  Qin et al. (2004) have derived a formula of count rates based on a model of
highly symmetric expanding fireballs, where the Doppler effect is the key
factor to be concerned. In this paper, we employ the formula to both the Qin
model and the uniform jet model to study how the rising timescale,
$\Delta\tau_{\theta,r}$, and the decay timescale, $\Delta\tau_{\theta,d}$, of a
local pulse affect the light curve of GRBs. Our analysis shows that they do
make contributions to both rising and decay portions of the light curve of
GRBs. Associated with a local pulse with both rising and decay portions, the
light curve of GRBs in the rising portion is expected to undergo a concave
phase and then a convex one, which we call a "concave-to-convex" character,
whereas that in the decay portion is expected to evolve an opposite process
which is called a "convex-to-concave" character, regardless of being in Qin
model or in the uniform jet model. These characteristics are independent of
local pulse shapes and their rest frame radiation forms. The diversity of light
curves are caused by different forms of local pulses and different ratios of
$\Delta\tau_{\theta,r}$ to $\Delta\tau_{\theta,d}$. We study a sample of 86 GRB
pulses detected by the BATSE instrument on board the Compton Gamma Ray
Observatory and find that the "concave-to-convex" (expected in the rising
portion of the light curve) and "convex-to-concave" (expected in the decay
portion) characters, which result from the curvature effect of spherical
surface (or the Doppler effect), do exist in the light curve of some GRBs.
