Between 1831 and 1847, the debt was below 40 million. This is too low for the Y-to-Y % change method to represent trends well. 
For instance, the debt went from $37,513 in 1836 to $336,957 in 1837, both miniscule amounts, but a 798% change!
Graphing as a % of GDP is a much better indicator, for this and I think other reasons, but we do not have GDP before depression-era financial reforms.
The graph is misleading as to the severity of the debt in non war years because of the immense scale