  We study parametric estimation for a second order linear parabolic stochastic
partial differential equation (SPDE) in two space dimensions driven by a
$Q$-Wiener process based on high frequency spatio-temporal data. We give an
estimator of the damping parameter of the $Q$-Wiener process of the SPDE based
on quadratic variations with temporal and spatial increments. We also provide
simulation results of the proposed estimator.
