## 3 The Diurnal Reference Check (DRC)
### Setting Maximum Amplitude of the Diurnal Signal  
Figure 5a shows the time series of the total monthly number of 24-h segments in the \(T_{IS}\) records, and the total number of those segments in which the DS was identified as described above. The typical monthly fraction of segments with identifiable diurnal signal is (90 \(\pm\) 3)%. Figure 5b shows the fraction of segments with ADS exceeding a given threshold, \(D\). This fraction quickly decreases with increasing \(D\). In rare extreme cases, the ADS may reach 40 K. In addition to the sensor's malfunctioning, another possible source of unrealistically large ADS is direct solar heating of buoys' hulls [31; 32]. We establish the \begin{table}
\begin{tabular}{c c c} \hline
**Satellite Instrument** & **Number of Matchups** & **Local Equator Crossing Time** \\ \hline Metop-A AVHRR FRAC & 2.47 \(\times\) 10\({}^{6}\) & 9:30 a.m. \\ Metop-B AVHRR FRAC & 2.47 \(\times\) 10\({}^{6}\) & 9:30 a.m. \\ Terra MODIS & 2.46 \(\times\) 10\({}^{6}\) & 10:30 a.m. \\ Aqua MODIS & 2.46 \(\times\) 10\({}^{6}\) & 1:30 p.m. \\ S-NPP VIIRS & 2.48 \(\times\) 10\({}^{6}\) & 1:30 p.m. \\ NOAA-15 AVHRR GAC & 2.45 \(\times\) 10\({}^{6}\) & 4:30–6:50 p.m. \\ NOAA-18 AVHRR GAC & 2.45 \(\times\) 10\({}^{6}\) & 2:30–8:20 p.m. \\ NOAA-19 AVHRR GAC & 2.45 \(\times\) 10\({}^{6}\) & 1:30–4:30 p.m. \\ \hline \end{tabular}
\end{table} 
Table 2: Total number of matchups of DTM in situ with satellite ‘Subskin’ SSTs and LEXT for eight satellites in 2012–2018. The LEXT bounds for the NOAA-15/18/19 were determined from the NOAA Sensor Stability for SST (3S) system [21]. threshold for'realistic' ADS, beyond which the DS is likely caused by extraneous factors other than variations in the water temperature, from the analysis of statistics of \(T_{SAT}\) vs. \(T_{IS}\) within the MDSs listed in Table 2.  
Figure 6a shows the median \(M(T_{SAT}-T_{IS})\) computed over segments with ADS corresponding to the \(D\pm\) 0.5 K bins as a function of \(D\). For all satellites, the \(M(T_{SAT}-T_{IS})\) is close to 0 K in the first \(D\) bin centered at 0.5 K, because the regression coefficients of the ACSPO SST equations were trained against \(T_{IS}\) with \(i\)Quan QL = 5, which rejects those \(T_{IS}\) counts that are significantly affected by the diurnal warming. Within a range of 0.5 K \(<\)\(D\) < 5.5 K, the medians vary from \(-\)0.05 K to 0.15 K, and then at \(D\) > 5.5 K, they drop to essentially negative values due to increased fractions of segments with the ADSs caused by the extraneous factors. Figure 6b shows the RSDs, \(S(T_{SAT}-T_{IS})\), as a function of \(D\). The RSDs are consistent across all satellites for \(Ds<\) -3.5 K, gradually increasing to \(-\)0.6 K. At \(D\) > 3.5 K, the RSDs grow at a faster rate. The largest RSDs correspond to the 'pm' satellites (S-NPP, Aqua, and NOAA-19), which observe the ocean at times close to the peak of the SST diurnal cycle, whereas the 'am' satellites (Metop-A/B) exhibit the lowest RSDs. Figure 6c shows the correlation coefficients \(C_{NIGHT}\) of \(T_{SAT}-T_{NIGHT}\) versus \(T_{IS}-T_{NIGHT}\), calculated within the same \(D\) bins. The \(C_{NIGHT}\) for Aqua, NPP, and NOAA-15/18/19 satellites show pronounced maxima at \(D\) = 3.5 K, followed by a sharp decline at \(D\) = 5.5 K. For the 'am' satellites Metop-A/B and Terra, the \(C_{NIGHT}\)s are relatively small and do not show distinct maxima. This is because significant'realistic' ADSs, with \(D\) < 5.5 K, most often occur near the peak of the diurnal cycle, whereas in the morning or evening, such ADSs are mostly caused by factors other than variations in the water temperature. Considering that at \(D\) > -5.5 K, the medians \(M(T_{SAT}-T_{IS})\) in Figure 6a start decreasing, and the correlations \(C_{NIGHT}\) in Figure 6c converge for all satellites, we adopt 5 K as the upper threshold for realistic ADSs for the water temperature at the buoys' depth. Figure 5b shows that this threshold rejects approximately 0.7% of all segments with identifiable DS.