Climate change scientists have shown concerns about possible sudden changes due to crossing a temperature threshold. Many authors emphasized the importance of sea level rise due to melting ice sheets of Greenland and west Antarctica and its large economic consequences. We study the economic consequences and policy implications of assuming a certain and uncertain thresholds at 2oC of global warming where it could result in a sudden sea level rise. We introduce these thresholds to the Dynamic Integrated model of Climate and the Economy (DICE model, Nordhaus 2009) and assess their policy impacts. We further modify the DICE model and assess the impacts of the thresholds using a reactive damage function. Results show that certain and uncertain thresholds have different impact on the optimal policy for different years. If the threshold is uncertain, the optimal carbon tax before 2025 is higher than certain threshold. However, optimal carbon tax assuming a certain threshold becomes higher than uncertain threshold from year 2025 and sharply increases between years 2035 to 2100.