It depends on the definition of the appraisal or valuation problem. That starts with the purpose and use (not the same) of the valuation. Why is it being done (use)? This points to the type of value (often, purpose).
Start with the obvious. Regardless of where they are if you want to know what that log is worth as timber (on the stump, cut and brought to the road, at the mill, whatever) then timber value applies.
If it is a tort damage case (a tort is a non-contractual, civil wrong under the law) then what does the law say the remedy is? In some states even of the tree is in prominent landscape use, timber or cordwood value is all that applies. In other states trees that are clearly "landscape," that is in managed settings in association with structures might be valued with CTLA methods using a Depreciated Replacement Cost (DRC). But that is not the only definition of landscape. Landscape can stretch to as far as the eye can see. Is a park, reserved from timber production a landscape? Often it is. Conceptually, if a non-timber value is allowed, the trees closer in would have higher location ratings and those farther out lower. At some point the low ratings start to create values that are more like timber values. But it is not just distance that matters. It is use and density or marginality. If you lose one tree out of a dozen near he house, is it missed? If you lose half an acre far from the house, but at a critical viewpoint on a nature trail, is timber value sufficient? Go back to the Timbetax.org website. Search on Bowers v Commissioner. An interesting case. The tax court ruled that a casualty loss deduction was wrongly denied because a vacation house was located in the woods. The IRS had said because there were so many other trees the ones lost didn't matter. The court said the marginality argument did not play and that the trres near the house were not timber trees.
So, in summary it depends on a complex of factors, not just distance. The "reasonable" value will be related to the facts by a process of reason.
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