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The occurrence and properties of hail smaller than severe thresholds (diameter < 25 mm) are poorly understood. Prior climatological hail studies have predominantly focused on large or severe hail (diameter at least 25 mm or 1 inch). Through use of data from the Meteorological Phenomena Identification Near the Ground project, Storm Data, and the Community Collaborative Rain, Hail and Snow Network the occurrence and characteristics of both severe, and sub-severe hail are explored. Spatial distributions of days with the different classes of hail are developed on an annual and seasonal basis for the period 2013-2020. Annually, there are several hail-day maxima that do not follow the maxima of severe hail: the peak is broadly centered over Oklahoma (about 28 days per year). A secondary maxima exists over the Colorado Front Range (about 26 days per year), a third extends across northern Indiana from the southern tip of Lake Michigan (about 24 days per year with hail), and a fourth area is centered over the corners of southwest North Carolina, northwest South Carolina, and the northeast tip of Georgia. Each of these maxima in hail days are driven by sub-severe hail. While similar patterns of severe hail have been previously documented, this is the first clear documentation of sub-severe hail patterns since the early 1990s. Analysis of the hail size distribution suggests that to capture the overall hail risk, each dataset provides a complimentary data source. 

This paper synthesizes multiple methods for machine learning (ML) model interpretation and visualization (MIV) focusing on meteorological applications. ML has recently exploded in popularity in many fields, including meteorology. Although ML has been successful in meteorology, it has not been as widely accepted, primarily due to the perception that ML models are “black boxes,” meaning the ML methods are thought to take inputs and provide outputs but not to yield physically interpretable information to the user. This paper introduces and demonstrates multiple MIV techniques for both traditional ML and deep learning, to enable meteorologists to understand what ML models have learned. We discuss permutation-based predictor importance, forward and backward selection, saliency maps, class-activation maps, backward optimization, and novelty detection. We apply these methods at multiple spatiotemporal scales to tornado, hail, winter precipitation type, and convective-storm mode. By analyzing such a wide variety of applications, we intend for this work to demystify the black box of ML, offer insight in applying MIV techniques, and serve as a MIV toolbox for meteorologists and other physical scientists.