The advantage of these approaches is that it does not require sorting.
1
idxmin, groupby. , .
df.loc[df.groupby('Date').Distance.idxmin()]
Date PlumeO Distance
0 2014-08-13 13:48:00 754.447905 5.844577
13 2014-08-13 16:59:00 754.447905 5.844577
2
pd.DataFrame.nsmallest , .
df.groupby('Date', group_keys=False).apply(
pd.DataFrame.nsmallest, n=1, columns='Distance'
)
Date PlumeO Distance
0 2014-08-13 13:48:00 754.447905 5.844577
13 2014-08-13 16:59:00 754.447905 5.844577