  We consider parameter estimation of the reaction term for a second order
linear parabolic stochastic partial differential equation in two space
dimensions driven by a $Q$-Wiener process under small diffusivity. We first
construct an estimator of the reaction parameter based on continuous
spatio-temporal data, and then derive an estimator of the reaction parameter
based on high frequency spatio-temporal data by discretizing the estimator
based on the continuous data. We show that the estimators have consistency and
asymptotic normality. Furthermore, we give simulation results of the estimator
based on high frequency data.
