Climate vs Weather J. J. Hack/A. Gettelman: June 2005

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1 Climate vs Weather J. J. Hack/A. Gettelman: June 2005

2 What is Climate? J. J. Hack/A. Gettelman: June 2005

3 Characterizing Climate Climate change and its manifestation in terms of weather (climate extremes) J. J. Hack/A. Gettelman: June 2005

4 Climate vs Weather Question 3: Why can t we predict weather? Weather is an inherently chaotic system Classic example: the Lorenz system

5 Characterizing Climate!"#$%"&'($)($*"#$+#&*"#, -.#/$)/$012)3#/()'/&4$(5(*#3(6$/#&,75$ )/)*)&4$%'/2)*)'/($)/$&$25/&3)%&4$(5(*#3$%&/$ "&.#$8-9:$2);;#,#/*$2#(*)/)#(<$ A',#/B$C**,&%*',!"#$&**,&%*',$)($*"#$%4)3&*#!"#$&**,&%*',$)*(#4;$#/='5($(*,>%*>,#$&/2$)*$)($ *"#$?&,&3#*#,($';$*"#$&**,&%*',$+#$&,#$&;*#,$ Jones

6 Evidence of a Changing Climate Intergovernmental Panel on Climate Change (IPCC):!"#$!%&!'()'*'&+*%,#%,'&-#.*/! Warming is unequivocal

7 Pandora s Box / : $;283<:!"#$% &'(%)#% =53089>79>56?81@;232 A3229;8B12>2CC2=6 *+),*-#* &.*,)#$)/ A>62?@2356B321?56;2?567=5D>?8E2D1 Jones

8 Why do we try to predict?!/*0,12$,3$456$71,8&*0 Jones

9 Why use computational models? 1-,0 < Friday: Natalie Mahowald will talk about full climate models Today: Intro to most basic concepts of energy balance models Jones

10 Simplest Energy Balance Models Energy gains Energy gains equal

11 Simplest Energy Balance Models Black Body Radiation Planck Energy gains Spectral Intensity vs Wavelength For black bodies at different temperatures (0 C=273K) Energy gains equal Sun: ~6000K, emits mainly in visible spectrum (shortwave) Earth: ~300K, emits mainly in IR (longwave) Integrate over wavelength for temp T to get total emission flux σt Stefan Boltzmann

12 Energy Balance, No Atmosphere Hypothesis: Earth s temperature is a consequence of 1. Blackbody radiation 2. Distance from Sun 3. Size 4. Albedo (reflectivity) Energy gains equal Energy gains -t 1,2. Solar flux S solar Wm 2 -t t Rays approx. parallel 4. Albedo α / 1. Terrestrial flux σt terrestrial ff r* e { 3. Surface Area 4πa 2 welf!o=1iel2 3. Area = πa 2 Following Marshall and Plumb

13 Energy Balance, No Atmosphere Hypothesis: Earth s temperature is a consequence of 1. Blackbody radiation 2. Distance from Sun 3. Size 4. Albedo (reflectivity) Energy Gain Solar flux * cross sect area = Sπa 2 W Energy gains equal Energy gains -t 1,2. Solar flux S solar Wm 2 -t t Rays approx. parallel 4. Albedo α / 1. Terrestrial flux σt terrestrial ff r* e { 3. Surface Area 4πa 2 welf!o=1iel2 3. Area = πa 2 Following Marshall and Plumb

14 Energy Balance, No Atmosphere Hypothesis: Earth s temperature is a consequence of 1. Blackbody radiation 2. Distance from Sun 3. Size 4. Albedo (reflectivity) Energy Gain Solar flux * cross sect area = Sπa 2 W Energy loss by Terrestrial Radiation Terrestrial flux * surface area = σt e4 4πa 2 Energy gains equal Energy gains -t 1,2. Solar flux S solar Wm 2 -t t Rays approx. parallel 4. Albedo α / 1. Terrestrial flux σt terrestrial ff r* e { 3. Surface Area 4πa 2 welf!o=1iel2 3. Area = πa 2 Following Marshall and Plumb

15 Energy Balance, No Atmosphere Hypothesis: Earth s temperature is a consequence of 1. Blackbody radiation 2. Distance from Sun 3. Size 4. Albedo (reflectivity) Energy Gain Solar flux * cross sect area = Sπa 2 W Energy loss by Terrestrial Radiation Terrestrial flux * surface area = σt e4 4πa 2 Energy gains equal Energy gains Energy loss by Albedo Reflected solar radiation = αsπa 2 -t 1,2. Solar flux S solar Wm 2 -t t Rays approx. parallel / 4. Albedo α 1. Terrestrial flux σt terrestrial ff r* e { 3. Surface Area 4πa 2 welf!o=1iel2 3. Area = πa 2 Following Marshall and Plumb

16 Energy Balance, No Atmosphere Hypothesis: Earth s temperature is a consequence of 1. Blackbody radiation 2. Distance from Sun 3. Size 4. Albedo (reflectivity) Energy Gain Solar flux * cross sect area = Sπa 2 W Energy loss by Terrestrial Radiation Terrestrial flux * surface area = σt e4 4πa 2 Energy gains equal Energy gains Energy loss by Albedo Reflected solar radiation = αsπa 2 Balance Sπa 2 = αsπa 2 + σt e4 4πa 2 (1 α)s = 4σT e T e = 255K = 18 C -t 1,2. Solar flux S solar Wm 2 -t t Rays approx. parallel / 4. Albedo α 1. Terrestrial flux σt terrestrial ff r* e { 3. Surface Area 4πa 2 welf!o=1iel2 3. Area = πa 2 Following Marshall and Plumb

17 Energy Balance, No Atmosphere Hypothesis: Earth s temperature is a consequence of 1. Blackbody radiation 2. Distance from Sun 3. Size 4. Albedo (reflectivity) Energy Gain Solar flux * cross sect area = Sπa 2 W Energy loss by Terrestrial Radiation Terrestrial flux * surface area = σt e4 4πa 2 Energy gains equal Energy gains Energy loss by Albedo Reflected solar radiation = αsπa 2 Balance Sπa 2 = αsπa 2 + σt e4 4πa 2 (1 α)s = 4σT e T e = 255K = 18 C Too Cold Snowball Earth! -t 1,2. Solar flux S solar Wm 2 -t t Rays approx. parallel / 4. Albedo α 1. Terrestrial flux σt terrestrial ff r* e { 3. Surface Area 4πa 2 welf!o=1iel2 3. Area = πa 2 Following Marshall and Plumb

18 Energy Balance, No Atmosphere Hypothesis: Earth s temperature is a consequence of 1. Blackbody radiation 2. Distance from Sun 3. Size 4. Albedo (reflectivity) Energy Gain Solar flux * cross sect area = Sπa 2 W Energy loss by Terrestrial Radiation Terrestrial flux * surface area = σt e4 4πa 2 Energy gains equal Energy gains Energy loss by Albedo Reflected solar radiation = αsπa 2 -t 1,2. Solar flux S solar Wm 2 Balance -t Sπa 2 = αsπa 2 + σt e4 4πa 2 (1 α)s = 4σT t e T e = 255K = 18 C Observed global average surface temp T s = 288K = 15 C Rays approx. parallel / 4. Albedo α 1. Terrestrial flux σt terrestrial ff r* e { 3. Surface Area 4πa 2 welf!o=1iel2 3. Area = πa 2 Following Marshall and Plumb

19 Energy Balance, No Atmosphere Hypothesis: Earth s temperature is a consequence of 1. Blackbody radiation 2. Distance from Sun 3. Size 4. Albedo (reflectivity) Conclusions: With these hypotheses, surface temp is 33 C too low We need to include atmosphere to correct this 255K is a good estimate for the top of the atmosphere. Which does satisfy the hypotheses more closely. Energy gains equal Energy gains -t 1,2. Solar flux S solar Wm 2 Balance -t Sπa 2 = αsπa 2 + σt e4 4πa 2 (1 α)s = 4σT t e T e = 255K = 18 C Observed global average surface temp T s = 288K = 15 C Rays approx. parallel / 4. Albedo α 1. Terrestrial flux σt terrestrial ff r* e { 3. Surface Area 4πa 2 welf!o=1iel2 3. Area = πa 2 Following Marshall and Plumb

20 Aside: DE Viewpoint Hypothesis: Earth s temperature is a consequence of 1. Blackbody radiation 2. Distance from Sun 3. Size 4. Albedo (reflectivity) Energy Gain Solar flux * cross sect area = Sπa 2 W Energy loss by Terrestrial Radiation Terrestrial flux * surface area = σt e4 4πa 2 Energy gains equal Energy gains Energy loss by Albedo Reflected solar radiation = αsπa 2 Balance Sπa 2 = αsπa 2 + σt e4 4πa 2 (1 α)s = 4σT e T e = 255K = 18 C Observed global average surface temp T s = 288K = 15 C Aside: as a differential equation for temp T e Sign(dT e /dt) = energy gain energy loss = ((1 α)s σt e4 ) πa 2 when T e = 255K, dt e /dt = 0 when T e > 255K, dt e /dt < 0 when T e < 255K, dt e /dt > 0 Energy balance corresponds to attracting equilibrium.

21 Energy Balance, No Atmosphere Hypothesis: Earth s temperature is a consequence of 1. Blackbody radiation 2. Distance from Sun 3. Size 4. Albedo (reflectivity) Conclusions: With these hypotheses, surface temp is 33 C too low We need to include atmosphere to correct this 255K is a good estimate for the top of the atmosphere. Which does satisfy the hypotheses more closely. Energy gains equal Energy gains -t 1,2. Solar flux S solar Wm 2 Balance -t Sπa 2 = αsπa 2 + σt e4 4πa 2 (1 α)s = 4σT t e T e = 255K = 18 C Observed global average surface temp T s = 288K = 15 C Rays approx. parallel / 4. Albedo α 1. Terrestrial flux σt terrestrial ff r* e { 3. Surface Area 4πa 2 welf!o=1iel2 3. Area = πa 2 Following Marshall and Plumb

22 Atmospheric Absorption Spectrum CIMSS/ U Wisc

23 Energy Balance, 1 Layer Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Energy gains Space Atmosphere Following Marshall and Plumb Surface Solar Terrestrial

24 Solar Flux Energy gains Recall total solar radiation (W) Solar flux * cross sect area = Sπa 2 Solar flux (W/m 2 ): Total solar in / surface area = Sπa 2 /4πa 2 = S/ Energy gains equal -t 1,2. Solar flux S solar Wm 2 -t t Rays approx. parallel 4. Albedo α / 1. Terrestrial flux σt terrestrial ff r* e { 3. Surface Area 4πa 2 welf!o=1iel2 3. Area = πa 2 Following Marshall and Plumb

25 Energy Balance, 1 Layer Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Solar flux (W/m 2 ): Total solar in / surface area = Sπa 2 /4πa 2 = S/ Energy gains Space Atmosphere Following Marshall and Plumb Surface Solar Terrestrial

26 Energy Balance, 1 Layer Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Solar flux (W/m 2 ): Total solar in / surface area = Sπa 2 /4πa 2 = S/ Energy balance of total system: S/= αs/+ σt a Energy gains (1 α)s/= σt a 4 Space Atmosphere Following Marshall and Plumb Surface Solar Terrestrial

27 Energy Balance, 1 Layer Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Solar flux (W/m 2 ): Total solar in / surface area = Sπa 2 /4πa 2 = S/ Energy balance of total system: S/= αs/+ σt a Energy gains (1 α)s/= σt a 4 So, as before, T a =255K Space Atmosphere Following Marshall and Plumb Surface Solar Terrestrial

28 Energy Balance, 1 Layer Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Solar flux (W/m 2 ): Total solar in / surface area = Sπa 2 /4πa 2 = S/ Energy balance of total system: S/= αs/+ σt a Energy gains (1 α)s/= σt a 4 So, as before, T a =255K Energy balance at surface: S/+ σt a = αs/+ σt s σt s = (1 α)s/+ σt a Space Atmosphere Following Marshall and Plumb Surface Solar Terrestrial

29 Energy Balance, 1 Layer Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Solar flux (W/m 2 ): Total solar in / surface area = Sπa 2 /4πa 2 = S/ Energy balance of total system: S/= αs/+ σt a Energy gains (1 α)s/= σt a 4 So, as before, T a =255K Energy balance at surface: S/+ σt a = αs/+ σt s σt s = (1 α)s/+ σt a = 2σT a4 Space Atmosphere Following Marshall and Plumb Surface Solar Terrestrial

30 Energy Balance, 1 Layer Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Solar flux (W/m 2 ): Total solar in / surface area = Sπa 2 /4πa 2 = S/ Energy balance of total system: S/= αs/+ σt a Energy gains (1 α)s/= σt a 4 So, as before, T a =255K Energy balance at surface: S/+ σt a = αs/+ σt s σt s = (1 α)s/+ σt a = 2σT a4 So, T s = 2 ¼ T a 1.19 T a = 303K = 30 C Following Marshall and Plumb Space Atmosphere Surface Solar Terrestrial

31 Energy Balance, 1 Layer Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Solar flux (W/m 2 ): Total solar in / surface area = Sπa 2 /4πa 2 = S/ Energy balance of total system: S/= αs/+ σt a Energy gains (1 α)s/= σt a 4 So, as before, T a =255K Energy balance at surface: S/+ σt a = αs/+ σt s σt s = (1 α)s/+ σt a = 2σT a4 So, T s = 2 ¼ T a 1.19 T a = 303K = 30 C Surface is 15 C warmer than observed. Space Atmosphere Surface Solar Terrestrial

32 Energy Balance, 1 Layer Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Solar flux (W/m 2 ): Total solar in / surface area = Sπa 2 /4πa 2 = S/ Energy balance of total system: S/= αs/+ σt a Energy gains (1 α)s/= σt a 4 So, as before, T a =255K Space Energy balance at surface: S/+ σt a = αs/+ σt s σt s = (1 α)s/+ σt a = 2σT a4 Atmosphere So, T s = 2 ¼ T a 1.19 T a = 303K = 30 C Note: downwelling from atmosphere is at magnitude of solar flux. Surface Solar Terrestrial

33 Energy Balance, 1 Layer Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Solar flux (W/m 2 ): Total solar in / surface area = Sπa 2 /4πa 2 = S/ Energy balance of total system: S/= αs/+ σt a Energy gains (1 α)s/= σt a 4 So, as before, T a =255K Energy balance at surface: S/+ σt a = αs/+ σt s σt s = (1 α)s/+ σt a = 2σT a4 So, T s = 2 ¼ T a 1.19 T a = 303K = 30 C Note: Atmosphere is cooler than the surface. Space Atmosphere Surface Solar Terrestrial

34 Energy Balance, 1 Layer Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Conclusions: With these hypotheses Top of atmosphere is 255K (observed 250K) Surface temp is 15 C too high Atmosphere is cooler than surface Energy gains Space Atmosphere Following Marshall and Plumb Surface Solar Terrestrial

35 Energy Balance, With Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Conclusions: With these hypotheses Top of atmosphere is 255K (observed 250K) Surface temp is 15 C too high Atmosphere is cooler than surface Energy gains New Hypotheses: Atmosphere partially opaque to terrestrial IR Conclusion: With realistic ε, surface temp is still too high Space Atmosphere Following Marshall and Plumb Surface Solar Terrestrial

36 Energy Balance, With Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Energy gains equal Conclusions: With these hypotheses Top of atmosphere is 255K (observed 250K) Surface temp is 15 C too high Atmosphere is cooler than surface Energy gains New Hypotheses: Atmosphere partially opaque to terrestrial IR Many layers of atmosphere Accurate ε for each layer Accurate ε for each wavelength Space Atmosphere Conclusion: With realistic atmosphere, surface temp is still too high Following Marshall and Plumb Surface Solar Terrestrial

37 Energy Balance, With Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Do get qualitative reproduction of temperature distribution in atmosphere. Atmospheric temperature with height New Hypotheses: Atmosphere partially opaque to IR Many layers of atmosphere Accurate ε for each layer Accurate ε for each wavelength Conclusion: With realistic atmosphere, surface temp is still too high

38 Energy Balance, With Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Radiative energy balance is NOT enough to explain surface temperature. Atmospheric temperature with height New Hypotheses: Atmosphere partially opaque to IR Many layers of atmosphere Accurate ε for each layer Accurate ε for each wavelength Conclusion: With realistic atmosphere, surface temp is still too high

39 Energy Balance, With Atmosphere Hypotheses: Earth s temperature is a consequence of 1. Radiation, distance from sun, size, albedo 2. Single layer, uniform atmosphere 3. Atmosphere transparent to solar radiation 4. Atmosphere opaque to terrestrial radiation Why? Cold fluid above hot fluid is an unstable equilibrium, so convection sets in fluid dynamics and weather in troposphere New Hypotheses: Atmosphere partially opaque to IR Many layers of atmosphere Accurate ε for each layer Accurate ε for each wavelength Atmospheric temperature with height Conclusion: With realistic atmosphere, surface temp is still too high

!"#$%&'()*"#+",+%#%&54!"#$%&'#$'())'*+,-"'."*/-&&-& 6*$!

40 Numerical Climate Model Du # $ %#! 2&' u" %( p ) # gk ) * Dt )!!"#$%&'()*"#+",+-($$!.()%&+'(/"&+0()-"$/1%&%2! $(3*#*)4+0"!%(#2++!!"#$%&'()*"#+",+%#%&54!"#$%&'#$'())'*+,-"'."*/-&&-& 6*$!&%)*7% 0/8)+"#+5&*92+!!"##%!)+/*%!%$+",+-"9%3+0:"8#9(&4+!"#9*)*"#$2+! *#*)*(3*7%+! $"3'%+!"-/8)()*"#(334

41 Climate Model Grid Size 1 x1 3 x2 Jacobson

42 Hypothesis Testing Observations: 20 Century Warming Model Solutions with Human Forcing J. J. Hack/A. Gettelman: June 2005

43 1 Dimensional Energy Balance Budyko Sellers North. Hypotheses: 1. Rotational symmetry of earth 2. Energy balance calculated for each latitude x i, with temp T i 3. Atmospheric dynamics provide heat transport between layers 4. Albedo depends on T i (ice or not) captures ice albedo feedback Solve equations for T i profile, and for location of ice line

44 1 D Energy Balance Equations Latitude x, temperature T 6&')*$7)4()-&%$ 8,+&/>"#*(.$)%4$&.#)%(.$"#),$,*)%/>&*,5$ 8'3#4&9$*#:#.,#4$'(1",$(%.*#)/#/$ (0$!;<=$4*&>/$3#'&?$0*##@(%1A$ B(%#)*(@)-&%$&0$CD,1&(%1$!#**#/,*()'$7)4()-&%$ 8//D+#$,"),$),+&/>"#*(.$)%4$&.#)%(.$ +&E#+#%,/$/+&&,"$,"#$,#+>#*),D*#$>*&F'#$$ Abbot

45 Budyko Sellers Model Predictions

ice melts and reverse ice-albedo feedback occurs Runaway ice-albedo feedback Very

46 Snowball Earth: 700M yrs ago!"#$%&'()*)"+#',-.#*/'0$-.1+#/')'2341$+)5-"'.3)%$)6'78)7' 63%87'#90*)3"'78#'%#-*-%3+)*'-2/#$:)5-"/;'' CO 2 draw down Tropical ice melts and reverse ice-albedo feedback occurs Runaway ice-albedo feedback Very low weathering allows CO 2 to build up to ~10% of atmosphere over 1-10 million years Abbot

47 More recent: last 600K yrs 10 deg variation in temperature 100 ppm variation in carbon dioxide Martin 2

48 Climate archives:! what information do we have?" Ruddiman, W. F., Earth's Climate: past and future" Martin

49 Temperature Record 2M yrs Glacial-interglacial cycles!

50 Sun Milankovich cycles: Variation in orbit & axis, 20K, 40K and 100K years Thousand years before present Combine Budyko model with Milankovich cycles As orbit changes slightly, amount of solar radiation received changes. Can explain timing of end of ice ages Cannot explain speed or amplitude of rise

Sun SUN Temp Milankovich cycles: Variation in orbit & axis, 20K, 40K and 100K years 400 300 200 100 0 Thousand years before present Green

51 Sun SUN Temp Milankovich cycles: Variation in orbit & axis, 20K, 40K and 100K years Thousand years before present Green house Gases Geol. Carbon Cycle CO 2 Include Temp CO 2 feedback from geological carbon cycle to help understand speed and amplitude of rise.

52 Temperature Record 2M yrs Glacial-interglacial cycles!

53 PaleoClimate Record 70M years Temperature Carbon What models capture this behavior? Especially abrupt changes. Million years ago Instructive to develop a hierarchy of models of increasing complexity. When do robust behaviors of simple models persist as we increase complexity? Zachos Use different levels of model hierarchy to give insight into feedback interactions between climate processes.

Radiation in climate models.

Lecture. Radiation in climate models. Objectives:. A hierarchy of the climate models.. Radiative and radiative-convective equilibrium.. Examples of simple energy balance models.. Radiation in the atmospheric