## Abstract

Drought mitigation and prevention require a broader knowledge of the spatio-temporal characteristics and return periods of droughts over several years. In this research, drought characteristics (severity, duration, frequency and areal extent) have been analysed in northern Algeria by using the Standardized Precipitation Index to identify drought events from 194 precipitation stations. For frequency analysis, three Archimedean copula families were used to find a relationship between drought duration and severity. The severity–duration–frequency (SDF) and the severity–area–frequency (SAF) curves were obtained. The SDF and SAF curves are then used to build three-dimensional surfaces of drought severity, drought duration and cumulated percentage of the affected area (SDA) for each return period. It has been shown that the return periods of maximum drought events severity vary according to their durations. To address the issue of long-term droughts, a new classification of dry events based on drought severities is proposed. The obtained results show that the western part of Algeria is the most sensitive to severe/extreme droughts of short durations and high probabilities of exceedance. For long-term durations, the study area was sensitive to mild droughts with lower probabilities.

## INTRODUCTION

Drought is a natural phenomenon resulting from a prolonged absence of precipitations. It has negative economic, environmental and social effects (WMO 2006). Drought is generally classified into four categories: meteorological drought, hydrological drought, agricultural drought and socio-economic drought. Meteorological drought is defined as the decrease in precipitation in an area over a prolonged period of time (Chang 1991; Eltahir 1992). Hydrological drought happens when the water supply becomes low in streams, reservoirs and groundwater levels. Agricultural drought occurs when crops become affected by the deficit in precipitation, while socio-economic drought occurs when the demand for an economic good exceeds supply as a result of a weather-related shortfall in water supply (Wilhite & Glantz 1985; WMO 2006; Mishra & Singh 2010).

The simplest way to monitor drought conditions is to use drought indices. These indices provide a quantitative method for determining the onset and end of a drought event and help in assessing its severity (Zargar *et al.* 2011).

Droughts have three specific features: severity, duration and spatial extent. Severity refers to the degree of the precipitation shortfall and/or the level of impacts associated with the shortfall. It is generally measured by a departure from the normal condition of a climatic parameter such as precipitation, a hydrological indicator such as the reservoir level or a drought index such as the Standardized Precipitation Index (SPI; McKee *et al.* 1993; Reddy & Ganguli 2013).

In the last decade, the copula approach has been widely used to perform multivariate analysis of drought characteristics (Shiau 2003; Shiau & Modarres 2009; Montaseri *et al.* 2018). Shiau (2006) shows that copulas are useful tools in exploring the associations of the correlated drought variables, i.e. duration and severity.

Shiau & Modarres (2009) used a copula-based approach to derive a drought severity–duration–frequency (SDF) relationship. Their analysis showed that drought severity in the humid region can be greater than that of semi-arid regions, for a given duration of drought and recurrence interval, if the region experiences high rainfall fluctuations. Mirabbasi *et al.* (2011) analysed drought duration and severity using the SPI in the northwest of Iran. They found that the bivariate probabilistic properties of droughts, based on the derived copula-based joint distribution, can provide useful information for water resource planning and management.

On the other hand, Ayantobo *et al.* (2018) used the bivariate Archimedean copulas to assess drought risk in mainland China. Using the Standardized Precipitation Evapotranspiration Index (SPEI), the analysis of the drought characteristic probabilities and return periods indicates that the drought risks were observed in both western and southeastern parts of the region, with a higher probability of droughts of longer durations, shorter return periods and greater severity.

The multivariate copula-based approach is also a valuable tool in the spatio-temporal analysis of drought. Reddy & Ganguli (2013) analysed the meteorological drought in India. In order to model the bivariate frequency of two drought characteristics, intensity and area, they evaluated the performance of Gumbel–Hougaard, Frank and Plackett copulas and derived the drought intensity–area–frequency curves for the region. These results were helpful in risk droughts evaluation. Xu *et al.* (2015) demonstrated that for a valuable evaluation of the drought spatio-temporal variability, it is necessary to consider three characteristic parameters (i.e. duration, affected area and severity). They used a copula-based trivariate frequency analysis to estimate the drought return period and concluded that the Joe and Gumbel copulas are the most suitable to estimate the joint distribution of drought duration, affected area and severity.

Several studies focused on the analysis of drought events in Africa. Ward *et al.* (1999) studied climate variability in Northern Africa. Their results showed that since the late 1970s, the north of Africa has witnessed a continuous deficit of precipitations compared with the previous decades. Touchan *et al.* (2010) analysed the spatio-temporal variability of drought in north-western Africa using the Palmer drought severity index, and they observed a shift towards dry conditions in recent centuries in this region. However, only few studies have been carried out on drought analysis in Algeria. Meddi *et al.* (2010) used five climate indices to analyse the temporal variability of annual precipitation in two catchments located in north-western Algeria. They showed that the total annual rainfall has been decreased at least by 20% at all the five considered stations. Hamlaoui *et al.* (2013) analysed the spatio-temporal trends in annual rainfall time series by using three nonparametric tests, namely Spearman's test, Mann–Kendall test and Pettitt test in western Algeria. The results indicate that the central part of the region was affected by the rainfall deficit. Meddi *et al.* (2013) used SPI-12 and three climate indices to analyse drought transition probabilities in the north-western and central plains of Algeria. Despite the increasing risk of droughts affecting the entire region of north Algeria, it should be noted that in the past decades, most of the works focused on the western part (Meddi *et al.* 2010; Hamlaoui *et al.* 2013; Djelloli *et al.* 2016; Habibi *et al.* 2018) and only a few of them dealt with the entire region (Taibi & Souag 2011; Lazri *et al.* 2015).

The analysis of the spatio-temporal drought features in northern Algeria including spatial extent, severity and duration is important for understanding the nature of drought and evaluating the region's vulnerability as well as for developing models to investigate different drought properties. Despite several papers addressing the analysis worldwide, it has never been explored to date in Algeria. In fact, the previous studies had the major drawback that they were limited to the identification of periods of droughts and affected regions. So, no attention has been paid to the spatio-temporal evolution of drought characteristics in this region, and studies on this field are still lacking. Thus, the goal of this paper is to investigate drought characteristics (severity, duration frequency and areal extent) over all northern Algeria and provide a valuable scientific reference for drought monitoring and management. To do so, copula-based multivariate frequency analysis is performed using the SPI at 3-month timescale (SPI-3) from 194 monthly precipitation time series. The SPI is one of the most commonly used indices for drought analysis. It is a powerful and flexible index that is simple to calculate. The main advantage of using the SPI is that it is only based on monthly precipitation series, which is the most available data at both the spatial and temporal scales. This advantage is especially important for this work, involving a study area of a large spatial extent and where numerous basins have very loose gauging networks with limited hydro-meteorological data. However, the main drawback of the SPI is its classification of the drought established according to the maximum intensity of drought event, regardless of its severity and its duration. So, to overcome this limitation, this work aims also to suggest a new classification of drought events.

## MATERIALS AND METHODS

The present paper investigates the analysis of drought characteristics (severity, duration, frequency and areal extent) in northern Algeria. The procedure adopted for this analysis is illustrated in Figure 1.

### Study area and data

The study area is the northern part of Algeria, which covers 12.72% of the total area. The limits are shown in Figure 2. The region has two types of climate; it is influenced by the Mediterranean Sea in the north (temperate Mediterranean climate) and by the desert in the south (a semi-arid climate). The average annual rainfall varies generally between 100 and 800 mm. The region exhibits a large variability of rainfall patterns, particularly between the north and the south and between the east and the west of the study area as shown in Figure 2.

In this study, the monthly precipitation data were provided by the National Agency of Hydraulic Resources (ANRH). 194 rainfall stations distributed over 16 catchments and covering the period 1970–2006 have been used. They are located at different climatic regimes; in the north of Algeria, there are three climatic zones such as humid and sub-humid in the central and eastern coastal zones, semi-arid in the western coastal areas and in the internal lands and the highlands and arid in the southern part of the study area. The general features of the 16 catchments are presented in Table 1.

Catchment code . | Name . | Area (km^{2})
. | Number of rainfall stations . |
---|---|---|---|

01 | Cheliff | 43,750 | 43 |

02 | Cotiers Algerois | 11,958 | 36 |

03 | Cotiers Constantiois | 11,566 | 12 |

04 | Cotiers Oranais | 5,831 | 13 |

05 | Chott Hodna | 25,843 | 09 |

06 | Chott Melghir | 68,750 | 10 |

07 | Hauts plateaux Constantinois | 9,578 | 11 |

08 | Chott Chergui | 52,090 | 08 |

09 | Isser | 4,149 | 07 |

10 | Kebir Rhumel | 8,815 | 03 |

11 | Macta | 14,389 | 11 |

12 | Medjerda | 7,785 | 05 |

14 | Seybouse | 6,475 | 05 |

15 | Soummam | 9,125 | 12 |

16 | Tafna | 7,245 | 06 |

17 | Zahrez | 9,141 | 03 |

Catchment code . | Name . | Area (km^{2})
. | Number of rainfall stations . |
---|---|---|---|

01 | Cheliff | 43,750 | 43 |

02 | Cotiers Algerois | 11,958 | 36 |

03 | Cotiers Constantiois | 11,566 | 12 |

04 | Cotiers Oranais | 5,831 | 13 |

05 | Chott Hodna | 25,843 | 09 |

06 | Chott Melghir | 68,750 | 10 |

07 | Hauts plateaux Constantinois | 9,578 | 11 |

08 | Chott Chergui | 52,090 | 08 |

09 | Isser | 4,149 | 07 |

10 | Kebir Rhumel | 8,815 | 03 |

11 | Macta | 14,389 | 11 |

12 | Medjerda | 7,785 | 05 |

14 | Seybouse | 6,475 | 05 |

15 | Soummam | 9,125 | 12 |

16 | Tafna | 7,245 | 06 |

17 | Zahrez | 9,141 | 03 |

### Standardized Precipitation Index

The SPI, developed by McKee *et al.* (1993) and recommended by Guttman (1999), remains a popular choice for researchers. Since its development, it has been widely used in various parts of the world. The SPI has the advantage of being simple to calculate and is solely a function of the precipitation amount.

The SPI calculation for any location is based on the fitting of a cumulative probability distribution (generally gamma distribution function) on monthly precipitation time series. It quantifies the deficit of precipitation for multiple timescales such as 1, 3, 6 and 12 months. This study adopted SPI-3, which uses 3-month aggregated precipitation data. The SPI relies on a long-term precipitation record, typically at least 30 years (McKee *et al.* 1993).

The drought event is defined by a period where the SPI is continuously negative. Dry conditions classified according to the SPI values are given in Table 2.

SPI values . | Drought category . |
---|---|

Mild dry | |

Moderate dry | |

Severe dry | |

Extreme dry |

SPI values . | Drought category . |
---|---|

Mild dry | |

Moderate dry | |

Severe dry | |

Extreme dry |

### Drought characteristics

Drought events are characterized by four main variables, namely duration (*D*), severity (*S*), return period (*T*) and affected area (*A*). The duration and severity are directly determined from the variation of the SPI values.

*Drought duration (D)*is defined as the number of months where SPI remains below the threshold value 0.*Drought severity (S)*is defined as the cumulated negative SPI values in drought duration*D*.

, where SPI* _{i}* is the SPI value in the

*i*th month (SPI

_{i}*<*0)

### Copula-based joint distributions

Sklar (1959) showed the role played by the copulas to construct the functions that link multivariate distribution functions to their univariate marginal distribution functions.

Copula . | C (u, v)
. | C
. | . |
---|---|---|---|

Clayton | |||

Frank | |||

Gumbel–Hougaard |

Copula . | C (u, v)
. | C
. | . |
---|---|---|---|

Clayton | |||

Frank | |||

Gumbel–Hougaard |

### Estimation of copula parameter

*n*is the sample size.

*et al.*(1995) as follows:

### Goodness-of-fit test for copulas

*u*is given by:where is a d-dimensional kernel,

*H*is a non-singular symmetric matrix of smoothing parameters,

*u*

*=*(,

*n*is the sample size and is the vector of the transformed variables. The test statistic is given by:where * denotes the convolution operator and is a weight function(see Zhang

*et al.*2016). The

*P*-value of the kernel-based GOF test was computed by the R package g of copula (Okhrin

*et al.*2018). It is computed by the formula:where

*M*and

*T*denote the number of bootstrapping loops and the bootstrapped test statistic, respectively.

_{b}The rejection rule of the kernel GOF test for copula is that: if *P*-value is lower than a significance level *α*, the null hypothesis is rejected.

The Akaike Information Criterion (AIC) has been assessed to select the best type of copula, which corresponds to the lowest value of AIC.

### Conditional return period

*et al.*(2007) have defined the conditional return period

*T*as an average of the recurrence time between two successive events. It is expressed as follows:where is the number of drought episodes per year,

*n*is the number of drought episodes and

*N*is the total length (in years) of SPI time series.

*C*is the conditional copula for

## RESULTS AND DISCUSSION

### Frequency analysis of drought severity

The drought duration and drought severity were calculated from observed droughts using SPI-3 values for all of the 194 rainfall time series. The severity values vary between 0.01 and 42.71. The shortest drought event lasted for 1 month and the longest one lasted for 32 months (about 3 years).

_{d}and CFD

_{s}are given by Equations (11) and (12), respectively.where

*λ*is the parameter of the exponential distribution;

*α*and

*β*are shape and scale parameters of gamma distribution, respectively;

*f(s*,

*α*,

*β*) is the gamma probability density function (PDF).

The Chi-square (*χ*^{2}) GOF test at the 5% significance level was used for the validation of the fitted models. The results indicate that the proposed distribution functions are adequate models for all the used drought severity and drought duration series.

Archimedean copula families were then used in order to link the fitted models and to derive the joint cumulative distribution functions, which model the dependence between drought severity and drought duration. According to the Kernel-based GOF test, it has been found that Clayton and Frank copulas have been accepted for 94.3% and 88.7% of the analysed stations, respectively. On the other hand, only 60.3% of the stations fitted the Gumbel–Hougaard copula. The final selection of the more adequate copula was based on the AIC, which revealed that 80% of couples (*u*, *v*) are best fitted by the Clayton copula, 20% by the Frank copula and no couple was fitted by the Gumbel–Hougaard copula.

For all the stations and for each duration, the variation in drought severity (*S*) according to the return period (*T*) is represented by logarithmic relationships of the form: *S**=**a* ln(*T*) *+**b*, with determination coefficient *R*^{2} varying between 0.89 and 0.99. Drought SDF curves given by the relationship between the severity of drought and its duration corresponding to different return periods were then established.

Among the derived results from 194 rainfall stations, one rainfall station is selected in order to illustrate the analysis results, namely the Tifelfel rainfall station located in the south-eastern part of the study area (Chott Melghir catchment) was selected to illustrate the analysis. According to SPI-3 time series, the main drought characteristics were as follows:

The maximum duration:

*D*_{max}= 14 monthsThe maximum severity:

*S*_{max}= 15.28Number of drought episodes:

*n**=*56, so*γ*= 1.51

Drought severity and drought duration were fitted by the gamma and exponential distributions, respectively. The maximum-likelihood estimation was used to calculate the parameters of these distributions (Bardossy & Pegram 2009). The results of the GOF test and estimated parameters are described in Table 4.

. | Distribution . | Critical values . | Parameters . | P-values
. |
---|---|---|---|---|

Duration | Exponential | 11.07 | λ = 0.27317 | 7.75 |

Severity | Gamma | 9.49 | α = 0.85914β = 3.3121 | 3.81 |

. | Distribution . | Critical values . | Parameters . | P-values
. |
---|---|---|---|---|

Duration | Exponential | 11.07 | λ = 0.27317 | 7.75 |

Severity | Gamma | 9.49 | α = 0.85914β = 3.3121 | 3.81 |

The kernel-based GOF test for copulas was used to check for the adequacy of three copula models (Clayton, Frank and Gumbel–Hougaard). According to the *P*-values (greater than a significance level (*α* = 0.05)) and the AIC, it has been found that the Clayton copula is the most adequate because its AIC value is the lowest compared with those of Gumbel–Hougaard and Frank copulas. Table 5 summarizes the results of the GOF test for the used copulas (GOF).

Copulas . | Kernel P-value
. | Parameter . | AIC . |
---|---|---|---|

Clayton | 0.607 | 4.84 | − 87.20 |

Frank | 0.181 | 11.78 | −65.78 |

Gumbel–Hougaard | 0.727 | 3.42 | −83.9 |

Copulas . | Kernel P-value
. | Parameter . | AIC . |
---|---|---|---|

Clayton | 0.607 | 4.84 | − 87.20 |

Frank | 0.181 | 11.78 | −65.78 |

Gumbel–Hougaard | 0.727 | 3.42 | −83.9 |

Bold values correspond to the most adequate copula.

For all durations, the variation of drought severity according to the return periods *T* = 1, 2, 5, 10, 20 and 50 years has been determined. It has been found that they are well fitted by a logarithmic relationship , with a coefficient of determination *R*^{2} varying between 0.89 and 0.99 (Figure 3).

Table 6 summarizes the results obtained from the frequency analysis, and the derived SDF curves of this station are illustrated in Figure 4. From this figure, it can be seen that drought severity increases rapidly for short-term drought events. But for longer drought events, drought severity shows a slight increasing trend and then approximates to a constant value.

Duration (months) . | S=f (T)
. | R^{2}
. |
---|---|---|

d = 1 | 0.212ln(T) + 0.118 | 0.988 |

d = 2 | 1.059ln(T) + 0.361 | 0.933 |

d = 3 | 1.959ln(T) + 1.304 | 0.974 |

d = 4 | 2.74ln(T) + 2.048 | 0.979 |

d = 5 | 3.408ln(T) + 2.556 | 0.961 |

d = 6 | 3.912ln(T) + 2.900 | 0.942 |

d = 7 | 4.272ln(T) + 3.132 | 0.927 |

d = 8 | 4.523ln(T) + 3.289 | 0.916 |

d = 9 | 4.698ln(T) + 3.396 | 0.908 |

d = 11 | 4.907ln(T) + 3.521 | 0.898 |

d = 14 | 5.047ln(T) + 3.605 | 0.891 |

Duration (months) . | S=f (T)
. | R^{2}
. |
---|---|---|

d = 1 | 0.212ln(T) + 0.118 | 0.988 |

d = 2 | 1.059ln(T) + 0.361 | 0.933 |

d = 3 | 1.959ln(T) + 1.304 | 0.974 |

d = 4 | 2.74ln(T) + 2.048 | 0.979 |

d = 5 | 3.408ln(T) + 2.556 | 0.961 |

d = 6 | 3.912ln(T) + 2.900 | 0.942 |

d = 7 | 4.272ln(T) + 3.132 | 0.927 |

d = 8 | 4.523ln(T) + 3.289 | 0.916 |

d = 9 | 4.698ln(T) + 3.396 | 0.908 |

d = 11 | 4.907ln(T) + 3.521 | 0.898 |

d = 14 | 5.047ln(T) + 3.605 | 0.891 |

### Spatial analysis of drought severity

The obtained results from the previous section are used in this part of the study. In order to establish the relationship between the severity and the cumulated affected area (Ac), the spatial variability of drought severity was analysed for each return period and for all durations. Figure 5 presents drought severity, affected area *A* (%) and cumulated affected area Ac (%) variations for the observed drought events corresponding to 3-month threshold duration and a return period of 10 years. The obtained results showed that extreme values of drought severity occur only in less than 5% of the whole study area. Hence, for reasons of simplification, the spatial variability analysis of drought severity is carried out over the interval [5%, 95%] of the total area. For each return period, there is a linear relationship between *S* and Ac with a determination coefficient *R*^{2} greater than 0.95 for all duration thresholds as illustrated in Figure 6 for *T* = 10 years and *D* ≤ 3 months.

### Frequency analysis of drought severity

The results described above showed that the degree of drought severity varies in time and space. In order to illustrate the spatio-temporal evolution of drought severity for different return periods, three-dimensional surfaces of drought severity, drought duration and cumulated percentage of the affected area (SDA) for each return period are constructed. Figures 7(a)–7(f) represent the SDA surfaces corresponding to the return periods of 1, 2, 5, 10, 20 and 50 years, respectively.

As seen in Figure 7, the severity values for threshold duration less than or equal to 1 month are between 0.14 and 0.31 for the return period of 1 year; between 0.32 and 0.67 for 2 years; between 0.54 and 1.24 for 5 years; between 0.71 and 1.66 for 10 years; between 0.89 and 2.07 for 20 years and between 1.12 and 2.63 for 50 years. On the other hand, for the higher threshold duration of less than or equal to 32 months, the severity values vary between 3.61 and 4.62 for the return period of 1 year; between 7.18 and 9.84 for 2 years; between 11.84 and 16.94 for 5 years; between 15.32 and 22.35 for 10 years; between 18.96 and 27.4 for 20 years and between 23.35 and 34.97 for 50 years. Thus, as threshold durations of drought events increase, their severities and return periods also increase. Extreme drought events correspond to high return periods or low probabilities of exceedance.

For each return period, the drought severity was mapped in the study area and split into four classes of the same amplitude (quartiles). The results show that the catchments Cotiers Constantinois (in the East), Chott Chergui (in the west) and ChottMelghir (southeast) are the most affected by higher drought severity (greater than 75% of the maximum value). Hence, for each return period, the longer the duration, the lower the sensitivity of these basins to drought and the smaller the affected area. For example, Table 7 indicates, for each quartile, the cumulated percentage of the affected area with a return period of 10 years and for durations of 3, 6, 12, 24 and 32 months as well as the maximum drought severity values corresponding to these durations.

. | 3 months . | 6 months . | 12 months . | 24 months . | 32 months . |
---|---|---|---|---|---|

S_{max} | 8.67 | 20.22 | 29.1 | 35.21 | 35.61 |

First quartile | 0.68 | 0.73 | 0.87 | 4.28 | 5.20 |

Second quartile | 30.49 | 64.23 | 75.12 | 89.75 | 88.99 |

Third quartile | 66.52 | 34.12 | 23.40 | 5.57 | 5.49 |

Fourth quartile | 2.31 | 0..92 | 0.61 | 0.40 | 0.32 |

. | 3 months . | 6 months . | 12 months . | 24 months . | 32 months . |
---|---|---|---|---|---|

S_{max} | 8.67 | 20.22 | 29.1 | 35.21 | 35.61 |

First quartile | 0.68 | 0.73 | 0.87 | 4.28 | 5.20 |

Second quartile | 30.49 | 64.23 | 75.12 | 89.75 | 88.99 |

Third quartile | 66.52 | 34.12 | 23.40 | 5.57 | 5.49 |

Fourth quartile | 2.31 | 0..92 | 0.61 | 0.40 | 0.32 |

### Frequency analysis of maximum drought severity

The observed maximum drought severity corresponding to different durations and for all stations is analysed. It has been found that the spatial distribution of observed maximum severity values was irregular for short threshold durations (*D* ≤ 3 months). However, for long durations, the southern part of the study area was the most affected by the maximum severity. The percentage of the affected area by these severity values for each duration threshold was then derived in order to establish the maximum drought severity–duration–area surfaces as illustrated in Figure 8. For the cumulated percentage of the affected area Ac over the interval [5%; 95%], the values of maximum drought severity vary between 1.06 and 1.73 for *D* ≤ 1 months and between 15.12 and 28.2 for *D* ≤ 329 months.

The return period of the observed maximum drought severity was estimated from the graphical superposition of *S*_{max}DA curves and the derived (using copula) SDA curves. So, we chose the largest return period for the threshold duration *D* ≤ *d*, where the *S*_{max}DA curve was located between two surfaces of different return periods *T*. Figures 9(a)–(e) illustrate the results obtained from the superposition between the surfaces; it shows that the return periods of maximum severity for durations such as *D* ≤ 12, 12 < *D* ≤ 20 and 20 < *D* ≤ 32 months are *T* ≤ 5, 5 < *T* ≤ 10 and 10 ≤ *T* ≤ 20 years, respectively. Thus, the return period of the maximum severity varies according to its duration, so that the longer the drought lasts, the longer the return period is.

### Drought classes for maximum severity

A drought event of *D* duration is generally characterized by its maximum intensity according to the SPI classification (given in Table 2), even when this latter was observed only during 1 month over all the event duration *D*. This can be acceptable for short duration events. However, for long durations, there is a tendency to overestimate the category of the drought event. This study proposes, therefore, a new classification of drought events based on the relationship linking the drought severities *S* to their corresponding average SPI values (Figure 10).

Equation (15) gives the relationship between the average SPI value, the drought severity *S* and duration *D*. So, it is sufficient to multiply the SPI average classes, given in Table 2, by −*D* to deduce the new drought classes according to the drought severity of the event. Table 8 presents the derived drought classification.

SPI . | Severity of D months
. | Drought category . |
---|---|---|

D>S> 0 | Mild dry (MID) | |

1.5 D+S≥D | Moderate dry (MOD) | |

2 D+S≥ 1.5 D | Severe dry (SD) | |

S≥ 2D | Extreme dry (ED) |

SPI . | Severity of D months
. | Drought category . |
---|---|---|

D>S> 0 | Mild dry (MID) | |

1.5 D+S≥D | Moderate dry (MOD) | |

2 D+S≥ 1.5 D | Severe dry (SD) | |

S≥ 2D | Extreme dry (ED) |

We found that short-term dry events (*D**≤* 3 months) were the most severe (third and fourth categories corresponding to severe and extreme dry). The western part of the study area was the most affected and the most sensitive to severe and extreme droughts (Figure 11(a)). Figures 11(b) and 11(c) show that as threshold durations increase (3 < *D* ≤ 20 months), the drought was moderate to mild over the entire study area. For long threshold durations, the eastern part of the study area was shown to be the most sensitive to moderate droughts, while the north-western part was mainly affected by mild droughts. For threshold durations greater than 20 months, the severity of drought is reduced. There are just small areas, randomly distributed over the study area, that are sensitive to moderate droughts (Figures 11(d) and 11(e)). Indeed, according to Table 8, it appears clearly that for the threshold duration of 24 months, the percentage of the affected area by mild droughts is of 94.03%, which is greater than that of the area affected by moderate droughts (5.97%).

The sensitivity to moderate droughts in these singularities is mainly caused by drought episodes of high severity values as illustrated in Table 9. For the eastern part of the study area, the areas adjacent to stations Bou Hadjar and Roum El Souk in the Cotiers Constantinois catchment have a moderate drought. These two regions are located in coastal areas and are subject to a humid climate. This unexpected result requires more in-depth investigation and further analysis. However, the other regions with moderate and extreme droughts such as Oued Cheliff in the Chott Melghir catchment; Timgad and Boulhilat in the Hauts plateaux Constantinois catchment, the stations Mechedellah and Ain Arnat in the Soummam catchment (central part), and stations Modzbah and Stitten in the ChottChergui catchment (western part) are all regions with a semi-arid climate.

Station name . | Latitude (DMS) . | Longitude (DMS) . | Altitude (m) . | D (months)
. | S_{max}
. | Return period (years) . | Drought cat. . | Drought period (month/year) . |
---|---|---|---|---|---|---|---|---|

Bou Hadjar | 36°30′36″N | 8°6′36″E | 300 | 25 | 34.86 | 10.62 | MOD | Jul 1992–Jul 1994 |

Roum El souk | 36°47′24″N | 8°33′00″E | 150 | 24 | 32.55 | 10.90 | MOD | Sep 2004–Aug 2006 |

Oued-Chelih | 35°31′48″N | 6°00′00″E | 1180 | 32 | 35.54 | 20 | MOD | Dec 1999–Jul 2001 |

Timgad | 35°28′48″N | 6°28′12″E | 1040 | 20 | 25.97 | 6.90 | MOD | Aug 1976–Mar 1978 |

Bouhlilat | 35°43′12″N | 6°40′12″E | 985 | 23 | 38.11 | 12.40 | SD | Jun 1982–Nov 1984 |

Michedella | 36°22′12″N | 4°16′12″E | 465 | 20 | 33.10 | 9.19 | SD | Sep 1990–Apr 1991 |

Ain Arnat | 36°10′48″N | 5°18′36″E | 520 | 25 | 37.79 | 11.15 | SD | Mar 1976–Mar 1978 |

Modzbah | 34°25′12″N | 0°06′00″E | 1075 | 30 | 39.77 | 14.31 | MOD | Aug 1999–Jan 1994 |

Stitten | 33°45′36″N | 1°13′48″E | 1410 | 12 | 17.90 | 4.50 | MOD | Sep 1999–Aug 1994 |

Station name . | Latitude (DMS) . | Longitude (DMS) . | Altitude (m) . | D (months)
. | S_{max}
. | Return period (years) . | Drought cat. . | Drought period (month/year) . |
---|---|---|---|---|---|---|---|---|

Bou Hadjar | 36°30′36″N | 8°6′36″E | 300 | 25 | 34.86 | 10.62 | MOD | Jul 1992–Jul 1994 |

Roum El souk | 36°47′24″N | 8°33′00″E | 150 | 24 | 32.55 | 10.90 | MOD | Sep 2004–Aug 2006 |

Oued-Chelih | 35°31′48″N | 6°00′00″E | 1180 | 32 | 35.54 | 20 | MOD | Dec 1999–Jul 2001 |

Timgad | 35°28′48″N | 6°28′12″E | 1040 | 20 | 25.97 | 6.90 | MOD | Aug 1976–Mar 1978 |

Bouhlilat | 35°43′12″N | 6°40′12″E | 985 | 23 | 38.11 | 12.40 | SD | Jun 1982–Nov 1984 |

Michedella | 36°22′12″N | 4°16′12″E | 465 | 20 | 33.10 | 9.19 | SD | Sep 1990–Apr 1991 |

Ain Arnat | 36°10′48″N | 5°18′36″E | 520 | 25 | 37.79 | 11.15 | SD | Mar 1976–Mar 1978 |

Modzbah | 34°25′12″N | 0°06′00″E | 1075 | 30 | 39.77 | 14.31 | MOD | Aug 1999–Jan 1994 |

Stitten | 33°45′36″N | 1°13′48″E | 1410 | 12 | 17.90 | 4.50 | MOD | Sep 1999–Aug 1994 |

These findings are in agreement with those of previous studies carried out in the same study area. Indeed, Taibi & Souag (2011) calculated SPI values for 102 rainfall stations covering the north of Algeria over a period of 74 years (1936–2010). Their results showed that the western part of the region is the most affected by severe droughts. In addition to the previous results, the present research depicted that this particular region experienced the most extreme droughts corresponding to short duration thresholds and the return period of 5 years. Whereas, as the drought durations increase, the sensitivity of this part of the study area to severe and extreme droughts decreases as shown in Figure 11.

## CONCLUSION

Drought is one of the natural disasters that seriously affects the management and planning of water resources. The analysis of the spatio-temporal drought characteristics plays an important role in the effective predication and risk management of this phenomenon. This study aims to analyse drought event variables over North Algeria using the SPI for 194 rainfall stations.

The analysis of the frequency of drought severity, based on the derived SDF curves, for different return periods and for all stations, has shown that there is a direct relationship between the severity and drought duration. Drought severity increases fast for short drought durations, while it increases mildly and then remains constant for longer drought durations.

The results obtained from the derived maximum drought severity–area (*S*_{max}*A*) and drought severity–area–frequency (SAF) curves also showed that over the interval [5%, 95%] of the total area, there is a linear and increasing relationship between drought severity *S* and the cumulative affected area Ac. Moreover, we found that, for 90% of the study area, the return period of maximum severity increases with the threshold duration.

To address the issue of long-term drought event classification, we propose a new categorization based on drought severities. According to this new classification, the western part of the study area is the most sensitive to severe/extreme droughts of short threshold durations, but most of the remaining parts of the study area are sensitive to moderate/mild droughts. The entire study area is affected by mild and moderate droughts for threshold durations not exceeding 20 months. Droughts of greater duration can be classified as mild for most regions, except for some singularities randomly distributed over the study area, and classified as moderate.

The developed methodology applied for a multi-dimensional analysis of droughts (frequency, spatial and temporal analysis) provided very useful information for drought monitoring and management and can be applied to other regions.