Peru Coupled Experiment - Serena Illig

for both systems using altimetric data over the 2000-2008 period. ..... performed following the new methodology developed and described in the companion paper. 286 ...... helped us improve our French literary writing. We are ..... Name, Equatorial forcing, alongshore wind-stress forcing and wave dissipation specifications.
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Sub-seasonal Coastal Trapped Wave propagations in the

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southeastern Pacific and Atlantic Oceans

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Part II: Wave characteristics and connection with equatorial

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variability

8 9 Serena Illig1,2, Marie-Lou Bachèlery2,3, and Emeline Cadier2

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Laboratoire d’Etudes en Géophysique et Océanographie Spatiale (LEGOS),

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CNRS/IRD/UPS/CNES, Toulouse, France 2

Department of Oceanography, MARE Institute, LMI ICEMASA, University of Cape Town,

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Cape Town, Rondebosch, South Africa. 3

Nansen-Tutu Centre, Marine Research Institute, Department of Oceanography, University of

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Cape Town

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Submitted to Journal of Geophysical Research in October 2017

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Revised Manuscript submitted in January 2018

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Revised Manuscript submitted in March 2018

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________________________________

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* Corresponding author address

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Serena Illig, IRD, LEGOS at UCT

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University of Cape Town (UCT), Department of Oceanography, Private Bag X3, Rondebosch

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7701, South Africa

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Email: [email protected]

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Abstract

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The objective of this study is to compare the characteristics of the oceanic teleconnection

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with the linear equatorial dynamics of two upwelling systems along the southwestern South

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American and African continents at sub-seasonal time-scales (60 m.km-1) are

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observed north of the Angola Benguela Frontal Zone (ABFZ) between 13°S-17°S. To summarize

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and compare coastal bathymetric profiles on the shelf and slope of both regions, we defined a

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topographic slope index (𝛼 3000) as the ratio between the depth 3000m and the distance from the

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coast at which the 3000m isobath is encountered (𝛼3000 = 3000/ 𝐿3000 ). 𝛼 3000 portrays the

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bathymetric profiles described previously (black line in Fig. 5). The combined effect of

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stratification, topography, and latitude (through f) affecting the CTW nature are then quantified

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through the estimation of S2. Results show that large values of S2 are encountered along the SEP

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coast (Fig. 5a), especially off central Peru. Lower S2 values are estimated along Southwest Africa

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and in particular in the Northern Benguela upwelling system (Fig. 5b). Increasing latitude also

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favors small S2 values associated with barotropic structures [Brink, 1982], especially along the

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South Chilean coast.

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Pressure modal structures of the four gravest CTW modes are derived from ROMS mean

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stratification and topography along the southwestern coasts of the South American and African

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continents (cf. #2.5). Examples of CTW pressure structures are shown in Fig. 3 and Fig. 12 of

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the companion paper [Illig et al., 2018] for cross-shelf sections along the Peruvian (16°S) and

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Namibian (27°S) coasts. According to the Burger number estimations associated with the deep

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and steep bathymetry along the Peruvian/Chilean coasts (Fig. 5), the CTW modal structures are

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baroclinic, with isopleths slanting outward. The modal structure and phase velocity of the gravest

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CTW mode approach the characteristics of a deep ocean internal Kelvin wave (consistently with

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Brink [1982]). Conversely, in the Benguela upwelling system, modal structures show nearly

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vertical isopleths over the shelf and slope, consistent with nearly barotropic dynamics associated

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with small S2 values. Accordingly, phase speed values are larger in SEA than in SEP and

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latitudinal variations of the phase speed (Fig. 4 of the companion paper [Illig et al., 2018]) are

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inversely proportional to S2 values.

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3.3. CTW mode contribution to coastal sub-seasonal variability

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By projecting ROMS pressure sub-seasonal anomalies onto the CTW modal structures,

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we estimate the amplitude of the first four CTW modes (cf. # 2.5), following the methodology

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validated in the companion paper [Illig et al., 2018]. The contribution of each CTW and their

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summed-up contribution to the coastal SSLA and Sub-seasonal Along-Shore Current Anomalies

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(SASCA) are quantified in the SEP and SEA. Fig. 7c-d of the companion paper [Illig et al.,

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2018] presents the coastal SSLA RMS of the first four CTW modes. Here, Fig. 6 presents their

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explained variance relative to the coastal SSLA and SASCA variability. In agreement with the

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shape of the CTW modal structures, the maximum amplitude of the modes is trapped at the coast.

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In both systems, the summed-up contribution of the four gravest CTW modes explains more than

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50% of the coastal SSLA variability (grey lines in Fig. 6c and Fig. 6g), emphasizing the

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importance of the sub-seasonal CTW dynamics in the coastal fringe. North of 7°S (10°S) in the

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SEP (SEA), the alongshore-current dynamics is more complex and cannot be explained purely

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by the summed-up contribution of the gravest CTW modes (grey lines in Fig. 6d and Fig. 6h).

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Results also show that there are important differences in the relative contribution of each CTW

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mode between the two basins. In agreement with the characteristics of the remote equatorial

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forcing, CTW mode 1 is dominant in the SEP. It explains more than 50% of the coastal (0-50km)

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SSLA and SASCA variability over much of the coast (Fig. 6a and black line in Fig. 6cd),

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showing a local minimum near 8°S. The contribution of the second CTW mode remains very

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weak, except north of 6°S, where its contribution is comparable to the one of the first CTW mode

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(Fig. 6b and red line in Fig. 6cd). In contrast, in the SEA, the second CTW mode is the most

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energetic north of ~13°S, while poleward, the first CTW mode dominates the sub-seasonal

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coastal variability (Fig. 6 lower panels). These differences between the two systems in terms of

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the relative contribution of each CTW mode are in agreement with the dynamics of the linear

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coastal model (cf. Fig 10cd and Fig. 7ab of the companion paper [Illig et al., 2018]).

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In conclusion, the dynamics in the SEP is straightforward: the sub-seasonal equatorial

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forcing, consisting of the dominant first EKW mode, is transmitted southward along the coasts

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of Peru/Chile as a first CTW mode. This mode remains dominant along the entire coast of western

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South America, enabling a consistency with the equatorial variability at high latitudes. In the

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SEA, the second EKW carries most of the sub-seasonal equatorial forcing. Its energy is

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transmitted poleward along the southwestern coast of Africa as a second CTW mode. However,

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its contribution to the coastal sub-seasonal variability drastically diminishes between 12-15°S,

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where CTW mode 1 amplitude increases. This transition in the dominance between in the two

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gravest CTW modes corresponds exactly to the latitude where the connection between coastal

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and equatorial variabilities fades out (Fig. 1b and Fig. 2). In the following section, we will

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investigate the processes that explain the fading of the SEA second CTW mode.

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3.4. CTW frictional dissipation

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Along their propagations, CTW modes experience dissipation and scattering due to

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bottom friction (Eq. 2). CTW frictional decay coefficients (ann) and frictional coupling

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coefficients (𝑎 𝑚𝑛 ) are estimated in the SEP (Fig. 7ab) and SEA (Fig. 7cd), based on CTW

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eigenfunction values (cf. Clarke and Van Gorder [1986] and Eq. 4.7 of the companion paper

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[Illig et al., 2018]). Coefficients are represented using a matrix, such as the amplitude of a given

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CTW mode of order n will be affected by the amplitude of a mode of order m through the

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frictional coefficient amn (Eq. 2). Diagonal elements are the frictional decay coefficients (ann).

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Coefficients have been averaged over 5° latitudinal bands, within 5°S-10°S, where CTW mode

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2 is dominant in the SEA, and further south within 20°S-25°S, where the contribution of SEA

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CTW mode 1 becomes dominant. Results show that in both systems and at all latitudes along the

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coasts, higher-order CTW modes dissipate more strongly than gravest modes (diagonal values in

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Fig. 7). Also, for each CTW mode the dissipation is stronger in the SEA than in the SEP (average

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within 5°S-25°S, not shown). As a consequence, the SEA dominant CTW mode 2 which carries

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the equatorial forcing signal will dissipate considerably faster than the SEP remotely-forced

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−1 CTW mode 1. Between 5°S and 10°S, the alongshore decay scale of the second CTW mode (𝑎22 )

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−1 in the SEA is 714 km, while in the SEP, 𝑎11 is equal to 2564 km.

𝑛≠𝑚

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This suggests that CTW frictional dissipation may explain the early fading of the

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coherence between coastal and equatorial sub-seasonal variabilities in the SEA compared to the

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SEP sector. This hypothesis is further tested out using the SEP and SEA linear coastal model

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configurations (cf. #2.6). We performed two sensitivity experiments (cf. Table 2) in which sub-

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seasonal CTW are forced at the equator but are not impacted by the coastal wind-stress forcing

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𝐸𝑄 (𝑏𝑛 = 0 in Eq. 2). They differ by the way friction affects CTW propagations: 𝐿𝐶𝑀𝑛𝑜𝐷𝐼𝑆𝑆 is the

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frictionless case (𝑎𝑛𝑛 = 𝑎 𝑚𝑛 = 0 in Eq. 2) and in 𝐿𝐶𝑀𝑛𝑜𝑆𝐶𝐴𝑇 , CTW dissipate along their

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propagation (𝑎𝑛𝑛 ≠ 0) without modal scattering (𝑎 𝑚𝑛 = 0). In these experiments, Fig 8 shows

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the contribution of the CTW modes to the coastal SSLA. The latitudinal variations of the CTW

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eigenfunctions (𝐹𝑛 (𝑥 = 0, 𝑧 = 0)) are thus superimposed on top of the variations of the

𝐸𝑄

𝑛≠𝑚

𝑛≠𝑚

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amplitude of the modes (𝜙𝑛 ), which can give the false impression that CTW modes dissipate less

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in the SEA than in the SEP. As expected, in the frictionless case (not shown), CTW propagate

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straightforwardly up to the southern boundary of both domains. In agreement with the equatorial

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forcing characteristics (Fig. 4), in the SEP (SEA), CTW mode 1 (2) remains the most energetic

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all along the coast. The coherence between coastal and equatorial variabilities remains strong up

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to 40°S (30°S) in the SEP (SEA). When introducing the CTW linear dissipation, the amplitude

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of the weakly-dissipative first CTW mode remains strong all along the coasts of both basins

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(black lines in Fig. 8a and Fig. 8b), while the amplitude of the higher order modes decreases

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rapidly, in particular in the SEP. There, the coherence with the equatorial variability, estimated

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by the maximum lag correlation between equatorial SSLA forcing (summed-up contribution of

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the 4 CTW modes) and the LCM coastal SSLA, remains prominent until the southern boundary

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of the model domain. In the SEA, CTW mode 2 energy decreases along its propagation, to reach

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the level of the amplitude of the first CTW mode around 15°S, in agreement with ROMS

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solutions (Fig. 6). The coherence with the equatorial forcing is high (correlation>0.7) until 30°S,

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but lags are not monotonically increasing south of 19°S (dashed line without shading in Fig. 8b).

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This latitude is however too far south compared to the 12°S-15°S latitude estimated with

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altimetry (Fig. 1).

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3.5. CTW modal scattering due to bottom friction

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Bottom friction also triggers modal scattering (Eq. 2 and Clarke and Van Gorder [1986])

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which can contribute to the decrease in the consistency between coastal and equatorial

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variabilities. In Fig. 7, the largest values of frictional coupling coefficients 𝑎 𝑚𝑛 are found below

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the diagonal of the frictional coefficient matrix, implying that the magnitude of a given mode of

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order n will be affected by the amplitude of lower order modes (m5° in latitude) of a Hayashi [1982] space-time analysis (cf. Fig. 10 of the companion

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paper [Illig et al., 2018]). Results show that, in the SEP, the local atmospheric forcing primarily

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impacts sub-monthly CTW mode 1 coastal SLA within the [10-20]-day period (Fig. 12a), while

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in the SEA it impacts a broader frequency band ranging from sub-monthly to intraseasonal time-

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scales (Fig. 12b).

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Hence, our results suggest that sub-seasonal wind-stress forcing can account for the

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increase in the amplitude of the first CTW mode south of 25°S (15°S) in the SEP (SEA). It

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explains the loss of coherence between the coastal variability and the equatorial forcing at ~30°S

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in the SEP. In addition to the dissipation and scattering of the remotely-forced CTW mode 2 in

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the SEA, sub-seasonal wind-stress forcing also participates in the early decreasing of the

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equatorial teleconnection in the SEA.

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4. Conclusions and Discussion

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In this paper, we have investigated the sub-seasonal poleward coastal propagations in the

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southeastern Pacific and Atlantic Oceans. The main objective is to explain the 15° difference

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between the two systems in the maximum latitude at which the coastal variability remains

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consistent with the equatorial forcing, as observed from altimetry. Our methodology is based on

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the experimentation with a combination of regional ocean general circulation model simulations

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and simple linear CTW model simulations, for which twin configurations of the SEP and SEA

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coastal oceans have been developed. We first quantified the amplitude of the sub-seasonal

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oceanic forcing in both eastern equatorial basins in terms of eastward-propagating EKW. Results

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show that this forcing is only 20% larger in the Pacific than in the Atlantic. However, we reported

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important differences in the relative contribution of the different baroclinic modes: the first EKW

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mode dominates the EEP variability, while in the EEA, EKW mode 2 carries a greater fraction

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of the sub-seasonal energy. Then, a decomposition of ROMS model outputs into CTW

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contribution was performed following the methodology validated in the companion paper [Illig

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et al., 2018]. In both systems, the extracted CTW modes propagate at velocities close to the

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theoretical phase speeds (companion paper [Illig et al., 2018]). Notably, they propagate slightly

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faster in the Atlantic compared to the Pacific. This is due to the CTW structures being more

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barotropic in the SEA than in the Humboldt Current system, which is a consequence of the gentler

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and shallower topography slope encountered in the SEA. Our study shows that, in both systems,

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the linear CTW dynamics explains a great amount of the coastal SSLA and SASCA variability,

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consistently with the good agreement between the linear model and ROMS outputs highlighted

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in the companion paper [Illig et al., 2018]. The summed-up contribution of the first four CTW

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modes accounts for ~50-90% of the SASCA and SSLA coastal variabilities. In agreement with

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the equatorial forcing, in the SEP, the first CTW mode largely dominates the coastal sub-seasonal

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variability. The assumption of retaining only the first CTW mode characteristics is thus valid in

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the SEP, in agreement with Brink [1982]. In this context, coastal altimetric products or tide gauge

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measurements can be useful to monitor sub-seasonal CTW propagations. In the SEA, the second

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CTW mode is dominant north of 13°S, whereas poleward of 13°S, the first CTW mode is the

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most energetic. Note that Polo et al. [2008] estimated coastal propagation velocities along the

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coast of West Africa within 1.5-2.1 m.s-1 range, consistent with first and second CTW mode

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phase speeds. The transition between the two modes corresponds to the latitude where the

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connection between coastal and equatorial variabilities fades out in the SEA (Polo et al., [2008],

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Goubanova et al., [2014] and Fig. 1b). We identified three processes that contribute to explain

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this result. The damping of CTW mode 2 at ~13°S in the SEA is induced by the frictional

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dissipation. South of 13°S, the re-energization of the first CTW mode is triggered by frictional

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modal scattering and sub-seasonal alongshore wind-stress forcing. In the SEP, the less dissipative

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remotely-forced first CTW mode remains energetic at high latitudes. A smaller impact of the

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equatorial teleconnection is however reported along the southern Chilean coast [Shaffer et al.,

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1999; Belmadani et al., 2012; Illig et al., 2014]. It is attributed to the local wind forcing

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contribution that becomes more important south of 25°S, where it overshadows the equatorial

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signal, in agreement with the result from Hormazabal et al., [2001].

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In the SEA, we reported an alternation of the dominant CTW mode contributions, with

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the equatorially-forced second CTW mode being the most energetic equatorward of 13°S, while

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poleward of this latitude the first CTW mode is the dominant contribution to the coastal sub-

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seasonal variability. We attributed this change to the bottom friction which dissipates and scatters

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the second CTW mode. This allows for the propagation of the remotely-forced first CTW mode

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further south which is re-energized by the coastal wind variability south of 15°S. Surprisingly,

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we did not detect any drastic changes in the CTW characteristics, in terms of bottom friction

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dissipation or modal coupling, around the ABFZ (~17°S, not shown)., This could be linked to

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the fact that we consider ROMS stratification at 400km off-shore in the SEA which might differ

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from the stratification on the shelf. Nevertheless, ROMS stratification remains fairly constant in

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the 400-km coastal band in both systems (not shown). Instead, our results suggest that the

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changes in CTW structure and parameters associated with the coastal vertical stratification

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modification across the ABFZ are compensated by the deepening and steepening of the

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bathymetry off the Angolan coast between 13-18°S (Fig. 5). We further estimated scattering

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coefficients due to the changes in the shape of CTW eigenfunctions from one latitude to another,

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as introduced by Johnson [1991]. Indeed, when CTW encounter irregularities on the bottom shelf

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topography or changes in the coastal stratification along their propagation, energy can be

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transferred between modes. The values of the scattering coefficients estimated along the West

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African coast reveal that the changes in the vertical stratification associated with the presence of

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the ABFZ do not trigger significant modal scattering (not shown). In contrast, the passage over

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the Walvis Ridge (~19°S-21°S) and the steepening of the bathymetry off Angola coast are

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associated with a clear increase in scattering coefficients (not shown). This most likely

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contributes to the fading of the equatorial connection around 12°S. More thorough analyses are

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required to properly conclude on this specific point. In particular, it would be relevant to further

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quantify the effect of the changes in the bathymetry and stratification along the wave propagation.

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This would imply increasing the complexity of the LCM model by adding the modal scattering

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associated with the changes in the shape of CTW structure from one latitude to another as

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implemented by Jordi et al. [2005].

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In both systems, we reported a distinct contribution of the second CTW mode (more

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prominent in the SEA) in the northern part of the domains close to the equatorial band, whereas

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further south there is a dominance of the first CTW mode. Following the same assumption and

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using the outputs from similar ROMS experiment, Illig et al., [2014] suggested that a CTW mode

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alternation could explain the drastic increase in poleward coastal propagation velocity observed

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in the SSLA off Southern Peru (~18°S, cf. dashed line in Fig. 1a). However, we showed in this

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paper that the contrast between the first and the second CTW modes is weakly marked in the SEP

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and the 20% contribution of the second CTW mode fades out north of 10°S, which rules out this

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supposition. We then hypothesized that the CTW acceleration can be triggered by the synoptic

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sub-monthly variability of the coastal jet along the coast of Chile. The latter would force CTW

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simultaneously over an extended coastal region, creating an apparent acceleration of free coastal

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propagations. But again, the analysis of the ROMS sensitivity experiment in which

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𝐸𝑄 climatological surface wind-stress forcing is prescribed (𝑅𝑂𝑀𝑆𝑆𝐸𝑃 ) depicts the acceleration of

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the coastal propagations in the Southern Humboldt region (not shown), in agreement with Illig

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et al. [2014] (their Figure 3). This excludes the role of coastal winds in the increase of the CTW

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velocity. In the light of the results presented in this paper, we conclude that the acceleration of

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the coastal propagations is likely associated with the change in the nature of the CTW passing

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from baroclinic vertical structures along the coast of Peru to fast, nearly barotropic waves south

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of 20°S (Fig. 5), as depicted in LCM (Fig. 5 of the companion paper [Illig et al., 2018]) and

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ROMS modal decomposition (Fig. 8 of the companion paper [Illig et al., 2018]) outputs.

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Finally, this study emphasizes the importance of the vertical structure variability of the

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remote equatorial dynamics in the eastern equatorial Pacific and Atlantic Oceans. A first

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baroclinic EKW transmitted along the southwestern coasts of South American and African

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continents as a fast weakly-dissipative first CTW will propagate farther south than higher order

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modes. Hence, the characteristics of the remote equatorial forcing can modulate the maximum

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latitude at which the equatorial dynamics imprints the coastal variability. In this context, Dewitte

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et al., [2008] showed that the intraseasonal EKW activity undergoes a significant modulation

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along the equatorial waveguide. Likewise, at interannual time-scales, Dewitte et al. [1999, 2003]

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reported a different contribution for the dominant EKW modes in the EEP, with the dominance

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of the second and third baroclinic modes. Similar behavior can be anticipated for the EEA

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forcing, accounting for the strong low-frequency modulation of the oceanic variability in the

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Tropical Atlantic [Xichen et al., 2016]. As a consequence, the results presented in this study are

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valid for the 2000-2008 period and for sub-seasonal frequencies. Further analysis is required for

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the investigation of the characteristics of equatorial connection at different time-scales, such as

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the interannual variability. Similarly, the strength of the equatorial connection will be affected

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by the low-frequency modulation of the equatorial dynamics, which can call into question our

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results for past or future periods.

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Acknowledgements:

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We would like to thank the CNES (OSTST project EBUS-SOUTH) for financial support.

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Marie-Lou Bachèlery received funding from the EU FP7/2007-2013 under grant agreement no.

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603521 and the NRF SARCHI chair on modelling ocean atmosphere land interactions. The

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authors would like to thank Boris Dewitte for the valuable discussions throughout the course of

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this study. We sincerely acknowledge our native (English) scientist Ross Blamey, who kindly

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helped us improve our French literary writing. We are also grateful to Dr. Kenneth H. Brink and

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Dr. Stephen Van Gorder for sharing their programs and kindly answered some technical

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questions. The authors wish to acknowledge use of the Ferret program (NOAA PMEL,

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http://ferret.pmel.noaa.gov) for analysis and graphics in this paper. ROMS model and

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ROMS_TOOLS software can be downloaded from https://www.croco-ocean.org. The ROMS

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model grid, forcing, and initial conditions were built using the ROMS_TOOLS package [Penven

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et al., 2008] version 3.1. Computations were performed using facilities provided by the

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University of Cape Town's ICTS High-Performance Computing team (http://hpc.uct.ac.za).

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QuikSCAT wind-stress data, AVISO Altimetric data, SODA and ERA-INTERIM reanalysis

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outputs are freely available to the public on the dedicated websites of these programs. We thank

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the anonymous reviewers for their comments and suggestions that helped improved the

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manuscripts.

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946 947

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948

31

949 950 951 952 953 954 955 956 Domain Southeastern Pacific (SEP)

Southeastern Atlantic (SEA)

EXP-Name

OBC

Surface Forcing

𝐶𝑅 𝑅𝑂𝑀𝑆𝑆𝐸𝑃

Total

Total

𝐸𝑄 𝑅𝑂𝑀𝑆𝑆𝐸𝑃

Total

Monthly Climatologies

𝐶𝑅 𝑅𝑂𝑀𝑆𝑆𝐸𝐴

Total

Total

𝐸𝑄 𝑅𝑂𝑀𝑆𝑆𝐸𝐴

Total

Total within [4°S-7°N; 10°W-4°E] and Monthly Climatologies elsewhere

957 958 959 960

Table 1: Description of ROMS Experiments: Domain, Name, Open lateral Boundary Conditions (OBC), surface forcing specifications.

32

961 962 963 964 965 966 967 EXP-Name

EKW Forcing

ASWS Forcing

Dissipation

Scattering

𝐸𝑄 𝐿𝐶𝑀𝑛𝑜𝐷𝐼𝑆𝑆

Total

none

no

no

𝐸𝑄 𝐿𝐶𝑀𝑛𝑜𝑆𝐶𝐴𝑇

Total

none

yes

no

𝐿𝐶𝑀𝐸𝑄

Total

none

yes

yes

𝐿𝐶𝑀𝐶𝑅

Total

Total

yes

yes

968 969 970 971

Table 2: Description of LCM Experiments conducted with SEP and SEA configurations: Name, Equatorial forcing, alongshore wind-stress forcing and wave dissipation specifications.

33

972 973 974 975 976 977 978 979

Sector SEP SEA

f

̅ 𝑁

L3000



Latitude

10-5 s-1

10-4 s-1

km

m.km-1

S2 -

16°S

-4.0

22.8

59.64

50.3

8.22

27°S

-6.6

22.9

58.37

51.4

3.06

16°S

-4.0

22.05

101.8

29.5

2.62

27°S

-6.6

22.02

227.8

13.2

0.19

980 981 982 983 984 985 986

Table 3: Parameters controlling CTW vertical structures at 16°S and 27°S along the coasts of ̅ is southwestern South America and western Africa: f is the Coriolis frequency at the coast, 𝑁 ROMS mean (2000-2008) buoyancy frequency averaged within the first 3000 meters, L3000 is the distance between the 3000m isobath and the coast,  is representative of the shelf-slope ̅/𝑓)2 is the squared Burger number. gradient (𝛼3000 = 3000/ 𝐿3000 ), and 𝑆 2 = (𝛼𝑁

34

987 988

989 990 991 992 993 994 995 996 997 998 999 1000 1001

Figure 1: In color: maximum lagged correlation analysis (top scale) between 2000-2008 observed (AVISO) coastal (1° coastal band average) Sub-seasonal Sea Level Anomalies (SSLA) and observed equatorial SSLA averaged within [105°W-95°W; 1°S-1°N] and [15°W5°W; 1°S-1°N] in SEP (a) and SEA (b) sectors respectively, as a function of latitude. Lags (in days) are specified with color shading. A positive value indicates that equatorial variability leads. An absence of shading is indicative of a non-statistically significant correlation coefficient (at 95% level of confidence [Sciremammano, 1979]) or to non-monotonically increasing lags when going poleward. Dashed lines: coastal SSLA propagation velocity (m.s-1, bottom scale). At each latitude, the maximum lagged correlation between coastal SSLA at this latitude and coastal SSLA within a centered 7° latitudinal window is computed. For each 7°window, the linear regression coefficient that best fits the lag estimation is calculated. Grey shading indicates error in the linear regression coefficient estimation.

35

1002 1003 1004 1005 1006 1007 1008 1009

1010 1011 1012 1013 1014 1015 1016 1017

Figure 2: Maximum lagged correlation between ROMSCR coastal (0.5° width band) SSLA and SODA equatorial SSLA as a function of latitude. Plain (dashed) line is for the SEP (SEA) coasts, with equatorial SSLA averaged within [105°W-95°W (15°W-5°W); 1°S-1°N]. Lags (in days) are specified with color shading. A positive value indicates that equatorial variability leads. An absence of shading is indicative of a non-statistically significant correlation coefficient (at 95% level of confidence [Sciremammano, 1979]) or to non-monotonically increasing lags when going poleward.

36

1018 1019 1020 1021 1022 1023 1024

1025 1026 1027 1028 1029 1030

Figure 3: Equatorial remote forcing contribution to coastal SLA (averaged within 0.5° coastal fringe) variability sub-monthly (grey) and intraseasonal (blue) time-scales as a function of latitude in the SEP (top panel) and SEA (bottom panel). Colored shading represents the ratio of variance between ROMSEQ and ROMSCR SLA, while dashed lines show the explained variance of ROMSEQ with respect to ROMSCR (in %, cf. Eq. 1).

37

1031 1032 1033 1034 1035 1036 1037

1038 1039 1040 1041 1042 1043 1044 1045

Figure 4: Histogram of SODA Equatorial Kelvin Wave (EKW) SLA Root Mean Square (RMS, in cm) for the 3 gravest baroclinic modes and their summed-up contribution in a) the eastern Equatorial Pacific (EEP, averaged within [105°W-95°W; 1°S-1°N]) and b) in the eastern Equatorial Atlantic (EEA, averaged within [5°W-5°E; 1°S-1°N]) for sub-seasonal (white), intraseasonal (blue), and sub-monthly (grey) time-scales. For each frequency band and each baroclinic mode, the percentage listed corresponds to the explained variance of the EKW SLA contribution to SODA sub-seasonal SLA (in %, cf. Eq. 1).

38

1046 1047 1048 1049 1050

1051 1052 1053 1054 1055 1056 1057 1058 1059

Figure 5: Parameters controlling CTW vertical structures in function of latitude along the coasts of the SEP (top panel) and SEA (bottom panel) Oceans.  is representative of the shelfslope gradient (black lines, 𝛼3000 = 3000/ 𝐿3000 , where L3000 is the distance between the coast ̅ is the mean buoyancy frequency and the 3000m isobath, unit is m.km-1, black left scale). 𝑁 averaged within the upper 3000 meters (blue lines, unit is 10-2 s-1, blue left scale). 𝑆 2 = ̅/𝑓)2 is the squared Burger number (red lines, unitless, red right scale). To better visualize (𝛼𝑁 𝑆 2 ≫ 1 and 𝑆 2 ≪ 1, we use a Log2 vertical scale. Red and blue shadings correspond to S2 values larger and lower than 1.

39

1060 1061 1062 1063

1064 1065 1066 1067 1068 1069 1070 1071 1072

Figure 6: CTW mode contribution (explained variance in %, cf. Eq. 3.1) to SSLA and SASCA along the coasts of the SEP (top panels) and SEA (bottom panels) Oceans. Panels a/e (b/f) show the explained variance of the first (second) CTW mode contribution to model SSLA, as a function of the distance from the coast (km) and the latitude. Panels c/g and e/f present the explained variance of the first three CTW modes and the summed-up contribution of the four gravest CTW modes to coastal SSLA (averaged within 0.5° coastal fringe) and SASCA (averaged within 100km/200m depth coastal fringe) respectively.

40

1073 1074

1075 1076 1077 1078 1079

Figure 7: Frictional coefficients (anm, in 10-8 cm-1) along a) North Peruvian (averaged within [5°S -10°S]), b) the North Chilean (averaged within [20°S-25°S]), c) along North Angolan (averaged within [5°S -10°S]), and d) Namibian (averaged within [20°S-25°S]) coasts.

41

1080 1081 1082 1083 1084 1085 1086 1087

1088 1089 1090 1091 1092 1093 1094 1095 1096

𝐸𝑄 Figure 8: 𝐿𝐶𝑀𝑛𝑜𝑆𝐶𝐴𝑇 CTW mode contribution to Coastal (0.5° width band) SSLA (CSSLA) along the coasts of the SEP (a) and SEA (b). Root Mean Square of CTW mode 1, 2, 3 and 4 are in black, red, blue and green plain lines, respectively. Unit is cm. Maximum lagged correlation between equatorial and coastal SSLA as a function of latitude, with monotonically increasing lags (in day) is specified with color shading. A positive value indicates that equatorial variability leads.

42

1097 1098 1099 1100 1101 1102 1103 1104

1105 1106 1107

Figure 9: Same as Fig. 8 but for LCMEQ simulation.

43

1108 1109 1110 1111

1112 1113 1114 1115 1116 1117 1118 1119

Figure 10: a) Root Mean Square of QuikSCAT alongshore wind-stress (dyn.cm-2) for subseasonal time-scales in function of latitude along the coasts of the SEP (shading) and SEA (dashed lines) Oceans. b) Histogram of the wind projection coefficient (bn, in 10-2 [s.cm]-1/2) for the four gravest CTW modes in the southeastern Pacific (bright shading) and Atlantic (light shading) Oceans, averaged within [5°S-10°S] (left panel), averaged within [15°S-20°S] (middle panel), and averaged within [25°S-30°S] (right panel).

44

1120 1121 1122 1123 1124 1125 1126

1127 1128 1129 1130 1131 1132

Figure 11: Top panels: Root Mean Square of CTW mode contribution to Coastal (0.5° width band) SSLA (CSSLA, cm) along the SEP (a) and the SEA (b) coasts for ROMSCR (plain lines) and ROMSEQ (dashed lines) simulations. CTW mode 1 is in black and CTW mode 2 is in red. Bottom panels: same as Fig. 8, for LCMCR along the SEP (c) and SEA (d) coasts.

45

1133 1134 1135 1136 1137 1138 1139 1140

1141 1142 1143 1144 1145 1146 1147 1148

Figure 12: Space-time power spectra [Hayashi, 1982] summed over long spatial-scales (>5° of latitude) for ROMSCR (grey shading) and ROMSEQ (black line) CTW mode 1 Coastal SSLA (CSSLA) in the SEP (a) and SEA (b) Oceans. In the SEP (SEA) the analysis is performed within a 32°-length (24°-length) domain extending from 3°S to 35°S (from 3°S to 27°S). Unit is cm2. Grey dashed vertical lines indicate the separation between sub-monthly and intraseasonal frequencies.

46