I realize that mature trees typically have shallow roots that often go beyond the drip line of the tree. In a situation where there is not enough water going to a tree from its shallow root system, can you make up for that by just adding water close to the trunk and allowing the tap root of the tree to get access to that water? An example of where this could happen would be an established tree that grew up on water from a lawn, and the lawn is later removed and most of the yard is not receiving much Summer water.

Most trees start out with a tap root but it doesn't continue to grow. In the beginning the tap root offers stability but as the tree grows and the roots spread, the tap root isn't needed.

Tree roots follow water so if the tree was starved for water, the roots are either 2 acres away or non-existent.

These are generalizations. What kind of tree are we talking about? Can you post photos?

@Lucy68 The problem with underwatered trees is across a whole garden, but the main trees involved are Magnolia, Apple, and Mimosa.

I think I would get out the rainbirds and turn them on to try to soak the entire garden for two reasons: You want the roots to move away from the trunk and you want the roots already there to get water. Even though the roots were growing under a lawn, they were getting enough water to survive and support mature trees. The roots are down there but probably damaged due to the lawn removal.

I realize that mature trees typically have shallow roots that often go beyond the drip line of the tree. Very true. Roots of some trees have been traced back to a tree as far as a mile or more away. In a situation where there is not enough water going to a tree from its shallow root system, can you make up for that by just adding water close to the trunk and allowing the tap root of the tree to get access to that water? Many experiments have been done to determine how water supply affects roots. One thing we do know is roots are incapable of following or seeking out water and nutrients, including oxygen. They simply grow where there is an ample supply of resources and die back where the supply is inadequate. It was found that with regard to a particular red maple, >90% of the tree's fine roots were in the top 6" of soil in early spring, with fine roots disappearing in the top 6" and growing deeper and deeper as summer progressed such that by August's end more than 90% of fine roots were located at depths below 18". That shouldn't be read to mean that all trees are capable of being so nimble when it comes to adjusting to droughty conditions.

Many trees and shrubs don't have a tap root (root radical). Anything created by a cutting or layering won't have a taproot. Too, in many cases long taproots are severed when seedlings are potted individually, and will develop several anchor roots growing downward from horizontal roots radiating from the basal wound on the cutting.
Roots of a seedling:


Roots on cuttings or layered plants are normally much more tidy and balanced than those seen on seedlings:


Al

True. Roots grow where there is oxygen and water already available, they don't seek it out like a snake hunting a mouse.

So in that sense, if you continuously water in one spot, the majority of fine root hairs will be in that area.
Ofcourse watering the entire projected surface of the canopy and preferably beyond will be best, but sometimes less must do.

Lucy68 said:
Tree roots follow water so if the tree was starved for water, the roots are either 2 acres away or non-existent.

Apparently I used the wrong word (follow). How's this... roots don't grow in dry soil, they grow where there's water. I didn't say seek out, I said follow as in follow the water trail.

For clarity, roots grow where water is available as long as there is an adequate supply of nutrients and oxygen, and temperatures allow. They can't pass through the badlands to reach the nearest watering hole unless the 3 resources are adequately available all along the journey.

Trees are shedding organisms and as such they shed foliage as a response to drought. Shedding is a survival mechanism which helps to ensure the tree retains water enough that roots (the heart of the tree) don't dry and lose viability. I'm confused by the thought that roots of droughty trees must either be nonexistent or 2 acres away. Why put us in a prison of only 2 ideas? Couldn't a 20 ft tall tree with a 20 ft diameter canopy simply have a regular ol' root system roughly within a 40 ft circumference? Why would the roots go away, or, end up "2 acres away"?
Al

Thank you for once again clarifying what I said in the first place. Always a pleasure conversing with you.