VIL is short for vertically integrated liquid, essentially the amount of liquid (not ice) in the column (based on reflectivity). But, one can roughly correlate a VIL of the day with severe hail. In other words, once you get a severe hail report, you can cross reference that with the current VIL and use that as a rough predictor of additional severe hail reports. For example, a 3/4 hail report had a VIL of 65. It would be safe to assume that a similar storm with another VIL of 65 may also be producing severe hail that day. In fact, back in the 90s, it was one of the top predictors used, and "VIL of the day" programs were used to get the current day's value based on freezing level and local climatology, etc. Digital VIL is also useful for finding the core of the storm when looking for storm verification, etc. Often, after a storm moves though an area and we haven't received storm verification, we can use the DVIL to pinpoint a very small area (often a couple square miles) to call citizens to inquire of hail size.
More recently, mets are correlating 50dbz heights to the freezing level and the -20C level to predict severe hail which actually works quite well. Several studies have been done which connect a given freezing level with expected severe hail sizes, etc.
VIL Density is just a correlation of VIL to the storm echo top. It basically boils down to this, if you have a high VIL but a low echo top, that results in a higher VIL Density and a greater threat for hail. Or, if you have a low VIL with a high echo top results in a low VIL Density and a much less chance for hail. Studies have shown that VILD values of 4 or greater are usually associated with severe hail, but from my experience, it can vary quite a bit from site to site. Is it a slam dunk that you get severe hail with values of 4 or higher? No, but it's just a tool like anything else.
As far as the hail size that you see in GR3, that's just the NSSL hail algorithm output. I take it with a grain of salt. Again, back in the day, it was about all we had for guidance for predicting hail size. But, again, with recent science advancements by correlating 50dbz heights with the freezing and -20C level, and also by calculating storm top divergence comes up with more accurate hail size forecast.
One other predictor for hail size is wet bulb zero value. Heights of 7000-10000 feet are ideal for large hail. When wet bulb zero heights get to 12000-14000, it results in a large amount of melting of the hailstones before reaching the ground. You might have an algorithm output of 2" hail, but only 3/4" stones might be reaching the ground due to the longer available melting time.
):
