  Using the Hilbert-Huang transform technique, we investigate the midrange
periodicities in solar radio flux at 2800 MHz (F10.7) and sunspot areas (SAs)
from February 1, 1947 to September 30, 2016. The following prominent results
are found: (1) The quasi-periodic oscillations of both data sets are not
identical, such as the rotational cycle, the midrange periodicities, and the
Schwabe cycle. In particular, the midrange periodicities ranging from 37.9 days
to 297.3 days are related to the magnetic Rossby-type waves; 2) The 1.3-year
and 1.7-year fluctuations in solar activity indicators are surface
manifestations (from photosphere to corona) of magnetic flux changes generated
deep inside the Sun; 3) At the timescale of the Schwabe cycle, \textbf{the
complicated phase relationships} in the three intervals (1947-1958, 1959-1988,
and 1989-2016) agree with the produced periodicities of the magnetic
Rossby-type waves. \textbf{The findings indicate that the magnetic Rossby-type
waves are the possible physical mechanism behind the midrange periodicities of
solar activity indicators. Moreover, the significant change in the relationship
between photospheric and coronal activity took place after the maximum of solar
cycle 22 could be interpreted by the magnetic Rossby-type waves.
