Context. The comet Shoemaker-Levy 9 impacted Jupiter in July 1994, leaving its stratosphere with several new species, with water vapor (H₂O) among them.

Aims. With the aid of a photochemical model, H₂O can be used as a dynamical tracer in the Jovian stratosphere. In this paper, we aim to constrain the vertical eddy diffusion (K_zz) at levels where H₂O is present.

Methods. We monitored the H₂O disk-averaged emission at 556.936 GHz with the space telescope between 2002 and 2019, covering nearly two decades. We analyzed the data with a combination of 1D photochemical and radiative transfer models to constrain the vertical eddy diffusion in the stratosphere of Jupiter. Results. Odin observations show us that the emission of H₂O has an almost linear decrease of about 40% between 2002 and 2019. We can only reproduce our time series if we increase the magnitude of K_zz in the pressure range where H₂O diffuses downward from 2002 to 2019, that is, from ~0.2 mbar to ~5 mbar. However, this modified K_zz is incompatible with hydrocarbon observations. We find that even if an allowance is made for the initially large abundances of H₂O and CO at the impact latitudes, the photochemical conversion of H₂O to CO₂ is not sufficient to explain the progressive decline of the H₂O line emission, which is suggestive of additional loss mechanisms.

Conclusions. The K_zz we derived from the Odin observations of H₂O can only be viewed as an upper limit in the ~0.2 mbar to ~5 mbar pressure range. The incompatibility between the interpretations made from H₂O and hydrocarbon observations probably results from 1D modeling limitations. Meridional variability of H₂O, most probably at auroral latitudes, would need to be assessed and compared with that of hydrocarbons to quantify the role of auroral chemistry in the temporal evolution of the H₂O abundance since the SL9 impacts. Modeling the temporal evolution of SL9 species with a 2D model would naturally be the next step in this area of study.