Parameter estimation is a foundational step in statistical modeling, enabling us to extract knowledge from data and apply it effectively. Bayesian estimation of parameters incorporates prior beliefs with observed data to infer distribution parameters probabilistically and robustly. Moreover, it provides full posterior distributions, allowing uncertainty quantification and regularization, especially useful in small or truncated samples. Utilizing the left-truncated log-logistic (LTLL) distribution is particularly well-suited for modeling time-to-event data where observations are subject to a known lower bound such as precipitation data and cancer survival times. In this paper, we propose a Bayesian approach for estimating the parameters of the LTLL distribution with a fixed truncation point \( x_L > 0 \). Given a random variable \( X \sim LL(α, β; x_L) \), where \( α> 0 \) is the scale parameter and \( β> 0 \) is the shape parameter, the likelihood function is derived based on a truncated sample \( X_1, X_2, \dots, X_N \) with \( X_i > x_L \). We assume independent prior distributions for the parameters, and the posterior inference is conducted via Markov Chain Monte Carlo sampling, specifically using the Metropolis-Hastings algorithm to obtain posterior estimates \( \hatα \) and \( \hatβ \). Through simulation studies and real-world applications, we demonstrate that Bayesian estimation provides more stable and reliable parameter estimates, particularly when the likelihood surface is irregular due to left truncation. The results highlight the advantages of Bayesian inference outperform the estimation of parameter uncertainty in truncated distributions for time to event data analysis.

With the intensification of global climate change, accurate prediction of weather indicators is of great significance in disaster prevention and mitigation, agricultural production, and transportation. Precipitation, as one of the key meteorological indicators, plays a crucial role in water resource management, agricultural production, and urban flood control. This study proposes a multidimensional precipitation index prediction model based on a CNN- LSTM hybrid framework, aiming to improve the accuracy of precipitation forecasts. The dataset is sourced from Pune, Maharashtra, India, covering monthly mean precipitation data from 1972 to 2002. This dataset includes nearly 31 years (1972-2002) of monthly average precipitation, reflecting the long-term fluctuations and seasonal variations of precipitation in the region. By analyzing these time series data, the CNN-LSTM model effectively captures local features and long-term dependencies. Experimental results show that the model achieves a root mean square error (RMSE) of 6.752, which demonstrates a significant advantage over traditional time series prediction methods in terms of prediction accuracy and generalization ability. Furthermore, this study provides new research ideas for precipitation prediction. However, the model requires high computational resources when dealing with large-scale datasets, and its predictive ability for multidimensional precipitation data still needs improvement. Future research could extend the model to support and predict multidimensional precipitation data, thereby promoting the development of more accurate and efficient meteorological prediction technologies.

Study Region: Goslar and G\"ottingen, Lower Saxony, Germany. Study Focus: In July 2017, the cities of Goslar and G\"ottingen experienced severe flood events characterized by short warning time of only 20 minutes, resulting in extensive regional flooding and significant damage. This highlights the critical need for a more reliable and timely flood forecasting system. This paper presents a comprehensive study on the impact of radar-based precipitation data on forecasting river water levels in Goslar. Additionally, the study examines how precipitation influences water level forecasts in G\"ottingen. The analysis integrates radar-derived spatiotemporal precipitation patterns with hydrological sensor data obtained from ground stations to evaluate the effectiveness of this approach in improving flood prediction capabilities. New Hydrological Insights for the Region: A key innovation in this paper is the use of residual-based modeling to address the non-linearity between precipitation images and water levels, leading to a Spatiotemporal Radar-based Precipitation Model with residuals (STRPMr). Unlike traditional hydrological models, our approach does not rely on upstream data, making it independent of additional hydrological inputs. This independence enhances its adaptability and allows for broader applicability in other regions with RADOLAN precipitation. The deep learning architecture integrates (2+1)D convolutional neural networks for spatial and temporal feature extraction with LSTM for timeseries forecasting. The results demonstrate the potential of the STRPMr for capturing extreme events and more accurate flood forecasting.

A recent report from the World Meteorological Organization (WMO) highlights that water-related disasters have caused the highest human losses among natural disasters over the past 50 years, with over 91\% of deaths occurring in low-income countries. This disparity is largely due to the lack of adequate ground monitoring stations, such as weather surveillance radars (WSR), which are expensive to install. For example, while the US and Europe combined possess over 600 WSRs, Africa, despite having almost one and half times their landmass, has fewer than 40. To address this issue, satellite-based observations offer a global, near-real-time monitoring solution. However, they face several challenges like accuracy, bias, and low spatial resolution. This study leverages the power of diffusion models and residual learning to address these limitations in a unified framework. We introduce the first diffusion model for correcting the inconsistency between different precipitation products. Our method demonstrates the effectiveness in downscaling satellite precipitation estimates from 10 km to 1 km resolution. Extensive experiments conducted in the Seattle region demonstrate significant improvements in accuracy, bias reduction, and spatial detail. Importantly, our approach achieves these results using only precipitation data, showcasing the potential of a purely computer vision-based approach for enhancing satellite precipitation products and paving the way for further advancements in this domain.

Climate change is intensifying rainfall extremes, making high-resolution precipitation projections crucial for society to better prepare for impacts such as flooding. However, current Global Climate Models (GCMs) operate at spatial resolutions too coarse for localized analyses. To address this limitation, deep learning-based statistical downscaling methods offer promising solutions, providing high-resolution precipitation projections with a moderate computational cost. In this work, we introduce a bias-informed conditional diffusion model for statistical downscaling of precipitation. Specifically, our model leverages a conditional diffusion approach to learn distribution priors from large-scale, high-resolution precipitation datasets. The long-tail distribution of precipitation poses a unique challenge for training diffusion models; to address this, we apply gamma correction during preprocessing. Additionally, to correct biases in the downscaled results, we employ a guided-sampling strategy to enhance bias correction. Our experiments demonstrate that the proposed model achieves highly accurate results in an 8 times downscaling setting, outperforming previous deterministic methods. The code and dataset are available at https://github.com/RoseLV/research_super-resolution

The sparse and spatio-temporally discontinuous nature of precipitation data presents significant challenges for simulation and statistical processing for bias correction and downscaling. These include incorrect representation of intermittency and extreme values (critical for hydrology applications), Gibbs phenomenon upon regridding, and lack of fine scales details. To address these challenges, a common approach is to transform the precipitation variable nonlinearly into one that is more malleable. In this work, we explore how deep learning can be used to generate a smooth, spatio-temporally continuous variable as a proxy for simulation of precipitation data. We develop a normally distributed field called pseudo-precipitation (PP) as an alternative for simulating precipitation. The practical applicability of this variable is investigated by applying it for downscaling precipitation from \(1\degree\) (\(\sim\) 100 km) to \(0.25\degree\) (\(\sim\) 25 km).

Recently, deep-learning weather forecasting models have surpassed traditional numerical models in terms of the accuracy of meteorological variables. However, there is considerable potential for improvements in precipitation forecasts, especially for heavy precipitation events. To address this deficiency, we propose Leadsee-Precip, a global deep learning model to generate precipitation from meteorological circulation fields. The model utilizes an information balance scheme to tackle the challenges of predicting heavy precipitation caused by the long-tail distribution of precipitation data. Additionally, more accurate satellite and radar-based precipitation retrievals are used as training targets. Compared to artificial intelligence global weather models, the heavy precipitation from Leadsee-Precip is more consistent with observations and shows competitive performance against global numerical weather prediction models. Leadsee-Precip can be integrated with any global circulation model to generate precipitation forecasts. But the deviations between the predicted and the ground-truth circulation fields may lead to a weakened precipitation forecast, which could potentially be mitigated by further fine-tuning based on the predicted circulation fields.

Understanding local risks from extreme rainfall, such as flooding, requires both long records (to sample rare events) and high-resolution products (to assess localized hazards). Unfortunately, there is a dearth of long-record and high-resolution products that can be used to understand local risk and precipitation science. In this paper, we present a novel generative diffusion model that downscales (super-resolves) globally available Climate Prediction Center (CPC) gauge-based precipitation products and ERA5 reanalysis data to generate kilometer-scale precipitation estimates. Downscaling gauge-based precipitation from 55 km to 1 km while recovering extreme rainfall signals poses significant challenges. To enforce our model (named WassDiff) to produce well-calibrated precipitation intensity values, we introduce a Wasserstein Distance Regularization (WDR) term for the score-matching training objective in the diffusion denoising process. We show that WDR greatly enhances the model's ability to capture extreme values compared to diffusion without WDR. Extensive evaluation shows that WassDiff has better reconstruction accuracy and bias scores than conventional score-based diffusion models. Case studies of extreme weather phenomena, like tropical storms and cold fronts, demonstrate WassDiff's ability to produce appropriate spatial patterns while capturing extremes. Such downscaling capability enables the generation of extensive km-scale precipitation datasets from existing historical global gauge records and current gauge measurements in areas without high-resolution radar.

There is a great need to accurately predict short-term precipitation, which has socioeconomic effects such as agriculture and disaster prevention. Recently, the forecasting models have employed multi-source data as the multi-modality input, thus improving the prediction accuracy. However, the prevailing methods usually suffer from the desynchronization of multi-source variables, the insufficient capability of capturing spatio-temporal dependency, and unsatisfactory performance in predicting extreme precipitation events. To fix these problems, we propose a short-term precipitation forecasting model based on spatio-temporal alignment attention, with SATA as the temporal alignment module and STAU as the spatio-temporal feature extractor to filter high-pass features from precipitation signals and capture multi-term temporal dependencies. Based on satellite and ERA5 data from the southwestern region of China, our model achieves improvements of 12.61\% in terms of RMSE, in comparison with the state-of-the-art methods.

To facilitate effective decision-making, gridded satellite precipitation products should include uncertainty estimates. Machine learning has been proposed for issuing such estimates. However, most existing algorithms for this purpose rely on quantile regression. Distributional regression offers distinct advantages over quantile regression, including the ability to model intermittency as well as a stronger ability to extrapolate beyond the training data, which is critical for predicting extreme precipitation. In this work, we introduce the concept of distributional regression for the engineering task of creating precipitation datasets through data merging. Building upon this concept, we propose new ensemble learning methods that can be valuable not only for spatial prediction but also for prediction problems in general. These methods exploit conditional zero-adjusted probability distributions estimated with generalized additive models for location, scale, and shape (GAMLSS), spline-based GAMLSS and distributional regression forests as well as their ensembles (stacking based on quantile regression, and equal-weight averaging). To identify the most effective methods for our specific problem, we compared them to benchmarks using a large, multi-source precipitation dataset. Stacking emerged as the most successful strategy. Three specific stacking methods achieved the best performance based on the quantile scoring rule, although the ranking of these methods varied across quantile levels. This suggests that a task-specific combination of multiple algorithms could yield significant benefits.