The problem you have is that you have coordinates for contours one level at a time, however since you have multiple closed loops this solution looks silly:
load LATLONALT.dat
levels = unique(LATLONALT(:,3));
for iLevels = 1:numel(levels)
plot(LATLONALT(LATLONALT(:,3)==levels(iLevels),1),...
LATLONALT(LATLONALT(:,3)==levels(iLevels),2),'-')
hold on
end
However, if you put in rows with nan inbetween the different closed contour-level-loops this should work.
HTH
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