A streamer discharge is a highly reactive and dynamic non-thermal plasma. It has been used in many applications, including environmental remediation, medicine, and material processing. Although the physics of streamer discharges in gaseous media is well understood, its interaction with a solid and liquid dielectric surfaces remains under investigation, in particular when quantitative data are searched for. In this study, we investigate the influence of voltage amplitude (Va) and interelectrode air gap distance (d) on the pulsed discharge behavior at the surface of distilled water. Time resolved images show the formation and propagation of plasma dots (ionization front of streamers) at water surface. Because of its stochastical nature, a large number of discharge was performed to address the influence of Va and d on the number of plasma dots (NDots) as well on the charge per dot (QDot). As expected, for a given Va, the breakdown voltage is found to increase with d. Moreover, NDots decreases linearly with d at the rate of ~1 dot by 200 µm of increase, while the total injected charge decays linearly with a rate of ~8-9 nC by 200 µm of increase. Based on the measurement of the propagation velocity of the plasma dots and on the estimation of the electric field in the medium, an average mobility of plasma dots of ~1.5 cm2/Vs is evaluated. From both this value and the instantaneous measured propagation velocity, the temporal evolution of QDot and charge number are determined. The observations reported here are of interest for fundamental studies as well as for applications where well-controlled charge transfer to surfaces is crucial.