My opinion....
Only my opinion.....take it for what it's worth. Feel free to throw rocks at me. I won't get upset, nor will I respond.
Fundamentally, there are three kinds of hydroplaning (as mentioned). The formula mentioned is also valid, but misleading.
The 9 times the square root thing applies to a tire that is already spinning at the correct speed. If the tire is stopped (as just prior to landing), and you make a really nice touchdown, the tire may never reach the proper speed, and, at that point, hydroplaning can occur at speeds as low as 6 to 7 times the square root. Firm touchdowns will get the wheels spinning at the proper speeds.
The above formula applies only to "Dynamic" hydroplaning.
Reverted rubber hydroplaning occurs when the tire is allowed to skid. Steam (from boiling water) develops and changes the surface characteristics of the rubber. This new surface characteristic doesn't do as well in stopping the aircraft.
Finally, there is viscous hydroplaning. It occurs when there are contaminants on the runway, such as oil, fuel, rubber deposits, etc.
It is important for you to touchdown firmly at the proper speed and the proper point on the runway. Use maximum reverse thrust immediatley upon touchdown. It is also important to touch down with no lateral drift AND with the aircraft aligned with the runway. No crab. (In some cases, some aircraft, some circumstances, it is necessary to land with some crab, I know....)
If you begin to drift toward the downwind side of the runway, steering to get back to centerline is proper, but, with maximum reverse, you will drift even more. This is because the thrust vector has a lateral component when the aircraft is not perfectly aligned with the runway. So, steer to get back on centerline, and, at the same time, go into idle reverse. Once you're back on centerline and aligned with the centerline, go back to maximum reverse.
The new anti-skid systems are great. The older generation ones are not. You don't want to skid....that's the idea. If you do, you get into a reverted rubber problem. (And, possibly a control problem.)
It's quite possible to experience all three types of hydroplaning in the same landing. First, you make a really nice, smooth landing....the tire really never makes good, solid contact with the runway (dynamic). Then, you skid, for one or many of a number of reasons, and you get reverted rubber. Then, as the other end of the runway comes up, you get into a viscous hydroplaning problem....all the rubber build up from the landings coming the opposite direction...take offs in the opposite direction (oil, fuel, exhaust, etc.).....
Be aware that with reverted rubber...and most especially viscous hydroplaning, hydroplaning can and does occur at any speed...even as low as ten knots. And, many aircraft anti-skid systems do not function at slow speeds. So, this makes things worse.
Again, the idea is to use reverse thrust at max and as soon as possible after touchdown. You want to take advantage of this, as best you can, so the brakes and tires don't have to do as much work at these high speeds. As the speed decreases and reverse thrust effectiveness diminishes, the brakes, tires, and anti-skid system will have to do more of the work...which is OK, since, ostensibly, you're going slower....less chance of dynamic hydroplaning.
Follow SOP with regard to reverse thrust use....but, keep in mind, if you need it, use it. If the end of the runway is rapidly approaching, and your deceleration is not so good...use max reverse...to a full stop if necessary. While this may not comply with SOP, it's far more desirable to the alternative.
By the way, unless your aircraft tires have fancy tread designs (as automobiles have), the tread on your tires has little effect on dynamic hydroplaning. Proper inflation pressure is the critical factor. And, runway grooving is critical, as well.
As I re-read this for typos, I noticed I failed to mention the importance of getting the speed brakes out immediately upon touchdown, as well. The reason for this should be obvious.
Your company's SOP is a good benchmark for operation in adverse weather. Use of autobrake (Today's systems are great!) is desirable. Typically, autobrake, coupled with a good anti-skid system, will allow you to get maximum deceleration (for the conditions given to you), minimizing skidding, maximizing control. Again, follow your company's SOP.
Many times, under adverse conditions, you'll exit the runway at the end or a turn off near the end, where contaminants can be heavy. And, with ATC constraints, you'll be asked to 'expedite' to the next available turn off. Be careful with this, as you'll find that when it's time to slow for the turn off, you'll be unable to slow....anti-skid system is not active because of the low speed (20 Kts for the Bus)....a lot of rubber and oil, etc., on the runway....and you'll slide right past your turn off. (If you were planing to expedite to the last turn off, you'll have problems....obviously.) So, resist the 'go along, get along' with ATC. They know (or should know) to give a bit more spacing on aircraft on approach, as it'll take a bit longer for aircraft to decelerate and clear the runway under adverse conditions. If the aircraft behind you has to go around, it won't be your fault....it'll be ATC's fault. In other words...one of flying's golden rules: Don't let ATC fly your aircraft!
Just my two cents...
Fly safe,
PantLoad