Here is an article on how the specific type of street tree affects the urban heat island locally, focusing on plant area index.
The way a street tree is able to modify the local microclimate on pedestrian walkways may vary according to tree species according to key canopy and leaf characteristics, such as leaf angle, leaf size, canopy architecture or simply canopy density. Three similar north-south orientated streets, with three different tree species possessing different canopy and leaf characteristics were studied in summer 2014. Microclimatic parameters were measured on pedestrian walkways below and away from tree canopies between 06:00 and 20:00 on three cloudless days. Physiological Equivalent Temperature (PET) was estimated to indicate pedestrian thermal comfort. Microclimate conditions were measured below and away from trees at solar noon for a wide range of trees with different Plant Area Index (PAI) as determined using full-frame photography. In streets with Ulmus procera and Platanus x acerifolia trees, the microclimatic benefits were significantly greater than the street with Eucalyptus scoparia trees, however no significant differences in the estimated PET. Microclimate benefit increased with increasing PAI for all three tree species, however no significant difference in under-canopy microclimate amongst tree species when the PAI was similar. It appears that differences in PAI are paramount in determining the microclimatic and PET benefits. Obviously, certain tree species have a limit of the PAI they can achieve, and that should be considered when selecting or comparing tree species for shading and cooling benefits. This study assists urban planners and landscape professionals in selecting street tree species for cooling benefits based on the expected or managed tree canopy area.
I’d heard of Leaf Area Index before I read this abstract, but not Plant Area Index. A search for Plant Area Index on Google brings up a Wikipedia definition of Leaf Area Index as the top hit.
Leaf area index (LAI) is a dimensionless quantity that characterizes plant canopies. It is defined as the one-sided green leaf area per unit ground surface area (LAI = leaf area / ground area, m2 / m2) in broadleaf canopies.
The best explanation of the difference I could find on the internet is here:
Leaf (or needles in the case of conifers) should be seen here as a generic term for designing the above ground aeral extent of vegetation. if no distinction is made between leaves (needles) and the other elements, the proper term to use is PAI: Plant Area Index rather than LAI.
So I guess the plant area index accounts for the trunk, branches, stems, etc.