Osnove meteorologije z nalogami za študente 2. letnika programa Fizika Del 2: termodinamika vlažnega zraka in bilanca energije
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1 Osnove meteorologije z nalogami za študente 2. letnika programa Fizika Del 2: termodinamika vlažnega zraka in bilanca energije izr.prof.dr. Nedjeljka Žagar Fakulteta za matemaako in fiziko Univerza v Ljubljani Ljubljana, 2014
2 Tematski sklop 1: Osnovne spremenljivke za opis vlage Stabilnost in dviganje vlažnega zraka Termodinamični diagrami
3 Spremenljivke za opis vlažnega zraka e = ρ v R v T p = p d + e q = e p r = e p e R d R v R d R v = ε e p e = ε p e ε e p R = e e s 100 r r s 100 q q s 100 p = ρr d T v de s dt = Le s R v T 2 " T v = T e % $ ' # p & T d = " $ # 1 1 T o R v L ln e s e so = T ( r) % ' & 1
4 Enačba Clausius- Clapeyrona opisuje spremembe nasičenega tlaka vodne pare v odvisnosa od temperature de s dt = Le s R v T 2 Različne oblike C- C enačbe v uporabi v meteorološki praksi: npr. Tetenova formula, formula WMO Več na hsp:// /~voemel/vp.html Arhiv sondaž dostopen na spletu (University of Wyoming) hsp://weather.uwyo.edu/upperair/sounding.html
5 SaturaAon vapor pressure Količina vodne pare potrebna za nasičenje 1 kg suhega zraka na različnih temperaturah. Približno se podvoji vsakih 10 C 11/8/10
6 Naloga S pomočjo osnovnih plinskih zakonov pokaži, da je vlažen zrak lažji od suhega ρ v <ρ d
7 Merjenje vlažnosa zraka Določanje relaavne vlage v F s pomočjo psihrometra Izmerjene vrednosa: p = 980 hpa (dostopno s postaje pred FMF) T= 23.0 o C temperatura suhega termometra Tm = 18.0 o C temperatura mokrega termometra Naloga: Izračunaj relaavno vlago iz izmerjenih podatkov Postopek: Uporabimo 1. stavek termodinamike pri p=konst LΔq = C p ΔT ( ) = C p ( T T m ) L q s q q s določimo iz enačbe Clausius- Clapeyrona (ki da e s ) in izraza Iz zgornje enačbe (q s, T, T m ) določimo količino vlage v F4 RelaAvna vlaga R = q q s 100% q s = ε e s p
8 Naloga: izračun relaavne vlage Izračunaj relaavno vlago v učilnici F4 na Jadranski 19 iz naslednjih izmerjenih podatkov: Temperatura suhega termometra T=23 o C Temperatura mokrega termometra T m =18 o C Tlak p=980 hpa RH=? Rešitev: 86%
9 Nenasičeni adiabatni procesi
10 Odvisno je o količini vlage v zraku Dviganje vlažnega zraka Mokro- adiabatni dvig: ~5 C/km Suho- adiabatani dvig: 9.8 C/km
11 Ekvivaletna potencialna temperatura Lq s Cp T θ e θ Maksimalna temperature, ki jo delec zraka lahko doseže v primeru, ko se vsa vlaga kondenzira, sproščena latentna toplota preda okolici in delec adiabatno spusa nazaj na 1000 hpa. Ohranjena za mokro- adiabatne procese (nasičen zrak). Mokra adiabata=krivulja θ e = konst.
12 Termodinamični diagrami Različne vrste diagramov so v uporabi od konca 19. stoletja. Vsi so zgrajeni na istem principu in upoštevajo osnovne termodinamične zakone in povezave med T,p,q Osnovni princip konstrukcije diagrama: enake površine predstavljajo enako energijo v vsaki točki diagrama Vsaki diagram vsebuje pet vrst izolinij 5 izolinij: T, p, r s, Θ, Θe Diagrami omogočajo enostavno določanje nivoja kondenzacije, nivoja in temperature proste konvekcije, energije dostopne za konvekcijo itn.
13 the Emagram the Tephigram Vrste termodinamičnih diagramov the SkewT/Log P diagram (modified emagram) the PsuedoadiabaAc (or Stüve) diagram ** The emagram was devised in 1884 by H. Hertz. In this plot, the dry adiabaac lines have an angle of about 45degrees with the isobars; isopleths of saturaaon mixing raao are almost straight and veracal. In 1947, N. Herlofson proposed a modificaaon to the emagram which allows straight, horizontal isobars, and provides for a large angle between isotherms and dry adiabats, similar to that in the tephigram. ** The Tephigram takes its name from the rectangular Cartesian coordinates : temperature and entropy. The Greek leser 'phi' was used for entropy, hence Te- phi- gram (or T- F- gram). The diagram was developed by Sir William Napier Shaw, a BriAsh meteorologist about 1922 or 1923, and was officially adopted by the InternaAonal Commission for the ExploraAon of the Upper Air in 1925.
14 Vrste termodinamičnih diagramov (2) ** The Stüve diagram was developed circa 1927 by G. Stüve and gained widespread acceptance in the United States: it uses straight lines for the three primary variables, pressure, temperature and poten<al temperature. In doing so we sacrifices the equal- area requirements (from the original Clapeyron diagram) that are saasfied in the other two diagrams. ** The SkewT/Log(- P) diagram is also in widespread use in North America, and in many services with which the United States (various) weather services have had connecaons. This is in fact a variaaon on the original Emagram, which was first devised in 1884 by H. Hertz.
15 y = - RlnP x = T + klnp Termodinamični diagrami: SKEW- T/LOG(P) Parameter k se določi tako, da je kot med izotermami in suhimi adiabatmi priližno 90 o.
16 Termodinamični diagrami 5 vrst izolinij: T, p, r s, Θ, Θe SKEW- T/LOG(P) T p r s Θ Θe
17 Termodinamični diagrami T izoterme p izobare r s izograme Θ suha (nenasičena) adiabata: Θe mokra (nasičena) adiabata: Γ d Γ m
18 Stabilnost vlažnega zraka Γ = Γ d Nenasičeno nevtralno ozračje Γ = Γ m (B) Nasičeno nevtralno ozračje Γ > Γ d (D) Absolutno labilno ozračje Γ < Γ m (A) Absolutno stabilno ozračje Γ < Γ d in Γ > Γ m (C) Pogojno stabilno ozračje: labilno glede na nasičeno in stabilno glede na nenasičeno (suho) adiabato
19 Stabilnost vlažnega zraka pogojno stabilno labilno stabilno Θ suha (nenasičena) adiabata: Θe mokra (nasičena) adiabata: Γ d Γ m
20 Parametri, ki jih določamo s pomočjo termodinamičnega diagrama LCL kondenzacijski nivo CCL nivo konvekavne kondenzacije (baza oblakov Cu) LFC nivo proste konvekcije (točka poziavnega vzgona) EL ravnovesni nivo (točka ničlega vzgona, ~vrh konv. oblaka) CAPE energija, dostopna za konvekavni razvoj CIN energija, potrebna za dvig delca na LFC
21 Struktura ozračja nad Ljubljano, , ob 6
22 11/8/10 Struktura ozračja nad Ljubljano,
23 Udine: struktura ozračja , ob 12 UTC
24 Konvekcija
25 Energija, dostopna za konvekcijo CAPE = convecave available potenaal energy CAPE z LNB z LFC g T v,delec T v,okolica T v,delec dz CAPE = w 2 max 2 J/kg CIN = convecave inhibiaon CIN=energija, potrebna za dvig delca na nivo proste konvekcije
26 Razvoj konvekcije: Apična sondaža
27 Naloga: dviganje vlažnega delca na Jadranski 19 Nadaljevanje naloge za izračun relaavne vlage v F4 P=980 hpa T= 23.0 o C Tm = 18.0 o C 1) izračunaj naslednje spremenljivke: qs, q, in RH Rešitev: 86% 2) Določi kondenzacijski nivo delca F4: LCL (p,t)=? 3) Če delec nadaljuje z dviganjem za dodatnih 200 hpa, določi p,t na novem polozaju in količino vodne pare kondenzirane med dvigom
28 Tematski sklop 2: Globalni hidrološki cikel Klimatologija padavin
29 Globalni hidrološki cikel Ozračje oceani kopno Kon<uniran cikel!
30 Globalni hidrološki cikel E- evaporaaon, Q- atmospheric water vapour advecaon, P- precipitaaon, Ro- river runoff, Ru- undergraound runoff Q Q Q E C E P P Ro Ru Pet komponent sistema: Oceani, ledeniki in sneg, vode na kopnu, ozračje in biosfera Vodna bilanca sistema: S=P- E- Ro- Ru totalna količina vode v sistemu je ohranjena Vir: Peixoto&Oort
31 Globalni hidrološki cikel <0.1% ~97.5% ~2.4% Če kondenziramo vso vodo v ozračju višina stolpca vode znaša približno 2.5 cm Vir: Peixoto&Oort
32 Globalni hidrološki cikel
33 Globalni hidrološki cikel Procesi v oceanih so dominanten vir in ponor vode v ozračju 350,000 Volume of Water (km 3 ) 300, , , , ,000 50,000 0 Ocean Evap Ocean Precip Land Precip Evap/trans Runoff process Ocean Evap Ocean Precip Land Precip Evap/trans Runoff
34 Padavine: globalna klimatologija letno povprečje (mm/dan) Variabilnost na skali > leta Vir: reanalize ERA40 (
35 Izhlapevanje- Padavine (letno povprečje) Vir: reanalize ERA40 (
36 Padavine Globalno letno povprečje padavin: ~1 m vode Povprečna količina vode v zraku: ~2.5 cm Povprečna življenska doba vodne kaplje: 0.025/1 na leto kar znaša okoli 9 dni Sledi, da se voda v ozračju v povprečju izmeni vsakih 40 dni
37 Padavine v Sloveniji: (30- letno povprečje, mm/leto) Vir: ARSO
38 Klimatologija padavin na območju Alp Vir: hsp:// doc/rr_clim.htm Letno povprečje (mm/dan) Postaje Povprečje za november Povprečje za julij
39 Tematski sklop 3: Sevanje in njegove spremembe na poa do tal Energijska bilanca ozračja
40 Oblike energijske v atmosferi E=E i +E p +E k +E lh notranja energija potencialna energija kineačna energija energija zaradi sproščanja latentne toplote Skupna energija klimatskega sistema (atmosfera, oceani, tla) je ohranjena
41 Prenosi energije v klimatskem sistemu Totalna energija sistema je ohranjena sevanje, kondukcija, konvekcija
42 Prvi zakon termodinamike dq=mc v T+pdα opravljeno delo izmenjena toplota notranja energija dq=mc p T- Vdp 1 m dq dt = C p dt dt dp α dt dt dt dp = α C dt p 1 mc p dq dt
43 Sevanje Osnovne spremenljivke za opis prenosa energije sevanjem: valovna dolžina - λ (m) frekvenca - ν (s - 1 oz. Hz) c = λ ν c - svetlobna hitrost ( m/s) P = 1 A ΔE Δt P A = ΔE Δt gostota energijskega toka sevanja (v enotah J/sm 2 = W/m 2 ) energijski tok (v enotah W = J/s )
44 Spekter elektromagnetnega sevanja
45 Osnovni fizikalni zakoni, ki se uporabljajo za opis sevanja 1) Planckov zakon: porazdelitev gostote energijskega toka v spektru valovnih dolžin P λ 2hc ( T) dλ = / 2 d [ ] λ 5 ch kλt e 1 λ Intenziteta monokrom. sevanja (energija po enoa površine v enoa časa po enoa kota) c - svetlobna hitrost ( m/s) h - Planckova konstanta (6, Js) k - Boltzmannova konstanta (1, J/K)
46 Osnovni fizikalni zakoni, ki se uporabljajo za opis sevanja 2) Wienov zakon: spekter sevanja črnega telesa ima maksimum pri valovni dolžini λ T = c max W c W - Wien- ova konstanta (c W =2898 Kμm) λ max - valovna dolžina pri kateri telo seva največ (m) T - temperatura telesa (K) Torej, toplejša telesa sevajo več pri manjših valovnih dolžinah, kot hladnejša.
47 Osnovni fizikalni zakoni, ki se uporabljajo za opis sevanja 3) Stefan- Boltzmannov zakon (črno telo s T višjo od absolutne ničle, oddaja energijo s sevanjem): 0 P( T) = P ( T) dλ ~ T λ P( T)cosθ dωda = σt 4 4 Stefan- Boltzmannova konstanta σ σ= Wm - 2 K - 4 Za sivo telo: P = ε σ T 4 ε emisivnost ali sposobnost oddajanja
48 Gostota energijskega toka na vrhu ozračja na povprečni oddaljenosa od Sonca Sonce seva pri ~5800 K, Vidna (λ med 0,4 in 0,75 µm), IR (0,2-0,4 µm) in UV (0,4-24 µm) svetloba S o = Q =1367 Wm 2 2 4πr Q intenziteta sončnega sevanja (3, W) r povprečna razdalja Sonce- Zemlja ( m)
49
50 Sončno in terestrično sevanje λ max = 2898 T Kµm Sončno sevanje ima max v področju vidne svetlobe (~0.6 µm), teresačno v infrardečem delu (~14 µm)
51 Gostota energijskega toka na vrhu ozračja na povprečni oddaljenosa od Sonca: S o =1367 Wm - 2 Sonce seva pri ~6000 K, Na vrhu ozračja: ~46% energije je med 0.4 in 0.75 µm (vidno sevanje), ~46% energije je med 0.75 in 24 µm (IR, infrardece sevanje), ~7% energije je med 0.2 in 0.4 µm (UV, ultravijolicno sevanje).
52 Kaj se zgodi s S o na poa do tal? Vhodno sončno sevanje se delno - absorbira (upija) - sipa - odbija (reflekara) - prepušča (transmisivnost) Sposobnost absorpcije: Koeficient absorpavnosa Sposobnost oddajanja: Koeficient emisivnosa ε P = εσt 4 Odbita energija Upadla energija = α koeficient refleksivnosa (odboja), ALBEDO
53 Albedo
54 Albedo pri tleh Albedo is majhen za površino oceanov, (2-10)%, Večji za kopno, posebej za puščave, (35-45)%, Največji pa za območja ledu in pod snegom (80% in večji)
55 Albedo za različne površine
56 Emisijska temperatura Zemlje
57 Bilanca energije na vrhu ozračja Letno povprečje Vhodno sončno sevanje 340 W/m 2 Absorbirano sončno sevanje 240 W/m 2 Planetary albedo 0.30 Oddano sevanje Zemlje 240 W/m 2 Emisijska temperatura Zemlje 255 K
58 Bilanca energije na vrhu ozračja Sončno sevanje Albedo Sevanje Zemlje Bilanca Vir: Barkstrom et al., 1989
59 Bilanca energije in globalni tokovi
60 Vloga ozračja: transport Skupni transport energije skozi atmosfero in oceane proa poloma Petawatt=10 15 W
61 Vloga spodnjih robnih pogojev: T površine Temperatura površine morja januarja Temperatura površine morja julija
62 Vloga spodnjih robnih pogojev: vlaga Odvisnost e s od temperature Globalna porazdelitev e s Okoli 70% površine zemlje je mokro
63 Vloga spodnjih robnih pogojev: ostali faktorji Nadmorska višina (orografija) Toplotna kapaciteta Hrapavost podlage Vegetacija Morski led Kopenski led
64 Profil ravnovesne temperature
65 Kaj se zgodi s S o na poa do tal?
66 Ocena energijske bilance Zemljina klimatskega sistema (v W/m 2 ) Vir: AMS
67 Ocena energijske bilance Zemljina klimatskega sistema (v %)
68 Porazdelitev Sončnega sevanja pri tleh
69 Lokalna bilanca energije Bilanca = +SW (sončno vhodno) SW (odbito) +LW (IR) LW (IR)
70 Energijska bilanca Zemlje P = P SW + P Povprečni energijski tok (ang. LW energy flux) P SW ( ) 1 α P = PSW PSW = SW α povprečni albedo P LW = P LW PLW Vse skupaj: P ( ) 4 1 α P εσt + P = SW Z LW SW: kratkovalovno LW: dolgovalovno
71 Energijska bilanca Zemlje: vrh ozračja (1) P TA ( ) 1 α P ds P ds 0 = SW top top LW Energijska bilanca na vrhu ozračja (TOA=top of the atmosphere) α povprečni albedo πr Z ( ) α zemlja+ozračje, v povprečju α S = 238 4πR 2 2 Z o Wm - 2 Za Zemljo kot črno telo, ravnovesna temperatura za (1): σt 4 e = 238 Te = 255 K Wm - 2 emisivnost ε=1
72 Energijska bilanca pri tleh P T s T e ( ) 4 1 A P εσt + P = SW e LW = T e ΔT ΔT = 33 K K emisivnost ε=1 P Tok zaznavne toplote P SH P LH Tok latentne toplote P G P M Toplotni tok v globlje sloje = 0 Energija, porabljena za taljenje snega, leda ali zmrzovanje vode
73 Bilanca energije na površini Zemlje Letno povprečje Absorbirano sončno sevanje (SW) 176 W/m 2 Dolgovalovno sevanje proa tlom (LW ) 312 W/m 2 Dolgovalovno sevanje navzven (LW ) W/m 2 Totalno dolgovalovno sevanje (LW) - 73 W/m 2 Bilanca sevanja na površini (SW+LW) 103 W/m 2 Latentna toplota (LH) - 79 W/m 2 Zaznavna toplota (SH) - 24 W/m 2 Poznamo jo le približno (napaka znaša kakšnih 20%)
74 Meddelovanje med oblaki in sevanjem
75 Naloga: enostavni modeli toplogrednega učinka Predpostavi, da je atmosfera opisana z N slojev kot je predstavljeno na sliki: Vir: Naloga 2.5 iz učbenika Marshall in Plumb: Atmosphere, Ocean and Climate Dynamics: an introductory text. InternaAonal Geophysics Series.
76 Naloga: enostavni modeli toplogrednega učinka (2) Predpostavi, da je atmosfera popolnoma prosojna za kratkovalovno (sončno, SW) sevanje in da delno propušča dolgovalovno (zemljino, LW) sevanje. Vsaki sloj popolnoma absorbira sevanje LW. a) S pomočjo energijske bilance pri tleh pokaži, da temperatura pri tleh mora bia večja od temperature najnižjega sloja ozračja. T s > T N b) S pomočjo energijske bilance za n- A sloj pokaži, da v ravnovesju velja 2T n 4 = T n T n 1 T n je tempertura sloja n, za n>1. Iz tega lahko sledi, da je ravnovesna temperatura pri tleh T T n je emisijska T planeta. s = N +1 ( ) 1/4 T e [Navodilo: Za reševanje naloge b) uporabi rezultat naloge a), določi T 1 in uporabi (*) za določanje razlike T sosednih slojev.] (*)
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