*2.3. Run Theory*

The run theory proposed by Yevjevich [33] refers to the occurrence of consecutive comparable conditions, such as wet or dry periods, allowing the characterization of each spell by assessing some characteristics such as duration, frequency, severity, and intensity. Figure 2 shows an example of the run theory for a fixed threshold.

**Figure 2.** Example of drought characteristics evaluated using the run theory for a given threshold level [34].

A "run" is defined as an interval in which the values are all above (positive run) or below (negative run) the threshold [33]. Once the runs, and thus the dry (SPI below the threshold) or wet (SPI over the threshold) spells, have been identified, it is possible to extract some characteristics. The percentage of dry or wet spells over the study period constitute the dry (*DF*) and wet (*WF*) frequencies. The dry and wet durations (*DD* and *WD*) are the time period lengths in which SPI values are constantly below or above the threshold. Durations can be expressed in weeks, months, years or any other time period. The average drought and wet durations (*ADD* and *AWD*) are the ratio between the sum of the durations of all the drought and wet spells and the number of drought and wet spells (*ND* and *NW*). The cumulated drought and wet values during each spell represent the drought and wet severities (*DS* and *WS*). The average drought and wet severities (*ADS* and *AWS*) are the ratio between the sum of the *DS* and *WS* of all the spells and *ND* and *NW*, respectively. The drought and wet intensities (*DI* and *WI*) were evaluated, for each event, as the ratio between the *DS* and *DD* and the *WS* and *WD*, respectively, thus the average drought and wet intensities (*ADI* and *AWI*) are the ratios between the sum of the *DI* and *WI* of all the spells and *ND* and *NW*, respectively.

In this study, drought and wet periods were evaluated considering the SPI thresholds of −1 and 1, respectively. Moreover, duration, severity, and intensity were estimated using the run theory applied to the 12-month SPI series, and thus *DD* and *WD* are expressed in years. This methodology has been applied in past studies performed for several areas of the world [35].

#### *2.4. Theil–Sen Estimator*

Considering that precipitation is often non normally distributed, the Theil–Sen estimator is generally considered more powerful than the linear regression methods in trend magnitude evaluation, because it is not subject to the influence of extreme values [36]. Given *x*1, *x*2, ... , *xn* precipitation observations at times *t*1, *t*2, ... , *tn* (with *t*<sup>1</sup> < *t*<sup>2</sup> < ... < *tn*), for each *N* pairs of observations *xj* and *xi* taken at times *tj* and *ti*, the gradient *Qk* can be calculated as:

$$Q\_k = \frac{\mathbf{x}\_j - \mathbf{x}\_i}{t\_j - t\_i} \text{ for } k = 1, \dots, N\_\prime \tag{10}$$

with 1 < *i* < *j* < *n* and *tj* > *ti*.

The estimate of the trend in the data series *x*1, *x*2, ... , *xn* can then be calculated as the median *Qmed* of the *N* values of *Qk*, ranked from the smallest to the largest:

$$Q\_{mcd} = \begin{cases} \begin{array}{c} Q\_{\left[\left(N+1\right)/2\right]} \text{if } N \text{isodd} \\ \frac{Q\_{\left[\left(N+2\right)/2\right]} + Q\_{\left[\left(N+2\right)/2\right]}}{2} \text{if } N \text{iseven} \end{array}} \end{cases} \tag{11}$$

The *Qmed* sign reveals the trend behavior, while its value indicates the magnitude of the trend.

#### *2.5. Mann–Kendall Test*

As regards the MK test [37,38], in order to evaluate the trend significance, the statistic *S* based on the rank sums is calculated as:

$$S = \sum\_{i=1}^{n-1} \sum\_{j=i+1}^{n} \text{sgn}(\mathbf{x}\_{j} - \mathbf{x}\_{i}) \text{ where } \text{sgn}(\mathbf{x}\_{j} - \mathbf{x}\_{i}) = \begin{cases} 1 \text{ if } (\mathbf{x}\_{j} - \mathbf{x}\_{i}) > 0 \\ 0 \text{ if } (\mathbf{x}\_{j} - \mathbf{x}\_{i}) = 0 \\ -1 \text{ if } (\mathbf{x}\_{j} - \mathbf{x}\_{i}) < 0 \end{cases} \tag{12}$$

In which *xj* and *xi* are the observations taken at times *j* and *i* (with *j* > *i*), respectively, and *n* is the dimension of the series.

Under the null hypothesis *H*0, the distribution of *S* is symmetrical and is normal in the limit as *n* becomes large, with zero mean and variance:

$$\text{Var}(S) = \left[ n(n-1)(2n+5) - \sum\_{i=1}^{m} t\_i i(i-1)(2i+5) \right] / 18 \tag{13}$$

in which *ti* indicates the number of ties with extend *i*.

Given the variance of *S*, it is possible to evaluate the standardized statistic *ZMK* as:

$$Z\_{\rm MK} = \begin{cases} \frac{S - 1}{\sqrt{\text{Var}(S)}} \text{for } S > 0\\ 0 \text{for } S = 0\\ \frac{S + 1}{\sqrt{\text{Var}(S)}} \text{for } S < 0 \end{cases} \tag{14}$$

By applying a two-tailed test, for a specified significance level α, the significance of the trend can be evaluated.

#### **3. Results**

Figure 3 shows the boxplots with the main statistics of *DF*, *WF*, *ADD*, *AWD*, *ADS*, *AWS*, *ADI*, and *AWI*. Generally, similar values were evaluated between the dry and the wet spells although higher frequencies and durations of wet events were detected in the

minimum and in the maximum values across the 150 stations. In fact, as regards the frequency, the *DF* ranged between 0 and almost 23% while the *WF* ranged between 8.3 and 25%. Similarly, considering the duration, *ADD* and *AWD* showed almost the same median, but maximum values of 3 and 4 years were obtained for *ADD* and *AWD*, respectively. This behavior has been confirmed also for the severity and the intensity, with *AWS* and *AWI* showing minimum and maximum values higher than the ones obtained for *ADS* and *ADI*.

**Figure 3.** Characterization through boxplots of frequency (%), average duration (in years), average severity, and average intensity (year<sup>−</sup>1). The top and the bottom of the boxes are the third and the second quartiles, respectively; the band inside the box is the median and the ends of the whiskers represent the minimum and maximum of all of the data.

Figure 4 shows the spatial distribution of *DF*, *ADD*, *ADS* and *ADI*. With respect to the dry frequency, the highest values largely involved the northern side of the basin, although in one station on the southern side a *DF* value higher than 20% was detected. Conversely, the southern side of the basin, which is the area with the highest elevation in which few

rain gauges are located, was characterized by the lowest values of *DF*, and two rain gauges did not show any dry event (Figure 4a).

**Figure 4.** Spatial distribution of the (**a**) dry frequency in %, (**b**) average dry duration in years, (**c**) average dry severity and (**d**) average dry intensity in year<sup>−</sup>1.

The average dry duration did not present any noteworthy spatial behavior. In fact, the lowest values (≈1 year) were distributed across the basin, while the highest ones (>2.5 years) were localized in the central part of the basin, but without any clear connection with orography (Figure 4b).

A spatial behavior similar to *ADD* was detected for *ADS* (Figure 4c). Indeed, from the spatial distribution of the average dry severity it is not possible to identify definite areas characterized by the highest values (>3.5 year), which were spread across the central part of the basin.

Finally, the spatial distribution of the average dry intensity evidenced some differences between the northern and the southern side of the basin (Figure 4d). In fact, the *ADI* values showed a distribution quite similar to the one obtained for the *DF* values, with intensities lower than 1.2 localized in the southeastern part of the basin, especially in the stations characterized by the highest elevations.

Figure 5 is similar to Figure 4 but for the wet events and, thus, it shows the spatial distribution of *WF*, *AWD*, *AWS*, and *AWI*.

**Figure 5.** Spatial distribution of the (**a**) wet frequency in %, (**b**) average wet duration in years, (**c**) average wet severity and (**d**) average wet intensity in year<sup>−</sup>1.

Regarding the frequency of the wet events, values higher than 20% were detected in several areas of the basin, without any particular geographical difference and without any connection with the orography (Figure 5a). Similarly, the average wet duration did not show any significant spatial behavior with the lowest values (<1.5 years) distributed across the basin and only two stations showed *AWD* values higher than 3 years (Figure 5b).

Differently from *DF* and *ADD*, the spatial distributions of the average wet severity and intensity evidenced some differences between the northern and the southern side of the basin (Figure 5c,d). In fact, for both *AWS* and *AWI* the highest values were localized in the southern part of the basin, especially in the stations characterized by the highest elevations.

In order to detect the temporal evolution of drought in the period 1970–2018, the 12-month SPI series were tested for trends through the Theil–Sen estimator and the Mann– Kendall test. As a result, for a SL = 95%, 26 out of 150 stations (i.e., 39%) showed a negative trend while an opposite behavior was detected in 13 out of 150 stations (i.e., 19.5%). Spatially, the negative trend mainly involved the northern areas of the basin, with a maximum decrease of more than −0.3/10 years (Figure 6). On the contrary, a positive trend was evidenced in the southern part of the basin reaching values between 0.2 and 0.3/10 years.

**Figure 6.** Spatial results of the trend analysis performed on the SPI values. The trend magnitude has been evaluated with the Theil–Sen estimator; the statistical significance of the trends, with a SL = 95%, has been assessed with the Mann–Kendall test. Colored points indicate significant trends.

Finally, with the aim to assess the drought response to the global circulation variability, a correlation analysis between the SPI values and the NAO was computed for each station. As a result, a clear link between drought and the NAO was evidenced. In particular, negative correlation values (<−0.4) mainly involved the northern areas of the basin, while a positive correlation was evidenced in the southern part of the basin (Figure 7).

**Figure 7.** Spatial results of the correlation analysis computed, with the Pearson method and for each station, between the SPI values and the NAO. Large sized points reveal a significant correlation, while small points show non-significant correlations.

#### **4. Discussion**

Although a lack of precipitation can be considered an ordinary part of the seasonal climatic cycle within the Mediterranean basin, future climate projections have identified the Mediterranean region as an area particularly subject to water scarcity and drought [39]. In order to monitor the drought phenomenon and to assess the climate anomalies quantitatively in terms of intensity, duration, frequency, recurrence probability, and spatial extent, several indices have been developed [40]. Among the several indices, the SPI has been applied in the trend detection of drought in many areas of the world [41]. While a trend analysis on the SPI values can only point out the possible changes in the expected precipitation amount over the years, the study of some of the main drought characteristics such as frequency, duration, severity, and intensity is essential for politicians, local communities, and stakeholders to identify the most vulnerable areas and their drought features.

The detection of these characteristics is particularly relevant for Algeria, which some studies have identified as one of the countries in North Africa that will become a global hot spot for drought by the end of the twenty-first century [42]. In fact, the results of this study evidenced a great spatiotemporal variability in wet and dry episodes in the Cheliff Basin, with different results obtained between the northern side of the basin, characterized by the

highest annual rainfall values, and the southern part, where annual rainfall values below 250 mm have been registered. In particular, the results in this area could be influenced by the low total amount of precipitation, which makes it more difficult to accurately detect drought development. The main outcomes of this study allow an identification of the areas, in the northern side of the basin, that could also face water stress conditions in the future, thus requiring drought monitoring and adequate adaptation strategies. At the same time, in the area currently suffering from a water deficit, an increase in the wet episodes has been detected, which is an important result that can inform people involved in the water resource management of the changing potential for flooding and water storage. The different behavior between the northern and the southern part of the basin has been pointed out in previous works e.g., in [29], the authors of which evidenced an annual rainfall decrease of more than 20 mm/10 years on the northern side and an increase of about 5 mm/10 years on the southern side. These results can be influenced by both global and local factors. Global factors which impact on the intra-annual precipitation distribution include teleconnection patterns [43,44]. In fact, as evidenced in Figure 7, a clear link exists between drought and the NAO. This result agrees with the results obtained by several authors e.g., [29], which evidenced that the Mediterranean rainfall regime is strongly linked to general atmospheric circulation patterns such as the El Niño Southern Oscillation (ENSO), the Mediterranean Oscillation (MO), the Western Mediterranean Oscillation (WeMO), and especially the North Atlantic Oscillation indices that are negatively correlated with precipitation in Algeria [45]. Indeed, positive NAO phases can cause dry conditions across large parts of the Mediterranean Basin, from Spain and Morocco across to the Balkans and western Turkey [46]. Specifically, a predominant negative phase of the NAO occurred between 1940 and 1980, corresponding to a period when precipitation was above normal. This was followed by a predominant positive phase, which significantly contributed to the rainfall reduction observed from the beginning of the 1980s in the Mediterranean basin, and also in Algeria [29]. Moreover, another regional-scale system that could influence the rainfall conditions in North Africa is the well-documented Sahelian drought and its multidecadal variability, which resulted from the response of the African summer monsoon to oceanic forcing and was amplified by land–atmosphere interactions [47].

In order to better appreciate the results of this study, an important final remark must be made concerning the database. In this study a high-quality database in the period 1970–2018 has been used. Unfortunately, only annual data (evaluated for water year) were available and thus it was not possible to perform a detailed analysis at a monthly scale. This study is nevertheless a valuable contribution not only to the quality of the database but also to its spatial resolution, which covers almost all the basin, with some gaps only in the central area. Continuous and spatially distributed data allowed a reliable analysis of the drought characteristics in the basin. Although globally gridded satellite-based precipitation products have become available in recent years as potential sources of data, ground-based precipitation measurements still remain the main and most accurate source in any climatological analysis [48].

#### **5. Conclusions**

This study aimed to analyze some of the main characteristics of the wet and dry events affecting the Cheliff Basin in the period 1970–2018 using the 12-month SPI, which is a broad proxy for water resource availability, evaluated from 150 rain gauges distributed across the basin. Generally, the analysis of the main statistics of the frequency, severity, duration, and intensity were evaluated for both dry and wet events, and it was found that their median values were similar, although higher minimum and maximum values were detected for the wet events. These results clearly indicate that the Cheliff Basin is at risk for extreme wet events as well as dry events. From the spatial distribution of the wet and dry characteristics, the basin areas facing water stress were identified. Finally, the results of the trend analysis performed on the 12-month SPI values evidenced a decreasing trend on the

northern side of the basin and an opposite behavior on the southern side, characterized by the highest elevations and the lowest annual rainfall values, in which positive values were detected. These results, probably linked with the predominant positive NAO phase which significantly contributed to the rainfall reduction observed from the beginning of the 1980s in Algeria, could be highly relevant for people involved in natural resource management decision-making for sustainable long-term water resource management in semi-arid regions.

**Author Contributions:** Conceptualization, M.A.; methodology, M.A. and T.C.; software, M.A. and T.C.; formal analysis, M.A. and T.C.; validation: M.A., T.C., A.W. and N.Y.K.; investigation, M.A., T.C., A.W. and N.Y.K.; data curation, M.A.; writing—original draft preparation, M.A., T.C., A.W. and N.Y.K.; writing—review and editing, M.A., T.C., A.W. and N.Y.K.; visualization, T.C.; supervision, A.W. and N.Y.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding authors.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

