Merge multiple DataFrames Pandas

I would use append.

>>> df1.append(df2).append(df3).sort_values('depth')

        VAR1     VAR2    VAR3  depth    profile
0  38.196202      NaN     NaN    0.5  profile_1
1  38.198002      NaN     NaN    0.6  profile_1
0        NaN  0.20440     NaN    0.6  profile_1
1        NaN  0.20442     NaN    1.1  profile_1
2        NaN  0.20446     NaN    1.2  profile_1
0        NaN      NaN  15.188    1.2  profile_1
2  38.200001      NaN     NaN    1.3  profile_1
1        NaN      NaN  15.182    1.3  profile_1
2        NaN      NaN  15.182    1.4  profile_1

Obviously if you have a lot of dataframes, just make a list and loop through them.

A simple way is with a combination of functools.partial/reduce.

Firstly partial allows to "freeze" some portion of a function’s arguments and/or keywords resulting in a new object with a simplified signature. Then with reduce we can apply cumulatively the new partial object to the items of iterable (list of dataframes here):

from functools import partial, reduce

dfs = [df1, df2, df3]
merge = partial(pd.merge, on=['depth', 'profile'], how='outer')
reduce(merge, dfs)

   depth       VAR1    profile     VAR2    VAR3
0    0.6  38.198002  profile_1  0.20440     NaN
1    0.6  38.198002  profile_1  0.20440     NaN
2    1.3  38.200001  profile_1      NaN  15.182
3    1.1        NaN  profile_1  0.20442     NaN
4    1.2        NaN  profile_1  0.20446  15.188
5    1.4        NaN  profile_1      NaN  15.182

Consider setting index on each data frame and then run the horizontal merge with pd.concat:

dfs = [df.set_index(['profile', 'depth']) for df in [df1, df2, df3]]

print(pd.concat(dfs, axis=1).reset_index())
#      profile  depth       VAR1     VAR2    VAR3
# 0  profile_1    0.5  38.198002      NaN     NaN
# 1  profile_1    0.6  38.198002  0.20440     NaN
# 2  profile_1    1.1        NaN  0.20442     NaN
# 3  profile_1    1.2        NaN  0.20446  15.188
# 4  profile_1    1.3  38.200001      NaN  15.182
# 5  profile_1    1.4        NaN      NaN  15.182