Extreme precipitation models are crucial for understanding the characteristics of extreme weather, ensuring the risk of extreme events, and designing flood protection structures. Analytical relationships that link the risk of extreme precipitation with a specific duration at a given location (i.e. intensity-duration-frequency(IDF) relationships) are commonly used to characterize the extreme events. If homogeneous rainfall data with long records are available, reliable analytical relationships can be developed. Yet, this is often not the case and the gauge networks in many parts of the world are either short or sparse. As a result, uncertainties of the gauge-based analyses tend to be high. To alleviate these uncertainties, regional frequency analysis methods which pool the precipitation data from multiple sites with a homogeneous precipitation pattern are used for modeling extreme precipitations. Yet, defining these homogeneous regions requires making additional assumptions that in many cases are not met.

In this dissertation, I try to address the limitations of the conventional extreme precipitation modeling approaches by: 1) Employing remotely-sensed precipitation information, instead of gauge observations, to capture the spatiotemporal variability of extreme precipitation; and 2) Applying advanced statistical techniques that do not have the limitations of the conventional regional approaches and can accommodate additional information to enhance model's performance.

In the first part of this dissertation, suitability of remotely-sensed precipitation information for extreme precipitation modeling is explored. A bias-correction framework is introduced to adjust the biases in the satellite-based extreme precipitation estimates. It is shown that the proposed method can effectively reduce the biases in the remotely-sensed extreme rainfall data, especially at high elevation regions where ground-based observations are poor and satellite-based estimates are highly biased. Also, it is demonstrated that the satellite-based extreme precipitation estimates that are bias-adjusted with limited ground-based observations using the proposed method outperform the gauge interpolation estimates even at some densely-gauged regions. Results also demonstrate that the high quantile estimates from the bias-adjusted dataset are in agreement with the Frequency Atlas of the United States(NOAA Atlas 14) estimates across various durations and return periods.

In the next step of this dissertation, advanced statistical techniques are employed to model spatial and temporal characteristics of extreme precipitation from remotely-sensed information. A hierarchical Bayesian approach is used to model extreme precipitation and to generate spatially consistent quantile estimates with low estimation uncertainties. In addition to the Bayesian framework, Max-stable processes, as the generalization of the extreme value theory, are used to capture the marginal properties and tail dependence structure of the extreme precipitation data. The performances of the applied methods in modeling extreme precipitations are evaluated using various validation metrics. A comprehensive evaluation of the models' performances shows that the applied methods are capable of generating extreme return levels that are consistent with gauge-based observations.

Results of this dissertation demonstrate that the satellite-based precipitation information can be used for extreme precipitation modeling, especially at poorly instrumented regions. Also, this study serves as an introduction to the application of advanced statistical techniques for extreme precipitation modeling using remotely-sensed information. The applied methods resulted in outstanding performances in characterizing extreme precipitation from remotely-sensed information.

Among all natural phenomena, precipitation is the main driver of the hydrological cycle and the challenging task of precipitation estimation is an essential element for hydrological and meteorological applications. Recent developments in satellite technologies resulting in higher temporal, spatial, and spectral resolutions, along with advancements in Machine Learning (ML) algorithms and computational power, open the great opportunity to develop analytical and data-driven tools to characterize such natural phenomena and their future behavior more efficiently and accurately. In this dissertation, state-of-the-art data-driven frameworks are proposed based on advanced deep learning algorithms and computer vision tools to extract the most useful features from single or multiple spectral bands of satellite information.

Specifically, in the first part of the dissertation, a novel gradient-based cloud segmentation algorithm is proposed to effectively identify clouds and monitor their evolution towards more accurate quantitative precipitation estimation and forecast. This algorithm integrates morphological image gradient magnitudes to separate cloud systems and patches boundaries from single or multi-spectral imagery. This method improves rain detection and estimation skills with an accuracy rate of up to 98\% in identifying cloud regions compared to the existing cloud-patch-based segmentation technique implemented in the operational PERSIANN-CCS (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Network - Cloud Classification System) algorithm. Application of this method is extendable to hurricanes simulations and synthetic satellite imageries simulated by high-resolution weather prediction models.

In the second part, an end-to-end deep learning precipitation estimation framework is developed from multiple sources of remotely sensed information to provide half-hourly, 4-km by 4-km precipitation estimates over the CONUS. In the first stage, a Rain/No Rain (R/NR) binary mask is generated by classification of the pixels and then a Fully Convolutional Network (FCN), U-net, is used as a regressor to predict precipitation estimates for rainy pixels. Due to the complex structure of precipitation, and inability of traditional objective functions to capture the true rainfall distribution, a novel distribution matching approach is designed and implemented. The network is trained using both the conditional Generative Adversarial Network (cGAN), and the Mean Squared Error (MSE) loss terms to match the distribution of the generated results and observed data, and to relax the strict assumptions of the traditional and conventional loss function in DNNs. The newly developed precipitation estimation algorithm is introduced as an augmentation for PERSIANN-CCS (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Network - Cloud Classification System) algorithm for estimating global precipitation and is termed as PERSIANN-cGAN. Statistics and visualizations of the metrics for PERSIANN-cGAN represent an improvement of the precipitation retrieval accuracy compared to the operational PERSIANN-CCS product, and a baseline model trained using the conventional MSE loss term.

Precipitation is one of the key elements of the Earth's water cycle. Long-term precipitation observations in global scale and at high spatial and temporal resolutions are imperative for understanding how global warming has affected our climate system, particularly in terms of changes in the characteristics of precipitation. This dissertation contributes to the advancement of our understanding of the water cycle by 1) development of a new long-term high-resolution satellite-based precipitation product to be used for different hydrological and climate studies at a higher spatial and temporal resolution than previously possible, and 2) presenting a probabilistic framework to study the observed variations, trends and changes in global precipitation, particularly extreme precipitation events, in the course of time.

In the first part of the dissertation, using the Geostationary Earth Orbit (GEO) satellites Infrared (IR) channel observations of the brightness temperature of the cloud, and the Global Precipitation Climatology Project (GPCP) monthly product, a retrospective high-resolution (daily, 25km) satellite-based precipitation climate data record is developed and introduced. The product, namely Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks - Climate Data Record (PERSIANN-CDR), provides more than 30 years of global rainfall estimates from 01/01/1983 to delayed present covering the latitude band 60°S-60°N and longitude band 0°-360°. The results from a number of different verification studies (Hurricane Katrina, 1986 Sydney flood, precipitation probability density function, extreme precipitation indices, rainfall-runoff modeling) over different regions (U.S., Australia, China) are presented and are encouraging.

In the second part, a non-stationary probabilistic framework based on Extreme Value Theory (EVT) is developed to assess potential footprints of climate change on characteristics (intensity and frequency) of extreme precipitation events. The main goal was to investigate if there have been statistically significant changes and trends in the Probability Distribution Function (PDF) of precipitation extremes over time. The proposed probabilistic scheme which is based on Generalized Extreme Value (GEV) and Generalized Pareto (GP) distributions proved to be effective in stochastically modeling the behavior of precipitation extremes over the past three decades. The statistically significant trends in the time-variant GEV distribution are tested over the U.S. The results show that Eastern and particularly the Northeastern parts of the U.S. are experiencing positive trends in the intensity and frequency of extreme precipitation events.