Our ability to predict precipitation on climate time-scales (months–decades) is limited by our ability to separate signals in the climate system (cyclical and secular) from noise — that is, variability due to processes that are inherently unpredictable on climate time-scales. This dissertation describes methods for characterizing “weather” noise — variability that arises from daily-scale processes — as well as the potential predictability of precipitation on climate time-scales. In each method, we make use of a climate-stationary null model for precipitation and determine which characteristics of the true, non-stationary system cannot be captured by a stationary assumption. This un-captured climate variability is potentially predictable, meaning that it is due to climate time-scale processes, although those processes themselves may not be entirely predictable, either practically or theoretically. The three primary methods proposed in this dissertation are 1. A stochastic framework for modeling precipitation occurrence with proper daily-scale memory representation, using variable order Markov chains and information criteria for order selection. 2. A corresponding method for representing precipitation intensity, allowing for memory in intensity processes. 3. A semi-parametric stochastic framework for precipitation which represents intensity and occurrence without separating the processes, designed to handle the issues that arise from estimating likelihoods for zero-inflated processes. Using each of these methods, potential predictability is determined across the contiguous 48 United States. Additionally, the methods of Chapter 4 are used to determine the magnitude of weather and climate variability for the “historical runs” of five global climate models for comparison against observational data. It is found that while some areas of the contiguous 48 United States are potentially very predictable (up to ∼ 70% of interannual variability), many regions are so dominated by weather noise that climate signals are effectively masked. Broadly, perhaps 20–30% of interannual variability may be potentially predictable, but this ranges considerably with geography and the annual seasonal cycle, yielding “hot spots” and “cold spots” of potential predictability. The analyzed global climate models demonstrate a fairly robust representation of weather-scale processes, and properly represent the ratio of weather-to- climate induced variability, despite some regional errors in mean precipitation totals and corresponding variability.