## 2 Material and Methods
### MODIS Sea-Ice Concentration Retrieval  
For the MODIS SIC retrieval, accurate knowledge of the background temperatures is crucial. The background temperatures, hereafter referred to as tie-points, are the reference temperatures which a pixel would have if it were covered completely by open water (water tie-point \(tp_{water}\)) or covered completely by sea ice (ice tie-point \(tp_{ice}\)). For the tie-point retrieval, we follow the approach of the works in [1,8].  
The choice of \(tp_{water}\) is straightforward: we assume that the open water is constantly at the freezing point of salt water, \(-1.8\ ^{\circ}\)C. If it would be colder, the water would freeze to sea ice until thermal equilibrium is reached. If it would be warmer, it would melt the surrounding the sea ice and thereby cool down to the freezing point. However, until equilibrium is reached other water temperatures can also be observed, which is part of the \(tp_{water}\) uncertainty.  
The choice of \(tp_{ice}\) is less straightforward. The IST follows the air temperature and thus has large spatial and temporal variability, which renders it impossible to choose an Arctic-wide fixed \(tp_{ice}\). To account for the local variability, each pixel is assigned its own \(tp_{ice}\). For this, the IST field is split into cells of 48 pixels by 48 pixels. We assume only linear IST variation within these cells. Each cell is split into 3 by 3 subcells of 16 pixels by 16 pixels. Within a subcell, we assume negligible IST variations. In the next step, the 25 th percentile of the IST field in the subcell is selected as preliminary \(tp_{ice}\), so that there are 9 preliminary \(tp_{ice,tmp}\) values per cell. Once the \(tp_{ice,tmp}\) are selected, a linear regression with two variables is performed within the cell to express the \(tp_{ice}\) as function of the x/y position within the cell:  
\[tp_{ice}(x,y)=ax+by+c, \tag{1}\]  
where \(x\) and \(y\) are the indices of the respective pixel within the cell, \(tp_{ice}(x,y)\) is \(tp_{ice}\) at this pixel, and \(a\), \(b\) and \(c\) are the regression coefficients. Subcells are discarded entirely if more than 70% of the pixels are covered by clouds and cells are discarded entirely if more than four subcells are discarded entirely. The authors of [15] investigate the sensitivity of the retrieval towards the required fraction of cloud-free pixels within one subcell, the required number of valid subcells in one cell and the percentile for the estimation of \(tp_{ice,tmp}\). They confirm that the initial settings are a reasonable choice. So far, the approach directly follows that in [1]. They shift the cells by 48 pixels once the calculation is done,  
Figure 1: Locations of the Sentinel-2 scenes. The polygons mark the regions which are used for defining the marginal seas. Regions are indicated by colours and Months are indicated by the orientation of the triangles (see legend for details). All in all, 79 scenes are used.  
so that each pixel is covered once. As in [8], we shift the cell by 1 pixel before repeating the calculation, so that each pixel is covered 48 times. The mean of the 48 iterations is then selected as \(tp_{ice}\). Our approach allows to use the standard deviation of the 48 iterations as estimate for the uncertainty of \(tp_{ice}\). Once \(tp_{ice}\) for each pixel is determined, the IST is converted to SIC by linear interpolation:  
\[SIC=\begin{cases}1&\text{if }IST<tp_{ice}\\ \frac{IST-tp_{water}}{tp_{ice}-tp_{water}}&\text{if }tp_{ice}<IST<tp_{water}\\ 0&\text{if }IST>tp_{water}\end{cases} \tag{2}\]  
No SIC retrieval is performed in the current version of our retrieval if \(tp_{ice}\) exceeds 270 K.  
The SIC calculation is performed on granule level. Subsequently, each granule is gridded to the NSIDC projection with 1 km grid spacing. Then, granules which belong to the same orbit are merged together, so that there is one MODIS SIC array per orbit.