  In this work, we estimate extreme sea surface temperature (SST) hotspots,
i.e., high threshold exceedance regions, for the Red Sea, a vital region of
high biodiversity. We analyze high-resolution satellite-derived SST data
comprising daily measurements at 16703 grid cells across the Red Sea over the
period 1985-2015. We propose a semiparametric Bayesian spatial mixed-effects
linear model with a flexible mean structure to capture spatially-varying trend
and seasonality, while the residual spatial variability is modeled through a
Dirichlet process mixture (DPM) of low-rank spatial Student-$t$ processes
(LTPs). By specifying cluster-specific parameters for each LTP mixture
component, the bulk of the SST residuals influence tail inference and hotspot
estimation only moderately. Our proposed model has a nonstationary mean,
covariance and tail dependence, and posterior inference can be drawn
efficiently through Gibbs sampling. In our application, we show that the
proposed method outperforms some natural parametric and semiparametric
alternatives. Moreover, we show how hotspots can be identified and we estimate
extreme SST hotspots for the whole Red Sea, projected until the year 2100,
based on the Representative Concentration Pathways 4.5 and 8.5. The estimated
95\% credible region for joint high threshold exceedances include large areas
covering major endangered coral reefs in the southern Red Sea.
