Spatio-temporal analysis of meteorological drought return periods in a Mediterranean arid region, the center of Morocco

ABHOER

Oum Rbia Hydraulic Agency

ABHT

Tensift Hydraulic Agency

ARIMA

Assessment and simulation of present and future multi-hazard risk in the Marrakech-Safi region project

D

Duration

DRA

Regional Directorate of Agriculture

IDW

Inverse distance weighting

P

Peak

S

Severity

SPI

Standardized precipitation index

Environmental emissions from the agricultural, livestock, and industrial sectors are the main cause of extreme weather events (Abbas et al.,2022a, 2022b, 2023a; Elahi et al. 2022, 2024). In particular, drought, broadly characterized as a temporary period of dryness occurring in both arid and humid areas, constitutes a natural component of climate fluctuations. Throughout the past millennium, Africa, like many other regions globally (Abbas et al. 2021, 2023b), has experienced multiple instances of significant droughts on a large scale (Dai 2010). Sea-surface temperature pattern changes in the Atlantic are a well-known factor that causes droughts in Africa (Epule et al. 2014) along with the possible indirect effect of anthropogenic aerosols as has been suggested for the Sahel of North Africa (Rotstayn & Lohmann 2002). In the North African countries, Morocco in particular, numerous studies have pointed out that it has been affected by severe periods of drought over the past 50 years with increasing frequency (Mu et al. 2013; García de Jalón et al. 2014; Piras et al. 2014; Abahous et al. 2018; Merabti et al. 2018; Hadria et al. 2019, 2020; Zkhiri et al. 2019; Elkouk et al. 2021). These drought events will increase even more in the future due to climate change (Schilling et al. 2020). Consequently, for Morocco, this will generally raise the irrigation water demand, cause more crop water stress in rainfed areas, and reduce the availability of drinking water (Verner et al. 2018). The semi-arid Marrakech-Safi region, located in the mid-west of Morocco, is even more vulnerable to drought because of its climate that makes the rainfall amount in these regions critically dependent on a few rainfall events in addition to the quantity of stored renewable groundwater that is usually insufficient to compensate for the water resources shortages (Sun et al. 2006). In this context, drought analysis in the Marrakech-Safi region, one of the important Moroccan regions in terms of agriculture and tourism, is of utmost importance for effectively managing the water resources in this zone and for adapting to the drought effects and mitigating them.

Given its complexity, drought can be classified into different types, including these interrelated categories: meteorological, agricultural, and hydrological (Wilhite & Glantz 1985). As Wilhite (2000) put it, meteorological drought often refers to a period ranging from months to years with below-average precipitation. Agricultural drought on the other hand is related, in addition to precipitation shortages, to the soil moisture deficit and the difference between actual and potential evapotranspiration. As for hydrological drought, it is associated with the effects of precipitation shortages on surface and groundwater resources. In consideration of the definition of various types of droughts, many indices have been suggested to describe, monitor, and quantify them (Dai 2010): standardized precipitation index (SPI), Palmer moisture anomaly index, and surface water supply, to name a few. Particularly, SPI is widely used for drought monitoring and analysis due to its simplicity, low data requirement, and the different timescales over which it can be calculated (e.g., three months (SPI-3), six months (SPI-6), nine months (SPI-9), and 12 months (SPI-12)), which enables it to identify different types of drought (Vicente-Serrano et al. 2010).

In recent years, several studies have investigated the drought situation in the Marrakech-Safi region, focusing on different aspects, namely, the spatiotemporal analysis and assessment of drought vulnerability and risk (Fniguire et al. 2017; Cotti et al. 2022), the spatiotemporal characterization of future droughts (Zkhiri et al. 2019), the impact of drought on agriculture (Meliho et al. 2020), and multiscale drought monitoring using remote-sensing products (Hadri et al. 2021). However, to the best of our knowledge, no studies have conducted a spatial multivariate return-period analysis of drought in this region or in Morocco.

Since drought characteristics such as those defined using run theory (Liu et al. 2016) (duration, severity, and peak that can also be referred to as intensity or magnitude) are usually interdependent, a suitable frequency analysis is needed to account for the existent dependencies in a proper multivariate manner (Ayantobo et al. 2019). Prior to 2006, the assessment of drought frequency and return period relied heavily on univariate statistical analysis, which involved computing the frequency of drought duration, severity, peak, and area separately (Liu et al. 2016). To determine the joint distribution function, drought variables were typically treated as uncorrelated or expected to adhere to the same marginal distribution. However, as there is a certain degree of correlation between variables that describe the same drought event, these hypotheses may not always reflect reality. Among the most suitable tools for achieving such multivariate analysis are copulas, which enable the characterization of the joint behavior of drought characteristics (Mishra & Singh 2011; Mesbahzadeh et al. 2020) and which are behind the increased attention of researchers in multivariate modeling (Salvadori & De Michele 2015; Ayantobo et al. 2019). Copulas offer a means of modeling the probabilistic dependence structure without being limited by the marginal distribution. The key benefit of copulas is their ability to describe multiple variables using distinct marginal distributions. Originally designed for the insurance and finance industries to investigate exceptional risks, copulas have been adapted for use in hydrological research to assess flood hazards (Favre et al. 2004; Grimaldi & Serinaldi 2006).

In this research article, we introduce a transformative approach to analyzing and understanding drought frequency by harnessing the power of copula modeling. Droughts, a complex phenomenon influenced by multifaceted interactions, have long posed challenges in accurate prediction and assessment. Our study breaks new ground in Morocco by employing copulas, a sophisticated statistical tool capable of capturing intricate dependencies between variables, to unravel the underlying dynamics of drought occurrence. By integrating copula modeling into the study of drought frequency, we transcend traditional methods and reveal hidden correlations that conventional approaches often overlook. Through a comprehensive empirical analysis, we not only validate the efficacy of our novel methodology but also shed light on previously unexplored insights into the temporal and spatial patterns of droughts. As such, this article not only contributes to the advancement of drought research in Morocco and in semi-arid regions but also charts a course toward enhanced predictive capabilities and informed decision-making in water resource management and climate adaptation strategies.

The focus of this study is to examine, utilizing SPI and copula, how the drought return period is distributed across one of the biggest and most interesting regions in Morocco, the Marrakech-Safi region. This research aims to achieve three main objectives: (1) analyzing the SPI at three- and 12-month timescales to assess the dry and wet spells and their trends during the last five decades; (2) calculating the drought return periods, using the joint cumulative distribution function, based on their characteristics: duration, severity, and intensity; and (3) analyzing the spatial distribution of drought return period over the Marrakech-Safi region in Morocco for different scenarios.

Regarding the climatological context, the region has a highly varied climate, characterized by three climates: arid and semi-arid across most of the region and sub-humid in the High Atlas. It is influenced by the High Atlas Mountains range and the Atlantic Ocean (through the cold current from the Canary Islands), with an average maximum temperature of around 37.7 °C and a minimum of about 4.9 °C. There is also significant variability in rainfall across the region, although it remains low and irregular, ranging from 800 mm in the High Atlas to 190 mm in the plains. In recent decades, the region has witnessed a significant decline in rainfall, leading to increased drought occurrences. Research conducted by Fniguire et al. (2017) indicated that these drought events, characterized by insufficient precipitation over 12- to 24-month periods starting in 1975, have become more frequent and prolonged.

The agricultural sector is one of the pillars of the regional economy. Indeed, nearly 42.49% of the region's workforce works in this sector according to the 2017 National Employment Survey. According to the data of the Regional Directorate of Agriculture (DRA), the region of Marrakech-Safi contributes to national production at relatively high rates, including in particular olive trees (25%), citrus (13%), apricots (65%), walnuts (33%), melons (20%), almonds (15%), cereals (12%), and table grapes (10%). However, this sector is confronted with several problems, namely, the aridity of the climate, the poor structuring of irrigation water, and the salinization of agricultural land, which limits the development of modern agriculture with a high yield.

The data used to calculate the SPI index comes from series of daily rainfall measurements collected from 32 rain gauge stations. These stations are located in the action zones of the Tensift Hydraulic Basin Agency, the Oum Rbia Hydraulic Agency, and the National Meteorological Directorate. The characteristics of the station data are presented in Table 1.

Before initiating the process of calculating the SPI, particular attention was paid to the crucial phases of quality control and validation of the statistical data. These stages are of vital importance in our analytical approach, aimed at ensuring the accuracy, reliability, and validity of the data underlying the calculation of the SPI. The first phase of this procedure involved a rigorous check for data-entry errors. Careful examination of the data allowed us to identify any anomalies, such as outliers or missing values, which could affect the overall quality of the dataset.

The anomalies and missing data encountered in certain stations have been corrected, while stations with more than 20% of missing data have been eliminated from the analysis (Wan et al. 2015).

The SPI index (McKee et al. 1995) was calculated using precipitation data to represent meteorological drought in the Marrakech-Safi region. The SPI is an index that is powerful, flexible to use, easy to calculate, and just as effective at analyzing anomalies between wet and dry periods. Furthermore, this index is not affected by geographical or topographical differences (Lana et al. 2001).

The SPI index was designed to quantify the rainfall deficit at multiple timescales. These timescales reflect the impact of drought on the availability of different types of water resources. In this study, we have calculated the SPI index for time periods of three- and 12 months. The choice of SPI-12 and SPI-3 timescales was based on the need to capture both long-term and short-term drought conditions. SPI-12 is effective for identifying long-term droughts that affect hydrological systems and water storage, while SPI-3 is useful for detecting short-term droughts impacting agriculture and immediate water availability. These timescales provide a balanced perspective, capturing both the long-term impacts on plantations and the critical short-term effects on cereals (main crops practiced in the region). By concentrating on these two timescales, we aim to provide clear, actionable insights for water resource managers and agricultural planners in our study area. This focused approach allows us to deliver more precise recommendations tailored to the specific agricultural practices and climatic conditions of the region. Caccamo et al. (2011) used the classification system presented in the SPI index table in Table 2 to define the intensity of drought events based on the value of the index.

The SPI operates as a distribution-dependent metric, with no sole distribution universally suited for all regions. Among various options, the gamma distribution has demonstrated its resilience and dominance in scholarly works as the most reliable and frequently employed choice.

The analysis of SPI trends is carried out based on the nonparametric Mann–Kendall test and Sen's slope. The Mann–Kendall test made it possible to highlight the existence or not of an identifiable trend in the SPI time-series of the different studied stations.

In the recent literature on multivariate frequency and co-distribution analysis in hydrological statistics, great importance has been given to copula applications (Favre et al. 2004; Genest et al. 2007; Salvadori et al. 2007; Vandenberghe et al. 2010).

Copulas make it possible to describe the dependency structure between random variables and, at the same time, to combine univariate marginal distribution functions into their joint cumulative distribution function. The copula is classified into large families, of which the Archimedean copula family (Gumbel's copula, Clayton's copula, and Frank's copula) and the elliptic family (Gaussian copula, Student's copula) remain the most widely used in the case of studies of extreme events such as drought (Joe 1997). It should be noted that few studies are interested in modeling trivariate return periods. Indeed, most studies are limited to bivariate frequency analysis (Grimaldi & Serinaldi 2006; Kao & Govindaraju 2008; Pinya et al. 2009; Vandenberghe et al. 2010).

The copula is particularly adept at capturing the upper tail dependence, which is critical for modeling extreme events like severe droughts. It enables the characterization of the joint behavior of drought characteristics and offers a means of modeling the probabilistic dependence structure without being limited by the marginal distribution. The copula is able to describe multiple variables using distinct marginal distributions and is capable of capturing intricate dependencies between variables, to unravel the underlying dynamics of drought occurrence.

Indeed, the joint distribution function provides a comprehensive picture of the likelihood of simultaneous drought characteristics, enabling better risk assessment and management strategies. Moreover, by understanding the dependency structure, policymakers can allocate resources more effectively, targeting areas with a higher probability of extreme drought conditions. Also, improved modeling of drought variables aids in the development of targeted mitigation strategies, reducing the adverse impacts of droughts in arid regions.

The following is a step-by-step overview of the methodology:

• Data collection: precipitation time-series from the Marrakech-Safi rainfall stations.

• Fit appropriate marginal distributions to each drought variable (duration, peak, severity). This step involves identifying the best statistical distribution that describes the individual behavior of each variable.

• Use the Gumbel copula to model the dependency structure between the variables. The Gumbel copula is parameterized by a single parameter, θ, which captures the strength of dependency. The copula is defined as follows:

  

  (4)

  where u and v are the cumulative distribution functions of the marginal distributions.

• Estimate the parameter θ using methods such as maximum likelihood estimation.

• Construct the joint distribution function of the drought variables by combining the marginal distributions and the copula function.

For the calculation of multivariate joint periods, they are characterized according to two cases, namely, a joint return period marked by an ‘or’ condition, meaning that at least one variable is greater than or equal to a given threshold, and a joint return period defined by the ‘and’ condition, indicating that all variables remain greater than or equal to the various defined thresholds. For the estimation of the joint return period in the case of this study, we focus only on the second ‘and’ condition. Thus, the formula for determining the multivariate return period is defined as follows.

• For the bivariate case:

  

  (6)
• and for the trivariate case:

  

  (7)

The joint distribution of copulas is defined according to the Gumbel copula. Indeed, the Gumbel copula belongs to the family of Archimedean copulas and constitutes a copula of extreme values with the advantage of measuring the dependency of the rarest events. According to the literature, distributions based on the use of copulas remain the most efficient and effective compared with the other conventional distributions (Janga Reddy & Ganguli 2012). In a multivariate modeling study using copula and meta-heuristic methods, Janga Reddy & Ganguli (2012) applied a comparative study of four different copula families (Archimedean, Placket, extreme value, and elliptic copula families) to model drought characteristics. The results of this study allowed the authors to conclude that the Gumbel copula class, belonging to the Archimedean copula family, performed better than the other copula classes.

Taking the example of the Abadla station, representing the plain area, the analysis showed that during the period of 1972–2018, the extreme values of SPI-12 varied between a minimum of −3.06 in 1981 and a maximum of 2.95 in 1996. Analysis of the fluctuations in SPI-12 at this station revealed the existence of ten extremely dry periods (SPI < -2) and six extremely wet periods (SPI > 2). According to the period considered for the case of Abadla station, the results made it possible to highlight the appearance of 279 drought months (i.e., 51% of the study period), of which 4% were extremely dry, 30% were severely dry, and 67% were moderately dry. For SPI-3, results showed 272 drought months, of which 72% and 24% were considered moderate and severe, respectively. The same trend is also observed at the other stations mentioned earlier.

Tables 3 and 4 show the results of the nonparametric Mann–Kendall test and Sen's slope test applied to the SPI-3 and SPI-12 series. The results of these tests allow statistical rejection of the null hypothesis of the trend analysis (absence of trend) with a level of significance (alpha = 5%) in 50% of the stations with the SPI-12 series against 27% with the SPI-3 series. The results of these tests also show that 69% and 61% of the stations studied show an upward trend for the SPI-3 and SPI-12 series, respectively.

The analysis of univariate distribution of variables characterizing drought (severity, peak, and duration) consists in finding the best adjustment of the data of each variable to a cumulative frequency function.

The results obtained showed a diversification of functions that fit the variables studied. An example of drought variables of the Chichaoua station shows how data are adjusted to the cumulative frequency functions, and these results are obtained for each station.

Regarding the spatial distribution of return periods corresponding to severity of strictly 6 in the Marrakech-Safi region with SPI-3 and SPI-12, the return periods obtained for the severity vary between a minimum of two years and a maximum of 16 and seven years, respectively, for SPI-3 and SPI-12. Regarding SPI-12, the areas in the region with a long return period are mainly distributed in the coastal and mountain areas. On the other hand, for the short drought periods (SPI-3), except in the southwest area, the results show a more homogeneous spatial distribution with a dominance of short return periods over the whole region.

Finally, for the spatial distribution of return periods for drought intensity strictly above 1, the return period corresponding to such an intensity varies between two and 14 years for SPI-3 and between four and 33 years for SPI-12. The results of the univariate return periods obtained with an intensity higher than 1 show few areas with long return periods. They are mainly located in the northwestern part of the coastal zone.

For SPI-12, the return period of D > 6 months and P > 1 ranges from 23 to 168 years, with an average of 56.5 months. The shorter return periods are mainly found in the Bahira plain and Haouz plain in the plains area. On the other hand, the return periods are relatively longer in the northern part of the coastal strip, averaging more than ten years. In terms of the bivariate return period of D and S, the range is from 20 to 77 months, with an average of 44.1 months. The longer return periods are distributed throughout the western half of the Marrakech-Safi region. For S and P, the return periods are short with an average of four years, covering almost the entire region except for the northwestern part (Figure 7). For SPI-3, the situation of D and P is quite uniform, with longer return periods in the entire north and west of the region. However, in the mountainous region, shorter return periods were observed, with an average of less than four years. In terms of the bivariate return period of P and S, the range is from 26 to 426 months, with an average of 112 months (Figure 8). Longer return periods are found in the northern part of the region, specifically in the Bahira plain. Overall, these observations provide valuable insights into the spatial and temporal variations of drought events in the Marrakech-Safi region.

The deviation from the mean precipitation is a good indicator of the amplitude of the drought or wetness of a given area. This is why SPI gained potential and interest for monitoring drought and become more trustworthy when using long records of precipitation measurements. Its value is also obtained from its potential to make comparisons across different rainfall areas (McKee et al. 1995; Tan et al. 2015; Lee et al. 2021).

The results of our study confirmed the significant interannual fluctuation and evolution of wet and drought cycles in the Marrakech-Safi region. The 12-month-scale SPI exhibited six well-defined dry cycles in this region (1974–1976, 1978–1987, 1991–1995, 1999–2002, 2004–2008, and 2012–2018) and four wet periods (1987–1990, 1996–1998, 2003–2004, and 2009–2011), with the driest years being 1983, 1987, 1993, 2005, and 2015. The findings of this investigation are consistent with several drought assessment studies carried out in Morocco. Indeed, Ouatiki et al. (2019) showed that the Oum Rbia basin has been through a series of dry periods, interrupted by a few seasons with moderate to heavy rainfall. The first of these dry spells, lasting five to seven seasons, occurred in the early 1980s and affected the majority of the basin during the 1980s and 1990s. These extended droughts, which have been identified by Driouech et al. (2010) in various parts of Morocco, have had a significant impact on agriculture, resulting in a decrease in GDP and creating economic instability (Balaghi et al. 2007; Verner et al. 2018; Seif-Ennasr et al. 2020; Hadri et al. 2022). Meliho et al. (2020) stressed that the Tensift river basin suffered from droughts during two periods, from 1990 to 1995 and from 1997 to 2008, which had a significant impact on the amount of water flowing into the Takerkoust dam, leading to a decrease in the amount of water available for irrigation, electricity generation, and drinking-water purposes. Other authors showed the same behavior of wet- and dry-spell fluctuations in the Marrakech-Safi region (Fniguire et al. 2017; Cotti et al. 2022; Ouassanouan et al. 2022; Elair et al. 2023), in northern Morocco (Boudad et al. 2018), and in the Sebou basin (Hakam et al. 2022).

Regarding the drought trends, our findings are in agreement with the research of Hadria et al. (2019), Strohmeier et al. (2019), Hadri et al. (2021), and Elair et al. (2023), which indicate that the Mann–Kendall test detected a mixture of positive and negative trends across various regions in Morocco in the last four decades. Nonetheless, the sporadic positive SPI trend observed may be attributed to the increased rainfall levels brought about by local extreme rainfall events. During dry periods, significant deviations from the norm may occur (Hadri et al. 2021). Only 50% and 27% of SPI-12 and SPI-3 trends are statistically significant, respectively, which join the findings of other research about precipitation trends, stressing that historical precipitation trends are not statistically significant over the whole Mediterranean basin (Raymond et al. 2016; Tramblay et al. 2020; Vicente-Serrano et al. 2020). Indeed, the influence of long-term climate change that has altered precipitation distribution and intensity contributes to both positive and negative SPI trends in different regions and on different timescales. Notably, extreme rainfall events have had significant impacts, causing sharp changes in SPI values over short periods. These events can lead to temporary positive SPI values, even during prolonged drought periods, thus affecting the overall trends observed. Moreover, the region's topography, ranging from sea level to over 4,000 m (High Atlas Mountains), significantly influences local climate and SPI trends. Coastal areas experience different precipitation patterns compared with internal plains and mountainous regions. The internal plains, which are critical for agriculture, are particularly sensitive to precipitation during key periods (December to February), affecting cereal crops.

The results showed that the drought magnitudes of the study area were the highest in the stations of the plain area, with the values fluctuating between 2 and 25 and the drought lasting for 6–20 months for 75% of the drought events. For example, the longest 12-month SPI drought was recorded at Nkouris station, which lasted for 47 months with a magnitude of 32.1 and a maximum intensity (peak) of 1.4. At the same time, the drought peaks are in general low and do not exceed 1 in more than 61% of drought events in all studied stations. Only 20% of these events have attained more than 1.5 in terms of intensity (peak). Therefore, the Marrakech-Safi region is witnessing frequent drought with high magnitudes (cumulative SPI) but in general with low intensity, which is very insightful in terms of drought understanding and monitoring. Furthermore, the difference of the spatial distribution of drought severity over the region might be explained especially by the region's varied topography that significantly influences local climate and drought magnitude. Coastal areas experience different precipitation patterns compared with internal plains and mountainous regions covered by snow over several months of the year. These heterogeneous meteorological drought patterns coupled with local land-use features, urbanization, and water management practices exacerbate the problems of water availability and shortage in the plain areas (extensive agriculture) and coastal zone (big cities).

Bivariate and trivariate analyses make more sense and provide more information on the frequency of drought occurrence due to its multidimensional nature. Indeed, a drought event can last a long time but with low severity and intensity, making its impact more manageable unless its temporal extent exceeds a certain threshold. However, a drought with medium duration, high severity, and magnitude can be significantly more devastating (McKee et al. 1995; Mohseni Saravi et al. 2009; Liu et al. 2016).

Bivariate analysis maps are almost unanimous in showing the spatial distribution of drought return periods in the Marrakech-Safi region. Generally, it is the coastal strip of the region that experiences the lowest drought recurrences; return periods can exceed 20 years (as in the bivariate S-and-P case). However, the width of this strip varies slightly depending on the pair of drought characteristics analyzed. Also, a gradient of accentuation of the return periods toward the south is observed. For instance, severe drought events with a severity exceeding 6 and a peak of more than 1 are not very recurrent and take more than 15 years to reoccur over almost the entire western half of the Marrakech-Safi region. Following this coastal strip in terms of drought occurrence is the mountainous area of the High Atlas, which also proves to be quite resilient to the occurrence of drought events, especially those of high intensities and severities. However, the plain areas, particularly the Rhamena to Kelaa des Sraghna, experience the most recurrent occurrence of droughts. Similar results were proposed by Meliho et al. (2020) in the Tensift basin (the south of the Marrakech-Safi region), who found, after studying historical data spanning 47 years, that droughts occurred every two years, regardless of the timescale examined. Specifically, in the area being analyzed, at both seasonal and annual levels, there were two moderate droughts every three years, a severe drought every five years, and two extremely severe droughts every 25 years. The north–south variability of drought occurrence was emphasized by many other authors in Europe and Africa (Santos et al. 2010; Addi et al. 2021; Christidis & Stott 2021).

This landscape is somewhat unusual for short-term droughts (SPI-3), which typically have much higher return periods compared with long-term droughts (SPI-12) throughout the region. These droughts occur more frequently in the mountainous area of the High Atlas, especially for the pair S > 6 and P > 1. Mohseni Saravi et al. (2009) found in Karoun basin in Iran that short-term water supplies were affected more than long-term water resources. Henchiri et al. (2021), who studied the drought return periods over North and West Africa, has also stressed that wet and dry periods show greater temporal variability over shorter timescales of one or three months, whereas longer timescales of 12 months have a lower occurrence of wet and dry periods (Henchiri et al. 2021).

The likelihood of drought is lower when three conditions (S > 6, P > 1, D > 6) are verified; such a drought happens at a longer timescale. The copula and joint return years analysis confirmed that severe drought conditions do not occur frequently and usually take many years to recur. The findings of this investigation are consistent with the studies by Kalisa et al. (2020) and Mesbahzadeh et al. (2020) who confirmed that severe drought conditions do not occur at short time-intervals and the joint return period of drought when the variables (severity, peak, and duration) exceeded a certain value was longer than that of either variable. This critical finding has significant implications for water resource planning and drought preparedness. In terms of water resource planning, the extended return period guides the development of robust infrastructure, such as reservoirs and water distribution systems, designed to handle prolonged drought periods. It also informs water allocation policies, ensuring prioritization of critical needs before and during droughts. For drought preparedness, the results support crafting effective emergency response plans, including water rationing and public awareness campaigns tailored to extended drought periods. In the context of climate change, understanding these return periods enhances adaptive management and scenario planning, ensuring proactive responses to future climatic shifts. Accurate return-period analysis underpins evidence-based policymaking, guiding regulations for sustainable water-use practices.

This study analyzed the spatial distribution of the drought return period across the Marrakech-Safi region using SPI and copula. However, it should be noted that the precipitation stations used in the analysis cannot be considered completely representative of their spatial diversity due to certain factors. One of the main limitations is the low density of these stations in most parts of the Moroccan basins, coupled with a large number of missing data in several stations and with the short recording periods in some stations. This is mainly due to accessibility challenges faced during the installation and maintenance of meteorological stations (Boudhar et al. 2009; Hadria et al. 2019; Hadri et al. 2022). To note, events with longer return periods have greater uncertainty compared with more frequent events. This is because there is an inadequate record of data, which requires extrapolation of the fitted theoretical frequency distribution for extreme events. Nevertheless, with a reasonably long sample of more than 30 years of recorded data in the stations utilized in this study, the uncertainty of extreme events could not be considered high.

On the other hand, it should also be highlighted that the choice of drought characteristics thresholds was dictated by a bibliographic analysis in contexts similar to those of the study area. However, it may have been more advisable to test and analyze several thresholds for the duration, severity, and intensity of drought. This would be a way to verify how the probability of drought is affected by these thresholds.

Morocco, one of the most vulnerable drought-prone countries, has experienced a significant increase in the frequency of drought during the last few decades, particularly in arid and semi-arid regions. This rise has caused severe economic and societal losses, underscoring the need to better characterize drought and predict its variability for improving early warning and disaster risk management. This study demonstrates that in regions such as Marrakech-Safi, which experience low precipitation and are prone to drought, analyzing drought characteristics (including magnitude, intensity, and duration) using SPI can be applied to accurately assess drought variability. Our research in Morocco pioneers the use of copulas, an advanced statistical technique adept at capturing complex relationships among variables, to uncover the fundamental dynamic of drought occurrence. Through the incorporation of copula modeling in assessing drought frequency, we surpass conventional methodologies, uncovering latent correlations that traditional approaches frequently fail to detect.

The results of this study lead to the following conclusions:

• The drought severity in the region was highest in the plain area, with droughts lasting 6–20 months for 75% of all drought events.

• The coastal strip exhibited the lowest drought recurrences.

• Dry periods exhibited greater temporal variability over shorter timescales.

• Trivariate return periods of drought events were longer, averaging 93 months for SPI-12.

• The local nature of drought occurrence, duration, severity, and intensity reveal a huge potential for inter-basin water management or other adaptation strategies. Eventually, the heterogenic drought pattern of Morocco reveals options for a broader scale of water management, as anchored in the Moroccan Water Law (Strohmeier et al. 2019).

The development of monovariate, bivariate, and trivariate return periods of drought variables, using joint and conditional distribution functions, is important for hydro-climate and agro-climate design and planning of Moroccan basins witnessing recurrent drought events. Indeed, for improving drought resilience in the Marrakech-Safi region, enhancing water conservation measures is crucial. Promoting the use of efficient irrigation systems, such as drip irrigation, can significantly reduce water waste in agriculture. In addition, implementing rainwater harvesting systems can capture and store rainwater for use during dry periods. Investment in the maintenance and upgrade of water distribution infrastructure is also essential to minimize losses due to leaks.

Developing drought-tolerant crops is another vital strategy. Supporting agricultural research institutions to develop and introduce drought-resistant crop varieties suitable for the region's climate can improve agricultural resilience. Moreover, implementing sustainable land-management practices is essential for long-term drought resilience; encouraging soil conservation techniques, such as mulching, cover cropping, and reduced tillage, helps maintain soil moisture and health. In addition, promoting afforestation and reforestation initiatives can enhance groundwater recharge and reduce soil erosion.

Further research is required to deal with sparse rain-station distribution and to test other duration, severity, and peak thresholds for the analysis of monovariate and multivariate drought frequency. The use of long-term global precipitation datasets within the study region, such as satellite measurements or reanalysis data, could give an alternative to identify additional representative datasets for drought monitoring and to mitigate the shortcomings arising from the limited number of stations in the study area. Finally, future research studies must focus as well on the impact of climate change on drought patterns and on the effectiveness of various drought-mitigation strategies in arid regions, like Marrakech-Safi.

We sincerely thank all experts and institutions who assisted us in conducting this research. This research was supported by the grant of Mohammed VI Polytechnic University. This research was partially carried out in the framework of ARIMA project and GEANTech project. The authors would like to acknowledge the Tensift Hydraulic Agency (ABHT), the Oum Rbia Hydraulic Agency (ABHOER), and the National Directorate of Meteorology for providing data to this research. We gratefully thank David Cotti from the United Nations University (UNU-EHS) for useful discussions on the idea of the research paper.

This research received no external funding.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.