Drought Quantification in Africa Using Remote Sensing, Gaussian Kernel, and Machine Learning

Abstract

Effective drought management requires precise measurement, but this is challenging due to the variety of drought indices and indicators, each with unique methods and specific uses, and limited ground data availability. This study utilizes remote sensing data from 2001 to 2020 to compute drought indices categorized as meteorological, agricultural, and hydrological. A Gaussian kernel convolves these indices into a denoised, multi-band composite image. Further refinement with a Gaussian kernel enhances a single drought index from each category: Reconnaissance Drought Index (RDI), Soil Moisture Agricultural Drought Index (SMADI), and Streamflow Drought Index (SDI). The enhanced index, encompassing all bands, serves as a predictor for classification and regression tree (CART), support vector machine (SVM), and random forest (RF) machine learning models, further improving the three indices. CART demonstrated the highest accuracy and error minimization across all drought categories, with root mean square error (RMSE) and mean absolute error (MAE) values between 0 and 0.4. RF ranked second, while SVM, though less reliable, achieved values below 0.7. The results show persistent drought in the Sahel, North Africa, and southwestern Africa, with meteorological drought affecting 30% of Africa, agricultural drought affecting 22%, and hydrological drought affecting 21%.

1. Introduction

Drought is a persistent natural phenomenon characterized by extended periods of scant precipitation, which exerts detrimental effects on soil moisture, humidity, and temperature, culminating in reduced water availability within hydrological systems, and this combination has a parching effect on vegetation [1,2]. This phenomenon is evident in regions of West and North Africa, particularly with recurring droughts in the Sahel, Sahara, and surrounding areas between 2001 and 2020 [3]. In southern Africa, severe droughts occurred between 2015 and 2018, notably in South Africa’s Western Cape, where dam levels fell by 20%, and lake levels in Botswana and Zambia were also impacted [4,5].

Owing to their protracted nature, droughts rank among the most detrimental natural disasters, inflicting enduring environmental and socio-economic ramifications [6,7]. For communities reliant on natural weather patterns for sustenance, drought can pose regressive challenges, underscoring the urgency of thorough drought investigation and the development of advanced detection methods to enhance preparedness and resilience strategies [6].

Drought, as a physical phenomenon, is based on three classifications: meteorological, linked to reduced precipitation; agricultural, marked by declining soil moisture; and hydrological, arising from diminished water supply in streams and other water bodies, offering a clear framework for understanding and guiding spatial and temporal assessment [8,9].

Although prior studies have primarily concentrated on specific African regions, such as southern Africa, East Africa, or individual nations, a comprehensive assessment of agricultural, meteorological, and hydrological drought across the entire African continent remains conspicuously limited [10,11,12,13]. This study delves into an extensive examination of meteorological, agricultural, and hydrological drought phenomena across the entire continent.

Diverse drought indices and indicators have been systematically calculated and applied within their respective drought classification categories. These distinct metrics exhibit inherent strengths and weaknesses, collectively enhancing their relevance and efficacy in the scientific examination of drought occurrences [14]. A universal framework for the comprehensive study of drought remains elusive due to the intricate nature of spatial and temporal modeling associated with this phenomenon. Consequently, it is imperative to employ a diverse array of indicators to investigate drought within its three distinct physical classifications [15]. Unlike prior studies, which primarily used drought indicators and indices for comparison or concentrated on improving individual components of these indices, this study seeks to enhance an entire index by incorporating insights from other drought indices within the same drought classification category [16,17].

This study employs six meteorological drought indices, focusing on refining the Reconnaissance Drought Index (RDI) for precision in meteorological drought mapping. The RDI is well-suited for Africa due to its sensitivity, adaptability to different climatic conditions, and accurate representation of water balance deficits [18]. Moreover, its adaptability to compute values across various temporal scales aligns with the study’s 12-month timeframe [19]. Recent research has highlighted its effectiveness in meteorological drought assessment, reinforcing its superiority over alternative indices [20]. Eight agricultural drought indices are used in this study, with an emphasis on the Soil Moisture Agricultural Drought Index (SMADI). SMADI stands out as a comprehensive index that incorporates multiple indices and indicators, distinguishing it from other agricultural drought indices [21]. Research findings have consistently validated SMADI as a highly accurate drought indicator, making it a logical choice for this study [22]. Finally, four drought indices are employed to investigate hydrological drought with attention to the Streamflow Drought Index (SDI). SDI has been found to accurately represent hydrological drought over a 12-month period, which is appropriate for this study [23,24].

This study deals with extensive spatial and temporal data, resulting in numerous missing pixel data points across various indicator and index maps [25]. This substantial data gap poses a significant challenge when attempting to aggregate indicators for each drought classification. To address this issue, a Gaussian kernel is employed to convolve and amalgamate the diverse indices and indicators, effectively filling in the missing pixel data and producing a denoised composite image [26]. The process is repeated where the Gaussian kernel is used to convolve a singular drought index with the denoised composite image, yielding a refined drought index that is seamlessly smoothed with the pre-existing indices [27].

This improved Gaussian image serves as the predictor variable to train three machine learning models, namely classification and regression trees (CART), support vector machine (SVM), and random forest (RF), to further refine the single drought index. Prior studies on drought have employed machine learning methods but lacked a notably superior training product utilizing Gaussian kernel-based composite images. Furthermore, using three different machine learning models broadens the scope for an improved drought index [28,29]. This distinguishes the study, not only in Africa but also from any previous work done.

Across the African continent, the scarcity of reliable ground-based hydro-meteorological data arises from a complex interplay of political, social, and economic factors [30]. This dearth of data poses significant challenges for accurate drought investigation. The study addresses this gap by developing innovative methodologies that leverage satellite data to accurately investigate drought in Africa. The objectives of this study are: (1) to compute different drought indices and indicators for meteorological, agricultural, and hydrological drought; (2) to employ the Gaussian kernel to produce an enhanced singular drought index smoothed with other indices and indicators of the same physical classification; (3) to deploy three machine learning models, specifically CART, SVM, and RF, to further improve the enhanced singular drought index; and (4) to compare the accuracy of the machine learning models in predicting a drought index. An enhanced singular drought index refers to an individual index for each drought classification category that has been improved with this study’s unique methodology. We enhanced the RDI for meteorological, SMADI for agricultural, and SDI for hydrological droughts to improve quantification accuracy. The study advanced beyond current approaches that typically enhance a single index without accounting for related indices within the same drought classification category. Additionally, it utilized the Gaussian kernel and its output as predictor variables in machine learning models to further refine the index, leading to improved accuracy [31,32]. The study introduces innovative methods for accurately investigating droughts, eliminating the need for ground-based data, which are inadequate in Africa [33]. This comprehensive assessment covers all physical drought classifications, enabling enhanced intra-and inter-governmental planning for improved water storage, conservation, and the technical diversion of water for hydropower and irrigation. This approach is also transferable to other large, diverse climate regions.

2. Materials and Methods

2.1. Study Area

Africa comprises 54 countries with diverse topography and elevation (Figure 1). It spans the equator, straddling both the northern and southern hemispheres, resulting in a wide range of climates under the Köppen–Geiger classification: A (tropical), B (arid), C (temperate), D (continental), and E (polar) [34]. This diversity is exemplified by year-round snow-capped peaks like Mount Kilimanjaro and juxtaposed by extremely dry areas like the Sahara Desert [35]. Africa covers 33.5 million square kilometers and has a population of about 1.2 billion people [36]. Africa has 8% cropland and 26% forest with the dominant cropland being maize, wheat, soybean, sugarcane, cassava, and wheat (Figure 1) [37].

2.2. Dataset

Table 1. Datasets utilized in the study and their characteristics.

Product	Variables	Spatiotemporal Resolution	Reference
CHIRPS IMERG-Final version “06”	Rainfall Rainfall	0.05° × 0.05° (daily) 0.1° × 0.1° (monthly)	Arregocés et al. [38] Aksu et al. [39]
FLDAS FLDAS	Evapotranspiration Soil moisture	0.1° × 0.1° (monthly) 0.1° × 0.1° (monthly)	McNally et al. [40] Jung et al. [41]
MOD17A2H V6	GPP	0.005° × 0.005° (8 day)	Shirkey et al. [42]
MOD13A2 V6.1	NDVI	0.01° × 0.01° (16 day)	Bari et al. [43]
ERA5	Air temperature	0.25° × 0.25° (monthly)	Gomis-Cebolla et al. [44]
MOD11A2 V6.1	Land surface temp	0.01° × 0.01° (8 day)	Li et al. [45]
MOD16A2 Version 6.1	PET, ET	0.004° × 0.004° (8 day)	Qiao et al. [46]
TerraClimate	PDSI	0.04° × 0.04° (monthly)	Liu et al. [47]
MOD09A1 V6.1	Surface reflectance	0.001° × 0.001° (8 day)	Ma & Liang [48]
SRTM digital elevation data v4	DEM	0.0008° × 0.0008°	Dong et al. [49]
SPEIbase	SPEI	0.5° × 0.5° (monthly)	Das et al. [50]
USDA system	Soil texture	0.002° × 0.002° (yearly)	Corral-Pazos-de-Provens et al. [51]
MCD12Q1 V6.1 product	Land cover	0.004° × 0.004° (yearly)	Chirachawala et al. [37]

provides an overview of the datasets used in the study, detailing their variables, spatio-temporal resolutions, and references, all accessible via Google Earth Engine (GEE).

The Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS) provides rainfall data from 1981 to present, integrating satellite fields, gridded physiographic indicators, and in situ weather station data at 0.05° resolution. The Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG) covers 2000 to 2021, offering precipitation data from various satellites. The Famine Early Warning Systems Network (FEWS NET) Land Data Assimilation System (FLDAS) has operated since 1982, combining MERRA-2 and CHIRPS data for evapotranspiration and soil moisture.

MODIS products include gross primary productivity (GPP) and net photosynthesis (PSN) from 2000, vegetation indices (normalized difference vegetation index, NDVI) from 2000, land surface temperature from 2000, and evapotranspiration data from 2001. The European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis 5 (ERA5) spans 1979 to present, providing a consistent global dataset. TerraClimate offers the Palmer Drought Severity Index (PDSI), soil moisture, and potential evapotranspiration (PET) from 1958.

The MODIS Terra MOD09A1 provides surface spectral reflectance, while the Shuttle Radar Topography Mission (SRTM) digital elevation model from 2000 offers high-quality elevation data. The Global Standardized Precipitation–Evapotranspiration Index (SPEIbase) covers 1901 to 2021, and USDA soil texture classes data are available from 1950 to 2018. The MODIS Land Cover Type product covers 2001 to 2022.

All datasets were standardized to a 0.05° × 0.05° (monthly) resolution before export from Google Earth Engine, with FLDAS and IMERG data downscaled from 0.1° to 0.05°.

The datasets utilized in this study are reliable and robust, given their extensive temporal coverage and high spatial resolution. Sources like CHIRPS, IMERG, and MODIS are known for their accuracy. Combining data from FLDAS, ECMWF ERA5, and TerraClimate further enhances reliability. Standardizing all data to a 0.05° × 0.05° resolution ensures consistency and precision, making the dataset dependable for drought analysis.

2.3. Methodology

The methodology used in this study is as follows: (1) Key drought indicators and their trend over a 20-year period from 2001 to 2020 are examined as independent variables. (2) Drought index maps are created with drought indices dependent on drought indicators, categorized into meteorological, agricultural, and hydrological drought classifications. Each drought category is then treated individually within the methodology, ensuring separate computation for meteorological, agricultural, and hydrological drought, all utilizing the same procedural framework. (3) A Gaussian kernel is applied to index and indicator variables to generate a denoised composite drought map. (4). A Gaussian kernel is applied a second time to smooth a single drought index with the composite drought map to produce an improved drought index. (5) This new smoothed index is used as a predictor variable in training three machine learning models, aimed at predicting an even more improved drought index. (6) Random forest is employed to rank the importance of variables used in producing the predicted drought maps. (7) Accuracy assessment is carried out to assess the model performance using two evaluation parameters. The methodology design is shown in Figure 2.

Several machine learning models were considered for this study. However, after conducting an extensive literature review on machine learning in drought-related research, big data spatial analysis, and JavaScript applications in Google Earth Engine, we determined that CART, SVM, and RF were the most suitable for our objectives. The focus of the research is not to use as many machine learning models as possible, but rather to demonstrate a novel approach for accurately quantifying drought using remote sensing, the Gaussian kernel, and machine learning. Therefore, these three models align well with our research goals. Nevertheless, testing additional machine learning models with more advanced tools for big data in remote sensing is a valuable direction for future research.

Additionally, although other denoising techniques were considered, only the Gaussian kernel was ultimately used. This decision was driven by its computational efficiency and strong support in Google Earth Engine when working with large spatial datasets using JavaScript (ES5). Even with complex scripts, the Gaussian kernel’s processing times rarely exceeded 4 h, while other methods like principal component analysis and wavelet approaches often crashed or took more than 10 h to run, with a high risk of failure even then. Gaussian kernel smooths high-frequency noise, which is often caused by factors such as sensor errors, atmospheric interference, or environmental conditions that result in pixel-level irregularities, like sudden changes from light to dark between neighboring pixels. These irregularities can obscure meaningful spatial patterns, such as those related to drought. The Gaussian kernel minimizes this noise without distorting the underlying signal, ensuring the creation of accurate composite maps of drought conditions. Additionally, the kernel’s bandwidth can be easily adjusted, providing flexibility for different spatial resolutions in drought mapping. These characteristics, combined with its efficiency and accuracy in processing remote sensing data within Google Earth Engine, made it the optimal choice for this study.

2.3.1. Key Drought Indicators and Indices and Their Trends

To understand the drought conditions in Africa for a 20-year period from 2001 to 2020, it is important to understand the environment first. Eight environmental variables and their trends were computed and mapped through a spatial–temporal aggregation and visualization process in Google Earth Engine, including: rainfall, evapotranspiration (ET), gross primary productivity (GPP), normalized difference vegetation index (NDVI), air temperature (Ta), land surface temperature (LST), and soil moisture at 0–10 cm and 10–40 cm depth. These variables also double as key drought indicators, some of which are used in the subsequent methodological processes as independent variables to compute drought indices. Figure 3 displays the maps for each of the variables and the corresponding maps of Kendall’s Tau-b rank correlation showing the 20-year trend. Kendall’s Tau (τ) is represented by the formula:

$$\tau ={\displaystyle \frac{2\left(n_c-n_d\right)}{n(n-1)}}$$

(1)

where $n$ denotes the duration of the various parameter/variable time series, which spans 20 years in this study, $n_c$ is the number of concordant pairs, and $n_d$ represents discordant pairs. A positive τ value within the range of 0 to 1 is indicative of an ascending trend, while a negative τ value within the range of −1 to 0 signifies a declining trend [52].

2.3.2. Drought Influencing Indicators and Drought Indices Used in the Study

Eight agricultural, six meteorological, and three hydrological drought indices were calculated and mapped. Five indicators (environmental factors) that affect the spatial distribution of drought were also mapped. Slope and elevation are indicators derived from the SRTM product (Table 1), where slope is based on the terrain and elevation is represented by:

$$E(z)={\displaystyle \frac{1}{2}}\left({\displaystyle \frac{{\partial }^{2}E(z)}{\partial x^2}}\right)x^2+{\displaystyle \frac{1}{2}}\left({\displaystyle \frac{{\partial }^{2}E(z)}{\partial y^2}}\right)y^2+\left({\displaystyle \frac{{\partial }^{2}E(z)}{\partial x\partial y}}\right)xy+\left({\displaystyle \frac{\partial E(z)}{\partial x}}\right)x+\left({\displaystyle \frac{\partial E(z)}{\partial y}}\right)y+u$$

(2)

where x, y are geographical coordinates in degrees and u denotes the residual term. Slope is represented by:

$$\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}(\mathrm{G})=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\sqrt{{\mathrm{p}}^2+{\mathrm{q}}^2}$$

(3)

Safanelli et al. [53] explain the formulas in detail and their application in Google Earth Engine. The precipitation indicator is the principal instigator of drought conditions; however, other factors such as evapotranspiration and soil moisture enhance drought [54]. Precipitation data relied on the CHIRPS product, while evapotranspiration and soil moisture were derived from the FLDAS product (Table 1). Subsequently, computations were performed using Google Earth Engine (GEE) to obtain the annual average for each variable.

Drought indices are used to analyze different drought types.

Table 2. Drought indices used in the study for meteorological, agricultural, and hydrological drought.

Drought Index	Full Name	Formula	Reference
Meteorological Drought Indices
PDSI	Palmer Drought Severity Index	$\mathrm{P}\mathrm{D}\mathrm{S}\mathrm{I}(\mathrm{i})=0.897\mathrm{P}\mathrm{D}\mathrm{S}\mathrm{I}(\mathrm{i}-1)+{\displaystyle \frac{\mathrm{Z}(\mathrm{i})}{3}}$	Palmer [55]
SPI	Standardized Precipitation Index	$\mathrm{S}\mathrm{P}\mathrm{I}={\displaystyle \frac{(\mathrm{P}\mathrm{R}\mathrm{E}-\overline{\mathrm{P}\mathrm{R}\mathrm{E}})}{{\sigma }_{\mathrm{P}\mathrm{R}\mathrm{E}}}}$	McKee et al. [56]
SPEI	Standardized Precipitation Evapotranspiration Index	$\mathrm{S}\mathrm{P}\mathrm{E}\mathrm{I}=\mathrm{W}-{\displaystyle \frac{{\mathrm{c}}_0+{\mathrm{c}}_1\mathrm{w}+{\mathrm{c}}_2{\mathrm{w}}^2}{1+{\mathrm{d}}_1\mathrm{w}+{\mathrm{d}}_2{\mathrm{w}}^2+{\mathrm{d}}_3{\mathrm{w}}^3}}$	Vicente-Serrano et al. [57]
RDI	Reconnaissance drought index	${\mathrm{R}\mathrm{D}\mathrm{I}}_{\mathrm{s}\mathrm{t}(\mathrm{k})}^{(\mathrm{i})}={\displaystyle \frac{{\mathrm{y}}_{\mathrm{k}}^{(\mathrm{i})}-{\overline{\mathrm{y}}}_{\mathrm{k}}}{{\widehat{\mathsf{\sigma }}}_{\mathrm{y}\mathrm{k}}}}$	Tsakiris et al. [18]
MIDI	Microwave Integrated Drought Index	$\mathsf{\alpha }\times \mathrm{P}\mathrm{C}\mathrm{I}+\mathsf{\beta }\times \mathrm{S}\mathrm{M}\mathrm{C}\mathrm{I}+(1-\mathsf{\alpha }-\mathsf{\beta })\times \mathrm{T}\mathrm{C}\mathrm{I}$	Zhang et al. [58]
OMDI	Optimized Meteorological Drought Index	$\mathsf{\alpha }\times \mathrm{T}\mathrm{C}\mathrm{I}+\mathsf{\beta }\times \mathrm{P}\mathrm{C}\mathrm{I}+(1-\mathsf{\alpha }-\mathsf{\beta })\times \mathrm{S}\mathrm{M}\mathrm{C}\mathrm{I}$	Hao et al. [59]
Agricultural Drought Indices
NDDI	Normalized Difference Drought Index	$(\mathrm{NDVI}-\mathrm{NDWI})/(\mathrm{NDVI}+\mathrm{NDWI})$	Gu et al. [60]
VHI	Vegetation Health Index	$\mathsf{\alpha }\times \mathrm{V}\mathrm{C}\mathrm{I}+(1-\mathsf{\alpha })\times \mathrm{T}\mathrm{C}\mathrm{I}$	Kogan [61]
SMDI	Soil Moisture Deficit Index	${\mathrm{S}\mathrm{M}\mathrm{D}\mathrm{I}}_{\mathrm{j}}=0.5{\mathrm{S}\mathrm{M}\mathrm{D}\mathrm{I}}_{\mathrm{j}-1}+{\displaystyle \frac{{\mathrm{S}\mathrm{D}}_{\mathrm{j}}}{50}}$	Narasimhan and Srinivasan [62]
ETDI	Evapotranspiration Deficit Index	$\mathrm{E}\mathrm{T}\mathrm{D}{\mathrm{I}}_{\mathrm{j}}=0.5\mathrm{E}\mathrm{T}\mathrm{D}{\mathrm{I}}_{\mathrm{j}-1}+{\displaystyle \frac{\mathrm{W}\mathrm{S}{\mathrm{A}}_{\mathrm{j}}}{50}}$	Narasimhan and Srinivasan [62]
CMI	Crop Moisture Index	$\mathrm{C}\mathrm{M}\mathrm{I}={\mathrm{Y}}_i+{\mathrm{G}}_i$ $\mathrm{Y}=\mathrm{E}\mathrm{v}\mathrm{a}\mathrm{p}\mathrm{o}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{a}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{y} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}$ $\mathrm{G}=\mathrm{e}\mathrm{x}\mathrm{c}\mathrm{e}\mathrm{s}\mathrm{s} \mathrm{m}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}$	Palmer [55]
SMADI	Soil Moisture Agricultural Drought Index	$\mathrm{S}\mathrm{M}\mathrm{A}\mathrm{D}{\mathrm{I}}_{\mathrm{i}}=\mathrm{S}\mathrm{M}\mathrm{C}{\mathrm{I}}_{\mathrm{i}}{\displaystyle \frac{\mathrm{M}\mathrm{T}\mathrm{C}{\mathrm{I}}_{\mathrm{i}}}{\mathrm{V}\mathrm{C}{\mathrm{I}}_{\mathrm{i}+1}}}$	Sánchez et al. [63]
NMDI	Normalized Multiband Drought Index	$\mathrm{N}\mathrm{M}\mathrm{D}\mathrm{I}={\displaystyle \frac{{\mathrm{R}}_{860\mathrm{n}\mathrm{m}}-\left({\mathrm{R}}_{1640\mathrm{n}\mathrm{m}}-{\mathrm{R}}_{2130\mathrm{n}\mathrm{m}}\right)}{{\mathrm{R}}_{860\mathrm{n}\mathrm{m}}+\left({\mathrm{R}}_{1640\mathrm{n}\mathrm{m}}-{\mathrm{R}}_{2130\mathrm{n}\mathrm{m}}\right)}}$	Wang and Qu [64]
SDCI	Scaled Drought Condition Index	$\mathrm{S}\mathrm{D}\mathrm{C}\mathrm{I}=0.25\times \mathrm{V}\mathrm{C}\mathrm{I}+0.25\times \mathrm{T}\mathrm{C}\mathrm{I}+0.5\times \mathrm{P}\mathrm{C}\mathrm{I}$	Rhee et al. [65]
Hydrological Drought Indices
SDI	Stream flow Drought Index	$\mathrm{S}\mathrm{D}{\mathrm{I}}_{\mathrm{i},\mathrm{k}}={\displaystyle \frac{{\mathrm{V}}_{\mathrm{i},\mathrm{k}}-{\overline{\mathrm{V}}}_{\mathrm{k}}}{{\mathrm{S}}_{\mathrm{k}}}}$	Nalbantis and Tsakiris [66]
PHDI	Palmer Hydrological Drought Index	${\mathrm{P}\mathrm{H}\mathrm{D}\mathrm{I}}_{\mathrm{i}}=0.897{\mathrm{P}\mathrm{H}\mathrm{D}\mathrm{I}}_{\mathrm{i}-1}+\left({\mathrm{Z}}_{\mathrm{i}}/3\right)$ ${\mathrm{P}\mathrm{e}}_{\mathrm{i}}={\displaystyle \frac{\sum _{\mathrm{j}=0}^{\mathrm{j}={\mathrm{j}}^{\mathrm{*}}}{\mathrm{U}}_{\mathrm{i}-\mathrm{j}}}{{\mathrm{Z}}_{\mathrm{e}}+\sum _{\mathrm{j}=1}^{\mathrm{j}={\mathrm{j}}^{\mathrm{*}}}{\mathrm{U}}_{\mathrm{i}-\mathrm{j}}}}\times 100 \mathrm{percent}$ $\mathrm{For} \mathrm{PHDI}, \mathrm{drought} \mathrm{ends} \mathrm{when} {\mathrm{P}}_{\mathrm{e}}=1$ $\mathrm{For} \mathrm{PDSI}, \mathrm{drought} \mathrm{ends} \mathrm{when} {\mathrm{P}}_{\mathrm{e}}\ge 0\le 1$ PDSI, Palmer Drought Severity Index	Palmer [55]
SHDI	Standardized Hydrological Drought index	$\mathrm{S}\mathrm{H}\mathrm{D}\mathrm{I}={\displaystyle \frac{\mathrm{l}\mathrm{o}\mathrm{g}(\mathrm{x})-\mathsf{\mu }}{\mathsf{\sigma }}}$	Dehghani et al. [67]

categorizes these indices under three classifications with their formulae and references. These indices are computed and mapped in GEE.

2.3.3. Blending Drought Indices and Indicators Using the Gaussian Kernel

Merging various indices and indicators by drought classification (meteorological, agricultural, hydrological) provides a holistic drought representation. This blending uses a Gaussian kernel, computing a weighted average within the pixel neighborhood, where closer pixels have more influence. This method ensures that linear features and boundaries remain sharp and intact during the blending process. The Gaussian kernel convolution process of images involves [68]:

$$g[i,j]=\sum _{m=1}^M\sum _{n=1}^{N}f[m,n]h[i-m,j-n]$$

(4)

where $f\left[m,n\right]$ is the input image pixel location, $h\left[i,j\right]$ is the kernel, and $g\left[i,j\right]$ is the output image. The 2D Gaussian kernel is defined as:

$$n_{\sigma }\left[i,j\right]={\displaystyle \frac{1}{2\pi {\sigma }^2}}{e}^{-{\displaystyle \frac{1}{2}}\left({\displaystyle \frac{i^2+j^2}{{\sigma }^2}}\right)}$$

(5)

The radius of the Gaussian kernel, $r$, can be found using:

$$\mathrm{r}=\sqrt{-2{\mathsf{\sigma }}^2\ln \left(\mathsf{ϵ}\cdot 2\mathsf{\pi }{\mathsf{\sigma }}^2\right)}$$

(6)

where $ϵ$ is a minimal weight parameter. This ensures the Gaussian kernel’s effective radius encompasses the significant pixel influences, maintaining image detail and feature integrity. In GEE for this study,$ϵ=0.01$, $\sigma =2,$ and $r$ = 3 were used.

2.3.4. Machine Learning Models

Breiman [69] developed the random forest (RF) to address bias and overfitting in decision trees using an ensemble approach. RFs predict outcomes in regression and classify data using multiple decision trees. For classification, they use majority voting; for regression, they average individual tree predictions. Increasing the number of trees enhances accuracy but also raises memory usage and computation time, making the number of trees a critical parameter. Optimal results in this study were achieved with 10 trees. Bagging, which involves creating multiple datasets from the original dataset and averaging classifiers, underpins RFs:

$$h\left(x\right)={\displaystyle \frac{1}{m}}\sum _{\mathrm{j}=1}^m{h}_j\left(x\right)$$

(7)

where $h(x)$ is a classifier representing the final prediction made by the RF for an input $x$, and $h_j(x)$ represents the prediction made by the $j$-th individual decision tree in the RF for the input $x$.

RFs enhance this by training decision trees on random subsets of $k$ features, typically $k=\sqrt{d}$ (hyperparameter), to balance information capture and reduce feature relation. RFs estimate test error using out-of-bag error (${\epsilon }_{OOB})$, which averages the error for data points excluded from training subsets:

$${\epsilon }_{OOB}={\displaystyle \frac{1}{n}}\sum _{i=1}^n{\displaystyle \frac{1}{Z_i}}\sum _{j=1}l\left(h_j\left(x_i\right),y_i\right)$$

(8)

where $Z_i$ is the count of classifiers not trained on $\left(x_i,y_i\right)$ and $l\left(h_j\left(x_i\right),y_i\right)$ is the loss function that measures the difference between the predicted value $h_j\left(x_i\right)$ and the true value $y_i$. RF was also used to rank feature importance.

Support Vector Machines (SVMs), invented by Vapnik and Cortes [70], are supervised machine learning algorithms used for classification and regression, particularly effective for high-dimensional data. The main objective of SVM is to find a hyperplane that maximizes the margin $(\mathsf{\gamma })$, the distance between the hyperplane and the nearest data points of different classes, known as support vectors. SVMs use a regularization parameter $C$ to control the trade-off between a wide margin and misclassifications [71]. For linearly separable data, the hyperplane $H_{w,b}$ is defined as:

$$H_{w,b}=\{x:w^{T}x+b=0\}$$

(9)

where $w$ is the weight vector determining the orientation, and $b$ is the bias term representing the offset from the origin. The distance of a point $x$ from the hyperplane is given by:

$$\parallel d{\parallel }_2={\displaystyle \frac{w^{\mathrm{\top }}x+b}{\parallel w{\parallel }_2}}$$

(10)

To maximize the margin, we minimize $\parallel w{\parallel }_2$ subject to the constraint: $y_i\left(w^{\mathrm{\top }}{x}_i+b\right)\ge 1$. In practice, data might not be perfectly separable, so slack variables ${\xi }_i$ are introduced to allow for some misclassification:

$${\mathrm{m}\mathrm{i}\mathrm{n}}_{w,b}\parallel w{\parallel }_2^2+C{\sum }_{i=1}^n{\xi }_i \mathrm{s}.\mathrm{t}. y_i\left(w^T{x}_i+b\right)\ge 1-{\xi }_i,{\xi }_i\ge 0$$

(11)

This forms the SVM with soft constraints, balancing the margin maximization and classification errors. The loss function incorporating slack variables is:

$${\xi }_i=\mathrm{m}\mathrm{a}\mathrm{x}\left(\mathrm{0,1}-y_i\left(w^T{x}_i+b\right)\right)$$

(12)

In summary, SVM aims to find a hyperplane that maximizes the margin while minimizing misclassification, utilizing regularization to avoid overfitting.

Classification And Regression Trees (CART) are decision tree algorithms for classification and regression, developed by Leo Breiman [72]. A CART model is a binary tree, with nodes representing decisions based on feature values, built by recursively splitting the data. The objective is to create pure leaves where all points share the same label, using impurity functions to measure purity. In classification, common impurity functions include Gini impurity and entropy. For a dataset $S$ with $n$ data points, Gini impurity is defined as:

$$\mathrm{G}(S)={\sum }_{k=1}^K{P}_k\left(1-P_k\right)$$

(13)

where $P_k$ is the probability of a point belonging to class $k$ [73]. Entropy measures disorder, defined as:

$$H(S)=-{\sum }_{k=1}^K{P}_k\mathrm{l}\mathrm{o}\mathrm{g}\left(P_k\right)$$

(14)

where $P_k$ is the probability of class $k$ [74]. For regression, CART uses the square loss function:

$$L(S)={\displaystyle \frac{1}{\left|s\right|}}{\sum }_{(x,y)\in S}(y-\mu {)}^2$$

(15)

where $\mu$ is the mean of $y$ values in $S$. To find the optimal split, CART evaluates all possible splits to minimize the impurity of the resulting nodes. The computational complexity of this process is represented in Big $O$ notation as $O\left(DK{N}^2\right)$. This denotes the amount of work required to find an optimal split in the CART algorithm, where $D$ is the number of dimensions, $K$ is the number of classes, and $N$ is the number of data points. Optimized implementations reduce this complexity to $O(DKN)$ [75]. In summary, CART aims to split data into pure leaves, using impurity functions to guide the splitting process. The algorithm balances complexity and performance, ensuring efficient and accurate decision tree construction.

2.3.5. Model Performance

The performance of the machine learning models was evaluated using root mean square error (RMSE) and mean absolute error (MAE). Each metric provided unique insights into model proficiency. RMSE is the square root of the average of squared differences between predicted and actual values [76]:

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(y_i-{\hat{y}}_i\right)}^2}$$

(16)

MAE is the average of absolute differences between predicted and actual values:

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|y_i-{\hat{y}}_i\right|$$

(17)

RMSE is useful when large errors need to be penalized more heavily, while MAE provides a balanced view by treating all errors equally. Evaluating multiple metrics offers a comprehensive understanding of model performance, aiding in the selection and improvement of SVM, CART, and RF models [77].

2.3.6. Model Parameter Settings and Validation

The parameters for RF model included the number of trees (10), the mode of operation (regression), input features (drought indices and indicators), and training data sampling. The effectiveness of these parameter settings was validated using standard regression metrics, specifically RMSE and MAE. The validation process involved comparing the model’s predictions with observed values at independent validation points. To ensure robust performance testing on unseen data, the validation dataset was generated separately from the training set. A total of 100 random points were sampled across Africa, and both the predicted and actual index values were extracted for comparison. Seed values were applied for consistency in sampling, and a tile scale of 16 was used to improve computational efficiency. Further parameter tuning, such as increasing the number of trees or incorporating additional input features, remains a potential avenue for improving model performance.

For the SVM model, the parameters included the SVM type (NU_SVR for regression), cost (1.0), and nu (0.5), along with input features (drought indices and indicators) and training data sampling. The model was configured for regression, making it suitable for predicting continuous values such as the drought indices (RDI, SMADI, and SDI). Validation of parameters was done in the same way as explained with RF. Further tuning of SVM parameters, such as adjusting the cost or nu values or incorporating additional features, could enhance the model’s performance.

For the CART model, the parameters included the maximum number of trees (10), mode of operation (regression), input features (drought indices and indicators), and training data sampling. The CART model was configured for regression to predict continuous values, such as the drought indices. The validation of these parameter settings was conducted in the same way as RF and SVM. Further tuning of the CART model, such as adjusting tree depth or incorporating additional input features, could improve model performance.

In addition to the model configurations and validation using standard metrics, the approach leverages Google Earth Engine for efficient processing of large-scale spatial data across Africa. Using various Earth observation data enabled detailed drought index computations. Denoising with a Gaussian kernel improves input data quality and enhances model accuracy. The methodology’s flexibility allows for further parameter tuning and feature integration, offering potential for future model refinement.

3. Results

3.1. Performance Evaluation

In Figure 4a, CART shows the best performance, with RMSE values ranging from 0.08 to 0.3 and MAE values from 0.05 to 0.25. SVM follows, with RMSE values between 0.18 and 0.5 and MAE between 0.15 and 0.45. RF has the highest errors, with RMSE from 0.28 to 0.6 and MAE from 0.25 to 0.55, indicating CART as the most proficient model, followed by SVM and RF.

Figure 4b shows that CART consistently achieves the lowest errors (RMSE: 0.02–0.05, MAE: 0.01–0.03). RF ranks second (RMSE: 0.03–0.06, MAE: 0.02–0.04), while SVM shows the highest errors (RMSE: 0.10–0.40, MAE: 0.04–0.16), indicating CART’s superior accuracy.

Considering Figure 4c, CART yields mean values of 0.202 (RMSE) and 0.154 (MAE). RF shows slightly higher errors, with 0.235 (RMSE) and 0.185 (MAE). SVM has the highest mean error values: 0.276 (RMSE) and 0.22 (MAE), reinforcing CART’s superior predictive accuracy.

Thus CART consistently demonstrates the lowest error values across all metrics, for both training and validation datasets, making it the most effective model. RF follows closely, while SVM shows the highest error rates, indicating its comparatively lower effectiveness.

3.2. Drought Quantification Maps for Meteorological, Agricultural, and Hydrological Drought

The Gaussian kernel was used to improve the RDI, SMADI, and SDI. These enhanced indices were then applied in machine learning models including CART, SVM, and RF to further refine the drought indices.

3.2.1. Meteorological Drought Index

Figure 5a shows a computed map of the RDI, which categorizes hydrological drought on a standardized scale. Values range from 1 to −1, indicating conditions from extremely wet to extreme drought. Central Africa mostly avoids extreme drought except in 2020, while the Sahel region experiences persistent drought. No data are available for the Sahara, Namib, and Guban Deserts. In Figure 5b, the styled vector of RDI derived from Figure 5a follows the same drought classification. An empty image is painted with the dominant pixel color for each country’s geometry, providing a generalized meteorological drought picture. The Horn of Africa and southern/southwestern Africa experience frequent drought episodes. As depicted in Figure 5c, Kendall’s tau-b trend analysis for RDI over 2001–2020 shows an increasing drought trend in northwestern Africa, the Sahel, southern Africa, parts of Central Africa, and the Horn of Africa. The scale ranges from −0.5 (extreme drought) to 0.5 (extremely wet). From Figure 5d, a denoised composite of six meteorological drought indices and five indicators (using a Gaussian kernel) shows persistent drought in the Sahel, Sahara Desert, Horn of Africa, and southwestern Africa. The scale ranges from 0 (extreme drought) to 1 (no drought). Figure 5e shows improved RDI using all variables from the denoised composite and Gaussian kernel. The scale is −1 to 1, consistent with Figure 5a. The Sahel region shows persistent drought, while Central Africa remains mostly drought-free. Figure 5f displays predicted RDI using CART with predictor variables from Figure 5e. The Sahel endures persistent extreme drought, and Central Africa experiences mild drought. No data are available for the Sahara, Namib, and Guban Deserts. Figure 5g illustrates the predicted RDI using SVM, indicating that Central Africa generally experiences mild drought conditions, with significant moderate drought in 2020. The Sahel consistently experiences extreme drought. The wettest year across Central, eastern, and southern Africa is 2007. Figure 5h presents the predicted RDI using RF, showing that the Sahel consistently experiences droughts ranging from mild to severe, with an extreme drought occurring in 2006. Parts of southern Africa endure persistent moderate to severe drought. Central Africa faces mild drought pockets, except in 2020.

Africa’s drought patterns show Central Africa avoiding extreme droughts, while the Sahel experiences persistent severe droughts. Increasing drought trends from 2001–2020 highlight the need for targeted management in affected regions.

3.2.2. Agricultural Drought Index

Figure 6a illustrates SMADI, categorizing drought severity into five levels: near normal (0–0.19), mild drought (0.20–0.39), moderate drought (0.40–0.59), severe drought (0.60–0.79), and extreme drought (0.80–1) [63]. Figure 6b presents a styled vector version of Figure 6a, highlighting agricultural drought-affected areas more clearly on a scale from 0 (near normal) to 0.5 (extreme drought). North Africa and parts of the Sahel show consistent drought, while East and Central Africa experience minimal drought. Figure 6c shows Kendall’s Tau-b trend analysis for SMADI from 2001 to 2020, on a scale from −0.5 (extreme drought) to 0.5 (extremely wet). A significant trend indicates increasing drought in the Sahel, while Central, northwestern, and northeastern Africa show a decreasing drought trend. Figure 6d presents a denoised composite image using a Gaussian kernel, incorporating 13 drought indicators, with a scale from 0 (near normal) to 1 (extreme drought). Persistent droughts are evident in the Sahel and southwestern Africa. Figure 6e shows enhanced SMADI results using the composite image variables processed with a Gaussian kernel, on the same scale as Figure 6a. Persistent agricultural droughts are seen in North, Central, and southwestern Africa, with no significant changes over the 20-year period.

Figure 6f–h display predicted SMADI using CART, SVM, and RF models, respectively, on the same scale as Figure 6a. The results vary across models. In 2006, droughts affected Central Africa, the Sahel, and southwestern Africa. By 2010, droughts appeared in West and Central Africa, and in 2016, extreme drought hit southern Africa (Figure 6f). No data are available for northern Africa due to the Sahara Desert. Significant droughts occurred in 2001, 2011, 2012, 2017, 2019, and 2020 (Figure 6g). Extreme drought affected Central and southern Africa in 2001, West Africa in 2011, East and southern Africa in 2012, East, Central, and southwestern Africa in 2017, and various regions in 2019 and 2020. Figure 6h excludes data for the Sahara, Namib, and Guban Deserts. No extreme drought is observed over the 20-year span, except for spots in southwestern Africa in 2020.

3.2.3. Hydrological Drought Index

Figure 7a evaluates SDI on a 12-month scale, categorizing conditions into eight levels. SDI values of 2 or higher indicate extremely wet conditions, while values of −2 or lower denote extreme drought. Each year shows unique and erratic drought patterns, with significant droughts in East Africa in 2005 and 2008, and moderate to severe droughts in southern Africa in multiple years. The Sahel consistently faces severe droughts, except in 2012, while Central and East Africa mostly experience mild to moderate droughts. The Sahara Desert lacks data. Figure 7b offers a generalized interpretation of hydrological drought conditions across Africa, consistent with Figure 7a, on a scale from −2 (extreme drought) to 2 (extremely wet). North Africa, the Sahel, and West Africa show varying drought intensities over the 20 years. The Horn of Africa and southwestern Africa experience drought episodes in at least half of the years. Figure 7c shows Kendall’s Tau-b trend analysis of SDI from 2001 to 2020, with a scale from −0.5 (extreme drought) to 0.5 (extremely wet). Increasing drought trends are observed in North Africa, the Sahel, the Horn of Africa, and southwestern Africa, while Central and parts of West Africa show decreasing drought trends. Figure 7d presents a denoised composite image using a Gaussian kernel, incorporating four hydrological drought indices and five indicators. The scale ranges from −2 (extreme drought) to 2 (extremely wet). The Sahel and the Sahara face frequent droughts, except in 2012 and 2019. East Africa experienced significant droughts in 2003 and 2005. Figure 7e displays enhanced SDI results using the composite image variables processed with a Gaussian kernel. The drought patterns closely match those in Figure 7a.

Figure 7f–h show predicted and improved SDI results using CART, SVM, and RF models, respectively, with patterns similar to Figure 7e. Figure 7f is similar to Figure 7e, with differences in 2010, 2016, and 2020. Figure 7g shows more pronounced extremes, ranging from −2 to 2. Figure 7h is similar to Figure 7e, but without extreme drought.

3.3. Ranking of Predictor Variable Importance for Meteorological, Agricultural, and Hydrological Drought in Africa

RF is used to evaluate the significance of each predictor variable within the drought categories of meteorological, agricultural and hydrological drought when predicting enhanced RDI, SMADI, and SDI respectively.

Figure 8a displays the predictor variables for the RDI and their importance. RDI is most influential at 26%, followed by SPI at 20% and MIDI at 11%. Slope and precipitation are the least influential. Figure 8b shows the predictor variables for agricultural drought used in machine learning models (CART, SVM, RF) to predict and enhance SMADI. SMADI is most important at 27%, followed by CMI at 15% and NMDI at 10%. Slope and elevation have the least importance. Figure 8c Illustrates the predictor variables for the SDI representing hydrological drought. SDI is most significant at 37%, followed by SHDI at 24%, and PHDI at 11%. Slope and soil moisture deficit (SMD) are the least influential.

3.4. Evaluation of Meteorological, Agricultural, and Hydrological Percentage Drought Incidence in Africa from 2001 to 2020

Table 3. Meteorological, agricultural, and hydrological droughts classified by area coverage in Africa.

Meteorological Drought (RDI)
Grid code	Classification	Area (km2)	Percentage of grid codes	Percentage of grid code 1 and 2
1	Extreme drought	3,729,089	16.8%
2	Severe drought	2,945,023	13.2%
3	Moderate drought	3,958,149	17.8%
4	Mild drought	3,986,207	17.9%
5	Normal	3,489,032	15.7%	30%
6	Slightly wet	2,105,593	9.4%
7	Moderately wet	1,068,267	4.8%
8	Severely wet	594,071	2.7%
9	Extremely wet	371,569	1.7%
Agricultural Drought (SMADI)
Grid code	Classification	Area (km2)	Percentage of grid codes	Percentage of grid code 2, 3, 4, and 5
1	Near normal	25,062,048	77.7%
2	Mild drought	5,027,211	15.6%
3	Moderate drought	1,646,027	5.1%	22%
4	Severe drought	379,880	1.2%
5	Extreme drought	138,697	0.4%
Hydrological Drought (SDI)
Grid code	Classification	Area (km2)	Percentage of grid codes	Percentage of grid code 1, 2, and 3
1	Extreme drought	150,067	0.5%
2	Severe drought	1,123,144	4.0%
3	Moderate drought	4,702,164	16.7%
4	Mild drought	5,089,351	18.1%	21%
5	Mildly wet	6,283,784	22.3%
6	Moderately wet	3,831,560	13.6%
7	Severely wet	3,029,034	10.7%
8	Extremely wet	3,981,002	14.1%

categorizes drought conditions into three types: meteorological, agricultural, and hydrological based on severity classification level and affected area. Each category’s total of areas represents Africa’s spatial extent. Meteorological drought, associated with rainfall deficiency, shows that 30% of Africa experiences severe and extreme drought. Agricultural drought, which impacts soil moisture and crop production, indicates that while a significant portion of Africa is near normal, 22% faces mild to extreme drought. Hydrological drought, which affects water bodies, revealed that while many regions experience mild drought to extremely wet conditions, 21% of Africa suffers moderate to extreme drought conditions.

4. Discussion

The accurate prediction and monitoring of drought conditions are crucial for mitigating the adverse effects on water resources, agriculture, and ecosystems. This study incorporated a Gaussian kernel and applied three machine learning models, namely, CART, SVM, and RF, to improve the prediction accuracy of meteorological (RDI), agricultural (SMADI), and hydrological (SDI) drought indices across Africa.

The Gaussian kernel was used to convolve and blend various indices and indicators, filling in missing pixels to produce a denoised composite image. It was then applied a second time to convolve a single drought index with a denoised composite image, resulting in an improved drought index that is seamlessly integrated with the denoised image.

Using a Gaussian kernel with machine learning models helps to clean the input data by reducing noise and improving spatial consistency, leading to more accurate and reliable drought index predictions. This approach enhances the performance of the machine learning model compared to using the model independently on raw data, as the model can focus on meaningful, generalizable patterns rather than noisy variations. Noise in training data can cause machine learning models to overfit, meaning they learn patterns specific to the noise rather than generalizable trends. For instance, the Gaussian kernel helps ensure that indices are not overly influenced by local outliers, such as a single dry pixel having an outsized impact on an otherwise well-watered region. Denoising with the Gaussian kernel allows for the model to generalize new, unseen data, thereby improving the prediction accuracy. Hence, while the Gaussian kernel and machine learning models can be used independently, applying the Gaussian kernel as a preprocessing step before the machine learning process significantly improves prediction accuracy.

Shen et al. [31] used Gaussian kernel with NDVI high- and low-resolution images to improve the images, which is in line with this study. Rakovec et al. [32] analyzed a European continent-wide drought with spatio-temporal drought analysis using a soil moisture index and used the Gaussian kernel to obtain a better-quality prediction. However, this study goes further and looks at convolving complex multiple index and indicator-based images with different internal data sets with an aim of enhancing a single drought index, which is a unique approach specific to this study. The Gaussian kernel was especially selected for use, as it is not too complex to compute and effectively handles the complex process of incorporating multiple drought indicators, each of which is intricate on its own.

The image improved with the Gaussian kernel contains different predictor variable bands and is used as an input for CART, SVM, and RF to obtain an improved indicator result from the prediction, which is another characteristic approach used in this study. Machine learning model accuracy and error minimization are assessed using RMSE and MAE, which are the most ideal for predictive models unlike classification models that require different metrics such as area under the curve, efficiency, and true skill statistic [78]. In all cases, for agricultural, meteorological, and hydrological drought, the CART model outperforms RF and SVM, with SVM demonstrating the lowest predictive accuracy. These findings align with the results of Prasetyo et al. [79], who used meteorological drought indices (SPI, SPEI, and PDSI) with satellite-based data to assess drought risk in central java, and found that CART outperformed RF, which in turn was superior to SVM. The results of our study are also consistent with Piao et al. [80], who mapped droughts in the Gangwon-do forest areas in South Korea using spatial data and the SPI meteorological drought index and found CART to be most reliable. CART has a lower computational complexity compared to RF and SVM, enabling it to find optimal splits faster and deliver better predictions with fewer resources. Its straightforward approach is well-suited for handling spatial and temporal data, where RF may struggle with correlations and SVM with kernel optimization. This simplicity gives CART an advantage in managing noise effectively without overfitting, making it less sensitive to noise and outliers. Moreover, CART demonstrates exceptional performance across various data types, including nominal, interval, and ratio data, and is effective with non-parametric data that do not follow a normal distribution. It also supports hierarchical relationships among variables, excels in processing large datasets efficiently, and offers transparent, interpretable model outputs, making it a robust choice for data analysis tasks [81,82]. Although CART outperformed RF and SVM, all models demonstrated very good to good accuracy, indicating that RF and SVM remain reliable options [83].

This study provides a comprehensive understanding of meteorological, agricultural, and hydrological droughts by computing multiple indices in each category. These indices are then used to improve a single drought index using a Gaussian kernel and machine learning. The modeled drought events from 2001 to 2020 and the affected region, country or basin, and drought period are consistent with findings from various studies in

Table 4. Meteorological, agricultural, and hydrological drought occurrences from 2001 to 2020 in various regions, countries, and basins in Africa.

Drought Type	Region	Citation	Years	Remarks
Meteorological Drought	North Africa	Thi et al. [84]	2001–2005, 2015–2017, 2019–2020	Droughts detected in northeast Africa through the Standardized Precipitation Index (SPI).
	West Africa	Kasei et al. [85]	2001	Droughts in Mali, Burkina Faso, Ghana, Togo, and the Volta Basin per SPI assessments.
	East Africa	Ayugi et al. [86]	2005–2006, 2007–2009, 2011, 2017–2018	Below-normal rainfall in Kenya, Tanzania, Somalia, Ethiopia.
	Southern Africa	Chivangulula et al. [87]	2002–2004, 2015–2019	Extreme droughts in southern Africa, influenced by El Niño.
	Central Africa	Ntali et al. [88]	Various years between 2002–2019	Frequent droughts in northern Cameroon via SPI analysis.
Agricultural Drought	North Africa	Thi et al. [84]	2016–2017, 2019–2020	Severe drought in Morocco and Algeria observed using NDVI data.
	West Africa	Bhaga et al. [89]	2018	Crop failure in Senegal causing food insecurity for 245,000 people.
	East Africa	Rulinda et al. [90]	2005–2006	Drought across Burundi, Kenya, Rwanda, Tanzania, Uganda from September 2005 to January 2006.
	Southern Africa	Ndlovu & Mjimba [91]	2019	Approximately 70% drop in maize production in Zimbabwe due to drought.
	Central Africa	Chen et al. [92]	2001–2020	Declining productivity in the Congo rainforest with increasing drought frequency.
Hydrological Drought	North Africa	Henchiri et al. [93]	2001–2003, 2008–2010	Hydrological droughts in Morocco and Algeria.
	West Africa	Henchiri et al. [93]	2000–2003, 2008–2010	Hydrological droughts in Mali, Guinea, Ghana, Sierra Leone, Cote d’Ivoire, Niger, Burkina Faso, Nigeria.
	East Africa	Anderson et al. [94]	2010–2011	Hydrological drought in Ethiopia, Somalia, Kenya indicated by modeling.
	Southern Africa	Siderius et al. [5]	2015–2016	Hydrological droughts in southern Africa due to severe El Niño, affecting lake levels in Botswana, Zambia.
	Central Africa	Sorí et al. [95]	2001–2020	Drying trend in the Congo River Basin.

, hence validating the research findings in the real world.

This globally transformative approach can be used to comprehend meteorological, agricultural, and hydrological drought using remote sensing data, making it especially valuable for countries with limited ground data. By offering a groundbreaking solution for monitoring and managing drought conditions, it provides a robust foundation for formulating drought risk and water resource management policies. Hagenlocher et al. [96] emphasized that building drought-resilient societies requires future policies and research to be grounded in a comprehensive understanding of drought.

Ranking predictor variables for meteorological, agricultural, and hydrological droughts reveals that drought indices are the most influential in improving the final single drought index. RF analysis shows higher values for predictors with higher contributions to accuracy. Across all categories, the top three predictors were drought indices, not indicators like slope, elevation, or precipitation. Bachmair et al. [97] found similar results in Europe. While indicators sometimes contributed, the top drought indices consistently proved most important, enhancing drought assessment accuracy.

Over a 20-year period, Africa most frequently experienced meteorological drought, followed by agricultural and then hydrological drought. This pattern mirrors the hydrological cycle: low rainfall causes meteorological drought, which affects agriculture, leading to agricultural drought, and eventually reduces water percolation, causing hydrological drought. This finding aligns with studies by Feng et al. [98] in the Lancang–Mekong River Basin and Anjali et al. [99] in the Ganga River Basin, India.

The data sources used are generally reliable for large-scale analysis of Africa, but challenges related to data gaps, cloud cover, and regional climatic differences can impact accuracy. Hence, using a combination of indices and adjusting spatial and temporal scales significantly mitigated these challenges. However, for future research, the model can be fine-tuned to cater to different ecological zones, and ensuring access to complete datasets across regions can further improve the accuracy and reliability when applying this methodology across Africa or other large continents.

The approach utilized in our work is transferable to other large, diverse climate regions outside Africa, allowing for generalization with minimal adjustments. Potential limitations include the need to select more appropriate indices and indicators based on local ecology and climate. Additionally, adjusting spatial and temporal scales may be necessary to align with regional land use and ensure data availability over the desired period, helping the model run efficiently without performance issues.

5. Conclusions

Drought indices and indicators are essential for understanding drought. Each index for a specific drought classification category has unique input data and computation methods, considering spatial and temporal factors. This complexity necessitates finding the best way to understand drought while accounting for various drought index variables and their unique representations. A Gaussian kernel effectively convolves and amalgamates diverse indices and indicators to create a denoised composite image. This study uniquely extended this approach by also using the Gaussian kernel to convolve the composite with a single drought index for that drought classification category (meteorological, agricultural, or hydrological), resulting in the best possible reconstruction of the single drought index. Furthermore, the study used these improved single drought index predictor variables as input for three machine learning models to predict an even more refined drought index. Among the models, the CART model delivered the best performance, followed by RF and SVM. All models generally produced acceptable results, ranging from very good to good, as evaluated by RMSE and MAE metrics. This study diverged from previous studies due to its use of various indices and indicators to enhance an index utilizing the Gaussian kernel and using the results in machine learning for improved accuracy in drought quantification. The spatial and temporal drought patterns were significantly consistent throughout the various iterations of the results. Regions with chronic drought conditions had limited changes throughout the 20-year span of the study. This implies that there could be stronger influences for drought conditions beyond what the drought indices indicate, such as the impact of deserts on meteorological, agricultural, and hydrological drought. This approach allows any drought index within its specific drought classification category to be adopted and enhanced. This means the method can be applied to regions where a specific drought index may be more suitable. Additionally, the approach does not rely on ground-based data, making it adaptable for both localized and global drought assessments, including regions with limited ground data.