The het budget of the tmosphere nd the greenhouse effect 1. Solr rdition 1.1 Solr constnt The rdition coming from the sun is clled solr rdition (shortwve rdition). Most of the solr rdition is visible light (with wvelength of 8 to 77 nm) (Note tht 1 nm = 1 μm =.1 mm). ultrviolet visible infrred (The Ntionl Renewble Energy Lbortory) Figure 1: Spectrum of solr rdition (The top line indictes vlues t the top of the tmosphere, while the bottom one those t the ground surfce.) The totl mount of solr rdition per unit re is bout 17 W/m t the top of the tmosphere. This vlue is defined s solr constnt (hereinfter referred to s S ). At the men distnce of the erth from the sun 11 ( 1.5 m ), the solr constnt is S.7 W/m. 1. Shdow re of plnet The shdow re of the erth s disk which intercepts the solr rdition is given by erth is R. R where R is the erth s rdius, while the surfce re of the 1
Figure : Shdow re nd surfce re Therefore, verging the totl incoming solr rdition over the erth s surfce, it is reduced to qurter of the solr constnt ( W/m ). S R S S R 1. Plnetry reflectivity In ddition, we must consider the fct tht not ll of the solr rdition incident on the erth is bsorbed. In fct, bout % of the solr rdition is reflected bck to spce. This reflectivity is clled lbedo ( ). The erth s lbedo is.. Thus, the erth bsorbs only 7 % of the solr rdition. Therefore, the net incoming solr rdition verged over the erth s surfce is S 1 S S (1) For the present erth, S. W/m.. Terrestril rdition The erth lwys bsorbs the solr rdition. Nevertheless, the men temperture of the surfce or the tmosphere is lmost constnt. It is becuse the erth rdites s much energy s it receives. The rdition emitted from the erth to spce is referred to s terrestril rdition (longwve rdition). Most of the terrestril rdition is emitted s infrred light. In generl, n object emits electromgnetic wve such like infrred rdition, corresponding to its temperture. This rdition is clled blckbody rdition. The power of blckbody rdition F cn be written F T () where T is temperture (bsolute temperture; =7.15K) of n object. is the Stefn-Boltzmnn constnt, nd hs vlue of
5.67 lw. W/m K. This reltionship is known s Stefn-Boltzmnn s 8W/m W/m Figure : Stefn-Boltzmnn s lw The terrestril rdition follows this lw.. Het budget without greenhouse effect The surfce of plnet reches n equilibrium stte t temperture where the terrestril rdition F is equl to the net solr rdition S. Thus, S F Substituting (1) to S, nd () to F, the het blnce gives S T Dividing both sides by, we obtin S T By clculting the fourth root of both sides, we hve T 1 S where T is defined s effective rdition temperture. When S.7 W/m nd., (A)
1..7 T 55[K] ( 8 [ ]) 5.67 This vlue is much lower thn the globl men surfce temperture of the erth. S 1 1 S T T No greenhouse effect Atmosphere Temperture T Greenhouse effect T T Temperture T Ground surfce Figure : Schemtic digrm of greenhouse effect Tble 1: Effective rdition temperture nd men surfce temperture of the plnets Men distnce from the sun (AU) Solr rdition (W/m ) Albedo Effective rdition temperture ( ) Men surfce temperture ( ) Surfce pressure (Erth = 1) Min components Mercury.9 91.11 16 17 Venus.7 6.78-9 6 9 CO Erth 1. 17. -18 15 1 N O Mrs 1.5 58.16-58 -.6 CO Jupiter 5. 5.7-185 -1 H He. Greenhouse effect.1 Greenhouse gs The erth hs n tmosphere. The erth s tmosphere is lmost trnsprent for visible light. Thus, the solr rdition is not bsorbed by the tmosphere. However, some components of the tmosphere such like wter
vpor (HO) nd crbon dioxide (CO) re opque for infrred rdition. Therefore, the terrestril rdition is bsorbed by the tmosphere. These components re clled greenhouse gs.. Het budget Let us consider the het budget under the existence of n tmosphere including greenhouse gs. Assume tht the tmosphere is trnsprent for solr rdition, but is opque for terrestril rdition (see Fig. ). First, the energy blnce t the ground gives 1 S where T T T is the tmospheric temperture, nd T is the temperture of the ground surfce (see Fig. ). In ddition, the energy blnce of the tmosphere is written (B) T T (C) By doubling (B), nd dding it to (C), we cn eliminte S T or T 1 S T nd obtin Then, (C) gives S T For S.7 nd. W/m, 1..7 T [K] ( [ ]) 5.67 1..7 T 55[K] ( 8 [ ]) 5.67 The vlue of surfce temperture T ( [ ]) is much higher thn tht in the cse of no greenhouse effect ( 8 [ ] ). Note tht T is the ir 5
temperture verged over the whole tmosphere (not the surfce ir temperture). In the rel tmosphere, the ir nd the ground cn exchnge het directly becuse they re in contct with ech other. Tking this into considertion, we consistently understnd tht the globl men surfce ir temperture is 88K ( 15 ).. Greenhouse effect nd globl wrming In the previous subsection, greenhouse gs prevents the terrestril rdition from escping to spce. Conversely, infrred rdition emitted from the tmosphere to the ground surfce wrms the surfce. This is referred to s greenhouse effect. If the greenhouse gs is nthropogeniclly incresed, the greenhouse effect will become stronger. The surfce temperture will then rise. We cll this nthropogenic chnge in climte the globl wrming. Figure 5: Globl men surfce ir temperture (Jpn Meteorologicl Agency) 6