## 2 Data and Methods
### Implementation of the Regression NN
As aforementioned, selective scaling and normalization of the input features were considered in the input layer of the network, according to the individual distribution of the input features. Table 1 provides the summary statistics representing the final distribution and dispersion of the input features. After processing the data, a total of 348,009 and 63,330 instances were suitable for training the thin and full-range SIT models, respectively. Ground truth SIT\({}_{\text{SMOS}}\) and SIT\({}_{\text{CS2 MOS}}\) are only available from mid-October onwards and Pb data have a delayed delivery time of about one month. Therefore, the thin SIT model was trained with data from 15 October to 4 December, and the full-range SIT model was trained from 15 October to 21 November 2020, respectively. The thin and the full-range NN models were both trained based on Arctic T\({}_{B}\) and ancillary data, and the model with the best fit was stored. Figure 4: Kernel Density Estimation (KDE) charts of the NN training sets used to train the thin sea ice (**a**) and the full-range model (**b**), including the marginal probability density functions of the filtered datasets. The thin model is based on T\({}_{B}\), SIC, T\({}_{S}\) and ground truth thin SIT derived from Soil Moisture and Ocean Salinity (SMOS). The full-range SIT model is based on T\({}_{B}\), SIC, T\({}_{S}\), Pb, and ground truth SIT derived from CryoSat-2 and SMOS. Unlike in simple regression or process-based models, the results of a NN cannot be extrapolated, since its input features are non-linearly related. NNs are based on the underlying statistics of the observations and a trained model can only be applied to new data in case the corresponding range of values is covered by that of the original training set. Thus, a reliable model prediction requires the variable space of the available training data to include the predicted data as an already learned subset. This can be assessed by comparing the training and prediction datasets regarding its variable ranges and the density of values. In case the values of the new dataset are located within the multi-dimensional convex hull of the original training dataset, the model output can be considered to be reliable. The convex hulls around the points clouds of all combinations of input features are presented in a two-dimensional sub-feature space in Figure 5, for the Arctic data (blue markers and black solid line) and for the Antarctic data (orange markers and red dashed line). Both of the datasets are of the same quality and processed identically. The total number of valid observations for Arctic ice is higher because both the Fb and the T\({}_{B}\) observations are less dense at higher latitudes, which reduces the amount of data for Antarctic sea ice. Regarding the distributions of T\({}_{B}\), Fb and SIC, the ranges and densities of the observations in the Antarctic, are entirely covered within the hull of observations in the Arctic. Therefore, the full-range model, which was trained with Arctic data, is considered to be reliable for an application to the Antarctic data. It is important to mention that a small amount of T\({}_{S}\) values in the Antarctic dataset is close to the sea ice melting point (>270 K). This is because the Antarctic summer had already started and the temperatures are high enough, so that sea ice located at lower latitudes begins to melt. The corresponding subset is not located within the convex hull of Arctic training data, which limits the reliability of the model predictions for these particular values.