Lecture 13From last time:If the Sun’s emitting surface layer (the “photosphere”) were to warm up by 10%, byhow much would the solar flux increase (as a fractional increase)?Today:• Planetary energy balance• Atmospheric structure revisitedNext lecture:-What makes some gases greenhouse gases?- Snow, water vapor, cloudsSun-Earth Geometry, and a factor of 4The Earth intercepts the sameamount of solar energy as flatdisc of area pr2The Earth emits longwaveradiation over the surface area ofa sphere, 4pr2 EIN [Watts] = EOUT [Watts][S0(1-A)] pr2 = s Te4 4pr2 The solar constant, S0 = the flux of solar energy passingthrough space at the Earth's orbital distance.S0 = 1370 W/m2pr2i.e. [Solar flux absorbed] ¥ (disc area) = terrestrial flux ¥ (sphere area) rEnergy balanceEIN = EOUT S0(1-A) pr2 = s Te4 4pr2 Te = the “effective temperature”. Now divide both sides by thesurface area of the Earth, 4pr2. This will give the energy averagedover the Earth's surface. (1-A) = s Te4 4S0EIN = 240 W m-2The average flux of solar energy absorbed by the Earth system.(averaged over entire surface, including day/night)S0 = 1370 W m-2 ; s = 5.67 ¥10-8 W m-2 K-4The average albedo of the Earth is 0.30Calculate input of solar energy/sec averaged over Earth’ssurfaceEffective Radiating Temperature -1EIN = EOUT (1-A) = s Te4 4S0Given values for S0, A, and s, we can solve for Te:where S0 is the solar constantA is the planetary albedos is the Stephan-Boltzmann constantand Te is the "effective radiating temperature" Te4 = (1-A)4sS0 Te = (1-A)4sS0[ ]1/4Effective Radiative Temperature -2 s = 5.67 x 10-8 W m-2 K-4 [universal constant] For Earth: solar constant, S0 = 1370 W m-2albedo A = 0.30 Calculate Te Te = (1-A)4sS0[ ]0.25 Te = 255 K (or -18 C)"The Earth radiates as if it were a blackbody at 255 K”, i.e. givesout a spectrum characteristic of a body at 255K but...the Earth's actual surface temperature (Ts) is 288 K (or +15 C). How do we reconcile this?Greenhouse EffectIf the Earth had no atmosphere (and still had an albedo of 0.30),its surface temperature would be 255 K.The atmosphere acts like a blanket, trapping heat near the surfaceand keeping the surface much warmer than it would otherwise be.The magnitude of this "greenhouse effect" (DTg) is:DTg = Ts - Te = 288 K - 255 KDTg = 33 KDTg is a property of the atmosphere.(Should really be called "the atmosphere effect".)Sister planetsVenus(runaway greenhouse)Earth("just right")Mars(littlegreenhouse)You cannot "predict" surface temperature Ts from knowledge of Te.Te is a function of S0 and ATs = Te + DTgwhere, DTg is a property of the atmosphere of a planetEnergy Balance and Climate ChangeEnergy balance equation (F is energy flux, W/m2)…FOUTenergy emittedby EarthFINenergy absorbedby Earth=“Energy Balance Theory of Climate Change”if FOUT < FIN [imbalance]then Tsurface will go up until balance is restoredi.e., the case with global warmingColor-coded energy budget: top of atmosphere and surfaceSurface budget: IN = OUTTop-of-Atmosphere budget: IN = OUTFig 3-19Energy Budget: in the atmosphereAtmosphere budget: IN = OUTFig 3-19Satellite View of Energy Budgetvisible satellite infrared satelliteVertical structure of the atmospherePressure: the weight of air overhead (e.g. psi = lbs/in2)Note log scale on pressure graph.a. At what height are you above 99% of the atmospheric mass?b. What fraction of atmospheric mass is in the Troposphere?a. 30 kmb. 90%Lapse rate: The rate at which temperature changes with height in theatmosphere. A measure of vertical stability.c. What height corresponds to Te?c. 6 kmLapse rate and convectionLapse rate: The rate at which temperature changes with height in theatmosphere. A measure of vertical stability.Stable: Warm fluid on top of cold fluid.Unstable: Warm fluid below cold fluid.Fig. 3-103 forms of heattransfer:- conduction- convection- radiationA dialectic on atmospheric vertical structureWeather (clouds, rain) happensin the troposphere because thetroposphere is unstable.KKC Fig 3-9Because temperature decreases with height.Yes, but why does temperature decrease with height?Why is the troposphere unstable?Because it is heated from below.Yes, but how does it come about that it is heated from below?Because the atmosphere is mostly transparent to solar(shortwave) radiation, and this is absorbed by the groundAtmospheric constituents• main gases (O2, N2, Ar are 99.9% of dry volume of atmosphere)• variable gas (water vapor)• trace gases (CO2, O3, CFCs, SO2, etc, etc, etc)• particles (dust, seasalt, sulfate, soot, organics)Greenhouse gasesppmv = parts per million by volume:molecules of trace gas per million molecules of
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