Sea level rise is a key feature in a warmer world and its impact can be seen globally. Assessing climate change-induced sea level rise, therefore, is urgently needed particularly in small island nations, where the threats of sea level rise are immediate, but the level of preparedness is low. Here, we propose a stochastic simulator to link changes in Mean Annual Temperature (MAT) to Mean Annual Sea Level (MASEL) at the local scale. This is through what-if scenarios that are developed based on the association between local temperature and sea level. The model can provide a basis for a bottom-up impact assessment by addressing limitations of applying large-scale projections in small islands and facilitating the accessibility of the impact assessment to stakeholders. For this purpose, we decompose the MAT and MASEL signals into their linear trend and autocorrelation components as well as independent and identically distributed residual terms. We further explore the association between trend and residual terms of MAT and MASEL. If such dependencies exist, scenarios of sea level can be synthesized based on the trend and residual terms of temperature. We use linear regression to link trends of MAT and MASEL, and copulas to formulate dependencies between residuals. This allows stochastic sampling of MASEL conditioned to trend and random variability in MAT. This framework is used for retrospective and prospective simulations of MASEL in Nouméa, the capital city of New Caledonia, the Pacific. We set up six different model configurations for developing the stochastic sampler, each including various parametric options. By selecting the best setup from each configuration, we provide a multi-model stochastic projection of MASEL, assuming the persistence in current long-term trend in MAT and MASEL. We demonstrate how such simulations can be used for a risk-based impact assessments and discuss sources of uncertainty in future projections. Display omitted •A locally-relevant bottom-up method is suggested for assessing sea level rise.•This is based on linking trends and residuals of local sea level and temperature.•The method is applied to assessing sea level rise in Nouméa, New Caledonia.•Guidelines on developing and parametrizing copula models are provided.•Sources of uncertainty are explored, decomposed and quantified.