The Hlan watershed is located in the south-central region of Benin, between approximately 7˚07'N and 7˚29'N latitude and 1˚95'E and 2˚15'E longitude. It spans an estimated surface area of 560 km² and straddles two major urban agglomerations: Bohicon and Abomey, respectively the second and fourth most populated cities in the Zou Department. The watershed plays a vital hydrological role in draining stormwater runoff from these urban centers, particularly in a context of rapidly increasing soil imperviousness due to urban expansion (Figure 1).

The climate of the region is classified as Sudano-Guinean, characterized by a bimodal rainy season with a primary peak in rainfall occurring between April and July, and a secondary peak between September and October. Annual rainfall typically ranges from 1000 to 1200 mm, with daily intensities often exceeding 50 mm/day during extreme precipitation events [4]. This climatic regime, combined with unregulated urban growth, makes the area especially vulnerable to urban flooding.

Rainfall data recorded at the Bohicon synoptic station between 1980 and 2023 reveal high interannual variability in the number of rainy days. A downward trend is observed after the year 2000, which suggests a shift in rainfall patterns—reduced frequency of rainfall events coupled with increased intensity—consistent with the impacts of climate change (see Figure 2).

Moreover, monthly average rainfall distribution shows peak precipitation levels in June and September, with values gradually tapering off in the dry season (November to February). This rainfall pattern (Figure 3) further confirms the bimodal structure of the regional rainfall regime, which has critical implications for hydrological modeling and infrastructure design in the study area.

This study utilizes satellite-based precipitation data from the IMERG Final Run V07B product, developed under NASA’s Global Precipitation Measurement (GPM) mission. The data offer a temporal resolution of 30 minutes and a spatial resolution of 0.1˚ × 0.1˚ (approximately 10 km × 10 km), covering the period from 2000 to 2023.

Figure 1. Study area map showing the Hlan watershed and surrounding hydrographic context.

Figure 2. Interannual variability of the number of rainy days per year at Bohicon (1980-2023).

Figure 3.Monthly average rainfall at Bohicon, showing the bimodal rainfall regime.

Data were extracted using the NASA Giovanni portal (https://giovanni.gsfc.nasa.gov) for the spatial grid covering the Hlan watershed (latitudes 7.05˚N to 7.25˚N; longitudes 1.95˚E to 2.15˚E). To improve their local representativeness, the IMERG data were corrected for systematic bias using statistical calibration against ground-based rain gauge records.

2.2.1. IMERG Data Bias Correction

To reduce systematic errors associated with satellite-based precipitation estimates, a bias correction was applied to the IMERG data prior to their use in hydrological analyses. The method adopted relies on a quantile mapping approach, which adjusts the statistical distribution of satellite-derived precipitation to match that observed on the ground, correcting both the mean bias and distributional discrepancies. The adjustment was performed on a monthly basis to account for seasonal variability in precipitation. Performance evaluation using statistical indicators (R², RMSE, and MAE) showed a significant improvement in the agreement between the corrected data and ground-based observations.

2.2.2. Frequency Analysis Methodology

The frequency analysis began with a diagnostic assessment of the precipitation time series to verify their suitability for distribution modeling. Three standard statistical tests were applied:

Kendall stationarity test.Wald-Wolfowitz runs test for independence.Wilcoxon homogeneity test.

These tests have been widely applied in recent hydrological studies across Africa [5].

In modeling annual maximum precipitation values, five probabilistic distributions were considered:

Generalized Extreme Value (GEV).Gumbel.Log-normal.Pearson Type III.Weibull.

The Maximum Likelihood Estimation (MLE) method was used to estimate distribution parameters, following best practices in extreme value analysis [6].

Table 1 below presents the main probability density functions (PDFs) associated with these distributions, along with their characteristic parameters.

Table 1.Probability Density Functions (PDFs) of the tested distributions.

2.2.3. Model Selection Criteria

To identify the most appropriate distribution, both graphical fitting and numerical criteria were used:

Log-likelihood (normalized).Akaike Information Criterion (AIC).Bayesian Information Criterion (BIC).

The BIC, for instance, is defined as:

where:

L is the maximum likelihood of the model.k is the number of parameters.N is the sample size.

This approach follows recent recommendations for model selection under tropical hydrological conditions [7]. It was supplemented by modern Bayesian criteria such as DIC [8] and WAIC, now widely used in hydrological inference [9].

2.2.4. Empirical IDF Models

The Intensity-Duration-Frequency (IDF) curves are empirical models that relate extreme rainfall intensity i(T) to its duration d and return period T. Three common models were tested:

The analytical expressions of these models are presented in Table 2, which summarizes their mathematical formulations and the meaning of the parameters.

Table 2. Empirical IDF models.

where:

i(T) is the rainfall intensity (mm/h) for return period T.ddd is the rainfall duration (minutes).a(T), η(T), and θ(T) are empirical parameters.

2.2.5. Model Performance Evaluation

Each IDF model was calibrated using least squares fitting, and evaluated using the following objective criteria:

The mathematical formulas of these indicators are presented in Table 3, in order to clarify their calculation method and their role in evaluating the performance of IDF models.

The model that exhibited the highest R², lowest RMSE, and lowest MAE was selected for generating the final site-specific IDF curves for Bohicon. This method aligns with best practices established in studies by [10][11].

Table 3. Statistical performance indicators.

To ensure the validity of the annual maximum rainfall series by duration (ranging from 30 minutes to 24 hours), three standardized statistical tests were conducted: the Kendall test for stationarity, the Wald-Wolfowitz runs test for independence, and the Wilcoxon-Mann-Whitney test for homogeneity. These tests verify the fulfillment of core assumptions required for robust frequency modeling.

Stationarity: As shown in Table 4, the p-values obtained from the Kendall test exceed the conventional 5% significance threshold across all durations, indicating the absence of significant trends. This result confirms the stationary behavior of the time series, aligning with recommendations from [12] regarding IDF modeling in tropical climates.Independence: The Wald-Wolfowitz runs test values confirm that successive observations are statistically independent. All series fulfill this critical requirement, corroborating similar findings reported by [13] in studies involving GPM/IMERG satellite data.Homogeneity: Regarding homogeneity, the Wilcoxon-Mann-Whitney test results reveal no significant discontinuities in the means of sub-series. Except for the 2-hour and 24-hour durations, all p-values exceed 0.5, supporting the assumption of a globally homogeneous rainfall regime over the study period. These outcomes are consistent with the observations of [14] on bias-corrected satellite series in West Africa.

Table 4.Results of hypothesis testing for annual maximum rainfall intensities.

Taken together, these results demonstrate that the datasets satisfy the three fundamental statistical assumptions—stationarity, independence, and homogeneity—required for reliable frequency analysis. This procedure aligns with current best practices outlined in recent methodological reviews on hydrological extreme value modeling [15].

Table 4 presents the results of stationarity, independence, and homogeneity tests for the maximum rainfall series at different durations.

Following the fitting of classical probability distributions (Gumbel, Weibull, Pearson Type III, and Lognormal) to the annual series of maximum rainfall intensities for each duration, the quality of the fit was assessed using two complementary statistical criteria:

Kolmogorov-Smirnov Test (p_KS): This evaluates the maximum deviation between the empirical and the fitted theoretical distributions. A p-value greater than 0.05 indicates that the null hypothesis (good conformity) is not rejected, implying an acceptable statistical fit.Akaike Information Criterion (AIC): This criterion allows for an objective comparison of models by balancing goodness-of-fit with model complexity.

Table 5 below presents the values obtained for the p_KS and AIC criteria according to different recording durations. It allows identifying the probability distributions that best fit the annual maximum intensity series.

Table 5. Statistical metrics for goodness-of-fit evaluation.

These results confirm the necessity of duration-specific model selection, based on robust statistical indicators. They align with findings from [16][17], who emphasized the variability in the best-fitting distributions depending on the temporal scale considered.

Visual Validation with Q-Q Plots

To complement the numerical analysis, visual validation of the selected models was carried out using quantile-quantile (Q-Q) plots. These graphs compare the empirical quantiles of observed data with the theoretical quantiles of the fitted distributions. A strong alignment along the identity line (red dashed line) indicates a good fit.

As illustrated in Figure 4, the Q-Q plots generally confirm the suitability of the selected probability distributions, particularly the Weibull and Gumbel laws. These distributions successfully replicate the variability observed in maximum rainfall intensities across all durations.

Note: Subplots include Q-Q plots for durations of 30 minutes, 1 hour, 2 hours, 3 hours, 6 hours, and 24 hours. The empirical quantiles (blue dots) are plotted against the theoretical quantiles derived from the selected probability distributions.

Figure 4. Q-Q plots of empirical vs. theoretical quantiles for all durations.

The performance evaluation of three empirical Intensity-Duration-Frequency (IDF) models—Montana,Talbot, andKeifer-Chu—was conducted using the statistical indicators coefficient of determination (R²),Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). This methodology follows the recommendations, which emphasize multi-criteria performance evaluation of IDF formulations under varying return periods.

3.3.1. Talbot Model Performance

As shown in Table 6, the Talbot model consistently delivers the best fit across all return periods. For a 2-year return period, it achieves a very high R² value of 0.962, with relatively low error levels (RMSE = 4.90,MAE = 4.10). Even in the 100-year return period, its performance remains satisfactory (R² = 0.813), with significantly lower errors than those obtained from the Montana and Keifer-Chu models.

These results validate the robustness of the Talbot formulation in capturing both short- and long-duration rainfall extremes in the Bohicon region, consistent with findings by [18] on the importance of model resilience under extreme events.

Table 6 presents the performance metrics (R², RMSE, and MAE) of the IDF Talbot model for different return periods (T).

Table 6. Talbot model evaluation metrics.

Table 7.Keifer-Chu model evaluation metrics.

3.3.2. Keifer-Chu Model Performance

The Keifer-Chu model, while mathematically close to Talbot’s formulation, demonstrates slightly reduced predictive performance, particularly for high return periods. As shown in Table 7, the R² drops to 0.779 for T = 100 years, accompanied by larger RMSE and MAE values. This behavior aligns with observations by [18], who highlighted the sensitivity of empirical models to extremes and the limitations in extrapolation accuracy.

Table 7 presents the evaluation metrics (R², RMSE, and MAE) of the Keifer-Chu model for different return periods (T).

3.3.3. Montana Model Performance

The Montana model, though simpler and historically widespread due to its two-parameter structure, proves to be the least effective among the three models assessed. It shows significant limitations in representing high-intensity events and long durations. As detailed in Table 8, R² drops to 0.725 for a 100-year return period, and the associated error metrics (RMSE and MAE) are substantially higher than those of the Talbot and Keifer-Chu models. These limitations corroborate the findings of [19], who questioned the adequacy of low-parameter models in capturing tail behaviors of extreme hydrological distributions.

Table 8 presents the evaluation metrics (R², RMSE, and MAE) of the Montana model for different return periods (T).

Table 8. Montana model evaluation metrics.

These comparative results clearly support the Talbot model as the most appropriate choice for IDF curve construction in Bohicon’s context. Its superior fitting capacity across return periods, along with its low error metrics, make it a robust and reliable option for the design of urban drainage infrastructure under climate uncertainty.

The Intensity-Duration-Frequency (IDF) matrix (see Table 9) reveals a consistent pattern where rainfall intensity decreases as the duration increases, while intensity logically increases with the return period. This inverse relationship between intensity and duration, and the direct relationship with return period, is a characteristic behavior of tropical rainfall regimes, in which short-duration events tend to be more intense and violent [20].

In particular, the difference in intensity between short (e.g., 0.5 h and 1 h) and long return periods (e.g., 100 years) is most pronounced for shorter durations. This confirms that extreme events disproportionately affect short and highly concentrated rainfall episodes, a phenomenon that is critical in understanding flash flooding risks in tropical urban environments.

These findings are consistent with the conclusions, who emphasized the pivotal role of short-duration rainfall in urban flood modeling. Moreover, the influence of the return period tends to diminish as the duration increases, a trend widely recognized in recent hydrological literature [21]. Such behavior underscores the need for regionally calibrated IDF curves that reflect the spatio-temporal variability of extreme precipitation events.

The corresponding simulated intensity values for each duration and return period are presented in Table 9, which illustrates the quantitative distribution of precipitation intensities derived from the fitted IDF model.

Table 9. Rainfall intensity quantiles (mm/h) for various return periods and durations.

The structure observed in Table 9 aligns well with tropical hydrological dynamics and confirms the critical importance of accurate IDF curve calibration per region. Given the sensitivity of urban hydrological systems to rainfall intensity and concentration, especially for stormwater infrastructure design, these findings provide essential guidance for planners and engineers operating in similar climatic zones.

The analysis of the adjusted parameters of the Talbot model reveals consistent trends from a hydrological perspective. As shown in Table 10, the parameter a, which reflects the maximum rainfall intensity, increases progressively with the return period (T). This upward trend indicates the intensification of extreme precipitation events over time, highlighting the increasing magnitude of rare storms.

Conversely, the exponent parameter η exhibits a slight decrease as the return period increases, suggesting that intensity decreases more slowly with duration for rare events. This behavior implies that longer storm events remain relatively intense during extreme return periods.

In parallel, the offset parameter θ shows a decreasing pattern, indicating a greater concentration of rainfall over shorter durations as the rarity of the event increases. This tendency underscores the abrupt and focused nature of extreme precipitation in tropical regions; a phenomenon frequently associated with flash flooding risks.

These parameter evolutions confirm the Talbot model’s ability to capture the non-linear dynamics of extreme rainfall patterns in the studied region. They are consistent with hydrological expectations for tropical climates and validate the model’s applicability in the local IDF (Intensity-Duration-Frequency) framework.

The corresponding values of these parameters are presented in Table 10, which summarizes the estimated Talbot coefficients for the different return periods and the corresponding IDF curves.

Table 10. Calibrated talbot model coefficients by return period.

The IDF curve presented illustrates the evolution of rainfall intensities as a function of duration for different return periods (from 2 to 100 years). It highlights a classic but significant trend: the longer the rainfall duration, the lower the intensity, and the longer the return period, the higher the intensity. This dual temporal decrease and frequency increase accurately reflects the expected behavior of extreme events in a tropical urban context, such as that of Bohicon. The maximum intensity for a duration of 30 minutes varies from approximately 32 mm/h for T = 2 years to more than 66 mm/h for T = 100 years, representing an increase of over 100%, which demonstrates a high potential for urban runoff during rare events. This rapid increase in intensity over short periods and with high recurrence corroborates the recent, which highlight the increased vulnerability of African cities under the combined effect of climate change and rapid urbanization.

The use of a 30-minute temporal resolution for constructing IDF curves represents a significant methodological advancement compared to traditional approaches based on hourly or daily time steps. This temporal precision allows for a better capture of short-duration rainfall intensities, often responsible for flash floods in urban areas. In the context of the cities of Abomey and Bohicon, where drainage networks have limited capacity and very short times of concentration, taking into account high-frequency rainfall is essential to accurately reproduce runoff dynamics. Rainfall events lasting less than an hour generate rapid peak flows, which can overwhelm infrastructure and amplify flood risks. This approach thus strengthens the reliability of hydrodynamic simulations and the relevance of planning strategies aimed at reducing vulnerability to intense urban flooding.

The simulated rainfall intensities in Bohicon are compared to previous studies conducted in Cotonou [22][23], a comparison justified by the geographical proximity and similarity of the climatic regimes of the two southern Benin locations. Situated in the humid subequatorial zone, these cities exhibit a bimodal regime and often experience intense, convective rainfall. This regional perspective allows us to assess the spatial consistency of the IDF parameters, to understand the discrepancies related to topography or local rainfall dynamics, and to strengthen the validity of the results obtained in Bohicon, while also shedding light on the regional variability of extreme rainfall.

Compared to the empirical models used, the three-parameter Talbot model proves more robust than the two-parameter Montana model, particularly for short-duration, high-intensity events. This superiority is explained by the third parameter, which allows for better control of the hyetograph shape and rainfall concentration. In the context of Bohicon’s highly variable, convective tropical rainfall, this parameter gives the Talbot model greater flexibility in reproducing the rapid decrease in intensity over time and the increase with the return period. This results in higher R² values and lower errors (RMSE and MAE) compared to the Montana model. The addition of this parameter is not merely a statistical improvement; it provides a better physical representation of extreme events, essential for the realistic design of urban drainage structures.

Overall, the study shows that the IDF curves constructed at high temporal resolution (30 minutes), calibrated with the Talbot model, offer a reliable and robust representation of extreme rainfall in Bohicon. The regional comparison with Cotonou and the analysis of model performance confirm the scientific and operational relevance of this approach for the design of critical infrastructure and the management of urban flooding in southern Benin.

The curves shown in Figure 5 illustrate the relationship between intensity and duration for different return periods. They reveal an almost exponential decrease in intensities as duration increases, reflecting a marked concentration of extreme rainfall in short-duration events.

Figure 5. IDF curve—rainfall intensity vs duration.

Figure 6, plotted on a logarithmic scale, provides a clearer visualization of this trend and highlights the consistency of the Talbot model fits across all considered durations.

Figure 6. Log-scale IDF curves—intensity vs duration.