Location = menu('Please select a loaction',LocationID);
assigns to a variable named Location with an upper-case L
fprintf('On Day %d, at location %s, the ice thickness was %0.4f [m]\n',Days(day),LocationID(location),Ice(day,location));
reads from a variable named location with a lower-case L.
MATLAB is case sensitive. You are not using the variable you think you are.