  In this paper we first give a brief review of the variable cosmological
constant model and its scalar field description. We mainly discuss two types of
variable cosmological constant models: $a$ power law and $H$ power law models.
A method to obtain all of the equivalent scalar field potentials and the
effective equation of state of the two models is presented. In addition, the
dynamics of such scalar field potentials and effective equation of state are
discussed in detail. The parameters of the two models are constrained by
current 307 high-quality "Union" SN Ia data set, baryon acoustic oscillation
(BAO) measurement from the Sloan Digital Sky Survey (SDSS), 9 observational
\textrm{H(z)} data derived from the Gemini Deep Deep Survey (GDDS) and the
shift parameter of the cosmic microwave background (CMB) given by the
three-year Wilkinson Microwave Anisotropy Probe (\textrm{WMAP}) observations.
We also calculate and draw the picture of the Hubble parameter, the
deceleration parameter and the matter density of the two models. Then, we show
that the indices $m$ and $n$ in the two models have specific meaning in
determining properties of the models. Moreover, The reasons that indices $m$
and $n$ may also influence the behavior of effective equation of state and
scalar field potentials are presented.
