Localization with respect to a map is an essential objective for the development of highly automated and autonomous vehicles as well as of mobile robots. Commonly, localization solutions rely on static, semantic objects, like road signs or house corners. In this paper, we introduce a novel local descriptor characterizing neighborhoods of LiDAR point clouds without semantic information to be independent of those semantic infrastructure elements. In contrast to other descriptor methods, our system uses the LiDAR sensors' intensity information which is encoded into a novel gradients-of-intensities-based local descriptor, called GRAIL. The descriptor represents shapes of intensities of the point clouds' local neighborhoods. We use the proposed descriptor for global localization with respect to a map and compare it to other well-known geometry-based descriptors to complete the localization framework. The introduced method has been thoroughly evaluated on a large data set including both, our own and the KITTI raw data benchmark. The experiments presented in this paper show that the proposed method can achieve accuracy at the level of stateof-the-art descriptor algorithms, even though most of these descriptors use the more informative geometry information.