The economics of the thermohaline circulation—A problem with multiple thresholds of unknown locations

A potentially serious environmental threat facing humanity is the possibility of a collapse of the thermohaline circulation. Resulting climate changes, including absolute cooling near Greenland and northwest Europe, could be abrupt. Collapse of the thermohaline circulation may be triggered if the temperature or the rate of temperature change exceeds certain thresholds. The locations of these thresholds are unknown. Economic regulation of this problem requires solution methods for a class of dynamic optimization problems with multiple thresholds located in n-dimensional space. This class of problems has hitherto not been discussed in the literature. We present a model for the economic regulation of CO2 emissions in the presence of threshold-triggered risk of a collapsing thermohaline circulation and derive optimality conditions for regulation.