Using pandas groupby and pd.concat together to add rows to a column

I have a large data frame with ~20 years of data. I would like to group this data frame by YEAR, and then add the same set of new X values to each group. I'm having trouble figuring how to use pd.concat with groupby. How can I use pd.concat and df.groupby together?

Below is a subset of my data frame (I deleted a bunch of rows just to show that I have multiple years that I would like to group by.

my data frame: 
     XSNO    YEAR     X     Z
5     LOL001  1978   0.22 -0.44
6     LOL001  1978   0.95 -0.55
7     LOL001  1978   1.70 -1.01
8     LOL001  1978   2.10 -1.22
9     LOL001  1978   2.68 -1.34
10    LOL001  1978   3.27 -1.41
48    LOL001  1978  17.60 -1.86
49    LOL001  1978  18.21 -1.77
50    LOL001  1978  18.41 -1.65
51    LOL001  1978  18.67 -1.54
52    LOL001  1978  19.00 -1.5
68    LOL001  1978  23.60 -0.31
78    LOL001  1980   0.40 -0.56
79    LOL001  1980   1.50 -0.91
80    LOL001  1980   2.50 -1.25
81    LOL001  1980   3.20 -1.43
82    LOL001  1980   3.90 -1.44
83    LOL001  1980   4.50 -1.55
84    LOL001  1980   5.80 -1.22
101   LOL001  1980  21.50 -0.96
102   LOL001  1980  22.50 -0.69
103   LOL001  1980  23.60 -0.43
104   LOL001  1980  25.10 -0.09
107   LOL001  1981   0.30 -0.40
108   LOL001  1981   0.60 -0.56
109   LOL001  1981   2.40 -1.20
110   LOL001  1981   4.40 -1.34
111   LOL001  1981   7.00 -1.10
112   LOL001  1981   8.60 -1.49

What I would like the output to be (just a subset of the added values for one year):
XSNO    YEAR    X      Z
LOL004  1978    0     NaN
LOL003  1978    0.05  NaN
LOL002  1978    0.1   NaN
LOL001  1978    0.15  NaN
LOL000  1978    0.2   NaN
LOL001  1978    0.22  -0.44
LOL002  1978    0.25  NaN
LOL003  1978    0.3   NaN
LOL004  1978    0.35  NaN
LOL005  1978    0.4   NaN
LOL006  1978    0.45  NaN
LOL007  1978    0.5   NaN
LOL008  1978    0.55  NaN
LOL009  1978    0.6   NaN
LOL010  1978    0.65  NaN
LOL011  1978    0.7   NaN
LOL012  1978    0.75  NaN
LOL013  1978    0.8   NaN
LOL014  1978    0.85  NaN
LOL001  1978    0.95  -0.55


max = df.X.max()
x = np.arange(0, max, 0.05)
x = pd.DataFrame({'X': x})

concat_df = df.groupby(['YEAR']).apply(lambda x: x.concat([df1, x]))
# this doesn't work and gives me an error

concat = pd.concat([df1, x])
# this doesn't give me what I want, it just tacks all the 'x' values (new values) on at the end.  

I'm not sure how to use merge/join/concat functions with a grouped pandas data frame. I can't seem to find any other questions/answers on stack that get at what I'm looking for.