Related papers: Controlling the rain fall statistics using Mean-Re…
While deep learning methods have achieved strong performance in time series prediction, their black-box nature and inability to explicitly model underlying stochastic processes often limit their generalization to non-stationary data,…
Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and therefore the statistical normal distribution with implicit assumption of independence, fixed mean and…
In this article, we apply a probabilistic approach to study general mean field type control (MFTC) problems with jump-diffusions, and give the first global-in-time solution. We allow the drift coefficient $b$ and the diffusion coefficient…
Precipitation nowcasting, predicting future radar echo sequences from current observations, is a critical yet challenging task due to the inherently chaotic and tightly coupled spatio-temporal dynamics of the atmosphere. While recent…
Deep neural networks have made great achievements in rainfall prediction.However, the current forecasting methods have certain limitations, such as with blurry generated images and incorrect spatial positions. To overcome these challenges,…
Environmental phenomena are influenced by complex interactions among various factors. For instance, the amount of rainfall measured at different stations within a given area is shaped by atmospheric conditions, orography, and physics of…
An extreme event is a sudden and violent change in the state of a nonlinear system. In fluid dynamics, extreme events can have adverse effects on the system's optimal design and operability, which calls for accurate methods for their…
Epidemics are often modelled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions,…
Forecasts of monsoon rainfall for India are made at national scale. But there is spatial coherence and heterogeneity that is relevant to forecasting. This paper considers year-to-year rainfall change and annual extremes at sub-national…
Regional flood frequency analysis is a convenient way to reduce estimation uncertainty when few data are available at the gauging site. In this work, a model that allows a non-null probability to a regional fixed shape parameter is…
Inference on the extremal behaviour of spatial aggregates of precipitation is important for quantifying river flood risk. There are two classes of previous approach, with one failing to ensure self-consistency in inference across different…
A moisture process with dynamics that switch after hitting a threshold gives rise to a rainfall process. This rainfall process is characterized by its random holding times for dry and wet periods. On average, the holding times for the wet…
Many physical processes involve spatio-temporal observations, which can be studied at different spatial and temporal scales. For example, rainfall data measured daily by rain gauges can be considered at daily, monthly or annual temporal…
The paper introduces a new regression model designed for situations where both the response and covariates are non-stationary extremes. This method is specifically designed for situations where both the response variable and covariates are…
Assessing the availability of rainfall water plays a crucial role in rainfed agriculture. Given the substantial proportion of agricultural practices in India being rainfed and considering the potential trends in rainfall amounts across…
An unresolved problem of present generation coupled climate models is the realistic distribution of rainfall over Indian monsoon region, which is also related to the persistent dry bias over Indian land mass. Therefore, quantitative…
We perform a detailed comparison between a Markov Switching Jump Diffusion Model and a Markov Switching {\alpha}-Stable Distribution Model with respect to the analysis of non-stationary data. We show that the jump diffusion model is…
Precipitation nowcasting is an important spatio-temporal prediction task to predict the radar echoes sequences based on current observations, which can serve both meteorological science and smart city applications. Due to the chaotic…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…
Predicting precipitation maps is a highly complex spatiotemporal modeling task, critical for mitigating the impacts of extreme weather events. Short-term precipitation forecasting, or nowcasting, requires models that are not only accurate…