  We consider parametric estimation for a second order linear parabolic
stochastic partial differential equation (SPDE) in two space dimensions driven
by a $Q$-Wiener process with a small noise based on high frequency
spatio-temporal data. We first provide estimators of the diffusive and
advective parameters in the SPDE using temporal and spatial increments. We then
construct an estimator of the reaction parameter in the SPDE based on an
approximate coordinate process. We also give simulation results of the proposed
estimators.
