Set Value in Multiple Rows in Pandas Dataframe Based on Condition

IIUC, the following;

Create column 'C' and fill with nan's:

df['C'] = np.nan

count consecutive occurrences of 'precipitation' < 0.04 in column 'C_:

def rolling_count(val):
    if val < 0.04:
        rolling_count.count +=1
    else:
        rolling_count.count = 0
    return rolling_count.count
rolling_count.count = 0

df['C_'] = df['precipitation'].apply(rolling_count)

fill column 'C' with '1', where the first '4' is found and backward fill the other 3:

df.loc[df[df['C_'] == 4].head(1).index.item(), 'C'] = 1
df['C'] = df['C'].fillna(method = 'bfill', limit = 3)
df['C'] = df['C'].fillna(0)
df['C'] = df['C'].astype(int)

df

   temperature  precipitation  C  C_
0         1.26         0.0279  0   1
1         1.64         0.0330  0   2
2         1.98         0.0381  0   3
3         2.31         0.0406  0   0
4         2.61         0.0406  0   0
5         2.89         0.0381  1   1
6         3.15         0.0356  1   2
7         3.51         0.0305  1   3
8         3.78         0.0305  1   4
9         3.78         0.0305  0   5

Note; this result differs from what your example shows, but IIUC you need to find 4 consecutive rows below 0.04 and fill 'C'. Problem is that you have a '0.0406' value filled with '1' in 'C' which is not below 0.04.