The most recent deglaciation resulted in a global sea-level rise of some 120m over approximately 12000years. In this Part I of two parts, a moving boundary numerical model is developed to predict the response of rivers to this rise. The model was motivated by experiments at small scale, which have identified two modes describing the transgression of a river mouth: autoretreat without abandonment of the river delta (no sediment starvation at the topset-foreset break) and sediment-starved autoretreat with abandonment of the delta. In the latter case, transgression is far more rapid and its effects are felt much further upstream of the river mouth. The moving boundary numerical model is checked against experiments. The generally favourable results of the check motivate adaptation of the model to describe the response of the much larger Fly-Strickland River system, Papua New Guinea to Holocene sea-level rise; this is done in the companion paper, Part II.
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