Nonlinear Trend and Multiscale Variability of Dry Spells in Senegal (1951–2010)

Abstract

Dry spells occurring during the rainy season have significant implications for agricultural productivity and socioeconomic development, particularly in rainfed agricultural countries such as Senegal. This study employs various chaos-theory-based tools, including the lacunarity method, rescaled analysis, and the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) method, to investigate the distribution, predictability, and multiscale properties of the annual series of maximum dry spell length (AMDSL) in Senegal during the rainy season. The analysis focuses on 29 stations across Senegal, spanning the period from 1951 to 2010. The findings reveal persistent behavior in the AMDSL across nearly all stations, indicating that predictive models based on extrapolating past time trends could enhance AMDSL forecasting. Furthermore, a well-defined spatial distribution of the lacunarity exponent β is observed, which exhibits a discernible relationship with rainfall patterns in Senegal. Notably, the lacunarity exponent displays a south-to-north gradient for all thresholds, suggesting its potential for distinguishing between different drought regimes and zones while aiding in the understanding of spatiotemporal rainfall variability patterns. Moreover, the analysis identifies five significant intrinsic mode functions (IMFs) characterized by different periods, including interannual, interdecadal, and multidecadal oscillations. These IMFs, along with a nonlinear trend, are identified as the driving forces behind AMDSL variations in Senegal. Among the inter-annual oscillations, a 3-year quasi-period emerges as the primary contributor and main component influencing AMDSL variability. Additionally, four distinct morphological types of nonlinear trends in AMDSL variations are identified, with increasing–decreasing and increasing trends being the most prevalent. These findings contribute to a better understanding of the variability in annual maximum dry spell lengths, particularly in the context of climate change, and provide valuable insights for improving AMDSL forecasting. Overall, this study enhances our comprehension of the complex dynamics underlying dry spell occurrences during the rainy season and presents potential avenues for predicting and managing the AMDSL in Senegal.

1. Introduction

The latest report by the Intergovernmental Panel on Climate Change indicates that global average surface air temperatures are increasing at rates unlike any other period on record [1]. These temperature changes have resulted in extreme conditions, including droughts and food insecurity, in Africa, posing significant threats to water resources, agriculture, and public health management [2,3,4]. Consequently, there is an urgent need to deepen our understanding of hydrometeorological hazards. Among the regions that are most vulnerable to such risks is the African continent, which faces the compounded challenges of population growth, ecosystem interactions, and limited adaptive capacity [1,5,6,7,8].

The West African region, in particular, exemplifies this vulnerability due to the combination of escalating water scarcity, rapid population growth, and recurrent localized droughts [9,10]. According to the World Food Program (WFP) [11], Senegal is among the seven Sahelian countries experiencing a substantial increase in the number of food-insecure individuals (from 314,600 to 548,000). Given the prevalence of intense and frequent hydrometeorological events and the high population exposure, it is crucial to enhance our understanding of rainfall variations and regimes across different spatial and temporal scales [12,13,14,15,16,17].

Several studies have utilized ground truth rainfall data to examine the spatial and temporal variability in extreme events in the Sahel region and Senegal [18,19,20,21,22]. These investigations have shed light on the hybrid rainy seasons characterized by simultaneous dry and wet seasonal rainfall events, as highlighted by Salack et al. [23] and Fall et al. [21]. While numerous studies have focused on the spatial and temporal variability in dry and wet spells and their association with the West African monsoon [24], limited attention has been given to the components of these hybrid seasons. Moreover, understanding the timing and characteristics of dry spells is crucial for agricultural monitoring, as they primarily occur at the onset and end of rainy seasons [25]. Furthermore, dry spell length (DSL) series can serve as valuable indicators for characterizing drought regimes in specific regions [26]. Hence, gaining a better understanding of the spatial and temporal characteristics of DSLs is relevant for countries where agricultural productivity strongly depends on rainfall.

In this context, Dieng et al. [27] found a correlation between earlier long dry spells and lower accumulated seasonal rainfall (June to September) in northern Senegal, whereas a later dry spell correlated with higher rainfall, particularly in the southern part of the country. Osorio and Galiano [28] used data from regional climate models to investigate the nonstationary analysis of annual maximum dry spell lengths in the monsoon season within the Senegal River basin. Salack et al. [25] explored the relationship between extreme dry spell frequencies and oceanic fluctuations in the West African Sahel (including Senegal) from 1950 to 2010. Froidurot and Diedhiou [24] examined the climatological characteristics of wet and dry spells in the West African monsoon system using daily TRMM 3B42 rainfall data from 1998 to 2014. Fall et al. [22] analyzed and compared the characteristics of dry and wet spells across various datasets (observations, satellite data, and statistical models) in Senegal from 1998 to 2010. Ndiaye et al. [29] investigated the interannual and decadal variability in dry spells and different classes of dry episodes from 1950 to 2010 at twelve stations. Recently, Touré et al. [30] characterized the spatial and temporal variability in nine descriptors, including dry spells, during the rainy season in Senegal, and explored their predictability using global sea surface temperature (SST) patterns. However, these previous studies, in general, analyzed the main characteristics of DSL (variability and trend) using traditional statistical methods that assume linearity and stationarity in DSL series, or decomposition methods (e.g., Fourier transform, wavelet analysis) that typically address only stationary time series and rely on predetermined functions.

These assumptions do not accurately represent the physical reality and may lead to erroneous conclusions since the climatic system is dynamic and chaotic, deviating from linear and stationary processes [31,32]. While some studies attempted to address these limitations (e.g., [28]), no comprehensive research has yet investigated the spatial and temporal characteristics of DSL series, particularly the annual series of maximum dry spell length (AMDSL) during the rainy season in Senegal, using nonlinear and chaos approaches. Therefore, employing nonlinear decomposition methods that do not require predetermined basis functions, in combination with fractals and chaos concepts, could provide significant added value by enabling a better understanding of the nonlinear trends and complexity of the hydroclimatic system [32,33,34,35,36], such as dry spell regimes [37,38,39].

Based on the aforementioned considerations, the main objective of this paper is to analyze the AMDSL during the period of 1951–2010 in Senegal’s rainy season. The specific objectives are as follows: (1) to spatially uncover the inherent multiscale characteristics of AMDSL, (2) to spatially identify the nonlinear long-term memory properties within the AMDSL, (3) to quantify the nonlinear variability in the AMDSL, and finally, (4) to assess the distribution of the AMDSL and the temporal dynamics of drought regimes.

2. Materials and Methods

2.1. Study Area

Senegal is situated on the westernmost coast of West Africa, lying between latitudes 12°30 N and 16°30 N and longitudes 11°30 W and 17 30 W, and occupying a land area of approximately 197,000 km² (refer to Figure 1). The country exhibits a pronounced north-to-south precipitation gradient [25,27,40,41]. Studies [25,30] indicate that the rainy season starts in early May in the south (June–July in the north) and finishes in late October (early October in the north), while the duration of the dry season in the northern and central regions is longer than that in the southern region. Using the average annual rainfall during the 1951–2010 period, studies such as [25,29,41] partitioned the country into four distinct rainfall zones: northern zone (NZ), central north zone (CN), central south zone (CS), and southern zone (SZ). The NZ (SZ) is typified by an average annual rainfall below 400 mm (exceeding 800 mm), whereas the CN (CS) zone features average annual rainfall between 400 and 600 mm (between 600 and 800 mm). Additionally, according to Dieng et al. [27], the CN, CS, and SZ regions are distinguished by more frequent rainy days and higher rainfall intensity than the NZ region.

2.2. Data

We used in situ data of precipitation for the 1951–2010 period collected from the Regional Centre for the Improvement of Plant Adaptation to Drought (Centre Régional pour l’Amélioration de l’Adaptation à la Sécheresse (CERAAS)), as previously described and used by several studies (e.g., [41,42,43]). The dataset consists of daily rainfall series from the network of the former National Meteorological Agency (now designated as Agence Nationale de l’aviation Civile et de la Météorologie du Senegal (ANACIM)) integrating other rain gauges operated by the Senegalese Institute for agricultural research (Institut Sénégalais de la Recherche Agricole (ISRA)) and CERAAS for crop monitoring and forecasting. The available twenty-nine (29) stations are relatively well spread over the country except for less density in the North and the eastern part of the domain (Figure 1b). They are distributed in four rainfall zones as follows: eight (08) in the northern zone (NZ), seven (07) in the central north zone (CN), nine (09) in the central south zone (CS), and five (05) in the southern zone (SZ) (details are provided in

Table 1. Information for identifying studied stations in Senegal (see Figure 1b).

Station ID	Station Name	Station Rainfall Zone	Lon	Lat
1	Kedougou	Southern zone (SZ)	−12.19	12.56
2	Kolda	Southern zone (SZ)	−14.93	12.88
3	Oussouye	Southern zone (SZ)	−16.53	12.48
4	Velingara	Southern zone (SZ)	−14.10	13.15
5	Ziguinchor	Southern zone (SZ)	−16.26	12.55
6	Bakel	Central South zone (CS)	−12.47	14.9
7	Boulel	Central South zone (CS)	−15.53	14.28
8	Goudiry	Central South zone (CS)	−12.72	14.18
9	Kaffrine	Central South zone (CS)	−15.55	14.1
10	Kaolack	Central South zone (CS)	−16.7	14.13
11	Kidira	Central South zone (CS)	−12.22	14.47
12	Koungheul	Central South zone (CS)	−14.81	13.96
13	Nioro	Central South zone (CS)	−15.78	13.73
14	Tambacounda	Central South zone (CS)	−13.68	13.76
15	Dakar	Central North zone (CN)	−17.50	14.73
16	Diourbel	Central North zone (CN)	−16.23	14.65
17	Fatick	Central North zone (CN)	−16.40	14.33
18	Gossas	Central North zone (CN)	−16.08	14.50
19	Mbacke	Central North zone (CN)	−15.92	14.80
20	Thies	Central North zone (CN)	−16.95	14.80
21	Tivaouane	Central North zone (CN)	−16.82	14.95
22	Dagana	Northern zone (NZ)	−15.50	16.52
23	Dahra	Northern zone (NZ)	−15.48	15.33
24	Kebemer	Northern zone (NZ)	−16.45	15.37
25	Linguere	Northern zone (NZ)	−15.12	15.38
26	Louga	Northern zone (NZ)	−16.22	15.62
27	Matam	Northern zone (NZ)	−13.25	15.65
28	Podor	Northern zone (NZ)	−14.96	16.65
29	St-Louis	Northern zone (NZ)	−16.45	16.05

).

2.3. Methods

2.3.1. Dry Spell Computation

In this study, we adopt the definition of dry spell length (DSL) as the consecutive number of days with precipitation less than 1 mm. This definition has been widely used in previous investigations conducted in the Sahel and Senegal regions (e.g., [21,22,24,25,44]). The computation of DSLs is performed for each year within the study period, which spans from 1951 to 2010, specifically during the rainy season from June to September. Consequently, we determine the AMDSL, representing the highest value of DSL observed during the rainy season for each year. Throughout our analysis, the following methods are employed to analyze the AMDSL complex properties in Senegal.

2.3.2. Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN)

In recent years, the empirical mode decomposition (EMD) method and its different variants have proven successful in climate change research [45,46,47,48,49,50,51]. Notably, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) method stands out as particularly well-suited for revealing the intrinsic multiscale characteristics and overall nonlinear trend of climatic variables’ time series [46,49]. Compared to standard decomposition methods such as Fourier transform and wavelet analysis, ICEEMDAN is preferred for its intuitive, posteriori, direct, empirical, and adaptive nature, eliminating the need for predetermined basis functions [49,52]. Moreover, ICEEMDAN incorporates several improvements over classical EMD techniques [53,54,55,56,57].

For this study, we employed the ICEEMDAN method developed by Colominas et al. [52] to investigate the intrinsic multiscale characteristics and long-term nonlinear trends present in the variability of AMDSL.

The implementation of the ICEEMDAN algorithm is as follows:

Introduce Gaussian white noise to the original AMDSL S(n) as follows:

$$S^i\left(n\right)=S\left(n\right)+{\lambda }_0{E}_1\left({\nu }^i\left(n\right)\right)$$

(1)

where $E_k\left(·\right)$ represents the kth order intrinsic mode function (IMF) obtained through the EMD algorithm; ${\nu }^i\left(n\right)$ is a sequence of standard normal distribution white noise added at the ith time, and λ denotes the signal-to-noise ratio.

Calculate the first-order residue sequence, denoted as $r_1\left(n\right)$, through the local mean of $S^i\left(n\right)$ using EMD as follows:

$$r_1\left(n\right)=\langle M\left(S^i\left(n\right)\right)\rangle$$

(2)

where 〈·〉 and M(·) represent averaging and local mean, respectively.

Compute the first IMF component ($\widetilde{IM{F}_1}$) at the first stage (k = 1) as follows:

$$\widetilde{IM{F}_1}=S\left(n\right)-r_1\left(n\right)$$

(3)

Calculate the second-order residue sequence, denoted as $r_2\left(n\right)$, and its corresponding IMF component ($\widetilde{IM{F}_2}$) through the local mean of $r_1\left(n\right)+{\lambda }_1{E}_2\left({\nu }^i\left(n\right)\right)$ using EMD as follows:

$$r_2\left(n\right)=\langle M\left(r_1\left(n\right)+{\lambda }_1{E}_2\left({\nu }^i\left(n\right)\right)\right)\rangle$$

(4)

$$\widetilde{IM{F}_2}=r_1\left(n\right)-r_2\left(n\right)$$

(5)

Repeat the algorithm iteratively until the signal cannot be further decomposed, and calculate the k(3, 4,…, L) th-order residual $r_k\left(n\right)$ and its corresponding $IM{F}_k$ as follows:

$$r_k\left(n\right)=\langle M\left(r_{k-1}\left(n\right)+{\lambda }_{k-1}{E}_k\left({\nu }^i\left(n\right)\right)\right)\rangle$$

(6)

$$\widetilde{IM{F}_k}=r_{k-1}\left(n\right)-r_k\left(n\right)$$

(7)

where L is the total numbers of IMF. Thus, the AMDSL is decomposed into

$$S\left(n\right)={\displaystyle \sum }_{k=1}^L{\widetilde{IMF}}_k+r_L\left(n\right)$$

(8)

where $r_L$ is the residual representing the nonlinear long-term trend of the AMDSL, and the IMF components represent the intrinsic multiscale characteristics embedded within the AMDSL.

In summary, the IMF components capture the periodic or quasi-periodic changes in the AMDSL at different time scales, while the residual component represents the overall trend of the AMDSL over time.

2.3.3. Significance Test of IMF and Trend Components

In order to assess the significance of the obtained IMFs, we employ a widely used method developed by Wu and Huang [58], which has been utilized in numerous previous studies (e.g., [59,60,61]). This method relies on the Monte Carlo technique to establish statistical significance. To determine the actual IMF component, we examine the detailed energy distribution with respect to the period, represented as a spectral function. To clarify, if the energy of an IMF exceeds the confidence line at a specific confidence level (e.g., 95%), it indicates that the IMF contains statistically significant information at that chosen confidence level. In other words, the IMF is considered to possess meaningful statistical relevance at the selected confidence level when its energy surpasses the corresponding threshold.

2.3.4. Variance Contribution Rate

The contribution of each IMF component and trend to the AMDSL changes is carried out using the variance contribution rate (VCR), as described in Guo et al. [62] and Bai et al. [63].

$$VC{R}_k=\frac{100\ast var\left(IM{F}_k\left(t\right)\right)}{{{\displaystyle \sum }}_{k=1}^{L}var\left(IM{F}_k\left(t\right)\right)+var\left(r_L\left(t\right)\right)}$$

(9)

where var (·) denotes the variance sign and $r_L\left(t\right)$ represents the residue.

2.3.5. Spatial Evolution of ICEEMDAN Trend

In order to examine the spatiotemporal evolution of the AMDSL, we compute the average increment value of the ICEEMDAN trend within the time window X–Y. This analysis is conducted following the approach described in previous studies [59,64,65].

$$ICEEMDA{N}_{Trend}=\left(r_L\left(Y\right)-r_L\left(X\right)\right)/\left(Y-X\right)$$

(10)

X and Y are particular years. In this study four-time windows are used: 1951–1970, 1971–1990, 1991–2010, and 1951–2010. These four distinct time windows cover various temporal scales, ranging from historical to more recent years, enabling us to thoroughly investigate the AMDSL characteristics and identify potential shifts or trends that have occurred over time. This facilitates the analysis of the evolution of the AMDSL trend and allows for a more comprehensive understanding of the spatiotemporal dynamics of the AMDSL.

2.3.6. Rescaled Range (R/S) Analysis

The Hurst exponent is widely employed to predict the persistence of hydrological and climatological time series data [66]. Among the available approaches for estimating the Hurst exponent, the rescaled range (R/S) analysis is extensively used in the literature [67,68]. Notably, previous studies by Martinez et al. [37] and Lana et al. [38] successfully applied the R/S analysis method to investigate the predictability and long-term memory of dry spell regimes in the Iberian Peninsula and Europe.

The R/S method, as described in previous studies [38,67,68,69,70], involves the following steps:

Firstly, compute, respectively, the range $R_{\tau }$ and standard deviation $S_{\tau }$ using Equations (11) and (12)

$$R_{\tau }=\left[\underset{1\le i\le \tau }{max}{\displaystyle \sum }_{k=1}^i\left(y_k-\frac{1}{\tau }{\displaystyle \sum }_{k=1}^{\tau }{y}_k\right)-\underset{1\le i\le \tau }{min}{\displaystyle \sum }_{k=1}^i\left(y_k-\frac{1}{\tau }{\displaystyle \sum }_{k=1}^{\tau }{y}_k\right)\right]$$

(11)

$$S_{\tau }={\left[\frac{1}{\tau }{\displaystyle \sum }_{k=1}^{\tau }{\left(y_k-\frac{1}{\tau }{\displaystyle \sum }_{k=1}^{\tau }{y}_k\right)}^2\right]}^{1/2}$$

(12)

where 1 ≤ τ ≤ N, and $\left\{y_t|t=1,2,\dots ,N\right\}$ denotes the original DSL series.

Secondly, determine the Hurst exponent by plotting the $log{\left(R/S\right)}_{\tau }$ versus $log\left(\tau \right)$ as:

$$log{\left(R/S\right)}_{\tau }=loga+H.log\left(\tau \right)$$

(13)

According to Martinez et al. [37] and Lana et al. [38], the Hurst exponent (H) provides valuable insights into the characteristics of the AMDSL. A Hurst exponent close to 0.5 indicates a completely random series, where there is no discernible relationship between the current and future values of AMDSL. In contrast, when 0.5 < H < 1.0, it signifies persistent behavior in the AMDSL dynamics. This means that the time trends of future AMDSL values are more likely to be similar to the current values, indicating a positive autocorrelation in the series. On the other hand, when 0 < H < 0.5, it indicates anti-persistence, suggesting that the current time trend will reverse in the future. A Hurst exponent close to 0 represents strong anti-persistence, while values close to 1 indicate strong persistence in the series. By analyzing the Hurst exponent, we can gain insights into the temporal dependencies and predictability of the AMDSL.

2.3.7. Lacunarity Method

The lacunarity method, initially developed by Mandelbrot [71] and further extended by Allain and Cloitre [72], is utilized in this study to explore the temporal dynamics of and variability in dry periods in the AMDSL. The method is applied at different thresholds, specifically 10, 15, 20, and 25 days per year, to assess the occurrence and characteristics of extended dry spells. This approach has been previously employed in studies by [37,38,73] to investigate the distribution of dry spells in various regions such as the Iberian Peninsula, Europe, and Brazil, focusing on daily precipitation time series. However, in the present study, we apply the lacunarity method to the AMDSL to specifically characterize the time series of prolonged dry spell regimes, which can significantly impact agricultural productivity. The lacunarity method can be concisely described as follows [37,38,73]:

Firstly, determine the frequency distribution n(p, r), which is the number of boxes of length r (time steps, years) containing p-occupied sites (time steps in which the AMDSL value exceeds the chosen threshold).

Secondly, calculate the probability distribution Q(p,r) as

$$Q\left(p,r\right)=\frac{n\left(p,r\right)}{N\left(r\right)}$$

(14)

N(r) is the total number of boxes of length r.

Thirdly, calculate the first and second moments of Q(p,r) as:

$$M^{\left(1\right)}\left(r\right)={\displaystyle \sum }_{p}pQ\left(p,r\right)$$

(15)

$$M^{\left(2\right)}\left(r\right)={\displaystyle \sum }_p{p}^2·Q\left(p,r\right)$$

(16)

Fourthly, determine the lacunarity L(r) by:

$$L\left(r\right)=\frac{M^{\left(2\right)}\left(r\right)}{{\left[M^1\left(r\right)\right]}^2}$$

(17)

Finally, determine the lacunarity exponent β by linear regression of log(L(r)) versus log(r) curves as:

$$log\left(L\left(r\right)\right)=log\left(\alpha \right)+\beta log\left(r\right)$$

(18)

Therefore, in areas with greater heterogeneity (a higher rate of variability) in the series of AMDSL values above a chosen threshold, the resulting lacunarity exponent β tends to have lower absolute values. Conversely, in areas where the AMDSL values above the chosen threshold exhibit smaller variations and a more uniform distribution, the absolute values of β are higher.

3. Results and Discussion

3.1. Spatial Distribution of AMDSLs

The spatial distribution of the AMDSLs during the period 1951–2010 across Senegal is presented in Figure 2. The results indicate significant differences between the four rainfall zones in the country, with spatial heterogeneity observed in the maximum and minimum values of the AMDSL. Specifically, the lowest values of the maximum AMDSL were observed in the central south (CS) and the southern zone (SZ), with the lowest values mainly concentrated in the SZ. Conversely, the greatest values of the maximum AMDSL were observed in the northern zone (NZ) and the central north zone (CN), with the highest values mainly concentrated in the NZ. The minimum value of the multiyear maximum AMDSL ranged from 15 to 30 days, occurring mainly in the SZ and increasing northward, while the maximum value of the multiyear maximum AMDSL ranged from 90 to 100 days and was mainly distributed in the NZ. Regarding the multiyear minimum AMDSL, the minimum values ranged from 4 to 7 days and occurred mainly in the SZ and CS, increasing northward, while the maximum values were observed in the NZ and CN, ranging from 7 to 12 days. These findings are consistent with previous studies that reported longer dry seasons in the northern and central zones of Senegal than in the southern zone [25,27,40,41].

3.2. Multiscale Decomposition of AMDSLs Using ICEEMDAN

The contribution of each intrinsic mode function (IMF) fluctuation and trend component on the overall variability in the AMDSL is assessed using the variance contribution rate (VCR) and reported in

Table 2. The variance contribution rate (%) of each IMF for AMDSL in each station. * means significant at the 90% confidence level.

Station ID	Station Name	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	Trend
1	Kedougou	69.1 *	6.4 *	14.6 *	6.8 *	0.5	-	2.5
2	Kolda	65.5 *	11.2 *	2.7 *	3.6 *	13.2 *	-	4.0
3	Oussouye	72.4 *	6.1 *	4.6 *	1.2	2.2 *	-	13.6
4	Velingara	57.6 *	18.5 *	1.4	14.2 *	5.6 *	-	2.6
5	Ziguinchor	63.8 *	3.1 *	4.3 *	0.8	2.5 *	-	25.5
6	Bakel	59.3 *	13.2 *	2.6 *	8.2 *	4.5 *	-	12.3
7	Boulel	61.3 *	8.6 *	11.2 *	5.3 *	-	-	13.7
8	Goudiry	49.9 *	8.9 *	15.3 *	3.2 *	16.6 *	-	6.1
9	Kaffrine	62.3 *	2.7 *	13.3 *	3.6 *	8.9 *	-	9.2
10	Kaolack	60.6 *	1.3	13.8 *	3.8 *	18.0 *	-	2.5
11	Kidira	54.9 *	22.5 *	3.4 *	6.3 *	9.6 *	-	3.3
12	Koungheul	64.4 *	9.6 *	3.0 *	7.5 *	1.3 *	-	14.3
13	Nioro	63.5 *	10.1 *	5.8 *	11.3 *	5.5 *	2.7 *	1.2
14	Tambacounda	67.4 *	11.3 *	11.3 *	3.5 *	2.7 *	-	3.8
15	Dakar	47.8 *	39.5 *	1.4 *	1.2 *	1.2 *	-	8.8
16	Diourbel	60.6 *	20.8 *	5.5 *	2.6 *	4.6 *	-	6.1
17	Fatick	58.9 *	22.5 *	14.8 *	2.9 *	0.3 *	-	0.6
18	Gossas	46.0 *	4.9 *	2.7 *	13.1 *	10.3 *	-	23.0
19	Mbacke	47.3 *	9.6 *	10.2 *	11.5 *	2.9 *	-	18.4
20	Thies	62.5 *	10.4 *	3.3 *	6.1 *	11.4 *	-	6.5
21	Tivaouane	23.1 *	26.5 *	3.5 *	4.7 *	9.2 *	-	33.0
22	Dagana	74.8 *	5.4 *	3.0 *	5.5 *	2.3 *	-	8.9
23	Dahra	70.7 *	4.1 *	11.7 *	8.2 *	0.7 *	-	4.7
24	Kebemer	47.8 *	11.5 *	2.8 *	7.5 *	8.6 *	-	21.7
25	Linguere	55.1 *	14.6 *	7.5 *	13.4 *	-	-	9.4
26	Louga	71.4 *	11.7 *	4.6 *	2.7 *	2.40 *	-	7.1
27	Matam	50.1 *	15.2 *	5.0 *	5.8 *	7.2 *	-	16.8
28	Podor	52.8 *	14.4 *	21.9 *	1.0 *	1.4 *	-	8.5
29	St-Louis	64.8 *	10.8 *	5.4 *	8.6 *	4.8 *	3.8 *	1.7

. Results suggest that, irrespective of the rainfall zone, five IMFs and a residue (nonlinear trend component) govern the overall variability in the AMDSL in Senegal. This differs from the analyses of Libanda and Nkolola [74] in Zambia and Duan et al. [75] in China, which identified three and four IMFs, respectively, for the maximum consecutive dry days. The discrepancy may come from differences in the geographical location and the analytical method used. We employed the ICEEMDAN algorithm, which suppresses residual noise and spurious components effectively during the decomposition process [52]. Most of the extracted intrinsic functions are statistically significant, and there are marked disparities in the VCR of the IMFs between the examined stations. Across all stations, the VCR of IMF1 and IMF2 to the total variability in the AMDSL ranges from 49.6 to 87.3%, while that of IMF3 and IMF4 ranges from 2.6 to 22.9%. The VCR of IMF5 and the overall trend varies from 0.5 to 18.0% and from 1.0 to 33%, respectively.

Collectively, these findings reveal that the evolution of AMDSL variability is characterized by distinct IMFs with different time scales, as reported by Duan et al. [54,75] in China. Multiscale changes in the AMDSL differ across the studied stations, while each IMF exerts a distinctive influence on the overall characteristics of the AMDSL.

Figure 3 displays the spatial distribution of the variance contribution rates of the intrinsic mode functions (IMFs) and trends of the AMDSL in Senegal. The results show that IMF1 consistently contributes the most to the total variability in the AMDSL, ranging from 45% to 75%, except at Tivaouane (ID:21), where it contributes only 23%. Following IMF1, IMF2 contributes between 1.5% and 40%, the overall trend contributes between 1% and 33%, IMF3 contributes between 1.3% and 21%, IMF4 contributes between 1% and 14.3%, and IMF5 contributes between 0.5% and 18%. The dominance of IMF1 in the AMDSL variance is consistent across all stations, implying that it represents the most important component of the AMDSL variability. Furthermore, the trend component’s contribution to the variability is significant and considerable in some stations, making it the second or third contributor to AMDSL variance, depending on the station. Thus, the trend component represents a critical part of the overall AMDSL variability. The variance contribution rates of the IMFs and trends vary across the studied stations due to differences in the underlying climatic conditions and geographical factors. These results highlight the importance of considering the spatial distribution of the variability in the AMDSL and the different contributions of each component to better understand the dynamics of drought in Senegal.

Figure 4 illustrates the spatial distribution of the quasi-periodic fluctuations of the first four IMFs. Across the country, the AMDSL variability is characterized by interannual (3-year and 5–9-year quasi-periodic fluctuations), interdecadal (10-year, 12-year, and 15-year quasi-periodic fluctuations), and multidecadal (20-year quasi-periodic fluctuations). The interannual variations with 3-year, 5–6-year, and 7–9-year periods are, respectively, detected in IMF1, IMF2, and IMF3. In addition, interdecadal and multidecadal variations with 10-year, 12-year, 15-year, and 20-year periods are detected in IMF4, depending on the station. Although a single period of 3 years is detected on all the 29 stations for IMF1, the periods of other IMFs vary across the stations. IMF2 with 5-year periods is detected for 69% of the stations, while IMF2 with 6-year periods is obtained for the rest. IMF3 with, respectively, 7-year, 8-year, 9-year, and 10-year periods is detected for 24%, 56%, 17%, and 3% of the stations. Similarly, IMF4 with, respectively, 10-year, 12-year, 15-year, and 20-year periods is detected for 10%, 31%, 45%, and 14% of the stations. Combining the results obtained for the variance contribution rate and those related to the periodicity of IMFs, it is clear that the interannual oscillations, especially with the 3-year period, are the main components of and contributors to the AMDSL variability in Senegal. Specifically, the most significant AMDSL changes occur at the interannual scale in Senegal. These results are consistent with the frequent droughts occurring every two or three years in Senegal (e.g., [76]) and could also be indirectly related to the high variability in rainfall at interannual and interdecadal scales [40,77].

Considering all the studied stations, AMDSL variation trends obtained from ICEEMDAN decomposition can be classified into four morphological types of trends, which are shown in Figure 5. In fact, we observe morphological types of increasing (Figure 5a), increasing–decreasing (Figure 5b), increasing–decreasing–increasing (Figure 5c), and decreasing–increasing–decreasing (Figure 5d). Hence, the trends in the AMDSL during the 1951–2010 period are nonlinear in Senegal. Therefore, the commonly used linear trend can lead to erroneous results.

Figure 6 illustrates the spatial distribution of various types of AMDSL variation trends. Among the stations analyzed, 60% exhibit the increasing–decreasing type, 34% display the increasing type, 3% demonstrate the increasing–decreasing–increasing type, and 3% show the decreasing–increasing–decreasing type. Stations with increasing–decreasing trends are predominantly found in the central north and central south zone, while stations with the increasing trend are mainly located in the northern zone. In contrast, both the increasing–decreasing and increasing trends are observed in the stations located in the southern zone. However, the underlying reasons behind these findings are not explored in this study. Our results are consistent with the nonlinear characteristics of the AMDSL previously identified by Osorio and Galiano [28]. Overall, the findings affirm that relying solely on linear trend methods to identify trends and characteristics of drought indices may yield inaccurate results and misleading conclusions, particularly in studies that aim to understand the impacts of climate change.

Figure 7 displays the spatial distribution of the trends in the AMDSL based on ICEEMDAN analysis for four time periods, i.e., 1951–1970, 1971–1990, 1991–2010, and 1951–2010. In general, an increase in the AMDSL is observed for most stations during the first three time periods, except for the 1991–2010 time window where approximately 50% of stations show a decreasing trend. However, it should be noted that the rate of increase varies across stations, and the highest rates of increase are mainly observed in the northern and central northern parts of the country. This is consistent with previous studies that reported an increasing trend in dry spells in the Sahel region over the past decades [20,78].

3.3. Long-Term Memory in AMDSLs

The spatial distribution of Hurst exponents (H) for the dataset of the AMDSL is depicted in Figure 8, revealing a range of H values between 0.4 and 0.92. Among the 29 stations investigated, 28 stations exhibit H values falling within the range of 0.6 to 0.92. However, a single station (Kedougou, ID:1) shows an H value ranging from 0.4 to 0.5. Thus, except for the Kedougou station, the AMDSL demonstrates persistent behavior at all other stations, implying that future AMDSL trends are likely to resemble the present values. Nevertheless, the degree of persistence varies among stations, with some classified as exhibiting weak persistence (0.6 < H ≤ 0.7) and others classified as displaying strong persistence (0.7 < H ≤ 0.92). Specifically, out of the stations analyzed, 21 stations exhibit strong persistence, while 7 stations exhibit weak persistence. The identified persistent behavior in the Senegalese AMDSL aligns with previous studies by Wang et al. [79] in China (investigating the longest consecutive dry day in the dry season) and Lana et al. [38] in the Iberian Peninsula (exploring daily rainfall and dry spell series).

3.4. Lacunarity Analysis of AMDSLs

In this section, we analyze the lacunarity of the AMDSL at different thresholds. Figure 9 illustrates the spatial distribution of the lacunarity exponent β for various AMDSL thresholds. In Figure 9a, focusing on the 10-day/year threshold, stations in the extreme northern part of the country show β values near zero, indicating that all AMDSL values exceed this threshold. This suggests that agricultural production in this region may be more severely impacted by prolonged dry spells compared to other regions. Previous studies [80,81,82,83] emphasized the negative consequences of dry spells lasting more than 10 days during the rainy season on crop production.

Lower absolute values of β are observed in the northern, central northern, and central southern zones, with a particular emphasis on the northern and central northern regions. This indicates that the northern and central northern regions have a higher rate of variability in AMDSL values exceeding 10 days/year, resulting in a more diverse pattern of dry spells. On the other hand, the southern region exhibits the greatest reduction in lacunarity, suggesting a more uniform distribution of AMDSL values exceeding 10 days/year.

Figure 9b reveals a noticeable north–south gradient in the absolute values of β for the AMDSL threshold of 15 days/year. The lacunarity analysis shows high values still detected in the southern region. Moving on to the AMDSL thresholds of 20 (Figure 9c) and 25 (Figure 9d) days/year, it is observed that all AMDSL values obtained from stations in the southern part of the country consistently fall below 20 and 25 days, respectively. The north–south gradient in the absolute values of β remains evident, seemingly associated with rainfall patterns.

Overall, regardless of the considered thresholds, the rate of variability in the AMDSL values decreases significantly from the north to the south of Senegal. The northern and central northern regions exhibit a wide range of AMDSL values, indicating diverse dry spell patterns, while the central southern and southern regions display a more uniform distribution of AMDSL values for the considered thresholds. These findings align with previous studies [25,27,40,41] highlighting a stronger cumulative rainfall gradient from north to south in the country. Additionally, they are consistent with the spatial distribution of drought reported by Ndiaye et al. [29]. Therefore, the lacunarity exponent β proves to be useful in distinguishing different drought regimes across various regions.

4. Conclusions

This study investigated the behavior of AMDSLs during the rainy season in Senegal using daily precipitation data from 29 stations recorded between 1951 and 2010. The findings of this study are as follows:

Firstly, we observed a spatial gradient in the lacunarity exponent β, showing higher values in the northern regions compared to the southern regions. These values were associated with the rainfall regime and can help distinguish different drought regimes.

Secondly, we identified five significant intrinsic mode functions (IMFs) operating at different time scales and a nonlinear trend governing the overall variability in the AMDSL. IMF1 contributed the most to the variance in the AMDSL, followed by IMF2 and the overall trend. This suggests that IMF1 is the dominant component of the AMDSL variability, but the trend component also plays a significant role.

Thirdly, we found interannual, interdecadal, and multidecadal scale oscillations in the changes in the AMDSL. Interannual oscillations, particularly the 3-year quasi-periodic oscillation, contributed the most to the variability in the AMDSL.

Fourthly, we identified four morphological types of nonlinear trends in AMDSL variations. The increasing–decreasing type was the most prevalent, followed by the increasing trend. Linear trend methods may not accurately capture the characteristics of drought indices in Senegal due to the nonlinear behavior of the AMDSL.

Lastly, we observed a general persistence of the AMDSL in Senegal, with varying degrees among stations. Most stations exhibited strong persistence, while a few showed weak persistence or anti-persistence behavior.

Overall, this study provides valuable insights into the nonlinear trends, periodic characteristics, long-term memory, intrinsic mode functions, and lacunarity of the AMDSL in Senegal. The findings have implications for policy making and the validation of climate models. Future research could focus on extending the study to cover a longer period and a wider geographical area, as well as developing predictive models using machine learning techniques to enhance drought management and mitigation strategies in Senegal.