up to 50%.


Introduction
Rainfall is a fundamental element of climate which is, for several decades, in perpetual mutations.For most regions around the Mediterranean, these changes resulted in significant rainfall deficits [1,2] accompanied by an increase of exceptional events such as severe droughts and devastating floods [3,4].The Mediterranean environments, typical of semiarid regions that enjoy a rather pleasant climate with sunshine and its fine weather, can suffer hazardous situations since several regions are regularly struck by severe rainstorms.Such events are highly variable in the time and space [5] and often lasted less than one day [6].Therefore, the critical parameter of these rainstorms is the maximum daily rainfall rather than the total rainfall.The annual maximum daily rainfall is defined as an extreme instance, with critical duration for a watershed, region, or state [7].In the hydrological year, the daily maximum rainfall is the parameter considered to assess the immediate impact on the hydrological response of streams, flooding cities, soil erosion, dams silting, and agricultural production [8,9].Located on the southern shore of the Mediterranean, Algeria suffers a semiarid to arid climate.Despite a drought that has lasted for over three decades, brief, intense, and devastating floods often affect cities.Due to the intensity of rainfall events that typically last less than 24 hours and the vulnerability of urban areas, the floods have caused damage and significant loss of human lives.The only flood that occurred in the city of Algiers in November 2001 caused some 740 casualties [10][11][12].
The objective of this study is to contribute to the knowledge of the variability of annual maximum daily rainfall and its changes in the north of Algeria.A particular attention is paid to detect possible trends characterizing AMDR series and to evaluate changes in AMDR contribution to annual totals.

Study Area/Materials and Methods
The study area is the north of Algeria and covers 15% of the total surface of the country (2.38 million km 2 ).The length  of the Mediterranean coastline is about 1200 km.Because of its geographic position and its mountainous nature, rainfall shows strongest contrasts between the various areas.This region has a high spatial and temporal climatic variability known as the Mediterranean climate.Intra-annual rainfall is irregular and most rains fall between October and April, while infrequent and local storms occur in the dry season from July to October.

Algeria Study area
Rainfall data were collected by the National Agency of the Hydraulic Resources (ARNH) (http://www.anrh.dz/).Because there were too many gaps after colonial period in the 1960s and where the number of years of observations was too low for statistical purposes, many station series were discarded from the data set.As a result, only 35 rainfall series were selected (Figure 1).
The data collected are a set of daily rainfall series for the period after 1970.They include less than 5% of gaps.These are replaced by the values of the station which has the best correlation.The data were tested for their quality control.The suspect data were cross-checked with those of nearby stations (some are not used in this study).The arithmetic sum of daily heights recorded is the annual rainfall value (AR) while the daily maximum observed during the year represents the annual maximum daily rainfall (AMDR).Data were aggregated according to hydrological year from September to August.The selected stations are described by the geographical coordinates, number of years of observation, and statistical characteristics (Table 1).
In the Mediterranean region, it is unlikely that rainstorm lasts more than 24 hours [6].So, the annual maximum daily rainfall (AMDR) series may be introduced to study the distribution of extreme precipitation occurrences within a year.To examine the regularity for such series, we applied the seasonality as described by Burn [13].This method used to estimate the timing and regularity of floods was then transposed to extreme rainfall in particular AMDR [14].It assesses the degree of similarity of watersheds in relation to the hydrological response or the occurrence of extreme rainfall.Burn's vector defined by (, ) represents the variability of the date of occurrence of all extremes events.Its direction is the mean date of the occurrence of the extremes events and the modulus is the variability around the mean value.The dates of the AMDR occurrence are based on the calendar year.January 1 is the 1st day and December 31 is the 365th day.
Each date   was replaced by an angle: The obtained series covers the unit circle where each term can be described in polar coordinates as a vector (cos   , sin   ), where   indicates the direction expressed in radians.Following the Burn approach, the Cartesian coordinates,   = cos   and   = sin   , are used to evaluate Burn's vector defined by (, ) the mean direction and mean modulus given by the following equations: where When  decrease to zero, there is no single dominant season and the occurrence of extreme event can arrive at any time of the year, while  = 0 is a virtual value indicating that extreme events occur on the same day.The date of occurrence of extreme events is regular, as the modulus approaches the unit more.
The annual trend of AMDR series was analyzed by using two statistical methods: the Mann-Kendall test and the linear regression.The nonparametric Mann-Kendall test [15,16] detects the direction of trend patterns in hydrological variables.For a time series (  ) of  values, each value   is compared with all corresponding   to compute the sign, and the indices  and  take the respective values  = 1, 2, . . .,  − 1 and  = +1, +2, +3, . . ., .Kendall's -statistics is based on the sum and variance computation.In this study, an error risk of 5% is accepted; that means a probability threshold below which the null hypothesis, the trend series, is monotonic, will International Journal of Geophysics be rejected.Thereby, the Mann-Kendall test is expected to be less affected by the outliers because its statistic is based on the sign of differences rather than on the values of the random variable [17].
The linear regression procedure is a statistical technique for estimating the relationships among variables (e.g.,  and ).The straight line  = + is obtained by the least square regression method.The slope () indicates the average rate of change in the variable used.If the change is significantly different from zero, then a real change occurs.Positive slope defines increasing trend while the negative one indicates a decreasing trend.
The temporal series of the rate contribution of the AMDR to annual rainfall was subjected to the Buishand test to assess trends and date of departure of homogeneity [18].The test is a graphical method based on the evolution of the following equation: where   is the variable,  is the mean value of the series, and  is the standard deviation.
The statistical parameter max  |CS  | is a good indicator of the departure of homogeneity [19].The increasing or decreasing limbs of both sides of the extremum max  |CS  | correspond to surplus or deficit periods, respectively.So when significant change is confirmed, we applied the double mass curve to quantify the surplus or deficit [20].The curve is a straight line whose slope is the proportionality constant.A break in slope indicates a change of the proportionality [21].The break in slope and the angle formed by two straight lines indicate the date and the degree of change in the behavior of the phenomenon.

Results
In the study sites located in the north of Algeria where a division in increments of 150 mm is shown in Figure 1(a), the average annual rainfall varies from 194 mm (Ras El Ma station, code number 4) to 874 mm (El Milia station code number 24) (Table 1).Spatially, rainfall is distributed in four areas [22]: (i) The central highlands, Sersou and Ras El Ma regions, though situated at high altitude, are sheltered compared to wet currents, where rainfall is less than 300 mm.
(ii) The western region of the country is characterized by a relative sheltered position compared to maritime influences and the low volume of the relief.Annual averages are generally less than 450 mm.
(iii) The mountainous areas and high interior plains (mountains of Tlemcen in the west and the mountains of Zaccar and Dahras in the east) are characterized by the relative importance of total rainfall, with annual average exceeding 600 mm.
(iv) The Atlas Tellien region exposed to the north and northwest records rainfall amounts that can exceed 800 mm.
For AMDR values, a division in increments of 10 mm and the main statistical parameters estimated for all the stations are shown, respectively, in Figure 1(b) and Table 1.Spatial variability of intra-annual averages of AMDR ranges from a minimum of 25 mm (station Ras El Ma, code number 4) to a maximum of 71 mm (Station Meured, code number 14).Low values are concentrated on the west side while the high values are in the east and center of the country.Through the 35 studied stations, the temporal distribution of the annual maximum daily rainfall is irregular.The coefficients of variation, Cv, vary between 31% and 81%, with a spatial average of 44%.The most irregular series, Cv above 0.5, are found near the reliefs.The stations with the code numbers 1 and 24 are positioned facing the north and the stations with code numbers 2, 4, 8, 12, 14, 15, 24, 27, and 28 are positioned facing the south (Figure 1).The largest values of 255 and 210 mm were recorded, respectively, in the west region in station code number 1 in 1999-2000 and at the east in station code number 24 in 1990-1991.The spatial average of maximum daily rainfall is about 114 mm, which represents 24% of the spatial average of mean inter annual rainfall.
For stations under consideration, the skewness coefficient (Cs) has positive values fluctuating from 0.4 to 4.6 with a spatial mean of 1. 43.Thereby, at level confidence of 95%, there is rejection for normal distribution for a majority of stations since the values of skewness coefficient are above 0.62 for 31 of 35 stations.That means low values are more frequent while high values are still rare but excessive.The pronounced skewness coefficients occurred at the station Pierre du chat (code number 1).
The difference in positioning stations (near the coastline, facing the sea, at high altitude or between the mountains) prevents a relatively good correlation to the altitude.The spatial variability of rainfall (AR and AMDR) is mainly influenced by latitude (Figure 2).The average increase for AR and AMDR, respectively, is about 140 mm and 25 mm to 100 km latitude.
The occurrence of AMDR was more frequent during November, followed by December and January (Figure 3(a)), while the peaks in order of importance occurred in October, December, and November (Figure 3(b)).In addition, the seasonal concentration index  varies from 0.03 to 0.32 with an average of 0.15 (Figure 4).So, there is no single dominant season and the occurrence of an extreme event can arrive at any time of the year.On the other hand, Burn's method shows that AMDR were more concentrated in February through 40% of the stations, against 20% in October (Figure 4).
The results of the Mann-Kendall test are summarized in Table 2 and Figure 5(a).At the 95% confidence level, only 6 of 35 stations show significant trend.The stations Ras El Ma, Ain Berda, and Chelia show an increasing trend, whereas the trend is decreasing in Sarno, Ameur El Ain, and Djebabra, while in the remaining stations no significant trend is observed.This finding corroborates the results obtained by the linear regression analysis (Table 2 and Figure    The curves resulting from Buishand procedure were classified into four distinct cases.The first case concerns five rainfall stations (Ain Beida, Ain El Hadjer, Sidi Yahia, Aïn Mimoun, and Djebabra) where Cs  curve shows ascending and descending lambs, and the maximum of the Cs  curve corresponds to the date of change (Figure 6(a)).The decline of the AMDR contribution to annual rainfall, manifested by the falling lamb, was quantified by the double mass curve and varies between 12.1 and 22.7%.The dates of change were observed during the 1980s (Table 2).The second case grouped 20 rainfall series exhibiting opposite behavior (Figure 6(b)).The AMDR contribution has increased significantly (e.g., at El Milia station the increase reaches about 50%).The dates of change occurred from the end of 1970s to the end of 1990s.The third case represents seven of 35 rainfall series and is manifested by a complex form showing more than one date of the change.However, lambs of the Cs  curves were not sufficiently long to apply the double mass method (Figure 6(c)).For the last case, three of 35 rainfall series, no clear trend can be detected for any rainfall sequence (e.g., Ouzera, Batna, and Chelia) (Figure 6(d)).

Discussion and Conclusion
The data of 35 rainfall stations recorded after 1970 and covering the north of Algeria reveal that rainfall undergoes an overall downward trend.Deficit rate between 20 and 40% was estimated in several parts of the country [23][24][25][26][27].This decrease in annual rainfall was accompanied by a large temporal irregularity like the Mediterranean region [28,29].In terms of AMDR values, coefficients of variation for the different sites vary at ±12% around the average of 44% showing a more pronounced irregularity occurrence, but in the same proportions as in other regions [30][31][32].Indeed, the skewness values of the time series, which show if the empirical distribution of the data follows a normal distribution, are more important in the extreme east of the country than in the west and the center (a ratio of 1.66).All positive values of Cs found indicating that distribution shifted to the left of the median (Table 1) are of the same order as those of Chott-Chergui basin in western Algeria [33].In this analysis, we exclude Pierre du chat station for which an exceptional value of 255.4 mm has increased all coefficients.
For a better understanding of water availability, it is very interesting to demarcate the quasi-homogeneous climatic zones and identify the climatic subregions in an observation network [34].Nevertheless, in the north of Algeria, the proximity of the Mediterranean and the variety surrounding reliefs make it difficult to delimiting homogeneous areas.Moreover, the increased baroclinic instability in saturated air is closely related to latent heat release and thus to the development of convective phenomena.During the rainy season, northern Algeria is affected by the polar front, especially the east of the country.Further south, the highlands are generally affected by western disturbances following the orographic forcing that causes thunderstorms with heavy rainfall [35].Then, the correlation between rainfall and altitude is complex.It may be valid only for limited areas.Contrary to that, the rainfall is positively correlated with latitude and the east of the country is much wetter than the west (Figure 2).
For almost all stations, mean values of AMDR as well as AR are two to five times higher for particular years.This disparity between the average values and peaks combined with statistical parameters cited above is illustrated in Figure 4 according to Burn [13].The seasonal concentration index  varies between 0.03 and 0.32 showing that there is no single dominant season, and the time of the occurrence of an extreme event is distributed around the year.This demonstrates the extent of rainfall irregularity in the south of the Mediterranean.This is not always the case through other regions.In central Slovakia, for example, the phenomenon has a spatiotemporal occurrence more regular [14].Despite this, October and November are the months when the floods are the deadliest.It should be noted that Algeria is the country where the number of flood victims is the highest of the Mediterranean countries [36].
The examination of AMDR trends using the Mann-Kendall test and linear regression procedure shows that, unlike the annual rainfall undergoing a downward trend in most of the rainfall stations in Algeria [28,[37][38][39], there is no clear trend to rise or fall in the series of AMDR for the majority of the sites studied.The region of study is characterized by a great number of complexities related to geography and topography where the combination of the effects produced makes weather forecasting exceedingly difficult causing high spatiotemporal variability.So, like many other parts of the Mediterranean area, a majority of AMDR series recorded in the north of Algeria show nonsignificant trends [38,40,41].However, globally, AMDR series show an increase in tendency in the east of the country and a decrease in the center while in the west, the system is more complicated and there is no majority of stations that differs from others.In this context, the IPCC report confirmed that the behavior of extreme rainfall differs considerably from the annual totals by some considerable geographical differences in the frequency, timing, and magnitude of events [42].
The present study does not converge with the results developed by some authors and in the occurrence of extreme rainfall forecasts which predict an increase in extreme rainfall in many parts of the world, even in areas where the average annual rainfall has a downward trend [42][43][44][45].For some authors, this finding is apparently valid for Mediterranean countries that record rainfall deficits since 3-4 decades [3,28].However, our study reveals that not only does the trend of the AMDR series depend on global and regional settings, but also, it is highly influenced by local geographical characteristics.This result corroborates the finding of Tramblay et al. [38] and Jones et al. [46] who cited the orography influence as a main cause generating local climatic processes.Other International Journal of Geophysics investigations of extreme rainfall across many countries of the globe show that extreme rainfall trend is complex.For example, it had increased in the USA, China, Australia, Canada, Norway, Mexico, and Poland [47], where no clear trend was detected in other regions such as in Brazil and Ethiopia [7,48].Although a general trend for drought and a reduction in rainfall intensity was predicted for eastern Mediterranean [49], the extreme precipitation trend is more misunderstood as in Jordan [32].
Without having a provided dominant season, the AMDR occurred mainly between October and March (Figure 4) and the highest values were recorded in autumn (Figure 3).Similar results were observed in other Mediterranean sites where a slight increase in autumn rainfall was mainly felt in October [50,51], leading to more concentrated rainfall during the hydrological year [52].
The relationship between the values of the AMDR and AR in the north of Algeria has experienced significant temporal changes in most of the studied stations.However, four configurations of the relationship between AMDR and AR (Figure 6) are distinguished and seem to be related to the climate change which operated in the Mediterranean region.Despite the lack of trend in AMDR series, their contributions in the annual rainfall are on the rise.This occurred in 80% of stations spread from the east to the west (not taking into account the stations that submitted a complex or nonsignificant trend behavior).The rate of increase of this contribution will be from 8 to about 50%.Although the rates of reduction of annual precipitation in the post-1970 period are higher than 20% for most stations in Algeria, some very high rates of increase in the contribution of the AMDR in annual totals are amplified by extremely high values of the recorded AMDR (example of El Milia Station).In this context and by analyzing the contribution of events in annual precipitation in the north of the Mediterranean, De Luis et al. [53] reported that, in all the studied stations, more than 37% experienced an increasing contribution against 15% with decreasing contribution.
The start of the change leading to the increasing contribution of the AMDR to the annual rainfall occurred mainly during the 1980s and 1990s and the AMDR occurred principally in the autumn season.However, this observation is misleading because the decrease of annual rainfall is mainly due to the sharp diminution of the winter rainfall.Indeed, the values of the AMDR that occurred during autumn are in the same proportions observed in winter (Figure 3).In the Mediterranean region, Giorgi and Lionello [50] observed a sharp falling in the winter rainfall against a small increase in autumn.They mainly attributed the increase in extreme daily intensities to the reduction of annual precipitation.The rate of this reduction was estimated to be more than 30% in the northwest of Algeria [54].

Figure 1 :
Figure 1: Locations of rainfall stations in northern Algeria and mean values intervals of annual rainfall (a) and annual maximum daily rainfall (b). 5(b)).

Figure 5 :
Figure 5: Mann-Kendall (a) and linear regression (b) trend of AMDR over the period after 1970 in northern Algeria.

Figure 6 :
Figure 6: Buishand and double mass methods applied to AMDR contribution to AR.

Table 1 :
Descriptive statistic of AMDR in northern Algeria.
: years of record; Cv: coefficient of variation; Cs: coefficient of skewness.

Table 2 :
values and Tau of Mann-Kendall test, the slope () of linear regression analysis, and AMDR contribution to AR over the period after 1970 in the north of Algeria.