I am assuming here that the rows of the “Ice” matrix correspond to the “Days” and the columns correspond to the “LocationID” . You may use the following code to extract the required values.
[~, maxAvgIceLocation] = max(mean(Ice(:)));
maxIce = max(Ice(:));
[maxRow, maxCol] = find(ismember(Ice, maxIce));
maxDay = Days(maxRow);
maxLocation = LocationID(maxCol);
Here the variable “maxAvgIceLocation” correspond to the location of the highest average ice thickness. “maxIce”, “maxDay”and “maxLocation” gives the maximum overall ice thickness with the associated day and location respectively.