Mike Barcaskey said:
ISA recommends 2 to 4 inches of mulch
The ISA has some good literature and its publications and website are well thought out and quite educational. Over the years the ISA has many of its recommendations evolve, and some even change completely. As new research unfolds, we have new understandings, and new recommendations are made.
I work in the field (tree service) and although I'm not a researcher, I enjoy reading research and figuring out just how it applies to real life.
One thing I have noticed over my years in the tree business is how long it takes for changes to take place, at least in how trees are cared for.
A great example of this is planting depth. We've known for years about planting depth issues, and I still can't find a nursery that doesn't have the majority of its stock planted too deep, or a landscaper that plants trees at the proper depth.
Another example is mulching trees. I'd guess less than 50% of the mulch beds I see are done properly. By properly, I mean the bed is actually better than no mulch at all.
The most common mistake, mulching too deep.
As for the recommendation to apply 4" of new mulch to a stressed tree, it will do more harm than good. If the soils are clay and the mulch has leaves ground up with it, such a thick application could very well be a death sentence for the tree. If it didn't kill the tree outright, it would have disrupted the growth of the tree by changing soil gas exchange and chemistry.
There is no reason to add more than 2" of mulch in a single application (with the exception of temporary applications to prevent compaction, and then it becomes the better of two evils). Two inches will have all the benefits of adding more, but will have fewer adverse effects. Adding mulch is very much like adding soil to a root zone.
Adding a thick mulch layer slows the drying of the soil, which you might think is good, and it is in many situations, but with a tree that is getting regular irrigation, slowing evaporation only slows the soil gas exchange. We want the soil to cycle between wet and dry to pump out the CO2, created by plant and microbial respiration, and pump in O2 from the atmosphere.
You might also think the mulch keeps down weeds. Think about it, if you're creating an environment so hostile weeds can't even grow, what are you doing to roots?
The only time I would recommend 4" of mulch would be on well drained soils, with course chips, and on planting sites that will only get initial watering and then need to rely on rainfall. And then the recommendation would be given with the knowledge that the thick mulch was not optimal for the tree, but only being done to prevent drought damage (again, the lesser of two evils).
Two inches is what is optimal for this tree, in this situation.