Extreme meteorological events often occur in complex temporal configurations, where the impacts of one hazard may depend on the prior occurrence of others. Characterising such temporal dependencies is essential for understanding compound climate risks, yet remains challenging due to the discrete, heterogeneous, and clustered nature of extreme events. In this study, we extend and apply temporal point process methods to characterise dependencies among extreme meteorological events occurring within appropriately defined spatial regions across Europe, focusing exclusively on their temporal structure. We introduce an event-based framework in which extreme events are represented as marked temporal point processes, with marks describing key characteristics such as intensity or duration. Global first- and second-order temporal statistics are used to quantify clustering, co-occurrence, and directional dependencies between different types of extremes. We rely on directional cross-K functions to assess whether the occurrence of one type of extreme event systematically modifies the short-term probability of subsequent events of another type. Two complementary applications illustrate different facets of compound event analysis. First, we demonstrate the relevance of the framework for preconditioned or cascading compound events through a temporal analysis of wildfire-related meteorological extremes. Second, we examine temporal dependence between extreme precipitation, extreme wind, and extreme atmospheric instability across all European NUTS-2 regions. Building on these second-order statistics, we develop formal tests of temporal independence to assess the significance of observed directional interactions between different types of extreme events. Overall, this temporal point process framework provides a rigorous and interpretable approach to the analysis of compound climate extremes, with direct applications to climate risk assessment and early-warning systems.
Accurate prediction of ocean surface currents is essential for maritime safety in narrow waterways with strong tidal forcing. This study presents a three-phase evaluation of forecasting methods for high-frequency (HF) radar surface currents in the Sunda Strait, Indonesia, where tidal currents regularly exceed 150 cm s−1. Phase 1 compares twelve methods – persistence, tidal harmonics, classical time series, a reduced-rank spatio-temporal statistical model, shallow machine learning, and deep learning – for one-step-ahead prediction; evaluated consistently over all 291 grid cells and the full test period, the deep learning models achieve the lowest root-mean-square errors (RMSE) for both components, with the convolutional neural network (CNN) reaching 11.31 cm s−1 for the zonal component (skill score 0.50 relative to persistence) and the convolutional neural network–gated recurrent unit (CNN-GRU) reaching 15.44 cm s−1 for the meridional component (skill score 0.42); the pointwise classical statistical models (autoregressive integrated moving average, ARIMA; exponential smoothing) fall well below, while an empirical-orthogonal-function vector autoregression (EOF-VAR) that models spatial correlation closes most of the gap to deep learning, indicating that the neglect of spatial structure – not of nonlinearity – is the principal limitation of the classical baselines. Phase 2 examines lookback window length (T = 3, 6, 12 h); CNN-gated recurrent unit (CNN-GRU) improves monotonically with longer lookback, reaching 11.21 and 15.41 cm s−1 at T = 12, while standalone CNN and GRU show no benefit. Phase 3 extends prediction to six-hour nowcasting using direct multi-step and autoregressive (ConvLSTM-ED, BiEF) architectures; under a controlled comparison (five seeds, identical training budget on one GPU), accuracy is governed by model capacity and plateaus near 1 M parameters (the 1.00 M CNN-GRU-MS-Small reaching 18.39 and 22.07 cm s−1; skill scores 0.77 and 0.72), and at matched capacity the direct and autoregressive architectures are statistically indistinguishable. The direct multi-step model is nonetheless preferred for operational nowcasting because it trains ∼2.5 times faster and runs ∼4.5 times faster at inference (a single forward pass versus sequential decoding). Diurnal error analysis, corroborated by concurrent wind observations from three coastal weather stations, reveals that zonal prediction errors correlate positively with afternoon sea-breeze wind enhancement (Spearman rs = 0.48 across the 24 diurnal-mean hours), while meridional errors follow a distinct diurnal pattern not explained by wind forcing. Relative errors of 3 %–7 % of the observed speed range are of the same order as those reported in calmer environments – though this normalisation partly reflects the strait's very large speed range – suggesting that deep learning does not break down in energetic strait settings.
We define a generalized exponential distribution (G-ED) that overlaps with a generalized Pareto distribution (GPD). Then, we introduce the q-Pareto distribution (q-PD) with two-parameter family distribution (strict positive shape and scale parameters) via transforming the G-ED. We demonstrate that the q-PD can be used to model the exceedances over a threshold, and we focus to estimate the q-PD parameters. Often, the estimation is taken the maximum likelihood estimation (MLE) because have a consistent estimator with an asymptotic normal distribution and is asymptotically effective in many cases. We present an algorithm to compute the MLE for q-PD parameters with confidence intervals for each estimator. Numerical examples are given to illustrate the results obtained. Efficient numerically methods are developed for the MLE of the q-PD parameters to maximize the log-likelihood of the q-PD.
Recurrent flooding in the Marahoué region, particularly in Bouaflé and Zuénoula, underscores the need for reliable and operational tools to anticipate hydrological risks and support early warning systems. This study presents a rainfall forecasting framework based on Long Short-Term Memory (LSTM) neural networks, integrating satellite-derived precipitation products and reanalysis-based atmospheric variables to predict daily rainfall at the Bouaflé and Zuénoula stations at t + 1, t + 3, and t + 7 d lead times. The performance of the LSTM model was systematically evaluated and compared with commonly used reference models, namely Random Forest (RF), Extra Trees (ET), and XGBoost (XGB), using standard statistical metrics (R2, NSE, Pearson correlation coefficient R, normalized RMSE, and MAE). The results show that the LSTM model consistently outperforms the reference models across all forecasting horizons and at both study stations. At short and medium lead times (t + 1 and t + 3), LSTM exhibits strong predictive skill, with R2 and NSE values exceeding 90 %, indicating an accurate representation of daily rainfall variability. Although performance decreases at the seven-day horizon due to increasing uncertainty and challenges in capturing extreme events, LSTM remains more robust than tree-based models, whose accuracy degrades markedly with increasing lead time. These findings confirm the relevance of LSTM-based approaches for rainfall forecasting and early warning applications in flood-prone regions. Future work will focus on integrating additional atmospheric predictors and applying advanced hyperparameter optimization techniques to improve long-term forecast reliability.
Precipitation generators are statistical models used to produce synthetic sequences of (multisite) precipitation for hydrological applications such as flood risk assessment and water resource management. Among these, approaches based on generalized linear models (GLMs) are widely used and often perform competitively with state-of-the-art alternatives, but they face limitations in representing seasonal variation in extremes and in flexibly capturing covariate effects on the precipitation distribution. In this paper, we extend the GLM framework in two directions. First, we introduce generalised additive models for location, scale and shape (GAMLSS) for precipitation generation. These models allow the use of spline-based model terms to flexibly capture covariate effects and allow covariates to influence multiple distributional parameters, thereby increasing flexibility in representing variation in both the mean and variance of the precipitation distribution. Second, we adapt a transformed Gaussian fields approach to jointly account for spatial dependence in both precipitation occurrence and intensity, thus allowing for potential cross-dependence between the two. A further contribution is to investigate the sensitivity of model performance to data resolution, highlighting that rounding in data pre-processing can substantially affect the reproduction of extremes. Using a well-studied daily precipitation dataset, we demonstrate that these extensions improve the realism of simulated sequences, particularly with respect to extremes, and capture spatial dependence well in both occurrence and intensity.
