Coronal rain corresponds to cool and dense clumps in the corona accreting towards the solar surface, and is often observed above solar active regions. They are generally thought to be produced by thermal instability in the corona and their lifetime is limited by the time they take to reach the chromosphere. Although the rain usually fragments into smaller clumps while falling down, their specific spatial and temporal scales remain unclear. In addition, the observational signatures of the impact of the rain with the chromosphere have not been clarified yet. In this study, we investigate the time evolution of velocity and intensity of coronal rain above a sunspot by analyzing coronal images obtained by the AIA onboard the SDO satellite as well as the Slit-Jaw Images (SJIs) and spectral data taken by the IRIS satellite. We identify dark and bright threads moving towards the umbra in AIA images and in SJIs, respectively, and co-spatial chromospheric intensity enhancements and redshifts in three IRIS spectra, Mg II k 2796 Angstrom, Si IV 1394 Angstrom, and C II 1336 Angstrom. The intensity enhancements and coronal rain redshifts occur almost concurrently in all the three lines, which clearly demonstrates the causal relationship with coronal rain. Furthermore, we detect bursty intensity variation with a timescale shorter than 1 minute in Mg II k, Si IV and C II spectra, indicating that a length scale of rain clumps is about 2.7 Mm if we multiply the typical time scale of the busty intensity variation at 30 sec by the rain velocity at 90 $mathrm{km s}^{-1}$. Such rapid enhancements in the IRIS lines are excited within a time lag of 5.6 sec limited by the temporal resolution. These temporal and spatial scales may reflect the physical processes responsible for the rain morphology, and are suggestive of instabilities such as Kelvin-Helmholtz.
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