# Sea Surface Temperature in Global Analyses: Gains from the Copernicus Imaging Microwave Radiometer
## 2 Methods
The synoptically correlated uncertainty arises from correlations in the atmospheric conditions between SST retrievals. Both the adjustment and synoptic uncertainties are assumed to be correlated over 100 km for IR sensors and 1 day. Uncorrelated uncertainties arise from effects that are not correlated from location to location, such as random noise in the satellite sensors [26; 27]. Each of these contributions was considered in turn, and for each, a value was added to the SST in each cell in the perfect dataset with an appropriate magnitude and correlation properties. A single large-scale noise value was applied to all cells in a given L3U file by selecting a random number from the Gaussian distribution with a standard deviation given by the mean of the large-scale correlated uncertainty values in the corresponding file. Noise values corresponding to the adjustment and synoptically correlated uncertainties were generated using a common method. Here, a value was chosen at random for each cell on a 1\({}^{\circ}\)-resolution grid from a Gaussian distribution with a standard deviation given by the mean of these uncertainties over all the 0.05\({}^{\circ}\) resolution cells falling within the 1\({}^{\circ}\) cell. These values were then interpolated back down to the 0.05\({}^{\circ}\) resolution to give a noise value to add to each cell of an appropriate size that varied smoothly and had correlations over the correct length scale (\(\approx\)100 km) for synoptic weather systems. The uncorrelated uncertainty values for each cell were used directly by choosing a random number chosen from a Gaussian distribution with the given standard deviation. Representative daily level 3 collated (L3C) CIMR data were also generated based on the model \"truth\" dataset. An initial sea ice mask was applied on the same basis as for the IR data. The edges of the mask were extended by two additional cells in both latitude and longitude to represent the need to avoid side-lobe contamination when measuring SSTs. A median filter was subsequently applied over a \(3\times 3\) box to obtain an SST value as seen by an instrument with a 15 km footprint. These data were then subset to every third pixel in each direction to ensure the independence of each cell being fed to the OSTIA system and a mask was applied to eliminate cells within 25 km of land. Finally, a mask was applied based on the daily coverage expected for the instrument. Analogous to the IR instruments, the resulting data represented the SSTs that would be derived in the case of a perfect observing and retrieval system for CIMR. To ensure the correct weighting of the CIMR observations by the OSTIA system and in order to generate appropriate synthetic observational noise, values were derived for the same four uncertainty terms considered for the IR data. The uncorrelated uncertainties were taken from [PERSON] et al. [28] that looked at the result of the instrumental noise-equivalent temperature change (NeAT) on the expected retrieval uncertainty of the SST from CIMR. The dependence of this uncertainty on the SST was retained but, in the absence of specific meteorological information, it was calculated using fixed values of wind speed (7 m\(\cdot\)s\({}^{-1}\)), salinity (35 psu) and total column water vapour (14 kg\(\cdot\)m\({}^{-2}\)). A similar analysis to [PERSON] et al. [28] that tested the effect of the orbital instability (rather than radiometric) uncertainty on the retrieved SST was used to derive values for the synoptically correlated uncertainty in the SST. A value of 0.1 K for the adjustment uncertainty was assumed and the large-scale uncertainty term was set to 0 on the assumption of a well-designed and calibrated retrieval scheme that removed orbit-to-orbit biases. An assumption was made that uncertainties were independent across orbits and thus were reduced by \(\sqrt{N_{obs}}\) for cells with multiple observations on a given day.