Appendix 1.  Description of changes and evaluation of new NEMO-NAA10km model

A first batch of simulation was started in 2020, based on outputs of the NorESM2 climate model. The design of the atmospheric forcing, adapted from the NorESM2 climate model was straightforward, but required a re-design of the oceanic boundary conditions, as using them directly produces ocean modelling simulations with an unrealistic Atlantic Meridional Overturning Circulation (AMOC) of 60 to 80 Sverdrup. The runoff that can be extracted from the NorESM2 climate model turned out to be un-realistic, as its historical simulation exhibits a freshwater flow towards the ocean that is higher by 20% than that observed by Dai and Trenberth (2002) during the period 1950–2014. Its geographical distribution is also biased. Therefore, the downscaling simulations used a climatological runoff, which gives realistic results in terms of salinity in the simulation but does not take into account the expected increase of runoff and hydrological cycle towards the Arctic Ocean, during the 21^st century.

Within NorScen, we aimed at providing river runoff fields that are realistic, and that follow the inter-annual variability of the climate model runoff, to the climate downscaling simulations. Development time was therefore invested into this task. River runoff outputs of climate models are two-dimensional fields, which for every coastal point of the ocean component of a climate model, provide a runoff value to the ocean. Each point corresponds to a drainage area outlet, but the representation of drainage areas varies between grid and models. Meanwhile, it is impossible to represent river runoff as two-dimensional fields, as they are on one hand discrete distributions, and on the other hand runoff conservation is essential which does not permit any spatial interpolation to enable comparison. A method is needed to perform this comparison.

To perform this task, the runoff of the climate model is re-routed to the Nemo-NAA10km, this means that for a given runoff point of the climate model, the runoff is re-routed towards the closest coastal point of the Nemo-NAA10km grid. River outflow locations can differ from one model to another, but integrating the river runoff along a coastline, should lead to the same accumulated value.  Therefore, our strategy is to integrate along a coastline that spawns the entire coast of the Nemo-NAA10km grid.  To create this coastline, one starts at the edge of the domain, on a coastal point located on the US East coast, and an algorithm searches for the closest coastal point, and so on, until the entire coast of the Nemo-NAA10km is covered. Some unphysical connecting jumps to islands or disconnected coastal areas may occur, but prove to be unimportant, as they create a coastal index that is identical and will be applied exactly in the same manner to all runoff inputs. This algorithm provides a pointer that covers the entire coast of the Nemo-NAA10km domain. The mean climatological runoff provided to Nemo-NAA10km in hindcast mode, and extracted from Dai and Trenberth (2002), is projected on this coastal index axis, as well as the mean climate model runoff for the historical period 1950–2014. This projection is made from a cumulated point of view, so that runoff projection on the coastal axis index is a strictly increasing function. This choice also allows getting a continuous function, although its derivative is not, since not all coastal points are related with a runoff input, nor this runoff input can be considered as constant. Finally, using a cumulative approach, allows replacing similar runoff inputs (i.e. corresponding with the same river or drainage area) but rerouted to different grid cells, to be close to one another on the coastal axis index. Once the reference hindcast runoff, and the climate model, are placed as cumulated runoff along the coastal axis index, a transfer function between the two is computed, with the shape of a second-degree polynomial, which coefficients can be computed based on simple matrix inversion. This allows for the computation of a corrected cumulated runoff function. The correction algorithm, and more specifically the polynomial transformation (after minor adjustment), is then assumed to work for any runoff field, during all the simulation. This method provides a valid correction of climate model runoff, for a given climate model, for the historical period 1950–2014 as well as for climate projections.

This algorithm, once applied to the runoff fields of the NorESM2 and EC-Earth climate models, allowed for the creation of monthly runoff fields, for each year of the period 1950–2100. These fields follow the inter-annual variability of each climate model original runoff fields, while being bias corrected and consistent with the original runoff inputs of the Nemo-NAA10km hindcast simulations.

First attempts at downscaling the EC-Earth climate model led to unrealistic results, in which the North Atlantic and the Arctic Oceans were transformed into a brackish structure, with very low SSS values. However, such SSS values, are not simulated in the original EC-Earth simulations used as input for these climate downscaling. Sensitivity experiments revealed that the precipitation fields of the EC-Earth model were overestimated, and responsible for this freshening. The mechanisms through which these overestimated precipitation fields do not produce a strong negative SSS anomaly in the EC-Earth climate model are unclear.  One could speculate that the evaporation rate over the ocean is higher in EC-Earth, or that the export of freshwater through the AMOC is higher than in Nemo-NAA10km, perhaps due to a deeper mixed layer. But the point is that we cannot use the EC-Earth precipitation fields as they are for downscaling experiments. A strategy is therefore needed to bias-correct the EC-Earth precipitation fields, for the purpose of downscaling EC-Earth climate simulations using Nemo-NAA10km.

We first identify that at the beginning of the historical period, the EC-Earth precipitation fields are actually lower on average for the Nemo-NAA10km domain, than the ERA5 precipitation fields. The strong freshening is related with a very strong trend of increase of the EC-Earth precipitation fields towards the end of the 20^th century and through the 21^st century. A trend which is not observed in the ERA5 precipitation fields. However, the difference of trend for precipitation trends, between ERA5 and EC-Earth, is very different depending on location, with a strong dependence on latitude.

For each (discretized) latitude along the latitude axis of the precipitation field, one can therefore define a trend correction to make the trend of ERA5 and EC-Earth precipitation fields fit during the 1979–2014 period. This correction, in the form of a constant coefficient for each discretized latitude component, is applied throughout the entire simulation 1950–2100. First, what should be the linear trend of precipitation in EC-Earth is computed, for a given year, and a given latitude, based on the corrected linear trend. Second, this value is subtracted from the EC-Earth precipitation field, for the same given year, and the same given latitude.

A comparison between the original EC-Earth precipitation fields, and the corrected ones, shows that most of the correction is applied at latitudes above 40 °N.

The comparison is done for the intermediate greenhouse gas concentration scenario SSP2-4.5. The new model version, with improved runoff distributions, has increased surface salinities in parts of the Barents, Kara and Norwegian seas and decreased salinities north of Greenland and in the East Greenland Current (Fig. A1, middle panel). However, the difference between the surface salinity in the two versions for the SSP2-4.5 scenario at the end of this century (Fig. A1, right panel, indicates that NEMO-NAA10km-new has less increased salinities in the Barents, Kara, and Norwegian seas compared to NEMO-NAA10km-old and less decreased salinities north of Greenland and in the East Greenland Current than NEMO-NAA10km-old. We are yet unable to explain the very pronounced difference between models in the region north of Greenland (intense red in Fig. A1, right panel). However, note that the changes in surface salinities generally were more extreme in the old version. This is also true for SST in the Norwegian and Barents Seas (Fig. A2, right). The combined effects on mixed layer depth is biggest in the subpolar region and in the Norwegian and Barents seas (Fig. A3, right), with less deep mixed layer depth most places in the new version.

Figure A1. Average March sea surface salinity (SST) in NEMO-NAA10km-new (2015–2034, left panel), average SSS change in NEMO-NAA10km-new from period 2015–2034 to period 2080–2099, mid) and average difference in this SSS change between NEMO-NAA10km-new and NEMO-NAA10km-old, right).

Figure A2. Average March sea surface temperature in NEMO-NAA10km-new (2015–2034, left panel), average SST change in NEMO-NAA10km-new from period 2015–2034 to period 2080–2099, mid) and average difference in this SST change between NEMO-NAA10km-new and NEMO-NAA10km-old, right).

Figure A3. Average March mixed layer depth (MLD) in NEMO-NAA10km-new (2015–2034, left panel), average MLD change in NEMO-NAA10km-new from period 2015–2034 to period 2080–2099, mid) and average difference in this MLD change between NEMO-NAA10km-new and NEMO-NAA10km-old, right).