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Description: Sea level rises at an accelerating pace threatening coastal communities all over the world. In this context sea level projections are key tools to help risk mitigation and adaptation. Sea level projections are often made using models of the main contributors to sea level rise (e.g. thermal expansion, glaciers, ice sheets...). To obtain the total sea level these contributions are added, therefore the uncertainty of total sea level depends on the correlation between the uncertainties of the contributors. This fact is important to understand the differences in the uncertainty of sea level projections from different methods. Using two process-based models to project sea level for the 21st century, we show how to model the correlation structure and its time dependence. In these models the correlation primarily arises from uncertainty of future global mean surface temperature that correlates with almost all contributors. Assuming that sea level contributors are independent of each other, an assumption made in many sea level projections, underestimates the uncertainty in sea level projections. As a result, high-end low probability events that are important for decision making are underestimated. The uncertainty in the strength of the dependence between contributors is also explored. New dependence relation between the uncertainty of dynamical processes, and surface mass balance in glaciers and ice sheets are introduced in our model. Total sea level uncertainty is found to be as sensitive to the dependence between contributors as to uncertainty in individual contributors like thermal expansion and Greenland ice sheet.