Advanced Ocean Modelling: Using Open-Source Software

94 3 Basics of Nonhydrostatic Modellingflushing times based on an e-folding timescale and to compare the results with thepredicted age distribution.3.25 Exercise 15: Inverse Estuaries3.25.1 AimThe aim of this exercise is to explore the circulation of inverse estuaries being causedby a net evaporative loss of water. Since this loss of water creates a pressure gradientdirected into the estuary, the question is: What drives the outflow (see Fig. 3.50, rightpanel)?3.25.2 Task DescriptionThe model configuration is identical to that of the previous exercise with a fewmodifications outlined in the following. The estuary is closed on the left side and,for simplicity, tidal forcing is not included. An evaporation rate of 5 cm per day(which is fairly high) is prescribed along the estuary up to x = 110 km. This rateis decreased linearly to zero value over the the adjacent 20 km across the mouth ofthe estuary. Evaporation over the ambient sea is set to zero. This design is purelyacademic and its sole purpose is to create a salinity distribution along the estuarythat resembles that observed in real inverse estuaries.Evaporative water loss appears in the vertically integrated continuity equation as:∂η∂t=− 1 b∂(b h〈u〉)∂x− E (3.90)where E is the evaporation rate. Owing to a loss of freshwater, the salt concentration(i.e. salinity) in the water column increases. On the basis of conservation of volumeand salt mass, this salinity change can be calculated from:∂ S∂t= S E h(3.91)where h is the depth over which this salinity increase becomes distributed. We usea linearised equation of state expressed in terms of density anomaly ρ ′ :ρ ′ = ρ o β(S − S o ) (3.92)where temperature effects are ignored, the salinity coefficient β is taken as 8×10 −4 ,and S o is a reference salinity, taken as 35 g/kg. Accordingly, Eq. (3.91) can be convertedinto a density change according to: