This paper employs a circularity function to quantify the internal morphology of Martian watershed basins in Margaritifer Sinus region and to infer the primary erosional processes that led to their current geomorphologic characteristics and possible climatic conditions under which these processes operated. The circularity function describes the elongation of a watershed basin at different elevations. We have used the circularity functions of terrestrial basins that were interpreted as having been modified by (1) erosion related to primarily groundwater sapping and (2) erosion related to primarily rainfall and surface run-off, as well as the circularity functions of cratering basins on the Moon, in order to formulate discriminant functions that are able to separate the three types of landforms. The spatial pattern of the classification of Martian basins based on discriminant functions shows that basins that look morphologically similar to terrestrial fluvial basins are mostly clustered near the mainstream at low elevation, while those that look morphologically similar to terrestrial basins interpreted as groundwater sapping origin are located near the tributaries and at higher elevation. There are more of the latter than the former. This spatial distribution is inconsistent with a continuous Earth-like warm and wet climate for early Mars. Instead, it is more aligned with an overall early dry climate punctuated with episodic wet periods. Alternatively, the concentrated erosion in the mainstream could also be caused by a change of water source from rainfall to snowfall or erosion cut through a duricrust layer.