Major Portions in Climate Change: Physical Approach

Transcription

1 Intrnational Rviw of Physics (I.R.E.PHY.), Vol. 5, N. 5 Octobr 20 Major Portions in Climat Chang: Physical Approach Jyrki Kauppinn, Jorma. Hinonn, Pkka J. Malmi Abstract h dstroying of rainforsts can warm th climat vn mor than th doubling of CO 2 concntration can do. h tmpratur clos to th surfac of th arth can chang du to th chang of th fdback or th amount of watr in th atmosphr, without any forcing or chang in th concntration of CO 2 as wll as othr grnhous gass. his papr drivs physically th snsitivity and th rspons tim of th climat du to radiativ forcing and a chang in fdback. During th last cntury th tmpratur incras consistd of chang in solar activity (0.47 C), dstruction of rainforsts (about 0.3 C), incras of th concntrations of th grnhous gass (about 0. C) and incras of arosols (about C). About on half of th tmpratur incras was anthropognic. Copyright 20 Prais Worthy Priz S.r.l. - All rights rsrvd. Kywords: Climat Chang, Climat Snsitivity, Climat Rspons im Nomnclatur Global man tmpratur Global man tmpratur without grnhous gass 2CO2 mpratur incras du to doubling of CO 2 Q mpratur chang du to radiativ forcing G mpratur chang du to chang of fdback R Climat snsitivity R 0 Climat snsitivity without fdback R av Avrag climat snsitivity Q s Surfac ux Q Absorbd ux Q Radiativ forcing f Fdback factor F Fdback loop gain G Fdback proportionality cof cint p Partial prssur of watr vapor C Hat capacity g Stp rspons h Impuls rspons Phas diffrnc Rspons tim L Diffusion lngth D Diffusivity I. Introduction h main goal of this papr is to calculat th chang of th global man tmpratur of th arth s climat du to a forcing lik grnhous gass and also without forcing. In addition, w lik to know th corrsponding rspons tim. h tmpratur chang 2CO2 of th climat du to th doubling of th CO 2 concntration is still vry uncrtain. According to th Intrgovrnmntal Panl on Climat Chang (IPCC) th chang of th global man tmpratur 2CO2 is likly btwn 2 and 4.5 K, most likly 3.2 K []. Hansn t al. [2] hav rportd 2CO2 btwn 2 and 5 K, assuming that th prsnt tmpratur chang rsults from th incrasd concntration of grnhous gass. h major rason to th uncrtainty is that th snsitivity R = d/dq of th climat is not vry wll known. h snsitivity givs us th surfac tmpratur chang = R Q, whr Q (W/m 2 ) is th radiativ forcing. Valus of IPCC and Hansn imply that thr is a positiv fdback in th climat systm. Howvr, thr ar paprs by Douglass t al. [3],[4] and Idso [5], whr much smallr snsitivitis ar prsntd. hs rsults ar obtaind.g. from th annual solar irradianc cycl. Also Lindzn [6], Lindzn and Choi [7], Spncr and Braswll [8], [9] hav rportd a ngativ fdback. h rspons tims hav bn stimatd from obsrvd tmpratur pro ls. h IPCC valus ar on th ordr of 0-00 yars, Mhl t al. [] and Hansn t al. [2]. Using th autocorrlation study of th tmpratur curvs, much smallr valus lik from 0.4 to 0 yars ar prsntd by Scaftta [0] and Schwartz []. h problm with ths mthods is that th rspons tims of th climat and th forcing ar mixd. Rspons tims from to 2 months ar obtaind by Douglass t al. [3],[4]. II. Estimation of Climat Snsitivity and Nt Fdback h total ux Q = 326 W/m 2 absorbd from th longwav mission is th incidnt surfac ux Q s = 396 W/m 2 minus th transmittd on 70 W/m 2, s Fig. in [2]. h atmosphr absorbs a fraction =0.82 of th Manuscript rcivd and rvisd Sptmbr 20, accptd Octobr 20 Copyright 20 Prais Worthy Priz S.r.l. - All rights rsrvd 260

2 surfac radiation Q s upwlling from th ground, or Q = Q s. h absorbd ux Q = 326 W/m 2 incrass th tmpratur clos to th arth s surfac by about 34 dgrs, from 255 K to 289 K. hus, th avrag snsitivity R av is 34 K/(326 W/m 2 ) = 0.04 K/(W/m 2 ). Using linar approximation = R av Q, this givs for 2CO2 only about 0.39 K, if th forcing Q has th IPCC valu 3.78 W/m 2. h abov vry rough stimation of th snsitivity givs us a hint to carry out a mor dtaild study basd on th obsrvd valus of th climat. W d n th climat snsitivity R 0 without fdback as follows: R d 0 3 dqs 4 4Q whr Q s = 4 is th blackbody mission ux from th arth s surfac and is th Stfan Boltzmann constant. Intgration givs th total forcing curv: s 4 4 s () Q (2) whr is 255 K and th missivity is st to unity. h total forcing in Q s drivd from th nrgy budgt in [2] as th diffrnc btwn th surfac radiation 396 W/m 2 and th outgoing longwav radiation 239 W/m 2 is 57 W/m 2. Notic that Q s (289 K), from quation (2), is about 56 W/m 2, which is clos to th valu drivd from th nrgy budgt. aking into account all th possibl fdback mchanisms w may writ: d R0 dqs R0 dq f d R dq whr R() is th actual snsitivity with all th fdback and f() is a tmpratur dpndnt fdback factor. h forcing dq = d( Q s ). From quation (3) w gt: or: R d R0 R0 dq f R F dq f d R 0 h intgration of quation (5) should giv th curv Q(), which starts at point A in Fig. (a), th condition without grnhous gass, and gos through point B, th prsnt condition of th climat. W assum that th major fdback is proportional to th chang of th watr vapor concntration with tmpratur. Still simplifying, th fdback factor is 0 (3) (4) (5) assumd to b proportional to th drivativ of th watr vapor saturation prssur: dp f G d (6) whr p is th saturation prssur of watr vapor, and G is th proportionality cof cint. W assum also that th surfac albdo is constant. Intgration of quation (5) givs: dp Q G d R d s 0 Q G p p As a rst approximation, th watr vapor saturation prssur is givn by th Clausius-Clapyron quation. W us hr th Antoin quation, a simpl mpirical improvmnt to th Clausius-Clapyron quation, widly usd ovr limitd tmpratur rangs [3]. h paramtrs for th rang K match fairly wll with th xprimntal data down to = 255 K. In th rang undr considration th vapor prssur incrass narly xponntially with tmpratur, s Fig. 2. Watr vapor and clouds hav a positiv fdback in th longwav mission and a strongr ngativ fdback in incoming shortwav insolation. In addition, th latnt hat givs mor ngativ fdback. h slop of th curv (Q) in Fig. (a) rprsnts th snsitivity of th climat. At point A th snsitivity R(255 K) without grnhous gass is littl lss than R 0 (255 K), which is 0.26 K/(W/m 2 ) according to quation (). h rason is that vn at th tmpratur 255 K w hav a small drivativ dp/d and a wak fdback, which maks R(255 K) slightly smallr than R 0 (255 K), according to quation (4). his is clarly sn in Fig. (b). So, th snsitivity at 255 K is substantially largr than R av = 0.04 K/(W/m 2 ), th slop of th straight lin btwn points A and B. W assum that th fdback dos not chang sign. his also mans that th curvatur of (Q) dos not chang sign. Hnc, to go through points A and B th slop of (Q) at point B has to b substantially smallr than R av and th nt fdback has to b ngativ. h snsitivity at B in Fig. (a) or at B' in Fig. (b) dpnds slightly on th shap of (Q). Howvr, th shap dtrmins how much smallr than 0.04 K/(W/m 2 ) th prsnt snsitivity is. For xampl, in Fig. (b) th snsitivity at B' is K/(W/m 2 ) as calculatd from quation (4) with f = - Gdp/d, whr G = 03 W/(m 2 kpa). Anothr possibility to driv G is to us quation (7), whr G[p() - p( )] should b (326-56) W/m 2 = 70 W/m 2. It turns out that any monotonically dcrasing function f(), which forcs th curv Q() to go through th points A and B so that th slop of Q() at 255 K is vry clos to th slop of curv AC, has th drivativ at (7) 26

3 point B btwn K/(W/m 2 ). For xampl with 25 % largr or smallr G th drivativs ar K/(W/m 2 ) and K/(W/m 2 ), rspctivly. S also point B' in Fig (b). his is vry strong proof of th climat snsitivity. Consquntly th only possibl choic for f() is th amount of th watr vapor and clouds in th atmosphr. In addition th spd of th hydrologic cycl has an ffct on f() via latnt cooling. In th ral climat, both th forcing Q and th proportionality cof cint G can chang. hn R Q R G p p Q G (8) whr Q and G ar th changs in tmpratur du to th changs of th forcing and th fdback, rspctivly. Figs.. (a) mpratur curvs AC, (Q s ) without fdback and AB, (Q) with a nt fdback. h points A, B and C ar obsrvd ons. h proportionality cof cint G in curv AB is 03 W/(m 2 kpa). h two xtra curvs ar plottd with 25 % highr and lowr G, for a purpos of comparison. (b) h corrsponding snsitivitis R 0 (Q s ) and R(Q), th drivativs of (Q s) and (Q), rspctivly Fig. 3. h total tmpratur chang is th sum of th contributions of th radiativ forcing Q and th chang of th cof cint G. In th curvs (Q, G ) and (Q,G 2) th cof cint G is constant with G >G 2. In th curv (Q,G) th cof cint G is changing. h point B is th sam as th point B in Fig. (a) h ctional situation, as dmonstratd in Fig. 3, shows that th masurd snsitivity / Q, th slop of th curv (Q,G), can b much largr (or smallr) than th snsitivity du to th radiativ forcing, th slop of th curv (Q,G ) or (Q, G 2 ). So, th masurd tmpratur curv as a function of th masurd CO 2 concntration is not a vry good tool for th stimation of 2CO2, bcaus w cannot assum that G is zro. Fig. 2. h partial prssur of th saturatd watr vapor p and th drivativ dp/d as a function of tmpratur, according to Antoin quation III. Physical hory of th Rspons of th Climat On th basis of our simpli d stimation abov, w conclud that w hav to nd a physical climat modl i.. th rspons of th climat, which givs th snsitivity and rspons tim, as wll. In physics, w dscrib any systm by its impuls rspons h(t), which contains all th information about th prformanc of th systm in th domain t. Mostly t is tim. 262

4 h output signal S out (t) is givn by th convolution of th impuls rspons h(t) and th input signal S in (t) as follows: S t h t S t out in h t' S t t' dt' If th input signal is th Dirac dlta function (unit impuls) (t), thn th output signal is th impuls rspons of th systm. On th othr hand, if th input is a stp function givn by: H t in, t 0 0, t 0 (9) (0) th output signal is a stp rspons g(t) of th systm. h drivativ of th stp rspons givs th impuls rspons [4] i..: ht dg t dt () First w d n th climat systm, which consists of th whol atmosphr including all th grnhous gass, th surfac of th arth to th dpth of a fw mtrs, all th laks, and th mixing layr of th ocans to th dpth of about 80 m. Latr, w xtnd th thrmodynamic climat systm including th whol glob and atmosphr. W assum that th climat is in a thrmal quilibrium at th global annual man tmpratur 0 clos to th surfac. In addition, w hav an nrgy balanc on th surfac and at th top of th climat. All typs of nrgy circulation insid th systm hav a vry small ffct on th global man tmpratur valus, bcaus th nrgy is moving in th atmosphr and in th ocans from on plac to anothr so that th consrvation of nrgy is valid. Mor information is givn in th discussion. Of cours, ths circulations hav a grat impact on th wathr conditions. his thory dals with th global annual avrag valus only. So, th tmpraturs can chang locally, horizontally and vrtically, for xampl, lik th laps rat in th atmosphr. h air tmpratur clos to th arth s surfac rprsnts vry wll th tmpratur of th climat, bcaus th major hat nrgy is clos to th surfac. h hat capacity of th air dcrass xponntially with altitud. W calculat vrything corrsponding to an avrag vrtical parcl of th climat systm. h cross-sction of th parcl is on squar mtr. In ordr to nd th impuls rspons of th climat systm w driv rst a stp rspons. W assum that th climat at th quilibrium tmpratur 0 snss an abrupt forcing Q, which corrsponds to th tmpratur incras of. h initial nrgy ux to th climat systm is Q = /R. With tim th hating powr pr squar mtr is proportional to th diffrnc btwn th nal tmpratur 0 + and th currnt tmpratur (t). his procss can b dscribd by a simpl diffrntial quation: d t 0 t C (2) dt R whr C is th total hat capacity of th climat systm. If th snsitivity R is constant and th forcing starts at t =0, th solution of quation (2) is simply: t 0 t/ (3) whr = RC and = R Q. Equation (3) givs us th stp rspons, th drivativ of which is th impuls rspons of th climat systm: h rsponss ar shown in Figs. 4. t/ ht (4) Figs. 4(a). h stp rspons g(t) and (b) th impuls rspons h(t) of th climat systm 263

5 IV. Drivation of th Snsitivity R and th Rspons im In climat rsarch on possibility is to driv th climat paramtrs R and using glacial and rcnt tmpratur curvs, i.. S out (t) of th climat. Unfortunatly, this is a vry hoplss or vn an impossibl task, bcaus w cannot driv h(t) from S out (t)= h(t) * S in (t). W will obtain only complicatd information about both functions h(t) and S in (t), and it is dif cult to distinguish th impuls rspons h(t). W hav to know th forcing as a function of tim, bcaus S in (t)= R Q(t). In addition, a chang of th cof cint G can chang th tmpratur without any radiativ forcing. h othr possibility is to us thortical circulation modls to driv th possibl fdbacks and nally th snsitivity. S.g. [2], [5]-[22]. Furthrmor, in ral climat it is almost impossibl to arrang mrly th stp or unit impuls forcing. On possibility is to us a sinusoidal input. his is a common way to tst lctronic circuits. W hav two options, namly th tmpratur pro ls ovr day and night or ovr summr and wintr. h diurnal tmpratur bhavior may b too fast and it is not vry sinusoidal. Howvr, th annual tmpratur curv (not too clos to th pols and th quator) sms to b clos to sinusoidal. So, th forcing in th solar irradiation annual cycl is approximatly: Sin t RAcos t (5) whr =2 /yar and A is th amplitud of th solar forcing. Using quations (9), (4) and (5) w obtain: whr: Sout t RAcos t* ht RA cos t A out A out 2 Acos is th amplitud of th tmpratur cycl and: (6) (7) tan (8) is th phas diffrnc btwn th tmpratur and solar cycls. Finally, w obtain th rspons tim: tan RC (9) Bcaus thr is a nic analogy with an lctronic RCcircuit, w can us it as a modl as shown in Fig. 5. h analogy btwn th climat systm and lctronic circuit paramtrs is as follows: voltag tmpratur, lctric currnt hat currnt, lctric capacitanc hat capacity, lctric rsistanc hat rsistanc, and lctric charg hat nrgy. Fig. 5. RC-circuit modl of th climat systm h basic ida is to masur and to calculat th hat capacity C of th climat, taking into account th hat capacity of th mixd layr in th ocan. h capacity ovr th ocan is largr than ovr th land. hus, it is usful to apply th basic diffrntial quation (2) sparatly to th land and to th ocan. Aftr this w can calculat and R for land and for ocan using quation (9). h hat capacity ovr land is th sum of hat capacitis of air and a thin layr of th ground. h thicknss of th layr is a fraction of th diffusion lngth. Our simulations latr will giv mor information on th diffusion into th dp soil. h hat diffusion lngths for th sinusoidal and for th stp input ar givn by L sin = 2D/ and L stp =.264 Dt, whr D is th diffusivity of sandy soil, m 2 /s [23]. According to th abov quations th diffusion lngth for a stp rspons is 2.24 tims th diffusion lngth for a sinusoidal input with th sam tim scal. h hat capacity of th atmosphr is about 0.35 MJ/(Km 2 ) with a rlativ humidity of 70 %. h moistur of th soil incrass th hat capacity. h hat capacity ovr th ocan is a littl diffrnt, bcaus in th ocan thr is a mixd layr with a thicknss varying btwn 20 and 00 mtrs. h tmpratur of th mixd layr follows approximatly th surfac on. his mans that w hav to tak into account th hat capacity of th mixd layr. In addition, blow th mixd layr w add th capacity of th layr, which is a part of th diffusion lngth lik in th cas of th soil. So, th total hat capacity ovr th ocan without th diffusion is about 325 MJ/(Km 2 ), which is th sum of th hat capacitis of air and th mixd layr. h avrag thicknss of th mixd layr is 75 m [24],[25]. h contribution of th diffusion to th hat capacity will b stimatd in our simulations. h thrmal diffusivity of watr is.40 7 m 2 /s. h hat capacity ovr th ocan is about thirty tims th hat capacity of th atmosphr. 264

6 V. Exprimntal Drivation of R and W usd th rsults of [26]. his papr is vry hlpful, bcaus it givs th phas lags sparatly for th land and ocan. h man lags btwn th annual tmpratur and solar irradiation cycls, obsrvd from yar 954 to 2007, ar 29±6 days ovr th land and 56± days ovr th ocan. W prfr using phas information instad of amplitud information, bcaus th rfrnc phas is xactly known at solstics. hus, w nd to know only th dat of th annual tmpratur maxima or minima. Of cours, it is possibl to us th amplituds A and A out and to apply quation (7), but thn w hav to us two pro ls, which both hav masurmnt uncrtainty. h lags givn by [26] corrspond to th phas diffrncs land = 28.6 and ocan = Substitution to quation (9) givs th rspons tims land =.04 months and ocan =2.74 months, and th snsitivitis R land =0.244 and R ocan = K/(W/m 2 ). h rst of th rsults ar collctd in abl I. h aras of land and ocan ar roughly 29 % and 7 %, rspctivly. Bcaus th tmpratur chang ovr th land is on ordr of magnitud gratr than that ovr th ocan, th global snsitivity dpnds substantially on how much th tmpratur changs balanc out,.g. by winds. W dnot th xtrm cass, which corrspond to prfct imbalanc and prfct balanc by R glo and R glo2, rspctivly. In th rst cas th global tmpratur chang is simply th man chang wightd by th aras d =0.29 d land +0.7 d ocan. Dividing by dq w gt: K R glo 0. 29R land 0. 7R ocan (20) W/m 2 In th scond cas w assum that hat ows btwn land and ocan until th changs in tmpratur ar qual. Consrvation of nrgy rquirs that 0.29C land d land + 0.7C ocan d ocan = 0.29C land d + 0.7C ocan d, whr C land and C ocan ar th hat capacitis pr unit ara and d is th common tmpratur chang. Solving d and dividing by dq w gt: R glo C R 0. 7C R land land ocan ocan 0. 29C 0. 7C land K W/m 2 ocan (2) h prfct balanc is nvr rachd globally but th local snsitivity on th coast should b clos to R glo2. According to [26], th lag on th coast is 42 days ( = 4.4 ). Substitution of this valu to quation (9) givs coast =.685 months. h coast can b thought of as an ara, which is half ocan and half land. If w us th avrag hat capacity C coast =(C land +C ocan )/2 = 68 MJ/K w gt R coast =0.026 K/(W/m 2 ). his valu is in good agrmnt with th valu R glo2. h nal snsitivity is btwn R glo and R glo2 dpnding on how wll th diffrnc of th tmpratur chang btwn th land and ocan is balancd. h linar combination 0.544R glo R glo2 is qual to th snsitivity K/(W/m 2 ) drivd in Fig.. VI. Hat Diffusion Into th hrmoclin and Into th Ground h ocan consists of a mixd layr with an avrag thicknss of 75 m. Blow th mixd layr is th narly prmannt thrmoclin going down to 000 m. In th avrag thrmoclin th tmpratur dcrass from 6 C to 4 C. Blow th thrmoclin is th dp ocan, whr th tmpratur dcrass vry slowly a fw dgrs. Fig. 6. R'C'-chain connctd to th climat systm h diffusion into watr in th ocan can b modld by coupling an R'C'-chain paralll with th hat capacity of th mixd layr in th ocan C 0 ocan = MJ/K as shown in Fig. 6. Now th hat capacity C 0 ocan dos not includ th diffusion layr blow th mixd layr, so it is smallr than C ocan (325.0 MJ/K) as dmonstratd in simulations latr. h diffusion taks plac in th R'C'- chain. h hat rsistanc R' and th hat capacity C' of th watr layr dpnd on th thicknss of th layr. h hat rsistanc of on squar mtr parcl is.75 K/(W/m), and th hat capacity of th parcl is 4.9 MJ/(Km 3 ). h voltag at ach junction of th R'C'-chain modls th tmpratur of th corrsponding layr. Figs. 7 show a simulation xampl of th ocan coupld with th diffusion layrs. W usd 48 layrs with a thicknss of 0.04 m, in othr words 48 R'C' circuits in th chain. h topmost curv in Fig. 7(a) is th stp rspons of th coupld climat, and it is th tmpratur climat (0 m) at th condnsr C 0 ocan, whn th tmpratur input stp is on K. In addition, bfor th stp input to th circuit all th 48 condnsrs of th R'C'-chain hav bn chargd corrsponding to th tmpratur pro l of th thrmoclin. In th thrmoclin, just blow th mixd layr, th tmpratur dcrass about 0.03 K/m. Fig. 7(a) prsnts also th tmpratur pro ls at a dpth of m, 2 m, and 5 m. Not that vn at a dpth of 5 m warming is quit slow. Using a sinusoidal input in in th circuit of Fig. 6 with th angular frquncy of 2 /yar w can adjust R ocan so that th phas angl is th obsrvd on With this valu of R ocan w can calculat C ocan using th rlation ocan = R ocan C ocan. h 265

7 diffrnc C ocan -C 0 ocan (vry small = about 0.4 MJ/K) is th hat capacity of a part of th diffusion layr. his diffrnc is gratr (about MJ/K) for th stp input, bcaus th thrmal diffusion lngth is 2.24 tims largr than in th cas of a sinusoidal input. Fig. 7(b) dmonstrats th diffusion to th thrmoclin with th sinusoidal input. h phas diffrnc btwn th input and climat (0 m) is Not that th amplitud of th signal obys quation (7), vn though w did not us this information. Part b prsnts also th tmpraturs at a dpth of m, 2 m, and 5 m from th bottom of th mixd layr. Similar tratmnt and simulations as abov can b don for th climat ovr th land. In this cas, th condnsrs in th R'C'-chain ar chargd at highr tmpraturs, bcaus th tmpratur in th ground incrass about 0.03 K/m. h hat diffusion into th soil has a gratr ffct on th snsitivity, bcaus th capacity of th air (0.35 MJ/K) is much smallr than th capacity (324.6 MJ/K) in th cas of th ocan. In th simulations w hav usd for th soil R' =3.33 K/Wm 2 and C' =.28 MJ/Km. In th land cas th capacitis of th diffusion layr ar approximatly 0.4 MJ/K and 0.9 MJ/K for a sinusoidal and a stp input, rspctivly. Figs. 8 dmonstrat a big diffrnc btwn th continntal and marin climats. Most popl xprinc this ffct vry asily. Fig. 8(a) shows th stp rsponss of th climat ovr th land, ovr th ocan, th stp rspons of th global avrag climat without balancing th diffrnc of th tmpratur chang btwn th land and ocan (Glo), and th stp rspons with a 00 % Balancd climat (Glo2). In addition, Fig. 8(b) shows th nal global stp rspons and th stp rspons on th coast. h global stp rspons Global = Glo Glo2, s Fig. 8(b). From this curv w ar abl to stimat th global rspons tim.3 months. h stp rspons on th coast should b vry clos to Glo2 bcaus th mixing on th coast is clos to 00 %. Using th R'C'-chain it is asy to calculat th slop of th stp rspons at latr tims. h simulations show that th avrag climat warms about K btwn 0 and 20 yars aftr th stp of on K. his rquirs a forcing of 2 W/m 2. h corrsponding IPCC valu is 0. K/0 yars []. For th abov rsults w hav assumd that hat gos from th bottom of th mixd layr to th thrmoclin only by thrmal diffusion. Of cours, vrtical convction incrass hat conduction, as wll. Using our simulation, w can asily calculat th cas, whr th conduction in th thrmoclin is hundrds of tims th conductivity in hat diffusion in watr.his corrsponds to th Eddy diffusivity m 2 /s [27],[28] in th ocan. h rsults show that th snsitivity dcrass 2 % and th tmpratur of th climat incrass about K btwn tn and twnty yars from th stp of on dgr. his stp rquirs th forcing of 3 W/m 2. Of cours, with th forcing of.3 W/m 2 th tmpratur chang of th climat is only K/0 yars. Not that th IPCC valu is 0. K/0 yars. Figs. 7. (a). h stp rspons of th climat coupld to th diffusion layr, and tmpraturs at diffrnt watr layrs climat (0 m), m, 2 m and 5 m blow th mixd layr. b) h sam dmonstration using sinusoidal input with a yar priod. h phas diffrnc btwn Input and climat (0 m) is 55.2 Figs. 8. All th stp rsponss ar drawn with th forcing of Q = K/R land =4.2 W/m 2. (a) h stp rsponss ovr th land and ovr th ocan. h stp rspons Glo is th avrag wightd by th aras of land and ocan. h stp rspons Glo2 is th avrag whn th tmpratur diffrnc btwn land and ocan is smoothd. (b)h xtndd part including th stp rspons on th coast and th nal global stp rspons 266

8 VII. Application of th Modl to CO 2 h doubling of CO 2 concntration givs a forcing of 3.78 W/m 2 (IPCC). In th litratur, a smallr valu of 2.4 W/m 2 can b found [29]. Using our avrag annual global snsitivity and th abov forcings, w can calculat th chang of th global man tmpratur as follows or: 2 Rglobal Q K 0. 22K (22) CO K 0. 4K (23) CO2 hs numbrs ar much smallr than IPCC valus: K. In this application w hav to prform a small corrction to th snsitivity. Our radiativ forcing dq includs also small positiv fdbacks of watr vapor and clouds in longwav absorptions. hs ar.4 W/(m 2 K) and about zro, according to Fig. 3 in [9]. So, w hav to us th forcing Q 2CO2 + Q watr ( ) W/m 2 = 4.09 W/m 2. his givs 2CO K. A bttr way to carry out this small corrction is to add th watr vapor fdback dirctly to th loop gain F, which changs to R 0 = thus, th snsitivity of th climat for all grnhous gass, xcpt watr vapor, is R g =0.063 K/(W/m 2 ). Now th nal valus of 2CO2 ar 0.24 K and 0.5 K with th forcings 3.78 W/m 2 (IPCC) and 2.4 W/m 2, rspctivly. h rsults ar in good agrmnt with th rsults by [30]. VIII. Effct of th Dstruction of th Rainforsts on th Global Man mpratur Fig. shows also (Q)-and R()-curvs with 25 % smallr and largr cof cint G. hs curvs dmonstrat that tmpratur can chang much without any absorption forcing. Not that th snsitivity R changs vry littl. h tmpratur chang is givn by R G p p (24) G Approximatly a 0 % chang in G corrsponds to th tmpratur chang of K. A good xampl of this is a chang in th solar activity, which changs th cloudinss of th atmosphr. h clouds hav a strong ngativ fdback. his has a much biggr ffct on th tmpratur than a small radiativ forcing (about on pr mil) du to th chang of th insolation [3]. Also arosols can chang G. On mor important xampl about th us of th quation (24) is th stimation of th tmpratur chang du to th dstruction of th rainforsts. h fdback loop gains: dp F f R0 G R0 d (25) drivd for land, for ocan and for glob ar 0.25, -7.28, and -2.3, rspctivly, s abl I. hn th corrsponding cof cints G ar roughly: G land = -2 W/(m 2 kpa), G ocan = 348 W/(m 2 kpa) and G global = 03 W/(m 2 kpa). hs valus ar global man ons at th avrag tmpratur 289 K. In rainforsts vaporization is vry ffctiv, bcaus th vaporation is abundant du to th strati cation of larg-ara lavs in th vgtation. h rlativ humidity is high and also cloudinss is high du to thundrstorms. h hydrologic cycl is vry rapid. hus w can assum that G rainforst G ocan. If man dstroys th rainforst ovr an ara of A 0 and aftr th dstruction th ara is lik avrag land with G land = -2 W/(m 2 kpa), thn th total chang of G is G ocan -G land = 360 W/(m 2 kpa) or largr. his corrsponds to th chang of about: G global A 0 A W 360 m 2 kpa (26) whr A is th ara of th arth glob. For xampl if A 0 /A = % or A km 2, th global man tmpratur chang according to quation (24) is about 0.3 K. So, it is much asir for us to caus a biggr climat chang by dstroying rainforsts than by incrasing CO 2 concntration in th atmosphr. h abov xampl corrsponds to th cas, whr % of th ara of th arth is changd from ocan to land. ABLE I CLIMAE RESPONSE IMES, SENSIIVIIES R, HEA CAPACIIES C AND FEEDBACK LOOP GAINS F (month) R(K/(W/m 2 )) C(MJ/(Km 2 )) sinusoidal stp sinusoidal stp F Land Ocan Glo Glo Coast Global (Fig. ) Global

9 If w rplac th rlativ aras of 29 % and 7 % with 30 % and 70 % for land and ocan, rspctivly, quations (20) and (2) giv a nw global snsitivity R global = K/(Wm 2 ). his mans that th fdback loop gain F is changd from -2.3 to giving th chang of G about -4 W/(m 2 kpa). his rsult supports th valu -3.6 W/(m 2 kpa), givn in quation (26). Quit larg aras of th rainforsts hav bn dstroyd sinc 970 [32]. his xplains at last partly th rapid tmpratur incras in th sam tim priod. IX. Discussion Finally, w lik to point out that according to our rsults thr is no so calld faint young sun paradox [33]. Assuming that during th faint young sun th insolation was 25 % smallr than now th tmpratur chang was about K/(W/m 2 )( W/m 2 ) -5K. So th tmpratur was only 5 K lowr than now and our glob was not frozn. In addition, th cof cint G was smallr than 03 W/(m 2 kpa), bcaus th amount of biomass was smallr than now. In this papr w hav assumd that th surfac albdo and th cof cint G ar constants all th way from A to B in Fig. (a). It turns out that th chang of th surfac albdo would mak th curv AB to start with a littl highr and nd with a littl lowr slop. In our modl this mans that th cof cint G would chang from a littl lowr to a littl highr valu than 03 W/(m 2 kpa) on th way from A to B. Solar nrgy is also stord in mchanical forms lik wind, wavs and strams in th ocans, and potntial nrgy. hs nrgis ar vry small compard with th thrmal nrgy stord in th climat and ocan. Usually ths mchanical nrgis incras whn th tmpratur of th climat incrass, so thy incras th ngativ fdback slightly. W hav to point out that th snsitivity and rspons tims can chang slowly, for xampl, du to th changs of th surfac albdo and th tmpratur. As shown in Figs., th snsitivity of th climat dcrass, whn th tmpratur and forcing incras. his corrsponds to th xtra ngativ fdback in th climat. In th climat, th hat nrgy circulation dos not chang th avrag tmpratur, if th circulation taks plac along a path, whr th hat capacity is constant. For xampl, wind ovr th ocan or a stram in th ocan has a minor ffct on th avrag global tmpratur. Howvr, if th wind is crossing th coast, th avrag tmpratur can chang, bcaus th hat capacity ovr th ocan is thirty tims of that ovr th land. his is th gratst ffct on th avrag tmpratur, du to circulation. X. Conclusion W hav stimatd th global man snsitivity of th climat using two indpndnt physical mthods. h simpli d mthod uss thr wll-known points (Q, ), th points A, B and C in Fig. (a), and a singl adjustabl paramtr G. h othr mthod uss two xprimntal phas lags btwn th annual solar irradiation cycl and th annual tmpratur curv, on for th ocan and on for th land. Sinc th annual solar irradiation cycl is wll known th rspons tim of th climat is only a function of th phas lag. In this mthod w nd to know only th shaps of th irradiation and tmpratur curvs, th absolut amplituds ar not rlvant. So, th long-trm variation of forcings and fdback has a minor ffct on ths rsults. W apply only th consrvation of nrgy to th climat systm as a function of tim. h basic physics is in th diffrntial quation (2). Our valus for th snsitivity and rspons tim ar in good agrmnt with ach othr and much smallr than th valus rportd arlir by studis basd on th xprimntal tmpratur curvs. W should raliz that th tmpratur curv is a rsult of th solar activity and othr forcings as wll as th fdback. It is practically impossibl to sparat th rols of ths factors in climat chang mrly from th tmpratur curv. W bliv that th gratst changs in tmpratur ar du to th chang in th proportionality cof cint G, i.. th rlation btwn cloudinss and watr vapor concntration. h tmpratur incras of th last cntury can b xplaind almost compltly by th incras of solar activity and th dcras of cosmic ray ux togthr 0.47 K [3], th dstruction of rainforsts about 0.3 K, th incras of grnhous gas concntration about 0. K and incras of arosol about K []. h sum of ths contributions is 0.8 K, which is clos to th obsrvd tmpratur incras [34]. In th nd, w conclud that mayb on rason for th long history of lif on our glob is th ngativ fdback of th climat for th global tmpratur. Rfrncs [] G. A. Mhl,. F. Stockr, W. D. Collins, P. Fridlingstin, A.. Gay, J. M. Grgory, A. Kitoh, R. Knutti, J. M. Murphy, A. Noda, S. C. B. Rapr, I. G. Wattrson, A. J. Wavr, and Z.-C. Zhao. Global climat projctions. contribution of working group i to th fourth assssmnt rport of th intrgovrnmntal panl on climat chang. In S. Solomon, D. Qin, M. Manning, Z. 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How snsitiv is th world s climat? National Gographic Rsarch & Exploration, 9:42 58, 993. [6] J. Hansn, G. Russl, A. Lacis, I. Fung, and D. Rind. Climat rspons tims: Dpndnc on climat snsitivity and ocan mixing. Scinc, 229: , 985. [7] B. J. Sodn and I. M. Hld. An assssmnt of climat fdbacks in coupld ocan-atmosphr modls. Journal of Climat, 9: , [8] S. Bony, R. Colman, V. M. Kattsov, R. P. Allan, C. S. Brthrton, J-L. Dufrsn, A. Hall, S. Hallgatt, M. H. Holland, W. Ingram, D. A. Randall, B. J. Sodn, G. slioudis, and M. J. Wbb. How wll do w undrstand and valuat climat chang fdback procsss? Journal of Climat, 9: , [9] R. Colman. A comparison of climat fdbacks in gnral circulation modls. Climat Dynamics, 20: , [20] J.. Kihl. Atmosphric gnral circulation modling. In K. E. rnbrth, ditor, Climat Systm Modling, chaptr 0. Cambridg Univrsity Prss, Nw York, 992. [2] J. M. Grgory, R. J. Stouffr, S. C. B. Rapr, P. A. Stott, and N. A. Raynr. An obsrvationally basd stimat of th climat snsitivity. 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Gnhous ffct in smi-transparnt plantary atmosphrs. Idõjárás, : 40, [3] N. J. Shaviv. On climat rspons to changs in th cosmic ray ux and radiativ budgt. Journal of Gophysical Rsarch, 0: 5, [32] J. Parantainn. uultusta ilmastokskustluun: konvktio ja sadmtsin hupnvat ukkospilvt. itssä tapahtuu, 25, [33] D. Rind. h sun s rol in climat variations. Scinc, 296: , [34] B. Libmann, R. M. Dol, C. Jons, I. Blad, and D. Allurd. In unc of choic of tim priod on global surfac tmpratur trnd stimats. Amrican Mtorological Socity, pags , 200. Authors information Dpartmnt of Physics and Astronomy Univrsity of urku FI-2004 URKU, FINLAND. jyrki.kauppinn@utu. Jyrki K. Kauppinn was born in Finland in 944. H was rcivd his Bachlor of Arts dgr in 967, his M.Sc.dgr in Physics in 968, and th Ph.D. dgr in 975 from th Univrsity of Oulu. H startd his acadmic carr at th Univrsity of Oulu working in many positions from assistant to profssor. h National Rsarch Council of Canada appointd him a rsarch fllow in 980. Dr. Kauppinn was lctd as snior rsarch fllow at th Acadmy of Finland in 98. H has also workd at th chnical Rsarch Cntr of Finland and th Mtrology Rsarch Institut of Hlsinki Univrsity of chnology. In 990 h was a visiting scintist at th National Rsarch Council of Canada and at Kansas Stat Univrsity. At prsnt h is a profssor of Physics at th Univrsity of urku (sinc 986), a docnt in Physics at th Univrsity of Oulu, and a docnt in Optical Masurmnt chnology at Aalto Univrsity in Espoo. Profssor Kauppinn has publishd about 60 paprs in intrnational scinti c journals and has mad about 40 confrnc prsntations including about 50 invitd lcturs. H has writtn invitd rviwarticls in Encyclopdia of Applid Physics, in Encyclopdia of Spctroscopy and Spctromtry, in Spctromtric chniqus, in Optics Encyclopdia, and in Handbook of Vibrational Spctroscopy. His papr daling with Fourir Slf-Dconvolution has th highst citation numbr in th whol history of th Journal of Applid Spctroscopy. In 200 Kauppinn and Partann publishd a book Fourir ransforms in Spctroscopy (Wily-VCH). H has 22 patnts or patnts pnding. H has bn for xampl a mmbr of th program and string committs in th Intrnational Confrncs on Fourir ransform Spctroscopy, a mmbr of th working group of IUPAC for Uni d Wavnumbr Standards, a mmbr of Finnish Acadmy of Scinc and Lttrs, and a mmbr of th ditorial board of Applid Spctroscopy Rviws. H was th chairman of th program committ and a mmbr of th string committ for th rst Intrnational Confrnc of Advanc Vibrational Spctroscopy ICAVS- hld in urku. H was also a mmbr of th program and string committs for ICAVS-2. H has rcivd th Intrnational Bomm-Michlson Award in 992 and th Innovation Award (th Foundation for Nw chnology) in 999 and in 2005 for dvloping th commrcial FIR gas analyzr GASME with mt Instrumnts Ltd. His varid rsarch intrsts includ high-rsolution Fourir transform spctroscopy, dvlopmnt of high-rsolution intrfromtrs. H built his rst high rsolution FIR spctromtr at th Univrsity of Oulu. his spctromtr was th fth high rsolution FIR instrumnt in th world starting to rcord spctra in 97. All th tim th rsolution of th spctromtr has bn th highst on in th world. Latr Dr. Kauppinn modi d th intrfromtr using th rst tim hom mad cub-cornr mirrors. h modi d cub-cornr intrfromtr achivd th rsolution of 0.00 cm, which is still th highst practical rsolution. At th Univrsity of urku h has built a nw cub-cornr intrfromtr with a rsolution of cm. Furthr, h has producd infrard wavnumbr standards and studid a lot of rotationvibration spctra of molculs including all th grnhous gass with his high rsolution intrfromtr. H has dvlopd th gaug masuring intrfromtr for th Finnish standard of lngth, lowrsolution stationary intrfromtrs (without moving parts), small vry stabl low rsolution intrfromtrs for IR, NIR, VIS, and UV such as Carousl-intrfromtr, Pndium intrfromtr, and Diamond intrfromtr, an automatic, commrcial, portabl FIR gas analysr GASME. Dr. Kauppinn has dvlopd data procssing by various 269

11 sophistic mathmatical mthods such as rsolution nhancmnt using Fourir Slf-Dconvolution and th xtrapolation of signals. wo spinoff companis hav bn foundd basd on his rsarch work. His latst innovation was an optical microphon using silicon cantilvrs. his microphon has bn usd in photoacoustic spctroscopy to improv snsitivity. hr ar a fw commrcial instrumnts basd on his microphon. In principl, photoacoustic dtction of gass is basd on th grnhous phnomnon in a small gas chambr. Jorma. Hinonn rcivd his M.Sc. dgr from Univrsity of urku, Finland, in 974 and his Licnciat in Philosophy dgr in 980 from th sam univrsity. H works as a Laboratory Managr in th Dpartmnt of Physics and Astronomy. His rsarch intrsts hav bn in xploitation of solar nrgy and simulation and dvlopmnt of th photoacoustic cll. Pkka J. Malmi rcivd his M.Sc dgr from th Univrsity of urku, Finland, in 990 and his Ph.D. dgr in 999 from th sam univrsity. H works as an Univrsity Lcturr in th Dpartmnt of Physics and Astronomy. His rsarch intrsts hav bn in low tmpratur solid stat NMR and ESR, spcially in quantum crystals. His currnt intrsts ar in th ld of optical spctroscopy. 270