Related papers: Controlling the rain fall statistics using Mean-Re…

A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the…

Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time $t$…

We propose a general framework for studying jump-diffusion systems driven by both Gaussian noise and a jump process with state-dependent intensity. Of particular natural interest are the jump locations: the system evaluated at the jump…

Short-term (0-24 hours) precipitation forecasting is highly valuable to socioeconomic activities and public safety. However, the highly complex evolution patterns of precipitation events, the extreme imbalance between precipitation and…

A region under rainfall is a contiguous spatial area receiving positive precipitation at a particular time. The probabilistic behavior of such a region is an issue of interest in meteorological studies. A region under rainfall can be viewed…

We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…

Precipitation data collected at sub-hourly resolution represents specific challenges for missing data recovery by being largely stochastic in nature and highly unbalanced in the duration of rain vs non-rain. Here we present a two-step…

In this paper, we present the double smoothed nonparametric approach for infinitesimal conditional volatility of jump-diffusion model based on high frequency data. Under certain minimal conditions, we obtain the strong consistency and…

Despite the importance of quantifying how the spatial patterns of extreme precipitation will change with warming, we lack tools to objectively analyze the storm-scale outputs of modern climate models. To address this gap, we develop an…

Forecasting extreme precipitation is essential yet challenging due to its rarity and complexity. We develop a large deviation framework to estimate the return times of extreme precipitation events. We first find that the Landau…

In this paper we prove a necessary condition of the optimal control problem for a class of general mean-field forward-backward stochastic systems with jumps in the case where the diffusion coefficients depend on control, the control set…

In climate science and meteorology, high-resolution local precipitation (rain and snowfall) predictions are limited by the computational costs of simulation-based methods. Statistical downscaling, or super-resolution, is a common workaround…

In this paper, the complexities in the relationship between rainfall and sea surface temperature (SST) anomalies during the winter monsoon (November-January) over India were evaluated statistically using scatter plot matrices and…

Due to complex physical phenomena, the distribution of heavy rainfall events is difficult to model spatially. Physically based numerical models can often provide physically coherent spatial patterns, but may miss some important…

Extreme floods pose escalating risks in a changing climate, yet forecasting remains challenging due to peak flow underestimation and high uncertainty. We introduce DRUM, a diffusion-based probabilistic deep learning approach that advances…

In this study, we examine a Bayesian approach to analyze extreme daily rainfall amounts and forecast return-levels. Estimating the probability of occurrence and quantiles of future extreme events is important in many applications, including…

Extreme value theory is concerned with probabilistic and statistical questions related to very high or very low values in sequences of random variables and in stochastic processes. The subject has a rich mathematical theory and also a long…

Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Max-stable processes are a class of asymptotically-justified models that are capable of representing spatial dependence among extreme…

Climate change is increasing the frequency of extreme precipitation events, making weather disasters such as flooding and landslides more likely. The ability to accurately nowcast precipitation is therefore becoming more critical for…

Highly resoluted and accurate daily precipitation data are required for impact models to perform adequately and to correctly measure high-risk events' impact. In order to produce such data, bias-correction is often needed. Most of those…