We characterize near-surface ocean diurnal warm-layer events, using satellite observations and fields from numerical weather forecasting. The study covers April to September, 2006, over the area 11 degrees W to 17 degrees E and 35 degrees N to 57 degrees N, with 0.1 degrees cells. We use hourly satellite SSTs from which peak amplitudes of diurnal cycles in SST (dSSTs) can be estimated with error similar to 0.3 K. The diurnal excursions of SST observed are spatially and temporally coherent. The largest dSSTs exceed 6 K, affect 0.01% of the surface, and are seen in the Mediterranean, North and Irish Seas. There is an anti-correlation between the magnitude and the horizontal length scale of dSST events. Events wherein dSST exceeds 4 K have length scales of <= 40 km. From the frequency distribution of different measures of wind-speed minima, we infer that extreme dSST maxima arise where conditions of low wind speed are sustained from early morning to mid afternoon.