Climate Modeling Primer

Develop a model to predict the average surface temperature of Earth List 5 Factors Need to be Considered

Insolation: Energy from the Sun solar radiation Objects above 0K can emit radiation Max possible radiation for given temperature is blackbody Plancks law gives blackbody curves

Planck’s Law: SUN Wien’s Law:  = 2897 / T T = 5780 K max 6 X 10 Objects above 0K can emit radiation Max possible radiation for given temperature is blackbody Plancks law gives blackbody curves

SUN

Develop a model to predict the average surface temperature of Earth List 5 Factors Need to be Considered

Focus on a particular time scale of interest Time Scales Focus on a particular time scale of interest Factors that change very slowly relative to that time scale can be considered constant Stop and Think 03 DEMO: pendulum Momentum goes from + to - and 0 Same for angular When a ball hits a bat where doe the momentum go? What is “the system” Momentum goes to string to ceiling to earth Earth gets what pendulum looses Factors that are very fast relative to that scale can be considered to be in an “instantaneously” adjusting equilibrium called quasi steady state

Time Scales

Crudest, useful estimate of effective surface temperature of planet Te: Equate solar radiation it absorbs to the infrared radiation it emits  T 4 e T e incoming solar radiation Rate at which object radiates is proportional to its area and to the fourth power of its absolute temperature (Stefan-Boltzman law)

solar radiation terrestrial radiation Energy In Energy Out Stored

DYNAMIC EQUILIBRIUM variable time

 T T 4 e e incoming solar radiation Absorbed depends on: Solar Constant, Albedo (~0.3 for earth), Radius Emitted depends on: Effective Temperature, Radius, Stefan-Boltzmann Constant

Outgoing: E = 4R T Incoming: (1-A) SR 2 4 earth e e SUN 2 4 earth e e Incoming: How much solar radiation does the earth intercept? (1-A) SR 2 e

SUN = 4R T 2 4 e e (1-A) SR 2 e T = 255 K e

Model Refinement . cT = (1-A) SR - 4R T Radiation Re-Radiated Absorbed Radiation Temperature cT = e . (1-A) SR 2 2 4 - 4R T e e e

X 10 6 Wien’s Law:  = 2897 / T max T = 5780 K T = 255 K

SUN = 4R T 2 4 e e (1-A) SR 2 e T = 255 K e

= 4R T (1-A) SR  T T If the model equation for this system is given by: = 4R T 2 4 e e (1-A) SR 2 e  T 4 e T s incoming solar radiation Then what has been assumed ?

Model Refinement

SUN Greenhouse Effect CO2 Heating reradiated incoming Haze Effect vs Greenhouse Effect Heating

SUN Box 2 Greenhouse Effect CO2 Box 1 Heating incoming reradiated Haze Effect vs Greenhouse Effect reradiated Box 1 Heating

SURFACE ATMOSPHERE BOX BOX Energy In Energy Out Energy Out Energy In Stored Stored SURFACE BOX

 T T  T  T T T = T = 255 K  T =  T Consider an end-member atmosphere layer that’s opaque to infrared  T 4 A T A  T 4 A  T 4 S T S incoming solar radiation For radiative equilibrium: Incoming (sun) must = Outgoing (atmosphere) T A = T effect = 255 K If the atmosphere is at steady-state then incoming IR must equal outgoing  T = 4 S  T A

 T   T  T =  A S incoming solar radiation   T S incoming solar radiation Surface measurements show an average surface temperature of 288K  T = S  prediction is within 5%

Model Refinement

Atmospheric Window for Infrared Radiation

k T T k T T  T k T k) T 4 A A 4 A S incoming solar radiation  T 4 S k T 4 S k) T 4 S

Ingregrate over all Bands

 T   T  T =  T  T =  A   T S incoming solar radiation  T = 1/4 S  T eff  T = S  Is this Really the Maximum Greenhouse Effect?

Model Refinement

Consider a 1-D column that represents the average vertical structure of the atmosphere of the entire planet Air layers containing CO2, H20… incoming solar radiation Transport of heat & chemical constituents between layers Global average albedo 50% of atmosphere is below 6km Atmosphere thins with elevation Space

SUN Te = T1 T1 Layer 1 T2 Layer 2 T3 Layer 3 TG 4 4 4 4 Haze Effect vs Greenhouse Effect TG 4 Layer 3

 SUN TG = (1+) Te Te = T1 T1 Layer 1 T2 T2 = (2) Te T3 Layer 2 1/4 Te = T1 T1 4 Layer 1 T2 4 T2 = (2) Te 1/4 T3 4 Layer 2 Haze Effect vs Greenhouse Effect  T3 = (3) Te 1/4 TG 4 Layer 3 TG = (4) Te 1/4

Model Refinement

= 4R T (1-A) SR SUN solar radiation Low Albedo High 2 4 2 4 e e (1-A) SR 2 e

= 4R T (1-A) SR f (Temperature) SUN solar radiation Low Albedo High = 4R T 2 4 e e (1-A) SR 2 e f (Temperature)

. Big Deal or Small Deal? cT = (1-A) SR - 4R T Temperature Albedo 1 present day cT = e . (1-A) SR 2 2 4 - 4R T e e e f (Temperature)

Model Refinement . cT = (1-A) SR - 4R T Radiation Re-Radiated Absorbed Radiation Temperature cT = e . (1-A) SR 2 2 4 - 4R T e e e

Model Refinement . cT = (1-A) SR - 4R T f (Temperature) Re-Radiated Absorbed negative feedback Radiation positive feedback Temperature cT = e . (1-A) SR 2 2 4 - 4R T e e e f (Temperature)

Zonal Energy Balance Climate Model (cf. Budyko)

Model Refinement

Model Extension

Faint Young Sun

Faint Young Sun Paradox

Should We Expect Other Earth-like Planets At All? By Caleb A. Scharf “… long-term stability (read millions of years) of the Earth’s surface environment close to the ‘habitable’ state is a direct consequence of geophysical re-cycling.” “Geophysics is the dirty little secret here.”

Volcanic-Tectonic Driven Climate Model

from WHAK to BLAG Walket Hayes and Kasting Berner Lasaga and Gerrels

Coupled Volcanic-Tectonic Evolution and Climate Evolution Model

Solid Planet Dynamics Model Climate Model CO2 Cycling

Develop a model to predict the average internal temperature of Earth List 5 Factors Need to be Considered

Mantle Heat Production Qs Surface Mantle Heat Flux H H Mantle Heat Production

an expression for this is the key to this modeling exercise Ur = cV T = - Qs Convective Flux Qs Surface Mantle Heat Flow an expression for this is the key to this modeling exercise Mantle Heat Production H H Qs Ur = Ur=.21-.49 Continents back = .33-.76

Carbonate-Silicate Weathering Cycle Tectonics + Hydrologic Cycle Cycles are dynamic- Fluxes are critical. What does a snapshot say about a cycle? Tectonic factors - volcanism, uplift, and exposure - affect atmospheric pCO2 , but ultimately the stabilizing influence is the sensitivity of weathering rates to atmospheric pCO2 . Increases in relief in tectonically active regions increase Aex , and thus cause CO2 draw-downs. The attendant climate change reduces chemical weathering rates elsewhere, returning the carbonate-silicate cycle to steady state (Kump & Arthur 1997). The major effect of CO2 on weathering is indirect, and involved the greenhouse effect of atmospheric pCO2 on temperature and net precipitation. Kump et al., 2000