  The backreaction term ${\cal Q}_\CD$ and the averaged spatial Ricci scalar
$\average{\CR}$ in the spatially averaged inhomogeneous Universe can be used to
combine into effective perfect fluid energy density $\varrho_{\rm eff}^{\CD}$
and pressure $p_{\rm eff}^{\CD}$ that can be regarded as new effective sources
for the backreaction effects. In order to model the realistic evolution of
backreaction, we adopt the Chevallier-Polarski-Linder(CPL) parameterizations of
the equation of state(EoS) of the effective perfect fluid. To deal with
observations in the backreaction context, in this paper, we employ two metrics
to describe the the late time Universe, one of them is the standard
Friedmann-Lema\^{\i}tre-Robertson-Walker(FLRW) metric, and the other is a
template metric with an evolving curvature parameter introduced by Larena et.
al. in \cite{larena2009testing}. We also fit the CPL backreaction model using
type Ia supernova(SN Ia) data and observational Hubble parameter data(OHD) with
these two metrics, and find out that parameter tensions between two different
data sets are larger when the backreaction model is equipped with the template
metric, therefore we conclude that the prescription of the geometrical
instantaneous spatially-constant curvature $\kappa_{\CD}$ needs to be modified.
