Clustering impacts across the Brazilian shelf

The Brazilian coastline measures over 8000 km, with continental shelf widths between 10 km to330 km (Castro et al., 2006). Nevertheless, as seen from our results, some as-pects of anthropogenic impacts show general similarities over large areas. To capture those similarities, we aggregate regions into clusters using self-organizing maps (SOM). This, in turn, allows us to define a set of representative impacts’ magnitude and range over our

Figure 4.2: Historical climatology and change signal for the austral summer (left panel) and winter (right panel) of the potential energy anomaly (φP Ein J.m^-3) across the Brazilian shelf. Summer is defined as the averages for December, January and February, whereas for Winter is June, July and August. Warm (positive) values indicate increased stratification, whereas cold (negative) values indicates a shift towards well-mixed conditions. The shelf is sectioned in three sectors to allow an easier visualization, and each lettered sector is color-referenced on the general South America inset in subset A. The dotted line represents the 200 misobath and marks the shelf break.

domain, as well as explore the temporal evolution of the desired properties under anthro-pogenic forcing. For this reason, we define the SOM clusters using a combination of five properties: ∇ρmax, ∇ρdepth,φP E, sea surface temperature (SST) and sea surface salinity (SSS).

We tested different numbers of clusters, ranging from4to10, and a sample of those re-sults can be seen on Fig.4.4. As shown in Figs.4.2and4.3, the strongest impacts are found along south Brazil. The difference is such, however, that only by increasing the number of clusters above 7does SOM start separating the impacts along the central and north-ern coastlines. Even with10clusters, both regions are essentially assigned a single cluster

Figure 4.3: Historical climatology and change signal for the annual mean potential energy anomaly (φP Ein J.m^-3, left panel) and the maximum pycnocline gradient (∇ρmaxin kg.m^-4, central panel) and depth (∇ρdepthin m, right panel) across the Brazilian shelf. The shelf is sectioned in three sectors to allow an easier visualization, and each lettered sector is color-referenced on the general South America inset in subset A. The dotted line represents the 200 misobath and marks the shelf break.

each, at most. In the south, on the other hand, a cluster below the Patos Lagoon and a cross-shelf gradient over the remainder shelf is preserved across all tests. As the number of clusters increase, this region is further refined zonally and over the shelf break, reflect-ing the susceptible nature of this region to anthropogenic climate change. Based on these results, we chose6clusters as an adequate representation of the different levels of anthro-pogenic impact over the Brazilian shelf. Although this choice is essentially subjective, it ensures clusters are not too small and t-test statistics between them reveals that only2-3 and4-6are not significantly different from each other. The number of insignificant clus-ters increases in higher SOM configurations and even at4there was an insignificant pair (1-3).

Time series of theφP E for each cluster further illustrate the impacts on the vertical water column structure across the shelf (Fig. 4.5). For clusters1,5and6,φP E essentially oscillates around the historical average until the end of the21^st century, with roughly the same distribution between positive and negative trend phases (increase and reduction in stratification, respectively). These are the regions where changes inφP E were mostly in-significant across all time scales when we considered our control (Figs. 4.2and4.3). For the remainder clusters, however, anthropogenic impacts are clear. Clusters2and3show a

Figure 4.4: Cluster assignment using self-organizing maps (SOM) to model the change signal along the Brazilian shelf. Four test are shown, using4,6,8and10as the number of clusters to classify. The shelf is sectioned in three sectors to allow an easier visualization, and each lettered sector is color-referenced on the general South America inset in subset A (see Fig.4.1). The dotted line represents the200 misobath and marks the shelf break.

clear negative trend for almost all climatologies. These accumulate during the second half of the 21^st century and lead to the more well-mixed conditions seen around Cabo Frio’s coastline and the outer shelf of the South Brazil Bight (Fig. 4.2). Cluster4, on the other hand, shows the opposite behavior and accumulates mostly positive trends, leading to a more stratified water column at the inner region of the South Brazil Bight.

We can draw further insights on the shelf’s water column response to increased GHG emissions by looking at the relative contribution of temperature (φP E,T) and salinity (φP E,S) to theφP E, which is done by calculatingφP Ebased on their depth-averaged profiles at each cell and time step (Fig.4.6). Overall, temperature tends to be the dominating factor to the φP Eand increases in the order of5-10% at the end of the century. The exception is cluster 6, where both temperature and salinity act as equal drivers to theφP E balance. Even in this region, however, we still see a shift in dominance after around2050, with temperature overtaking salinity.

Figure 4.5: Left axis show the time series of the potential energy anomaly (φP E in J.m^-3, black line), whereas the right axis show the trend (J.m^-3.year^-1, colored line) for each defined cluster. The trend is estimated with a one-year running window for every30-year climatol-ogy between1980and2100, and referenced to the climatology’s halfway year (e.g.,1994 for the period between1980 and2009). Red indicates higher stratification and blue in-dicates a shift towards more well-mixed conditions. Gaps are present where the trend is essentially zero. The dashed gray line represents the calculated historical average, consid-ering the period between1980and2009, and is related to the left axis.

Among these results, we can see that some portions within cluster 5also showed an increase inφP E, specially around the southern shelf, but were grouped with regions where this impact was insignificant (Figs. 4.2 and4.3). This led to the approximately neutral change seen in this cluster’sφP Etime series. This happens because different properties can dominate the separation between clusters (Fig.4.7). Cluster1, which represents the largest portion of the Brazilian shelf in length, shows essentially no impact on stratification (both φP Eand pycnocline characteristics). SST increases on the order of1^◦C, with a SSS increase of0.5. Cluster6, located south of the Patos Lagoon, shows a similar low impact onφP E

but a slightly higher variance in pycnocline depth. It distinguish itself from other clusters mostly for the highest average salinity increase of≈1, alongside the highest SST variance.

Cluster4, located in the internal region of the South Brazil Bight, has the largest increase in pycnocline strength (∇ρmax,±0.2 kg m⁻⁴), a stronger increase inφP E and SST increase above 1^◦C. Clusters2, 3and 5all show a tendency towards shallower pycnoclines and reducedφP E, while having similar small increases in SSS. However, cluster2, located in the inner shelf near Cabo Frio, is also the only region to show an average SST decrease.

Figure 4.6: Time series of the relative contribution of temperature (red, left axis) and salin-ity (right, blue axis) to the potential energy anomaly (in %) for each defined cluster. We would like to draw the readers’ attention to both axes’ ranges.

This characteristic, in itself, distinguishes this cluster from number 3, even though they have insignificant t-test statistics between them when all properties are considered.