Circulation

The Simple Estuarine Response Model (SERM) treats circulation and exchange in highly simplified ways. Because we are not modelling individual, real estuaries (and in most cases have no data to do so), it is not possible to develop detailed hydrodynamic models. Instead, we have developed very simple, semi-empirical models to describe circulation and exchange for each estuary type.

Lagoon

The model represents lagoons in the simplest way possible – a single, well-mixed box, with fresh water replacement time, and exchange with the ocean. A plan view is shown below.

Flows and loads are specified relative to the volume and area of the estuary, so that the size (and shape) of the estuary are of no consequence to the model, for this estuary type. In reality, the rate at which a lagoon exchanges with the ocean depends greatly on the geometry, depth, and circulation, near the mouth of the estuary (which may also only be intermittently open). However, without detailed data sets, it isn’t possible to develop a generic model which can calculate such exchanges in any sort of predictive way. The oceanic flushing time is thus a fixed, specified, parameter for this estuary type.

The river inflow magnitude is given relative to the volume of the estuary by specifying the time taken (in days) for the annual mean river flow to deliver a volume of fresh water equal to the volume of the estuary, the fresh water replacement time. Similarly, the oceanic exchange is given by specifying the time taken (in days) for exchange processes at the mouth of the estuary to mix a volume of ocean water which is equal to the volume of the estuary, into the estuary. This is commonly termed the flushing time for the estuary.

The model combines the fresh water replacement time and oceanic flushing time to calculate total exchanges between the lagoon and the ocean. If the river time is much shorter than the oceanic time, then the lagoon will on average be fairly fresh. If the oceanic time is much shorter than the river time, the lagoon salinity will on average be fairly close to marine salinity. When river and oceanic times are about equal, the mean salinity inside the lagoon will be about half-way between fresh water and oceanic salinity values.

Tidal

Tidal estuaries are vertically well-mixed channels, split into 5 boxes along the length of the estuary, with fresh water replacement time, and diffusive exchange due to tides between each box. A plan view is shown below.

Again, without detailed data for each particular case, it is not possible to develop models which can predict exchanges in such a system. A number of gross simplifications have been made in the model, as follows:

• The depth is uniform throughout the estuary.
• The tidal range (and phase) is uniform throughout the estuary.
• The diffusive exchange between two adjacent boxes is proportional to the tidal flow volume which passes through the interface between the boxes.
• The total exchange between two adjacent boxes is the sum of the two-way tidal diffusive exchange, plus the downstream transport due to any river flow present.

Under these assumptions, the model calculates exchanges and transport based on the mean tidal range at the mouth, river inflows, and lengths and widths for each box.

Salt-wedge

The model represents salt-wedge estuaries as a stratified channel, split into 5 boxes along the length of the estuary, and two layers vertically. Circulation and exchanges occur due to fresh water replacement time, horizontal diffusive exchange due to any tidal motions present, vertical entrainment from the lower layer to the upper layer, and vertical mixing. Plan and section views are shown below.

The model makes the following gross assumptions:

• The depth is uniform throughout the estuary.
• The depth of the interface between the two layers is uniform throughout the estuary
• If present, the tidal range (and phase) is uniform throughout the estuary.
• Horizontal diffusive exchanges are calculated from tidal motions in the same way used for tidal estuaries.
• Entrainment from the lower layer to the upper layer is represented by a uniform upward velocity (calibrated to give realistic salinity distributions for focus estuary cases).
• Lower layer salinity is assumed to be uniformly 35.
• Vertical mixing between the lower and upper layers is calculated using a Richardson number based scheme (essentially based on the velocity and salinity difference between the lower and upper layers).

The salt-wedge estuary requires by far the most complex model calculations for transport and exchange, but the model is still highly simplified and empirical compared to a model which might be set up for a realistic, specific estuary. In a given box, the model proceeds by calculating seaward flow in the upper layer based on the seaward flow in the next most landward upper layer, plus flow entrained from the lower layer. Upper layer dilutions and salinities can then be calculated. The lower layer landward flow at each box interface is the sum of the entrainment flows further landward. Vertical mixing can then be calculated based on contrasts in velocity and salinity between upper and lower layers.