Is the early arrival of a migratory bird to its breeding or feeding ground an adaptation to climate change? Can we call these early arrival birds a positive match to climate change?
This is an interesting question. There is wide literature on this matter in several journals and monographs. It's clear that some species arrive sooner at the breeding grounds in comparison with previous decades, and this is due, at least in part, to climate change. One good example is the White Stork (Ciconia ciconia) in mainland Spain, where many birds don't migrate or arrive too early at the breeding territories after the migration routes, but many other interesting cases around the world demonstrate the effect of climate change on bird migration.
A scientist needs to use caution when interpreting the early arrival of migratory birds to feeding and/or breeding ranges. The "early arrival" might not have anything to do with climate change. Some individuals in a population might have a genetic predisposition to migrate earlier or later than the group as a whole, and as such, those behaviors would be within the normal range of variation for the population. Environmental factors on the wintering grounds (like decreased food availability, or competition from conspecifics) might influence some birds to migrate earlier. If conditions are favorable, some individuals might over-winter on the breeding range and not migrate at all; in that case, an observer might see those birds and assume that they "migrated into the area early", when in fact, the birds stayed all year long. [Snow Geese (Anser caerulescens), a highly migratory species from Alaska, sometimes stay all year long in the lower, continental USA.] Illness or injury can sometimes prevent birds from following migratory pathways as well. In short, a well-designed, long-term study might be able to determine general trends (i.e., a species is arriving earlier or later than baseline data suggests) but care is needed when interpreting the results because other factors might be involved that are not obvious to the researcher.
I agree with Dr. Novy's response, but at least in some cases, there are proofs of changes in the migration and timing of arrival of the birds to the breeding grounds due to climate change. Between other references, see this relating to the mentioned White Storks: