With dead-reckoning from velocity sensors, AUVs may construct short-term, local bathymetry maps of the sea floor using multibeam sensors. However, the position estimate from dead-reckoning will include some drift that grows with time. In this work, we focus on longterm onboard storage of these local bathymetry maps, and the alignment of maps with respect to each other. We propose using Sparse Gaussian Processes for this purpose, and show that the representation has several advantages, including an intuitive alignment optimization, data compression, and sensor noise filtering. We demonstrate these three key capabilities on two real-world datasets.