*2.4. Ocean Modelling*

The LAMBDA boundary products were implemented as proof of concept (PoC) in an updated version Portuguese Coast Operational Modelling System (hereafter referred as PCOMS, [22,23]) that covers the western Iberia regional ocean. Simulations were made for the period of October 2017–December 2018 that includes the extreme rain event of late March 2018.

The PCOMS system is a 3D full baroclinic hydrodynamic and biogeochemical regional ocean operational model application that uses MOHID Water as its numerical core. It is composed of two nested domains: WestIberia (2D) and Portugal (3D) covering the Iberian Atlantic coast and its contiguous ocean populated with bathymetric information derived from the EMODnet Bathymetry portal (Figure 3; https://www.emodnet-bathymetry.eu/, accessed on 15 April 2022). The WestIberia domain covers the area limited by specific latitudes (33.48◦ N, 45.90◦ N) and longitudes (4.20◦ W, 13.50◦ W), resulting in a grid of 207 × 155 cells with a maximum depth around 5600 m. The Portugal domain covers the area comprised of specific latitudes (34.38◦ N, 45.00◦ N) and longitudes (5.10◦ W, 12.60◦ W), resulting in a grid of 177 × 125 cells and a maximum depth around 5300 m. Both domains use constant horizontal spatial resolution of 0.06◦, resulting in 6.7 × 5.2 km cells. The Portugal domain is located at the centre of the WestIberia grid (Figure 3). Vertically, the Portugal domain uses a hybrid discretisation with near-surface, variable-thickness sigma layer with 7 levels, increasing from 1 m at the surface to 8.68 m of depth, above a layer with 43-z-levels increasing in thickness towards the bottom; this domain is based on the Mercator-Océan PSY2V4 vertical geometry [23].

Tides in the current configuration are also forced with FES2014 harmonic components along the WestIberia domain boundary. The Portugal domain receives tides from the WestIberia domain and uses CMEMS Global Ocean 1/12◦ Physics Analysis and Forecast updated Daily product (hereafter referred as CMEMS-Global) as initial and boundary condition for water levels, currents, temperature, and salinity. CMEMS-Global fields are relaxed in the first 10 cells of the open boundary, while the inner area the model runs free, without assimilation; these parameters rest on the assumption that the open ocean boundary condition does not affect the river-influenced areas. At the atmospheric boundary, the Portugal domain was forced by hourly results from a MM5 model application (Meteorological Model 5; [24]) based on two nested grids with a horizontal resolution of

27 and 9 km, respectively, implemented by the IST meteorological group (http://meteo. tecnico.ulisboa.pt/ [25], accessed on 15 April 2022).

#### **3. Modelling Results and Validation**

## *3.1. Watershed Modelling*

Each modelling domain was independently calibrated, which resulted in flow and temperature timeseries for the main 54 rivers discharging into the European Atlantic Ocean and the North Sea for the period of 2008–2019. To achieve a more comprehensive water budget entering the coastal areas, 70 extra discharges for Western Iberia and 364 extra discharges for the Ireland and UK region were obtained from the domains. However, these extra rivers could not be fully validated, since resolution may be too coarse to accurately reproduce out-river flowrates.

Observed data for each river was collected from several data sources including EMODnet physics NRT river database (https://portal.emodnet-physics.eu/, accessed on 15 April 2022) for recent data and the Global Runoff Data Base (GRDB; https://www.bafg.de/ GRDC/EN/01\_GRDC/13\_dtbse/database\_node.html, accessed on 15 April 2022) for historical data. Nevertheless, the lack of available observations for some catchments or presented incomplete datasets for the simulation period hampered efforts to validate and calibrate some domains. Moreover, the available hydrologic stations are in some cases located far from the coastal area, so that validation was only possible for the upper part of the catchment. Figure 4 shows the geographic distribution of the coefficient of determination between observed and modelled data for the stations used for validation in this study.

**Figure 4.** Coefficient of determination (R2) between observed and modelled river flow for the stations with available data for the period 2008–2019.

A well-calibrated and -configured watershed model will face difficulties in attempting to accurately simulate river runoff, since river flow is highly controlled by reservoirs managed by human behaviour. Watershed numerical models calculate natural river flow, and as such, their results tend to be closer to the observed values when the degree of human intervention is low [17].

To illustrate the results, the analysis of two large rivers in western Iberia, the Douro and Tagus rivers, are presented. The Douro and Tagus river mouths are the longest rivers discharging in the Atlantic Ocean, at 897 and 1007 km long respectively. They receive waters from the largest drainage areas in the Iberian Peninsula, with 98,400 and 80,000 km<sup>2</sup> for the Douro and Tagus respectively. The larger Douro catchment is located in the wettest region of the Iberian Peninsula and with a resultant average flow of ≈700 m<sup>3</sup> s<sup>−</sup>1, an average that is higher than the Tagus River, whose average flow is ≈440 m<sup>3</sup> s<sup>−</sup>1. The river mouths are separated by 275 km.

Another subject relevant to the watershed validation is the precision of river flow observations, especially since many hydrometric stations use rating curves (RC) to transform water levels into river flow. This method may introduce some errors in the context of extreme events, since RC must be extrapolated outside of the observed range [26]. Such is the case for the Almourol station in the Tagus River where flow is calculated from water levels with a rating curve. On the other hand, the Douro River monitoring station closest to the coastal area (Albufeira da Crestuma) is a hydroelectric power plant, which enables more precise observation. In both rivers, the numerical model reproduces the main flow peaks in the period timeseries; however, it presents higher average flow and lower extreme peaks (Figure 5). This excess of freshwater may be caused by human management, errors, or uncertainties in the meteorological and watershed model and observations that translate into a low coefficient of determination of around 0.6 and 0.3 for the Douro and Tagus rivers, respectively.

**Figure 5.** Observed (orange line) and modelled (blue line) river flow for the period 2014–2018 used for validation in (**a**) Douro River at Albufeira de Crestuma station; (**b**) Tagus River at Almourol station (Source for observed data: Portuguese Environmental Agency APA).

## *3.2. Estuary Modelling*

To evaluate the differences resulting from using observed versus modelled river flow in the coastal area, the estuarine proxies defined for the Douro and the Tagus rivers were forced with both datasets for the period of May 2017–December 2018. These estuaries

present large geomorphological differences (Table 1) relative to each other that affects their tidal prism size and substantially influences water volume and other properties reaching the open ocean (Figure 6). Mean maximum instant flow is around 1–1.5·10<sup>3</sup> m<sup>3</sup> s<sup>−</sup><sup>1</sup> and 40–70·10<sup>3</sup> m<sup>3</sup> s<sup>−</sup><sup>1</sup> for the Douro and Tagus estuaries, respectively. These values are similar to those found by Campuzano et al. [7] who used full-scale estuarine models. Larger volume fluxes do not imply larger momentum at the estuarine mouth. For example, the Douro estuary presents slightly larger instant velocities than the Tagus estuary that has larger estuarine flows (Table 2). During extreme events, as in March 2018, Tagus flow and velocity were barely impacted by the river discharge while the Douro estuary was highly affected by this type of event, with flows and velocities substantially affecting the plume momentum, shape, and extension.

The differing geomorphologies are also important for the water properties reaching the coastal area. When forced with the observed values of the river flow, the average salinity at the mouth of the Tagus estuary is around 33 salinity units, while in the Douro the average salinity is only 12.5 salinity units. In terms of the S-value range, the Douro has a greater variability than the Tagus estuary. During extreme conditions, freshwater conditions can almost be reached in the Douro mouth, as was also observed with the full-scale estuary model [7]. The Douro estuary temperature range is also widely impacted by the river's seasonal temperature evolution.

Proxies forced with LAMBDA watershed modelling results lead to fresher water for both estuaries. Nevertheless, salinity trends are well represented for both estuaries. The Douro estuary proxy, due to its smaller size, is more sensitive to differences in the imposed river flow.
