Artificial intelligence (AI) has been sparked by significant advancements in Graphic Processing Units (GPUs). Machine learning (ML) and deep learning (DL) models have been widely employed for Earth system modeling due to their ability to fit any contiguous functions. Especially for hydro-climate systems, DL models have been adopted to simulate the processes based on our current understandings. Although the accuracy and performance are comparable or even better than process-based models, DL models are often referred to as 'black box' models since people can not intuitively understand why and how the model produces the desired results, necessitating the need for explainable AI and trustworthy AI. Additionally, when generalizing the models to datasets out of the training range, the trust of DL models is lacking since unlike process-based models, DL models do not explicitly satisfy physical constraints, and as a result, they are more likely to generate nonphysical results. In this dissertation, ML and DL models are adopted to simulate and analyze the components of Earth's hydro-climate system, including snowpack, streamflow and precipitation. These studies focus on both accuracy and interpretations from the DL models. As for precipitation, it is analyzed with a feature-based analysis together with ML models to understand the precipitation characteristics and meteorological drivers.

Several DL models are benchmarked with 20 basins in California for streamflow simulations. The model sensitivities with respect to input variables and input time window size reflect the unique streamflow dynamics over the Sierra Nevada basins. Although there are no explicit physical constraints in the DL model, an idealized test proves the mass conservation, providing confidence in future projection analyses. The future projections validate the distinct dynamic features over the Sierra Nevada basins once again.

In the snowpack simulation, three DL models are developed and tested with observational stations across the Western US. The DL models can achieve comparable accuracy compared with a process-based dataset. A permutation-based explainable AI method is applied to understand the importance of each input variable, which highlights the critical roles of precipitation and temperature in snowpack modeling. When DL models are extrapolated to generate gridded snow estimates, the extrapolation problem arises. It is alleviated with a simple transformation to the output variable, and this method is proved to be applicable to all of the DL models that have been examined. Finally this generalized DL model is used to generate climate projections and investigate the response of snowpack with respect to climate change.

The precipitation analysis focuses on the mean precipitation and extreme precipitation events in the North American Monsoon area. The monsoon domain is first identified using a ML model from a gridded precipitation dataset, and it is further delineated into subregions to better represent local precipitation characteristics. A linear orthogonal method is used to decompose the mean precipitation time series and projects it onto various modes. The monsoon ridge and moisture surges along the Gulf of California are present in the first modes, representing the seasonal-background of precipitation, whereas the second modes are more associated with shorter-time phenomena, such as upper-level disturbances and mid-troposphere lows. Feature-based analysis is conducted to reveal the meteorological causes for extreme precipitation. Five synoptic features and one mesoscale feature are examined and assigned as potential drivers for extreme precipitation. Finally, the feature-based analysis are linked to the linear modes, and moisture surges are found to be more connected with the first mode whereas tropical cyclones are more correlated with the second modes, particularly for extreme precipitation events.

Atmospheric rivers (ARs) are filamentary systems which perform nearly all of the poleward moisture transport through the midlatitudes. When these systems are lifted---for instance when impinging on local topography---they can produce substantial precipitation which ranges from beneficial to destructive, sometimes providing essential water resources and sometimes leading to devastating floods. With this in mind, it is critical for planning and preparedness purposes to project the response of ARs to climate change. Open questions remain however, highlighting the need for a better understanding of the physical processes behind the AR response to climate change. To address these gaps in understanding, ARs are simulated in an aquaplanet, an idealized global climate model without land, sea ice, topography, or seasonality. A time-invariant ``Baseline'' sea-surface temperature (SST) distribution is prescribed for a reference run, while each test run applies a uniform increase (plus two, four, and six Kelvin) over the Baseline distribution to isolate the response of ARs to warming SSTs and assess sensitivities.

Under SST increases, zonal mean AR occurrence frequency increases everywhere, mostly due to enhancements in AR size. These AR occurrence frequency increases are greatest at higher latitudes as storm tracks shift poleward with SST warming. Zonal and areal means of AR integrated water vapor (IWV) show that AR moisture is enhanced at rates greater than predicted for surface moisture by the Clausius-Clapeyron relation with respect to SST warming. Vertical profiles of relative humidity (RH) and temperature show that this ``super-Clausius-Clapeyron'' IWV increase masks RH decreases at upper levels which are related to upper-tropospheric warming that far outpaces the prescribed SST increases. Zonal and areal means of AR IWV transport (IVT) show lower increases with SST warming than for IWV; a simple linear decomposition of AR IVT into moisture and wind components shows that a slowing of mean AR wind speeds attenuates the IVT response. Zonal mean AR precipitation rates exhibit a complicated response characterized by increases in some latitude bands and decreases in others. A linear decomposition of AR precipitation rates like that performed for AR IVT once again shows a compensatory relationship between AR moistening and weakening dynamics, in this case mid-tropospheric vertical velocities.

Increases in AR size as SSTs warm are examined separately. Cross-sections of AR IVT are approximated with Gaussian functions with three fit parameters: AR background IVT, AR IVT exceedance above the background, and the breadth of the AR IVT profile, defined as the distance through which 95\% of the IVT exceedance occurs. From both the AR IVT cross-sections and their Gaussian approximations are derived four measures of AR width in total. All widths are enhanced with SST warming, mostly as a result of enhanced background IVT statistics and increased AR IVT profile breadth. IVT profile breadth changes are driven mostly by Clausius-Clapeyron moderated moisture increases, though changes to AR wind profiles also play a role.

The significant impacts of climate change on extreme weather events have been widely demonstrated in past decades. As the most expensive climate disaster, the drought and its risks under the warming climate always attract people's attention. However, huge uncertainties exist in climate projections, mainly consisting of scenario uncertainty, model uncertainty, and internal variability. Moreover, drought is more difficult to assess in climate datasets, due to its long duration per event, relative to the length of a typical simulation. Meanwhile, since the infamous extreme drought of the 1960s, the climate of the Northeastern United States (NEUS) has generally trended towards warmer and wetter conditions. Nonetheless, there is mounting evidence that short-term droughts will continue to pose a significant risk for this region. Therefore, there is a growing need for a comprehensive framework with the most advanced climate techniques and datasets to investigate the impacts of climate change on drought over NEUS.

In this thesis, firstly, a comprehensive drought feature-based evaluation system, equipped with statistical hypothesis testing and Principal Feature Analysis, is put forward and is designed to be easily used for any climate datasets. With its help, people can choose climate models with fewer model uncertainties and biases in capturing droughts in the regions of interest. This system is applied to three characteristically distinct regions in the conterminous US and across several commonly employed climate datasets (CMIP5/6, LOCA, and CORDEX). As a result, insights emerge into the underlying drivers of model bias in global climate models, regional climate models, and statistically downscaled models.

Then to reduce the impacts of internal variability on drought projections, 7 large ensemble (LE) models and a novel drought index are employed to examine the changing trends of drought at different temporal scales. We find most LE models indicate the NEUS will experience a long-term wetting trend with more ``extremely wet'' months, but also more frequent short-term extreme droughts. These changes are associated with increasing precipitation, atmospheric water demand, and climate variability. We also conclude that discrepant trends in precipitation and evapotranspiration variability will lead to increasing anti-correlation of these variables, which is relevant to the intensification of rapidly developing drought -- particularly in the spring season. These changes are associated with an increase in evapotranspiration from plants, brought by an earlier emergence of the growing season and denser vegetation.

The northeastern United States (hereinafter, the Northeast) is home to a dense human population and encompasses a variety of agricultural and economic interests that are reliant on the available water resources and the replenishment of those resources via precipitation. Due to ongoing climate change, water availability is expected to be altered in this region. This expected change is particularly important at the ends of the precipitation spectrum (i.e., extreme precipitation and droughts), as these events can lead to devastating economic damages to infrastructure, property, and agriculture. Given the many problems that can be associated with an increased frequency of both wet and dry extremes, it has become increasingly important to gain a better understanding of the large-scale meteorology related to precipitation variability in the Northeast. Such insight provides meaningful insight for stakeholders and policymakers with interests pertaining to future resource allocations and water management practices in the region.This PhD work seeks to build upon the existing literature related to understanding the large-scale processes that are important in producing conditions favorable to precipitation in the Northeast, and uses that understanding to examine the meteorological conditions that accompany short-duration dry spells (droughts) that occur over the region. My dissertation establishes a unique framework by which to explore scientific questions related to Northeast precipitation variability by utilizing a novel linear orthogonal decomposition technique, large-scale meteorological pattern analysis, analysis of relevant dynamical and thermodynamical fields, and reanalysis and climate model datasets. Such a framework provides a comprehensive assessment of the meteorological conditions associated with different precipitation regimes over the Northeast. This research topic sits at the intersection of atmospheric science, regional climate, machine learning, and climate model validation, with the overall goal of improving our capabilities in regional climate analysis. Chapter 1 provides an introduction and background information related to precipitation in the Northeast. Chapter 2 focuses on identifying the large-scale drivers of precipitation over the Northeast using a novel linear orthogonal decomposition (LOD) approach. Chapter 3 examines the absence (or reduction) of those drivers during short-duration dry spells (droughts) over the region primarily using large-scale meteorological pattern (LSMP) analysis. Chapter 4 assesses the fidelity of current-generation general circulation models (GCMs) in representing different characteristics of the dry spells in comparison to those obtained from observations. Lastly, Chapter 5 summarizes the work discussed in this dissertation and provides insight into potential avenues for future work.