  Record-breaking temperature events are now very frequently in the news,
viewed as evidence of climate change. With this as motivation, we undertake the
first substantial spatial modeling investigation of temperature record-breaking
across years for any given day within the year. We work with a dataset
consisting of over sixty years (1960-2021) of daily maximum temperatures across
peninsular Spain. Formal statistical analysis of record-breaking events is an
area that has received attention primarily within the probability community,
dominated by results for the stationary record-breaking setting with some
additional work addressing trends. Such effort is inadequate for analyzing
actual record-breaking data. Effective analysis requires rich modeling of the
indicator events which define record-breaking sequences. Resulting from novel
and detailed exploratory data analysis, we propose hierarchical conditional
models for the indicator events. After suitable model selection, we discover
explicit trend behavior, necessary autoregression, significance of distance to
the coast, useful interactions, helpful spatial random effects, and very strong
daily random effects. Illustratively, the model estimates that global warming
trends have increased the number of records expected in the past decade almost
two-fold, 1.93 (1.89,1.98), but also estimates highly differentiated climate
warming rates in space and by season.
