  We investigate pointwise estimation of the function-valued velocity field of
a second-order linear SPDE. Based on multiple spatially localised measurements,
we construct a weighted augmented MLE and study its convergence properties as
the spatial resolution of the observations tends to zero and the number of
measurements increases. By imposing H\"older smoothness conditions, we recover
the pointwise convergence rate known to be minimax-optimal in the linear
regression framework. The optimality of the rate in the current setting is
verified by adapting the lower bound ansatz based on the RKHS of local
measurements to the nonparametric situation.
