An experimental study has been carried out on the dynamical process taking place in the plasma generated by a Q-switched Nd:YAG laser (1.064 nm, 8 ns, 175 mJ) on a water surface at atmospheric air pressure. Accurate dynamical characterization of the resulting plasma has been carried out using gated intensified optical multichannel analyzer. The occurrence of the hydrogen emission lines of H I 656.2 nm (Hα), H I 486.1 nm (Hβ), H I 434.0 nm (Hγ) and H I 410.1 nm (Hδ) was observed. Line broadening of hydrogen emission lines was studied in term of its emission time profile. In addition to reaffirming the role of the shock wave mechanism in the generation of atmospheric plasma, an analysis of the time-resolved spatial integrated of emission intensities and the time-resolved averaged temperature was made using the emission lines of Cu I 510.5 nm and Cu I 521.8 nm. As a result, the occurrence of two-stage emission processes, the shock excitation stage and cooling stage has been proved. The experimental result considering the characteristics of the atmospheric plasma can be well understood by considering the shock wave model instead of breakdown mechanism. Further application for quantitative analysis of calcium and sodium in water was also performed. A linear calibration curve was obtained without using any internal standardization and the detection limit in this stage of the experiment was estimated to be less than 1 ppm for calcium and sodium in water.