"closely correlates with" is a correct and usable phrase in written English.
You can use it when you want to describe a strong relationship between two different things. For example, "The number of ice cream sales closely correlates with the temperature outside."
Part 3 shows that the accounting evidence closely correlates with the history of American political ideology.
It helps that Mexican GDP closely correlates with America's industrial production, rather than its overall economy.
The adsorbing rate closely correlates with the pH of the solution, the temperature and the sequence length of ssDNA.
Results: We established that PDE III is abnormally upregulated in cerebral blood vessels of AD and CAA subjects and closely correlates with vascular amyloid burden.
The detection methodology gives a vibration response signature that closely correlates with and is very specific to the behaviour of the transverse surface crack in a horizontal rotor.
Activation of class I Phosphoinositide 3-kinases (PI3Ks) by mutation or overexpression closely correlates with the development of various human cancers.
C. elegans SYG-1's specification of proper synapse formation in vivo closely correlates with the heterophilic complex affinity, which appears to be tuned for optimal function.
This closely correlates with the idea of the Lyapunov-Schmidt reduction [2, 3].
The calcium distribution map closely correlates with the copper map in the foliage areas.
Moreover, the synthesis rate also closely correlates with the ultimate cholesterol level in different brain regions (Quan et al., 2003).
Corresponding temperature derived from luminescence dependence on temperature closely correlates with that from resistance measurement during heating.
