Please help solve this HW question!

1. A climate model Consider the following simple climate model: T: = Ttl + U1(Ft1 KTti 02 (Ttl 11111)) TtL = Trill + U3 (Ti1 Till1) where T; and Tf', respectively, denote the atmospheric and ocean temperature in period t, both mea- sured relative to a pre-industrial steady state. Ft is forcing in period t (change in energy balance relative to pre-industrial steady state) and Ii and the [HS are positive parameters. (a) (b) (C) (d) Suppose we observe that if forcing is constant at the level F = 4, the atmospheric temperature T eventually stabilizes at 3 degrees. Will also the ocean temperature stabilize? If so, at which temperature? Which parameter(s) if any is determined by the information in a., i.e., that Ft = 4 for all t, implies that T: converges to 3? Use the information to calibrate (put a number to) relevant parameter(s). Suppose F0 2 4 and To 2 E? = 0. What are T1 and Tf' in terms of the parameters? Suppose we observe that T1 = 1. Use this to calibrate the relevant parameter(s). Now consider the case of tipping points created by temperature dependent feedbacks. Specically, in the model above we have assumed that the energy outflow is proportional to temperature. Assume now instead that the pr0portionality factor falls discretely whenever T: > 2. Which parameter is affected and no longer a temperature independent constant? Draw a stylized graph with time on the xaxis and T: on the y-axis showing the dynamics of the atmOSpheric temperature in the case of tipping points. Assume as above that at the start of your graph, To = TOL = 0 and that Ft = 4 for all t Z 0