*2.3. Estuarine Modelling*

Since regional ocean models commonly impose direct river discharges into coarse grids with horizontal resolutions of several kilometres, an estuarine proxy was developed to include the tidal signal complexity, thus providing more realistic readings of salinity concentration and of discharged volumes reaching the coastal area. This proxy was adapted from a more complex approach where full scale estuarine models were used to estimate transport fluxes and related water properties [7].

A simple and scalable MOHID Water application was designed to represent estuaries schematically and to export the methodology where a full-scale estuary model is not available. The advantages of this type of application include low computing costs and the capacity to combine realistic open ocean and land boundary conditions with local tides. The proxy can calculate a realistic tidal mixing, considering each estuary's tidal prism, and different tidal cycles such as spring-neap and ebb-flow periods. Each proxy calculates cross-section water velocity that can later serve to impose momentum in the ocean model. Moreover, using a full numerical model to simulate in a simple grid, instead of tidal mixing empirical equations, allows for a future increase in complexity, i.e., adding atmospheric boundary conditions, biogeochemical modelling, etc.

The LAMBDA estuarine model proxy consists of a regular domain of 12 × 3 cells where the estuary is represented by 10 grid cells aligned in any cardinal direction plus a cell for the ocean open boundary conditions and the land boundary (Figure 2). Configuring each estuarine proxy domain requires some basic estuary geometry properties:


**Figure 2.** MOHID Water Estuarine schematic model design used for simulating an estuarine proxy. The domain consists of a 12 × 3 grid that receives land inputs (river flow, temperature and salinity) and ocean inputs from tides and regional ocean models (water level, currents, temperature, and salinity) to produce outputs at the estuarine mouth, outputs such as salinity, temperature, flow, and velocity.

At the open ocean boundary, the model generates water levels, using FES2014 tidal constituents, and receives ocean properties such as surface salinity and water temperature. Each estuarine proxy simulates its corresponding tides, supported by its georeferenced location, and using the FES2014 global tidal model [21]. Ocean-water properties at the

open boundary can be defined as constant or time-varying with either timeseries or more complex 2D/3D fields from ocean global or regional models. In the innermost cell, river flow, temperature, and zero salinity is imposed.

Each estuarine proxy produces timeseries of flow, velocity (u or v according to estuary mouth orientation), and water properties estimated at its outer estuarine cell. Water velocity serves to impose momentum on the estuarine plume in the regional ocean model. In contrast with river discharges, modelled estuarine flows have positive and negative values according to the tidal phase (ebb and flood). The receiving model should be capable of handling negative discharges to fully include this property as a land boundary condition. The proxy outputs are independent of the downstream ocean model and for this reason can be applied to any regional or global ocean model.

To evaluate the performance of the estuarine proxy, simulations using this method were applied to the main six estuaries in western Iberia (from South to North): Guadalquivir, Sado, Tagus, Mondego, Douro, and Minho (Figure 3). Fluxes, temperature, salinity, and velocity timeseries were obtained for the period of May 2017–December 2018. The geomorphology information used to configure each of these estuary proxies is included in Table 1.

**Figure 3.** PCOMS regional ocean operational system domains and bathymetry. The full domain corresponds to the WestIberia 2D Domain where tide is imposed. The red box indicates the outer limit of the Portugal 3D Domain. Pink dots indicate the location of the six main estuaries in western Iberia. Red dots indicate the location of extra 45 rivers implemented with direct discharges. The locations of Silleiro and A Guarda monitoring stations are indicated by orange dots.


**Table 1.** Proxy configuration for the main six estuaries in western Iberia ordered from South to North. The Tagus estuary is the only proxy configured with variable depth along its channel.

Two proxy scenarios were set according to observed and modelled land boundary conditions to assess human managemen<sup>t</sup> impact on river flows. Observed river flows for the Douro, Guadalquivir, Mondego, and Tagus rivers were obtained from EMODnet physics near real time data (NRT). These were the only rivers with data available for the analysed period when the simulations were made. Water temperature was forced in all proxies with watershed modelling results, since this variable is rarely monitored continuously. Salinity was considered as freshwater with zero salinity in all land scenarios. At the open ocean boundary, each proxy received surface temperature and salinity values according to the locations of its mouth from a regional ocean model without land inputs, and the values are described in the next section.
