Presentation on theme: "Introduction to Climate and Energy Balance Models"— Presentation transcript:
1 Introduction to Climate and Energy Balance Models July 22, 2013Samantha OestreicherUniversity of Minnesota
2 “Some say the world will end in fire…” Some say the world will end in fire, Some say in ice. From what I've tasted of desire I hold with those who favor fire. But if it had to perish twice, I think I know enough of hate To say that for destruction ice Is also great And would suffice.
3 Outline What is Climate? How do we observe climate? An Overview of Earth’s Climate System.Types of RadiationEnergy Balance ModelStefan-BoltzmannBudyko-Sellers
17 How do we model climate?There are two main view on how to model climate:“No detail is too small!”Leads to all-inclusiveGlobal Climate Models“The rest is details”Leads to simpleConceptualClimate Models
18 Complicated choices starting from how to grid the globe. Global Climate ModelsComplicated choices starting from how to grid the globe.
24 How do we model climate?There are two main view on how to model climate:“No detail is too small!”Leads to all-inclusiveGlobal Climate Models“The rest is details”Leads to simpleConceptualClimate Models
25 Energy Balance Models Temperature Change = Energy In – Energy Out Energy Out using Stefan-Boltzmann Law:Temperature of the Sun = 5,778 KPower flux (W/m2) = (5.67 x10-8 )*(5778)4 = 6.33x107 W/m2Question:What kind of energy is the Sun radiating?
27 Types of RadiationPlank’s Function gives a distribution of wavelengths based on the temperature of the body.Wein’s Law tells us the maximum frequency is inversely proportional to the temperature. ie: Hotter bodies produce shorter wavelengths.The Sun gives off shortwave radiation or ultraviolet.The Earth gives off longwave radiation or infared.
28 Types of RadiationThe Sun gives off shortwave radiation or ultraviolet.The Earth gives off longwave radiation or infared.
29 Energy Balance ModelsIn the “Global Energy Balance Models and the Goldilocks Zone” section of the MATLAB guide, you will use the Stefan-Boltzmann Law to derive the average incoming solar radiation (or insolation) to Earth.Earth’s Insolation = 342 W/m2 = QThus the simplest energy balance model is:Temperature change = energy in – energy outWhich has equilibrium solution:Q = sTeq4or(342/s)1/4=TeqThus Earth’s temperature is modeled to beTeq = 279K = 6 °C = 43 °F
30 Energy Balance Models Teq = 279K = 6 °C = 43 °F But the observed temperature of Earth is onlyT = 14 °CStefan-Boltzmann is black body radiation. We need to include albedo.Globally 30% of insolation is reflected back into space.
32 Energy Balance Models Thus the improved energy balance model is: Which has equilibrium solution:Q (1- a) = sTeq4or(342*(1-0.3)/s)1/4=TeqThus Earth’s temperature is modeled to beTeq = 255K = -18 °C = 0 °FQuestion:Why isn’t the Earth a snowball?
33 Energy Balance ModelsBudyko - Sellers Suggest new outgoing longwave radiation (OLR) formulation:OLR = A + BTA and B are determined from satellite observations.T is surface temperature (in Celsius).A = 202 W/m B =1.90 W/m KDynamicsphotospheretemperatureglobal meansurface temperatureQuestion:What is happening in the atmosphere to cause this discrepancy?
34 Energy Balance Models Budyko-Sellers Energy Balance Model is: With equilibrium solutionThis equilibrium solution is stable with eigenvalue –B. (Recall B>0.)Question:What if Earth’s albedo was not 30%?Budyko 1969