We present a new geomorphological analysis of the Tinee River tributaries in the southern French Alps based on numerical inverse and forward modelling of their longitudinal profiles. We model their relative uplift history with respect to the main channel, hence the incision rate history of this channel. Inverse models show that all tributaries have consistent incision rate histories with alternating high and low values. A comparison with global temperature curves shows that these variations correlate with quaternary climate changes. We suggest that during warm periods, a wave of regressive erosion propagates in the Tinee River, while its tributaries deeply incise their substratum to catch up with the falling base level. We also show that the post 140 ka history of this landscape evolution is dominated by fluvial incision. We then perform forward models of river incision and simulate the incision of the Tinee River system over a time span of 600 ka. This model allows us to extract time and space incision rate variations of the Tinee River. With a background of a few mm.yr(-1), incision rate can increase up to more than 1 cm yr(-1) during short periods of time due to climatic oscillations. This result is compatible with published cosmogenic nuclide based dating, which evidenced incision rates from 0.2 to 24 mm yr(-1). The part of the channel located between 12 and 20 km downstream from the source has undergone several periods of rapid incision rates, which could explain the steep hillslopes and the triggering of a landslide similar to 10 ka ago. (C) 2017 Elsevier Ltd. All rights reserved.