  Let $ (Z_{n})_{n\geq 0} $ be a supercritical branching process in an
independent and identically distributed random environment. We establish an
optimal convergence rate in the Wasserstein-$1$ distance for the process $
(Z_{n})_{n\geq 0} $, which completes a result of Grama et al. [Stochastic
Process. Appl., 127(4), 1255-1281, 2017]. Moreover, an exponential nonuniform
Berry-Esseen bound is also given. At last, some applications of the main
results to the confidence interval estimation for the criticality parameter and
the population size $Z_n$ are discussed.
