Performing statistical analyses with climate data requires accounting for many types of variability. This variability is complex and spatiotemporal in nature, and the variability often integrates overlapping processes at multiple spatial and temporal scales. While this makes climate a challenging setting for applying statistical methods, we can use scientific expertise to properly account for and leverage these spatiotemporal structures in our analyses. This dissertation develops statistical methods for performing large scale multiple hypothesis testing and uncertainty quantification in the climate setting. Chapter 1 introduces the climate setting and some of the particular challenges that methods face in this setting. Chapter 2 focuses on multiple hypothesis testing in a common regression setting in climate, where a univariate response variable is regressed against a spatial grid of covariates. The false discovery rate (FDR) control framework provides a practical method for controlling for multiple hypothesis testing, but popular FDR controlling methods, such as Benjamini-Hochberg, exhibit weak power when applied to data that is highly spatially correlated, as is often the case with climate data. This limitation motivates a proposed spatial smoothing method using learned local covariance structures to smooth covariate data as pre-processing step before the analysis. We demonstrate that our method still controls the FDR rate empirically, while substantially increasing power in simulation studies. Then, we apply the method on regressions of central US temperatures against sea surface temperatures. In Chapter 3, we consider the problem of quantifying uncertainty in estimates of precipitation extremes over the conterminous United States (CONUS). Due to the inherently rare nature of extreme events, extreme quantiles are difficult to estimate, and this process is made more challenging by the temporal structure of precipitation data, which is influenced by modes of variability. We expand upon observational large ensemble methods in the literature to generate synthetic spatiotemporal fields of precipitation over CONUS. These synthetic fields incorporate variability related to large scale modes of climate variability as well as unrelated short term variability to produce fields with realistic precipitation variability. This method is validated using data from climate model initial condition large ensembles, and we use these ensembles to estimate uncertainty in estimates of monthly extreme quantiles of the precipitation distribution across CONUS. In Chapter 4, we apply this observational large ensemble approach with regression models to better quantify variability in Colorado River streamflows at Lees Ferry. Streamflows of the Colorado River are heavily influenced by temperature and precipitation over the Upper Colorado River Basin. In order to understand how the variability in temperature and precipitation can influence the variability in streamflows, we apply the observational large ensemble to generate synthetic precipitation and temperature records for the Upper Colorado River Basin. And, using these records with the regression models, we produce a synthetic ensemble of streamflows. This synthetic ensemble is used to estimate annual variability for streamflows that properly integrate the variability of temperature and precipitation records. Then, we use estimates of future warming to explore how streamflows might change by 2050. Finally, Chapter 5 concludes the thesis with a discussion of these methods and future work.