Extending the Simple Model

Question 1

What terms from basic energy balance did Budyko linearise?

Answer 1

a - longwave emission to space at T_s = 273K
b - rate of change of longwave emission per K (similar to -lambda) as a function of latitude rather than response to climate.

Question 2

What is the meaning of insolation?

Answer 2

An object’s exposure to the sun’s rays.

Question 3

What does the Beta term represent in Budyko’s linearisation?

Answer 3

It represents the down-gradient of heat transfer from warmer equatorial regions to cooler polar regions.

Question 4

When do we utilise the Beta term in Budyko’s linearisation?

Answer 4

When forming the expression for T as a function of latitude. When considering the average surface temperature, we neglect this term and only consider the variables a and b.

Question 5

What is the expression relating a forcing and feedback with added time dependence (e.g. when equilibrium is non instantaneously reached.)

Answer 5

Q’ = -lambda T’_s + c dT’s/dt
where c denotes the specific heat capacity, so the added term is the energy storage,

Question 6

What is the expression relating a forcing and feedback with added time dependence (e.g. when equilibrium is non instantaneously reached.)

Answer 6

Q’ = -lambda T’_s + c dT’s/dt
where c denotes the specific heat capacity, so the added term is the energy storage.

Question 7

How do we solve the integral equation with added time dependence term?

Answer 7

Use an integrating factor, e^ alpha t, where alpha = -lambda/c, and the integration limits are between times t and t’.