  The CoRoT and Kepler missions provided a wealth of high-quality data for
solar-like oscillations. To make the best of such data for seismic inferences,
we need theoretical models with precise near-surface structure, which has
significant influence on solar-like oscillation frequencies. The mixing-length
parameter, $\alpha$, is a key factor for the near-surface structure. In the
convection formulations used in evolution codes, the $\alpha$ is a free
parameter that needs to be properly specified. We calibrated $\alpha$ values by
matching entropy profiles of 1D envelope models with those of 3D CO$^5$BOLD
models. For such calibration, previous works concentrated on the classical
mixing-length theory (MLT). Here we also analyzed the full spectrum turbulence
(FST) models. For the atmosphere part in the 1D models, we use the Eddington
grey $T(\tau)$ relation and the one with the solar-calibrated Hopf-like
function. For both the MLT and FST models with a mixing length $l=\alpha H_p$,
calibrated $\alpha$ values increase with increasing $g$ or decreasing $T_{\rm
eff}$. For the FST models, we also calibrated values of $\alpha^*$ defined as
$l=r_{\rm top}-r+\alpha^*H_{p,{\rm top}}$. $\alpha^*$ is found to increase with
$T_{\rm eff}$ and $g$. As for the correspondence to the 3D models, the solar
Hopf-like function gives a photospheric-minimum entropy closer to a 3D model
than the Eddington $T(\tau)$. The structure below the photosphere depends on
the convection model. However, not a single convection model gives the best
correspondence since the averaged 3D quantities are not necessarily related via
an EOS. Although the FST models with $l=r_{\rm top}-r+\alpha^*H_{p,{\rm top}}$
are found to give the frequencies closest to the solar observed ones, a more
appropriate treatment of the top part of the 1D convective envelope is
necessary.
