  We present an efficient score statistic, called the $\textsf{S}^3 \textsf{T}$
statistic, to detect the emergence of a spatially and temporally correlated
signal from either fixed-sample or sequential data. The signal may cause a men
shift and/or a change in the covariance structure. The score statistic can
capture both spatial and temporal structures of the change and hence is
particularly powerful in detecting weak signals. The score statistic is
computationally efficient and statistically powerful. Our main theoretical
contribution are accurate analytical approximations on the false alarm rate of
the detection procedures, which can be used to calibrate the threshold
analytically. Numerical experiments on simulated and real data demonstrate the
good performance of our procedure for solar flame detection and water quality
monitoring.
