Protoplanetary discs' infrared water spectra (e.g. as observed by JWST) encode information about the underlying water distribution and physical conditions. In this work, we examine and quantify the imprint of various dynamical processes (operating alone or in unison) on water abundances and emerging spectra using a new 2D model called Molecular emission Affected by Gas, Pebble, and Ice Evolution (MAGPIE). This model combines diffusion and advection for water (and associated species) and dust grains with aerodynamically decoupled pebbles, and photodissociation and a gas-phase water formation prescription. In general, we find that transport processes have a major impact on the inner disc's water content and can (re)plenish the layer above the ice reservoir which in static models is water-poor due to photodissociation. In particular, adding diffusion to a chemical model can result in strong changes in the spectrum (e.g. a flux increases of colder compared to warmer water lines) that recent work has associated with pebble drift. Adding pebble drift dramatically increases the inner disc water abundance but, surprisingly, does not readily lead to a further increase of cold water tracers as (1) efficient outward transport of water vapour is inhibited by a conveyor belt effect of incoming pebbles, and (2) the increase in hot water line fluxes overshadows smaller increases of colder lines. We conclude that dynamical processes have a significant but complex impact on water spectra. Future work should explore a range in stellar (e.g. UV irradiation) and disc properties to comprehensively understand the observed diversity of water emission.