2.1 Imagery

A DJI Phantom 4 Pro V2 aircraft and Pix4Dcapture flight-control software were used for image acquisition. The integrated, gimbal-mounted aircraft camera uses a 13.2 mm × 8.8 mm active-pixel sensor which provides 20M effective pixels, automatic exposure, and an autofocus lens with a focal length of 8.8–24 mm and maximum field of view of 84^∘. For the 26 November event, the aircraft was flown at an altitude of 10 m (relative to the take-off location) over a rectangular survey area of 1290 m² centred on 34.6459^∘ S, 68.4814^∘ W, providing a ∼2.7 mm ground sampling distance (Fig. 1a). Near-surface wind speed at the time of capture was noted by the authors to be a gentle breeze (3.5–5.5 ms⁻¹), reducing the likelihood of wind-induced motion blur. Images were captured with a 70 % overlap laterally and medially at a flight speed of 1 m s⁻¹ over a surface consisting of sparse grasses, small shrubs, gravel and dirt. A large image overlap and slow flight speed were selected to increase the number of quality matching points during orthomosaic construction and reduce motion blur (Bemis et al., 2014). The survey was initialized immediately once hail fall concluded and required approximately 4 min to complete. The location of images was measured using the integrated GPS receiver, which has an accuracy of ±1.5 m. Precise location measurements (e.g. real-time kinematic positioning) are not essential for improving the pixel size accuracy during photogrammetry processing (Küng, 2012).

The Pix4Dmapper software package was used to generate orthomosaic imagery and a digital elevation model (DEM) from the survey photos (Küng, 2012) with a ground sampling distance of 2.7 mm. The software is based on the structure-from-motion photogrammetry technique and uses the following automated steps:

1. Tie points between the survey images are identified. Each tie point must be matched in at least three images.

2. Tie points are combined with positioning and orientation information from the aircraft autopilot to reconstruct the camera perspective and position for each survey image. This information is used to verify the quality of matching points and calculate the 3-D coordinates of tie points.

3. The sparse point cloud of 3-D coordinates is interpolated to obtain a gridded DEM.

4. The DEM is used to project every image pixel and to calculate an orthomosaic.

An average of 181 081 matched tie points were found per cubic metre with a mean geolocation error of less than 1 mm. Analysis of the DEM indicates a gradual slope was present across the survey area with a total change in elevation of approximately 2.3 m (not shown). Two scale markers consisting of 300 mm × 300 mm black and white vinyl tiles were also placed into the aerial-survey area to provide a secondary check of pixel size within the orthomosaic.

2.2 Hail detection

To efficiently identify the many thousands of hailstones captured in the aerial imagery after the San Rafael hailstorm, automated feature detection techniques were explored. Simple thresholding of pixel luminosity for detecting hailstones performed poorly owing to similar luminosity from sparse grasses, light dirt patches, pale-coloured rocks and leaf debris and to instances when hailstones were in contact. Despite the low contrast, hailstones were easily identifiable in the imagery by human observers, motivating the application of the state-of-the-art Mask regional CNN (R-CNN) model (He et al., 2017). This technique combines the optimized selection and parallel processing of proposed feature regions (Fast R-CNN) with semantic segmentation, whereby each pixel is classified. Mask R-CCN architecture and implementation methods used are described in detail by He et al. (2017).

Figure 2Demonstration of hail size extraction from the 26 November 2018 survey orthomosaic (a) from a single tile (b: blue bounding box) for a single hailstone (c: black circle in b). Radial transects for extracting imagery lightness are shown in (c) as black lines radiating from hailstone centroid (blue marker), and hailstone edge pixels along transects are numbered. The subplot in panel (d) shows the normalized pixel lightness along the 12 transects shown in (c) with the corresponding edge pixels marked.

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Figure 3Orthomosaic RGB imagery from the 26 November 2018 survey overlaid with the outlines of tiles used for the extraction of hail size distribution statistics.

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To reduce memory requirements, the 489 MP aerial-survey orthomosaic was divided into 1961 tiles of size 600 pixels × 600 pixels, including a 50-pixel overlap along edges with neighbouring tiles to avoid cropped hailstones (Figs. 1b, 2a, b). To provide a sufficiently large sample of hailstones for training the Mask R-CNN model, 12 tiles were manually selected that in total contained more than 1000 stones and were annotated using the VGG Image Annotator (VIA) tool (Dutta and Zisserman, 2019). These tiles were also selected to sample the varying background types across the orthomosaic. Nine tiles were randomly selected for training (containing 729 annotated hailstones) and the remaining three for validation (Fig. 1c). The Mask R-CNN training was initialized with the pre-trained weights from the Microsoft COCO dataset (set of $>\mathrm{2}\times {\mathrm{10}}^{\mathrm{5}}$ labelled images; Lin et al., 2014), which capture many features in natural images. Utilizing these weights greatly reduces the training time required to recognize hail. The default learning and weighting configuration described by He et al. (2017) was applied, and training was performed on eight GPUs with one image per GPU for 3000 iterations (∼43 min of computation time). The trained model detected more than 94 % of the hailstones in each validation tile with a false-alarm rate of <1 %. When applied to all tiles, the trained Mask R-CNN model detected a total of 46 871 hailstones.

Figure 4Distribution of hail major-axis length, minor-axis ratio, and scatter plot of axis ratio and major-axis length from the (a) photogrammetry and (b) pad hail size retrievals for the 26 November 2018 survey. A fitted gamma distribution probability density function for the photogrammetry major-axis size distribution is shown (black line). Photogrammetry scatter plot observations are binned using 5 mm bin sizes and error bars represent ±1 standard deviation.

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2.3 Hail size measurement

The segmentation mask generated by the Mask R-CNN model was initially tested for hail size measurement but was found to contain small errors that rendered it unsuitable. To provide the pixel-level accuracy required for measuring hailstones, an edge detection algorithm was developed to find the steep lightness gradient¹ at the hailstone edge that occurs radially from the hailstone centroid (Fig. 1d). The HSL colour space is an alternative to the red–green–blue model (RGB; developed for colour displays) that is commonly used in computer vision applications for reducing the correlation between colours (Cheng et al., 2001). The hailstone centroids required to initialize the edge detection technique are derived from the segmentation mask. Two additional quality control steps are also applied to the centroids and image tiles:

1. Tiles where hail was obscured (e.g. under long grass or shrubs) or water had accumulated were removed, leaving 188 clean image tiles containing 15 983 hailstones over a total area of 342.6 m² for hail size measurement.

2. Hail centroids for the 188 clean image tiles were manually assessed and amended if required using the VIA annotation tool.

The clean image tiles are next transformed into the HSL colour space and the hailstone size is measured for every centroid using the following procedure. First, coordinates of 12 equally spaced radials of length 20 pixels from the centroid (p₀) are calculated (Fig. 2c), denoted as $p_i^k$, where i is the pixel index ($i=\mathrm{1},\mathrm{\dots }\mathrm{20}$) and k is the radial index ($k=\mathrm{1},\mathrm{\dots },\mathrm{12}$). For all points along a radial, the lightness values $L\left(p_i^k\right)$ are extracted. Then, the gradient of lightness values $L^{\prime }\left(p_i^k\right)$ along each radial are calculated. Starting from the centroid of each radial, the edge point is found at coordinate $p_i^k$ when the following criteria are met:

and

The required minimum lightness difference between the hailstone centroid and background (50) was found to perform well across all background types, including light-coloured soils. Once all edge points are found along the radials (Fig. 2d), the median distance $\stackrel{\mathrm{̃}}{d}$ from the centroid is calculated for each edge point. If an edge point falls outside the range $[\stackrel{\mathrm{̃}}{d}\times \mathrm{0.5}$ to $\stackrel{\mathrm{̃}}{d}\times \mathrm{1.5}]$, it is replaced by $\stackrel{\mathrm{̃}}{d}$. Finally, to measure the major- and minor-axis length of the hailstone, the minimum bounding box (allowing for rotation) is calculated for the set of edge points.