Need help understanding variables that relate to meterology terminology
Here are the answers that I received for anyone interested:

1) Regarding the question about 10th percentile: The 10th percentile of reflectivity in a 5x5 neighborhood of the gauge means that they take the 25 reflectivity values surrounding the gauge (horizontally), sort them, and return one of the lowest values. The table in the attached image shows an example of this. In this case, the gauge is assumed to be in the green box, and bold value to the bottom right is the 10th percentile value returned by Excel.

2) Regarding the question about the vertical column: The radar scans at multiple elevation angles (between 0.5 and 19.5 degrees above horizontal), and so each one of those scans will be at a different height when it passes over the location of the gauge, sampling a different set of particles (rain, hail, etc). So the vertical maximum reflectivity at that point is simply taking the maximum value at the gauge location from all the available elevations within a complete set of scans. This “maximum reflectivity in the vertical column” variable is sometimes referred to as “composite reflectivity”.

3) Pulse volume refers to the volume of air that is sampled by the radar beam at a given instant. This volume is defined by a horizontal extent, a vertical extent, and a range extent. The horizontal and vertical extents are determined by the characteristics of the antenna and the range being considered. For most radars, this cross-section is circular, since the horizontal and vertical beamwidths are the same, often around 1 degree. The range extent is determined by the amount of time the radar transmits between periods of listening. The physical length of the pulse is the speed of light times the amount of time the pulse is being transmitted, and is typically on the order of a couple hundred meters. The formula for pulse volume is pi(range*vertical beamwidth/2)(rangehorizontal beamwidth/2)(pulse length/2).