Impact of Evaporation and Precipitation on Estuarine Mixing

Recent studies could link the quantities of estuarine exchange flows to the volume-integrated mixing inside an estuary, where mixing is defined as the destruction of salinity variance. The existing mixing relations quantify mixing inside an estuary by the net boundary fluxes of volume, salinity, and salinity variance, which are quantified as Knudsen or total exchange flow bulk values. So far, river runoff is the only freshwater flux included, and the freshwater exchange due to precipitation and evaporation is neglected. Yet, the latter is the driving force of inverse estuaries, which could not be described by the existing relations. To close this gap, this study considers evaporation and precipitation to complete the existing mixing relations by including cross-surface salinity variance transport. This allows decomposing the mixing into a riverine and a surface transport contribution. The improved relations are tested against idealized two-dimensional numerical simulations of different combinations of freshwater forcing. The mixing diagnosed from the model results agrees exactly with the derived mixing relation. An annual hindcast simulation of the Persian Gulf is then used to test the mixing relations, both exact and approximated, e.g., long-term averaged, for a realistic inverse estuary. The results show that the annual mean mixing contributions of river discharge and evaporation are almost equal, although the freshwater transport due to evaporation is about one order of magnitude larger than the river runoff.