Earth’s energy budgets

ESE 101 2016 Global energy balance

Incoming Reflected Outgoing solar radiation solar radiation longwave radiation 340 100 240 TOA

Atmospheric Atmospheric Cloud reflection window effect 77 40 165 35 Clear Sky 75 Atmospheric absorption

188 23 24 88 398 345 Absorbed Reflected SH LH LW up LW down SW SW

F￿￿￿￿￿ 7.1: Earth’s global energy balance. The energy fluxes through the climate system are global averages estimated from satellite data and atmospheric reanalysis. They 2 are indicated in units of W m . At the top of the atmosphere, the energy fluxes are 2 best constrained and have errors of order 1Wm . The errors in surface fluxes, and 2 particularly latent heat fluxes are considerably larger, of order 10 W m . The indicated fluxes were adjusted within the measurement errors such that the energy balance closes.1 Climate_Book October 24, 2016 6x9

Climate_Book October 24, 2016 6x9

ENERGY BALANCES AND TEMPERATURES 109

ENERGY BALANCES AND TEMPERATURES 109

Surface energy balance

@Ts c ⇢ ⇤ S# L" F F div F s s @t 0 0 L S O F￿￿￿￿￿ 7.2: Absorbed solar radiative flux at the surface.

7.3 LATENTF AND￿￿￿￿￿ 7.2 SENSIBLE: AbsorbedSurface HEAT solar heat radiative FLUXES fluxes: flux at the surface. bulk aerodynamic formulae F ⇤ ⇢c ⇢C v T T z (7.2) 7.3 LATENT AND SENSIBLES p HEATd k FLUXESk [ s a( r)] assume transfer coefficient Cd equal to sensible heat and latent energy (not F ⇤ ⇢c ⇢C v T T z (7.2) necessarily true) S p d k k [ s a( r)] assume transfer coefficient Cd equal to sensible heat and latent energy (not ⇤ necessarily true) FL ⇢LCd v qs qa zr (7.3) k k ( ) ⇤ assume qs q⇤ Ts over wet surfaces ⇥ ⇤ ( ) F ⇤ ⇢LC v q q z (7.3) L d k k s a( r) assume q ⇤ q T over wet surfaces 7.4 BOWENs ⇤ RATIO( s) ⇥ ⇤

FS 7.4 BOWEN RATIO Bo ⇤ (7.4) FL F Bo ⇤ S (7.4) FL Climate_Book October 24, 2016 6x9 Net downward solar radiative flux at surface @Ts ENERGYc BALANCES⇢ AND TEMPERATURES⇤ S# L" F F div F 109 s s @t 0 0 L S O 90°N ANN 25 100 45°N

225 150 0 250 Latitude 45°S 125 300 90°S 120°E 120°W 0 200 90°N 250 DJF 45°N 25 200 100

200 −2 150 0 250 150

275 W m Latitude 45°S 100

90°S 120°E 120°W 0 200 50 90°N JJA 100 0 45°N 300 250 275 0

Latitude 125 75 45°S

90°S 120°E 120°W 0 200 Longitude W m−2

F￿￿￿￿￿ 7.2: Absorbed solar radiative flux at the surface.

7.3 LATENT AND SENSIBLE HEAT FLUXES

F ⇤ ⇢c ⇢C v T T z (7.2) S p d k k [ s a( r)] assume transfer coefficient Cd equal to sensible heat and latent energy (not necessarily true)

F ⇤ ⇢LC v q q z (7.3) L d k k s a( r) assume q ⇤ q T over wet surfaces s ⇤( s) ⇥ ⇤

7.4 BOWEN RATIO F Bo ⇤ S (7.4) FL Climate_Book October 24, 2016 6x9

AbsorbedENERGY BALANCES solar AND TEMPERATURES radiative flux at surface 109

90°N ANN 25 100 45°N

225 150 0 250

Latitude Climate_Book October 24, 2016 6x9 45°S 125

90°S 120°E 120°W 0 200 90°N 100 CHAPTER 4 TOA annual mean albedo a 90°N Total 65 45°N 25 30 0 15 35 Latitude 45°S

70 90°S 0 120°E 120°W 0 0 40 80

F￿￿￿￿￿ 7.2: Absorbed solar radiative flux at the surface.

7.3 LATENT AND SENSIBLE HEAT FLUXES

F ⇤ ⇢c ⇢C v T T z (7.2) F￿￿￿￿￿ 4.5: Earth’s annual-meanS albedop d k atk the[ s top ofa( atmosphere.r)] (a) Total albedo, obtained as the ratio of total upward to downward solar radiative energy flux at the assume transfer coefficient Cd equal to sensible heat and latent energy (not topnecessarily of the atmosphere. true) (b) Clear-sky component of the albedo, obtained as the ratio of upward solar radiative energy flux from cloudless regions to total downward flux. All radiative energy fluxes were measured by NASA’s space-based Clouds and Earth’s F ⇤ ⇢LC v q q z (7.3) Radiant Energy System (CERES)L instruments.d k k s They a( werer) averaged over the 13 years ⇤ 2 fromassume Marchqs 2000q⇤ T throughs over February wet surfaces 2013 prior⇥ to the computation⇤ of the albedos. The right panels show( the) zonal means of the left panels. The dashed red line in the upper right panel is the fit from the heuristic model in the box on p. 103. 7.4 BOWEN RATIO F land and Antarctica. Subtropical desertsBo ⇤ S such as the Sahara also stand out(7.4) as regions of high albedo compared with surroundingFL areas. But otherwise, land– ocean contrasts and other variations of Earth’s surface properties only leave a weak signature on top-of-atmosphere albedo variations. Instead, the dominant albedo variation is the gradual increase from 20% in the tropics, to 45% at ⇠ ⇠ 60N/S, to &70% near the poles. This is clearly evident in the zonal-mean albedo (Fig. 4.5a, right panel), which increases nearly symmetrically away from the equator—despite the strongly hemispherically asymmetric distribution of continents. The zonal albedo variations (the variations along latitude belts) are comparatively weak. They correlate with measures of cloudiness, such as cloud water path (Fig. 1.20) and cloud fraction (Fig. 1.22). For example, the albedo is elevated ( 30%) over the subtropical eastern Pacific with its high fraction of low clouds (cf.⇠ Fig. 1.22), and it is reduced over the subtropical western Pacific with its lower cloud water path and cloud fraction. These observations indicate that Climate_Book October 24, 2016 6x9 Net longwave radiative flux at surface

110 @Ts CHAPTER 7 c ⇢ ⇤ S# L" F F div F s s @t 0 0 L S O 90°N ANN

45°N 100 75 125 0 50 100 Latitude 45°S

50 150 90°S 120°E 120°W 0 100 90°N DJF 50 25 45°N 100 100 −2 0 50 W m

Latitude 125 100 45°S 50

90°S 120°E 120°W 0 100 90°N 0 JJA

45°N 125 125 50 150 0

Latitude 100 45°S

50 90°S 120°E 120°W 0 100 Longitude W m−2

F￿￿￿￿￿ 7.3: Surface longwave radiation.

how does it depend on climate

cp Ts Ta Bo ( ) (7.5) ⇠ L q T q T ⇤( s) H ⇤( a) assume fixed T T and fixed relative⇥ humidity ⇤. s a H

7.5 SURFACE ENERGY UPTAKE

7.6 TOP OF ATMOSPHERE ENERGY BALANCE

@E ⇤ S# L" div F (7.6) @t TOA TOA Surface radiation balance

Hartmann (2016) Climate_Book October 24, 2016 6x9 Surface sensible heat fluxes @Ts ENERGYc BALANCES⇢ AND TEMPERATURES⇤ S# L" F F div F 111 s s @t 0 0 L S O 90°N ANN -25 45°N 50 50 0

Latitude 75 25 45°S

25 200 90°S 120°E 120°W −25 25 90°N 150 DJF 125 45°N 100 100

50 −2 0 W m Latitude 125 200 50 45°S 0

90°S 0 120°E 120°W −25 25 90°N JJA −50 45°N 50 100 100 25 0 50 Latitude 45°S -50 90°S 120°E 120°W −25 25 Longitude W m−2

F￿￿￿￿￿ 7.4: Surface sensible heat fluxes. where

F ⇤ FA + FO

7.7 FORMS OF ENERGY

7.7.1 Atmosphere To atmosphere can be taken to be an ideal gas.

I￿￿￿￿￿￿￿ ￿￿￿￿￿￿

I ⇤ cvT (7.7) Climate_Book October 24, 2016 6x9 Surface latent heat fluxes

112 @Ts CHAPTER 7 c ⇢ ⇤ S# L" F F div F s s @t 0 0 L S O 90°N ANN 45°N 175 200 150 0 175 Latitude 100 45°S 50 250 90°S 120°E 120°W 0 100 90°N 200 DJF 45°N 250 250 150 −2 0 100

150 125 W m

Latitude 100 45°S 25

90°S 50 120°E 120°W 0 100 90°N JJA 0 45°N 75 125 100 0 200 150 Latitude 45°S 75

90°S 120°E 120°W 0 100 Longitude W m−2

F￿￿￿￿￿ 7.5: Surface latent heat fluxes.

P￿￿￿￿￿￿￿￿ ￿￿￿￿￿￿

⇤ gz (7.8)

L￿￿￿￿￿ ￿￿￿￿￿￿

Lq (7.9)

K￿￿￿￿￿￿ ￿￿￿￿￿￿

1 K ⇤ u 2 (7.10) 2 k k Climate_Book October 24, 2016 6x9 Surface fluxes residual

ENERGY BALANCES@ ANDTs TEMPERATURES 113 c ⇢ ⇤ S# L" F F div F s s @t 0 0 L S O 90°N ANN 45°N −125 −175

0 150

Latitude 125 45°S 25 300 −25 250 90°S 120°E 120°W −100 100 200 90°N DJF 150

45°N −250 −225 100 −75 50 −2 0 175 0 W m

Latitude 175 45°S 125 −50 −100 90°S 120°E 120°W −100 100 −150 90°N −200 JJA −250 45°N 175 200 75 0

Latitude −100 45°S −225 −125

90°S 120°E 120°W −100 100 Longitude W m−2

F￿￿￿￿￿ 7.6: [Update with Liu et al. 2015 estimates] Surface energy uptake, cal- culated as a residual of the fluxes in Figs. 7.2–7.5.2

C￿￿￿￿￿ ￿￿￿￿￿￿￿￿￿

Vertical integral

p 1 1 s dp ⇢Idz⇤ ⇢c Tdz⇤ c T (7.11) v v g π0 π0 π0 Climate_Book October 24, 2016 6x9

ENERGY BALANCES AND TEMPERATURES 109

Climate_Book October 24, 2016 6x9

110 CHAPTER 7

F￿￿￿￿￿ 7.2: Absorbed solar radiative flux at the surface.

7.3 LATENT AND SENSIBLE HEAT FLUXES

F ⇤ ⇢c ⇢C v T T z (7.2) S p d k k [ s a( r)] assume transfer coefficient Cd equal to sensible heat and latent energy (not necessarily true)

F ⇤ ⇢LC v q q z (7.3) L d k k s a( r) assume q ⇤ q T over wet surfaces s ⇤( s) Bowen Ratio⇥ ⇤

7.4 BOWEN RATIO

FS F￿￿￿￿￿ 7.3: SurfaceBo ⇤ longwave radiation. (7.4) FL how does it depend on climate

cp Ts Ta Bo ( ) (7.5) ⇠ L q T q T ⇤( s) H ⇤( a) assume fixed T T and fixed relative⇥ humidity ⇤. s a H

7.5 SURFACE ENERGY UPTAKE

7.6 TOP OF ATMOSPHERE ENERGY BALANCE

@E ⇤ S# L" div F (7.6) @t TOA TOA Climate_Book October 24, 2016 6x9

110 CHAPTER 7

Climate_Book October 24, 2016 6x9

ENERGY BALANCES AND TEMPERATURES 111

F￿￿￿￿￿ 7.3: Surface longwave radiation. how does it depend on climate

cp Ts Ta Bo ( ) (7.5) ⇠ L q T q T ⇤( s) H ⇤( a) assume fixed T T and fixed relative⇥ humidity ⇤. s a TOA energy balanceH

7.5 SURFACE ENERGY UPTAKE

7.6 TOP OF ATMOSPHERE ENERGY BALANCE F￿￿￿￿￿ 7.4: Surface sensible heat fluxes. @E ⇤ S# L" div F (7.6) @t TOA TOA where

F ⇤ FA + FO

7.7 FORMS OF ENERGY

7.7.1 Atmosphere To atmosphere can be taken to be an ideal gas.

I￿￿￿￿￿￿￿ ￿￿￿￿￿￿

I ⇤ cvT (7.7) Climate_Book October 24, 2016 6x9

114 TOA radiative fluxes CHAPTER 7

90°N SW 350 125 45°N 200 250 350 −2 0 275 W m

Latitude 150 45°S 175 75 50 90°S 120°E 120°W 100 300 90°N OLR 180 280

45°N 230 230 230 −2 0 255 280 W m

Latitude 180 45°S

180 130 90°S 120°E 120°W 100 300 90°N 100 Net −75 45°N −25 50 −25 75 0 −2 0 50 W m Latitude −50 45°S −100 −100 90°S 120°E 120°W −100 100 Longitude W m−2

F￿￿￿￿￿ 7.7: Annual-mean absorbed shortwave, outgoing longwave, and net radiation at the top of the atmosphere, based on space-based measurements.3

F￿￿￿￿￿ 7.8: Zonal- and annual-mean absorbed shortwave and outgoing longwave radi- ation. Climate_Book October 24, 2016 6x9

114 CHAPTER 7

F￿￿￿￿￿ 7.7: Annual-mean absorbed shortwave, outgoing longwave, and net radiation at the top of the atmosphere, based on space-based measurements.3

310 250 OLR −2 190

W m 130 70 Net Shortwave Down 90°S 45°S 30°S 15°S 0 15°N 30°N 45°N 90°N Latitude

F￿￿￿￿￿ 7.8: Zonal- and annual-mean absorbed shortwave and outgoing longwave radi- ation. Total energy transport

Hartmann (2016)