Theoretical background noise rate over water surface for a photon-counting lidar and its application in land and sea cover classification.

For photon-counting lidars, the classical theoretical rate of the noise photons reflected by the Earth's surface is under the assumption that the Earth's surface is a Lambert reflector, which is obviously not suitable for the water surface. In this paper, the specular reflection theorem is introduced to derive an analytical expression of noise photons arising from the water surface reflection. The verification uses the mean noise rate over water surface, calculated by the raw data photons measured by the Multiple Altimeter Beam Experiment Lidar (MABEL) near the East Coast in the North Carolina, USA. The measured result coincides well with the theoretical noise rate, as both of them equal to 8.4 kHz. In addition, the background noise model also indicates that the background noise rate over the land surface is one order of magnitude larger than that over the water surface, in certain conditions. Hence, a new method, based on the noise rates, is proposed for the Earth's surface type classification and it performs well in distinguishing all water surfaces from land surfaces in the coastal area. For space-borne or airborne photon-counting lidars, this paper not only fills the gap of theoretical rate of noise photons from the water surface but also provides a fast and effective method to classify the Earth's surface types. This method is also suitable for distinguishing ice and water in high-latitude sea-ice covered regions, which is the area of most interest of the Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) mission.