ERA5 SST day-to-day variance rose 4.9-fold at the 2007 HadISST2-to-OSTIA switch and biases its heatwave trends; with one common noise spectrum ERA5 and OISST agree on detrended trends (60S-60N)

Question: Daily NOAA OISST v2.1 has steps in fast (sub-monthly) variance at input changes, and these steps bias marine heatwave (MHW) statistics. Does ERA5, the other daily SST product that many MHW studies use, have the same problem? If two products receive one common correction, do they agree? Approach: We read ERA5 SST at 12 UTC for 1979-2025 from ARCO-ERA5 at 28,805 ice-free one-degree sample cells (60S-60N), collocated with OISST. We measured fast variance, searched for change points, compared both products with up to 173 moored buoys, and calculated Hobday et al. (2016) statistics (1983-2012 baseline) for published data and for versions matched to one common target spectrum at periods shorter than about 32 days. Results: ERA5 day-to-day variance increased 4.9-fold on 2007-09-01, when its SST input changed from HadISST2 to OSTIA. Before this date ERA5 has 0.00-0.05 times the buoy power at 2-8 days. OISST steps go the other way. At 127 buoys, published ERA5 has a too-low MHW frequency trend (-0.135 events per year per decade, p = 2e-6), a too-high peak-intensity trend (+0.085 C per decade, p = 8e-12) and a false memory loss; after homogenisation these biases are not significant. Over the ocean, published ERA5 minus OISST trend differences are +0.090 C per decade for MHW peak intensity, -0.26 events per year per decade for frequency and +0.095 and -0.184 C per decade for the annual maximum and minimum anomaly. Homogenisation reduces them to -0.016, -0.12, -0.023 and -0.059. With each product's own linear trend removed, homogenised ERA5 and OISST agree on MHW and cold-spell duration, frequency and peak intensity within 0.06 per decade. A 0.043 C per decade slower mean warming in ERA5 remains and explains most of the remaining MHW-day and duration differences; at the buoys OISST drifts warm (+0.034 C per decade) and ERA5 does not (-0.009). Limitations: the correction fixes spectra, not event timing (day-level agreement stays near 0.3 before 2007); pre-2007 ERA5 fast variance after correction is synthetic; buoys feed both products and sample only the tropics and US waters; the study does not decide which mean warming rate is correct.