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Abstract The role of ocean dynamics in Atlantic climate variability and predictability is often studied through the lens of sea surface temperature (SST). Unlike SST, sea surface salinity (SSS) is not directly damped by surface fluxes, and its low-frequency variability responds primarily to oceanic processes. This study investigates the drivers of SSS variability using a stochastic model hierarchy to disentangle oceanic and atmospheric contributions to Atlantic climate variability, in particular, the role of local vertical processes. Representation of SST and SSS persistence and variance is especially improved by the introduction of damping of anomalies below the mixed layer, though SSS anomalies remain too persistent. The effect of SST–evaporation feedback on SSS is comparatively smaller except in regions with strong SST–SSS correlation. Despite the lack of representation of geostrophic advection, the stochastic model successfully reproduces spatial patterns of recurring SST/SSS anomalies in the Community Earth System Model 1 (CESM1) Large Ensemble at monthly to interannual time scales. At multidecadal time scales, the stochastic model is unable to simulate the amplitude of SST/SSS variability, but their spatial patterns are broadly reproduced, suggesting that direct atmospheric forcing and local vertical processes are important for capturing these features. Further analysis of the processes missing from the stochastic model suggests that the lack of geostrophic advection is largely responsible for too persistent SSS in the stochastic model, while the lack of interannual mixed-layer depth variability explains the underestimated persistence and variance in some regions for both SST and SSS.