Climate Modeling In Class Discussion Energy Balance Models

Climate Modeling In -Class Discussion: Energy Balance Models

Energy Balance Equation 1. Net radiation in/out at any latitude balanced by dynamical divergence/convergence 2. Still require global radiative balance Solve this equation to get Ts( ). Suppose Earth has interior source of heat, like Jupiter. How does the balance equation change?

Energy Balance Equation

Balance Equation to Solve Where Boundary Conditions: (i) Dynamic flux = 0 at poles (x = 1) (ii) Dynamic flux = 0 at x = 0 (hemispheric symmetry) (iii) xi = x(Ts= -10˚C) => xi = x(Ii =195. 7 W-m-2)

Balance Equation to Solve Where What happens to the solution? Suppose the interior heating gradually disappears. How do the balance equation and the equilibrium solution change?

Solar Flux - 2 S(x) is an even function about 0. Suppose Earth's tilt of axis changes. How does this picture change?

Solar Flux - 2 S(x) is an even function about 0. Suppose Earth's tilt of axis changes. How does this picture change, if …

Solar Flux - 2 S(x) is an even function about 0. … the earth has zero tilt? (no seasons)

Solar Flux - 2 S(x) is an even function about 0. … the earth has 90˚ tilt? (like Uranus)

Annual Cycle - Representation For any variable use, e. g. , § Units for t: year § P 1 captures seasonal asymmetry about equator (e. g. SH warm when NH cold. ) § Sizes of T 1 C and T 1 S determine amplitude and phase of annual cycle § Fit observed T, I, albedo and S: rms error < 5%

Annual Cycle - Representation For any variable use, e. g. , § P 1 captures seasonal asymmetry about equator (e. g. SH warm when NH cold. ) § Sizes of T 1 C and T 1 S determine amplitude and phase of annual cycle § How do these change for the cases of no axial tilt or 90˚ tilt?

Albedo - 2 xi = ice/snow edge = 0. 95 (lati = 72˚)

Albedo - 2 How would this change if clouds were different?

In-Class Discussion ~ End ~