Ing. Pavel Oupicky Institute of Plasma Physics AV ČR ,v.v.i.

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Processes with the influence on Earth’s temperature and their modelling
Ing. Pavel Oupicky Institute of Plasma Physics AV ČR ,v.v.i. Department of Optical Diagnostic Turnov Keywords: TSI (total solar irradiation), black and grey body, albedo, greenhouse effekt ,effektive temperature, climate modeling, Daisyworld, Greenhouseworld , Wimovac,Moses radiometers, spectroradiometers, satellites

Procesy ovliňující teplotu Země a jejich modelování
Ing. Pavel Oupický Ústav fyziky plazmatu AV ČR ,v.v.i. Oddělení optické diagnostiky Turnov Klíčová slova: TSI (total solar irradiation), černé a šedé těleso, albedo, skleníkový efekt ,efektivní teplota, klimatické modely, Daisyworld, Greenhouseworld , Wimovac,Moses radiometry, spektroradiometry, satelity

Sun + Earth Earth reflection + irradiation -> ….. <- Solar irradiation [1]

Energy comming <=> Enegry leaving
Climate Change and Greenhouse Effect. A briefing from the Hadley Centre for Climate Prediction Professor John Mitchell et al, Chief Scientist, Met Office December 2005

Black body - Planck law (for wavelength)
I is irradiation of black body of temperature T on wavelength λ

Planck law (for wave number)
I is irradiation of black body of temperature T on wave number ν l=1/ν [l in meters ] l=10000/ν [l in micrometers ]

Stefan-Boltzman law derivation
I is total irradiation of black body of temperature T

Prof. Mike Barnsley, University of Wales Swansea

Sun and Earth as black bodies
Earth irradiation (T effective ~ 14ºC) = 385W/m2

Earth radiation The amount of energy radiated by the surface of the Earth depends only on the temperature of the surface of the Earth. The type of radiation is also determined by the temperature of the Earth, most of the energy it loses is in the form of infrared radiation. The quantity of radiation lost is proportional to T ^ 4, where T is the Earth’s temperature in kelvins (K).

Black, grey and real body
Black body: EBB = σ T s 4 Grey body: EGB = ε σ T s 4 ε (or α) < 1 Emisivity (or absorbance) ε (λ) = const Real Body: ERB = ε (λ) σ T s 4

Sun <---> Earth Power Balance
PDISK = PSR ~ PEI = PKOULE

Sun + {geothermal + fosil} power
π r 2 ETSI {+ 4 π r 2 EGI + 4 π r2 EFI }

Earth outgoing power (Earth as real body) PEI (λ) = 4 π r 2 ε (λ) ETEI
ε (λ) = ( 1 - G (λ) ) / ( 1 – A (λ) ) PEI (λ) = 4 π r 2 (( 1 - G (λ) ) / ( 1 – A (λ) )) ETEI

Sun <---> Earth Power Balance
π r 2 ETSI + {4 π r 2 EGI + 4 π r 2 EFI } = 4 π r 2 (( 1 - G ) / ( 1 – A )) ETEI Next: dividing by 4 π r 2 and multipling by (1-A) :

(1- A) ( ETSI / 4 + {EGI + EFI} ) = (1- G) ETEI where : ETEI = σ T e 4 A(l,φ,t,h,etc.) is albedo, A<1 G(l,φ,t,etc.) is greenhouse “albedo”, G<1 Te is effective temperature in Kelvins

EGI= 0 , EFI = 0 (1 - A) ETSI / 4 = (1- G) σ T e 4 Basic equation of Solarworld (of black and grey bodies)

Effective (emissive) temperature definition
Te ~ ETSI / 4 ESI (φ) = ETSI cos2(φ)/ 2 (change between day and night, φ is latitude) on equator ( φ = 0 ) ESI (0) = ETSI / 2 ETSI cos2(φ)/ 2 = ETSI / 4 => φ cos 2(φ) = 1/2 => cos(φ) = => 45º ~ Te

Effective and global temperature
Temperature is monitored on the many places on Earth for the long time “Global temperature” is the average from many measurement

On earth globe temperature
Observed mean temperature from January to December

TSI data from NASA Next data were obtained from the NASA Langley Research Center Atmospheric Science Data Center.

TSI data from SORCE / TIM
TSI on the top of earth orbit on the earth distance from Sun and re-count on A.U. TSI data from SORCE / TIM

TSI on the top of earth orbit in A.U. and earth distance from Sun
TSI data from SORCE / TIM / detail

TSI on the top of earth orbit in A.U.
TSI data comparison from ACRIM and SORCE satelites

TSI on the top of earth orbit in A.U.
TSI data comparison from ACRIM and SORCE satelites - detail

TSI on the top of earth orbit in A.U.
Data Quality Description (updated 13 December 2005) To date the TIM is proving very stable with usage and solar exposure, and long-term relative uncertainties are estimated to be less than W/m2/yr (10 ppm/yr). Present absolute accuracy is estimated to be 0.48 W/m^2 (350 ppm), largely determined by the agreement between all four TIM radiometers. There remains an unresolved 4.5 W/m2 difference between the TIM and other space-borne radiometers, and this difference is being studied by the TSI and radiometry communities.

TSI on the top of earth orbit in A.U.
TSI data from ACRIM / ACRIM3 satelite - detail

TSI in three solar cycles
TSI from the maxima of 21. solar cycle to the minima of 21.solar one

Data from ACRIM3 - example

Sun and Earth as ideal black body radiators
Theoretical count of spectra

Sun and Earth as ideal black body radiators
Theoretical count of normalised spectra

On the top of atmosphere and on the Earth in sea level

Measuring on the Earth surface Malá Skála (near of Turnov city, Czech Republic)

Earth reflection and absorption (Campbell and Norman 1998)
Shortwave radiation budget [1] Reflection : a) Atmosphere c) clouds e) surface Absorption: b) atmosphere d) clouds f) surface

342 = 1368 / 4 [ W/m2]

Picture from NASA / Satellite Terra/Modis measuring

Longwave irradiation budget a) absorbed by atmospheric gases b) lost to space c) from atmospheric gases d) sensible heat flux e) from clouds f) latent heat flux

Satellite measuring (Modis) (Data from NASA, Earth Observatory)

Total Sun <-> Earth radiation balance

Total Sun <-> Earth radiation balance
Picture from NASA / Earth Observatory

Total Sun <-> Earth radiation balance

Earth incoming <-> outgoing energy balance all in W/m2
What is the net energy at the top of the atmosphere? Incomming : 1368/4 = 342–77(clouds)–30(surface) = 235 W/m2 Outgoing: 165(a)+30(c) + 40(w) = 235 W/m2 The Earth (planet and atmosphere) receives as much energy from the Sun as it loses to space What is the net energy of the centre of the atmosphere? Incoming : 67(aa) + 78(vap) + 24(thermal) + 350(es) = 519 Outgoing: 324(back)+165(e)+30(c) = 519 The atmosphere receives as much energy from the Sun as it loses to Space What is the net energy of the surface of the Earth? Incoming: 168(Sun) + 324(gases) = 492 Outgoing: 390(surface) + 78(vap) + 24(thermal) = 492

Earth incoming <-> outgoing energy balance
Atmosphere

Earth incoming <-> outgoing energy balance results
The surface of the Earth receives as much energy from the Sun as it loses to space All the elements of the Earth/atmosphere system lose as much energy as they gain. Therefore, their temperature stays stable.

Climate models Zero-dimensional models Higher Dimension Models
Radiative-Convective Models EMICs (Earth-system Models of Intermediate Complexity) GCMs (Global Climate Models or General Circulation Models

Zero-dimensional models
A very simple model of the radiative equilibrium of the Earth is (1 − a) S πr2 = 4πr2 ε σT4 where the left hand side represents the incoming energy from the Sun the right hand side represents the outgoing energy from the Earth, calculated from the Stefan-Boltzmann law assuming a constant radiative temperature, T, that is to be found, and

Zero-dimensional models
The constant πr2 can be factored out, giving (1 − a) S = 4 ε σ T 4 This yields an average earth temperature of 288 K. This is because the above equation represents the effective radiative temperature of the Earth (including the clouds and atmosphere).

Zero-dimensional models
S is the solar constant - the incoming solar radiation per unit area - about 1367 W·m-2 a is the Earth's average albedo, measured to be 0.3 [1] [2] r is Earth's radius — approximately 6.371×106m π is well known, approximately σ is the Stefan-Boltzmann constant — approximately 5.67×10-8 J·K-4·m-2·s-1 ε is the effective emissivity of earth, about 0.612

( 1/Ghf(λ) ) = 1- G(λ) = ε (λ)
Greenhouse effect EEI = ε (λ) σ T s 4 EEI = (1- G(λ)) σ T s 4 ( 1/Ghf(λ) ) = 1- G(λ) = ε (λ) EEI = σ T s 4 ε < 1, G<1 , Ghf >1 Greenhouse factor or emissivity or Greenhouse “albedo” equivalents

Greenhouse factor derivation – equation (1),(2)

Greenhouse factor derivation – equation (3),(4),(5)

4 * Ghf = 2 / (1+ τau ) ?? 1 / Ghf = 2 / (1+ τau ) Ghf = (1+ τau ) Ghf > 1, τau < 1 Greenhouse factor derivation – result ?

Climate modelling (1- A) ETSI /4 + {EGI + EFI} = ( 1- G ) σ T e 4

Basic counts from the basic equation and constants
Solarworld Basic counts from the basic equation and constants

=> Tef earth = 288ºK (15ºC)
Solarworld T solar ~ 5780ºK A = 0, G = 0 T ef earth ~ 279ºK (6ºC) A = 0.3, G = 0 T ef earth = 255ºK (-18ºC) A = 0.3 , 1 – G = ( G = ) => Tef earth = 288ºK (15ºC)

Water -> vapor -> clouds + reflection
Cloudsworld Water-Clouds-Cycle Water -> vapor -> clouds + reflection -> rain -> Water … and so one

Daisyworld (John Lovelock, Gaia hypothese)
Daisyworld (according to Phillipe Senssini-Gill from University of Calgary)

Daisyworld – close to reality
Dark green and light green plants

Daisyworld (according to prof. Mike Barnsley)
Globally-averaged temperature of Daisyworld

Daisyworld (according to prof. Mike Barnsley)
Example of canopy

Daisyworld (according to prof. Mike Barnsley)
Albedo of leaf and soil

Daisyworld from prof. Mike Barnsley
Optimal (local) temperature for black and white daisies

Daisyworld (according to prof. Mike Barnsley)
Daisies - growth and death rate

Daisyworld (according to prof. Mike Barnsley)
New area of black and white daisies

Daisyworld (according to prof. Mike Barnsley)
Temperature stability with daisies

Daisyworld from prof. Mike Barnsley
Spectral reflectance of leafs and soil

Daisyworld ? / leafs and plants
Transmitance of leafs

Daisyworld ? / leafs and plants
Relative reflectance of leafs (100% = glass)

Daisyworld ? / leafs and plants
Measuring of leaf reflectance - device

Daisyworld ? / leafs and plants
Absolute reflectance of leafs (100% - Al, USB2000)

Daisyworld ? / leafs and plants
Absolute reflectance of leafs (NIR) (100% = Al , NIR512)

Daisyworld ? / tiles and plant

Daisyworld ? / tiles and plant

Daisyworld ? / tiles and plant
Spectroradiometer USB 2000 with cosine extender

Daisyworld ? / tiles and plant
Measuring of plant reflectance - schema

Daisyworld ? / tiles and plants
Measuring of direct and reflected solar radiation Sun / Yellow , shadow / black, tile / brown, grass / green

Daisyworld ? / tiles and plant
Measuring of direct and reflected solar radiation - detail

Daisyworld ? / tiles and plants
SPMOORAD/10/task SPM-N-Sun-P par Spectrum of Sun and refl. from grass and tile Time: ,14:40,SEC User: autor Spectrometer:OO-USB2000,USB2G13027 Inputs:4 WDB/300/849/BS,GREEN/500/599/BS, RED/600/699/BS,NIR/700/799/BS ( BS = Band Sum )

Daisyworld ? / tiles and plants
Table nr.1: results / reflected radiation from grass and tile in W/m2 | | |Time | WIDE | GREEN| RED | NIR |Ang.| Comment | |13:38:10.17| | 2.648| 0.390| 2.684| -45| reflectance of grass | |13:40:01.75| | 2.696| 0.409| 2.830| 0| - “ | |13:39:19.80| | 3.272| 0.570| 2.954| 45| - “ | |13:54:39.20| |42.001|11.088| 8.322| -0| Sun direct on Earth | |13:55:01.79| |14.582| 3.457| 2.495| -0| cloudy | |13:55:20.63| | 3.939| 1.151| 1.644| 0| reflectance of tile | |13:56:04.53| | 4.657| 1.349| 1.908| -45| - “ | |13:56:30.54| | 4.486| 1.326| 1.884| 45| - “ | Measuring in bands – Wide, Green, Red, NIR

Daisyworld ? / leafs and plants
Table nr.2 : Spectrum of Sun and reflection from grass and tile / Malá Skala / File : Sun MS-forenoon.ftm Input : 4 (WDB,GREEN,RED,NIR) W/m2 Cas abs || WDB || GREEN || RED || NIR || Comment | | | 10:37: || || || || || shadow | | 10:37: || || || || || horizont | | 10:38: || || || || || perpend. | | 10:39: || || || || || shadow | | 10:39: || || || || || grass | | 10:39: || || || || || tile | | 10:40: || || || || || shadow | | | Measuring in bands – Wide, Green, Red, Nir

Daisyworld ? / tiles and plants
Measuring of direct and reflected solar radiation - detail

Daisyworld ? / tiles and plants
Programm: SPMOORAD10/data/spr Data file: Spr-Sun-MS ftm Description: Spectrum of Sun and reflection from grass and tile Parameters: 2,1,1,0 Date and time: *9:27:50*SEC Place: Mala Skala / near of the Turnov, Czech Republic Data: Time * WDB, GREEN, RED, NIR * comment 09:28:40.25 * , , , * Sun hor. 09:28:54.72 * , , , * Sun perp. 09:29:10.09 * , , , * shadow 09:29:50.27 * , , , * tile 09:30:12.79 * , , , * grass Measuring in bands – Wide, Green, Red, Nir [W/m2]

Daisyworld ? / tiles and plant
Measuring with spectroradiometer USB 2000 with cosine extender direct and reflected sun light

Daisyworld ? / tiles and plant
Measuring with spectroradiometer USB 2000 with cosine extender direct and reflected sun light

Daisyworld ? / forest and wood
Mala Skala / spruce and wood tile

Daisyworld ? / forest and wood
Mala Skala / spruce and wood tile - spectra

Daisyworld ? / forest and wood
File: Spr-Sun-MS ftm Description: Radiation of Sun and plants and wood refl. Parameters: 2,1,1,0 Date*Time: *9:41:20*SEC Place: Mala Skala / near of Turnov, Czech Republic Device: USB2000,USB2G13027,Spm-Kal-N-Hal-W kal Bands: 4*WDB,GREEN,RED,NIR, Data: Time * WDB , GREEN , RED , NIR * comment 09:41:43.14* , , , * dark 09:41:58.83* , , , * horizont. 09:42:22.85* , , , * direkt 09:42:44.31* , , , * forest 09:43:12.27* , , , * wood 09:43:35.12* , , , * grass =========================================================

Daisyworld ? / forest and soil
Flux Tower from BOREAS project

Daisyworld ? / forest and soil
Ground Flux from BOREAS project

BOREAS / forest and soil
Interaction between the BOReal Forest and the AtmoSphere

Bartlett flux tower during spring-early summer 2004
J.P.Jenkins / Agricultural and Forest Meteorology 143 (2007) 64–79

Bartlett flux tower during spring-early summer 2004
J.P.Jenkins / Agricultural and Forest Meteorology 143 (2007) 64–79

NASA / Satellites Launching of Terra

NASA / Satellites / ERBS, TERRA, GLORY
ERBS / ERBE Earth Radiation Budget Experiment Scanner - A set of three co-planar detectors (longwave, shortwave and total energy), all of which scan from one limb of the Earth to the other, across the satellite track (in it's normal operational mode). Nonscanner - A set of five detectors; one which measures the total energy from the Sun, two which measure the shortwave and total energy from the entire Earth disk, and two of which measure the shortwave and total energy from a medium resolution area beneath the satellite.

NASA / Satellites / ERBS, TERRA, GLORY
Terra / ACER, MODIS, CERES, ….. MODerate-resolution Imaging Spectroradiometer (MODIS) , Clouds and Earth's Radiant Energy System (CERES) Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER)

Satellite Terra

TERRA / MODIS

CERES / Clouds and Earth Radiation Energy System

CERES / Clouds and Earth Radiation Energy System

Albedo of ecosystems without snow
Satellite/Modis – snow free albedo Shortwave reflection

Albedo of ecosystems with snow
Satellite/Modis – albedo with snow

Albedo of ecosystems with snow
Ecosystems that have some vegetative canopy generally have a lower albedo. Canopied ecosystems exhibit a peak around 0.86 μm that suggests contribution by the snow on the canopy (leaf/needle or otherwise). Evergreen needleleaf forests have the lowest overall spectral albedo, undoubtedly due to the relatively lush winter canopy that obscures the ground-level snow. The deciduous broadleaf and deciduous needleleaf forests have nearly identical spectral signatures, as their winter canopies (of dense branches) are similar. These results are in accordance with modeling studies that show canopies that cover snow reduce the surface albedo during winter times (Bonan,1997; Bounoua et al., 2000). Effect of evergreen needleaf forests with snow

Albedo of ecosystems with snow
Graph of albedos of different ecosystems

Albedo of ecosystems with snow
The research reported in this article was supported by EOS MODIS support, the MODIS Science Team under NASA contract H4, and to Goddard Space Flight Center (E.G. Moody, M.D. King, D.K. Hall, S. Platnick) and NASA contract NAS to Boston University (CBS).

Principle of Greenhouseworld

Greenhouseworld ILW = (1- G) σ T4 G = kGE CE C ~ CO2
CO2 + light => photosynthesis dC/dt = - kG N Tmin < T < Tmax dC/dt = kM N T < Tmin , T > Tmax G = kGE CE Where N is number of leaf population (or leaf index), kG is constant of photosynthesis, kM is constant of mortality

Greenhouseworld (Lee Worden)
A (albedo) = konst, (1–G) is function of resources R and population N

Greenhouseworld (Lee Worden)
h0, h1 is amount of „greenhouse effect“ potential, R0 is resource, R1 is waste product N0 is population of individuals t0 is optimal temperature ( ~ 50F ), Mtotal is total mass in system ( R0 + R1 + N0 = 1.0 )

Greenhouseworld (Lee Worden)
Social - ecological System of Individuals

Greenhouseworld (Lee Worden)
General model parameters

Greenhouseworld (Lee Worden)
Model phenotypic and resource-specific parameters

Greenhouseworld (Lee Worden)
Basic equations

Greenhouseworld (Lee Worden)
Result ( y is relative time, x is temperature [ºF] )

Greenhouseworld – carbon balance
Carbon is stored on Earth in a number of major reservoirs: Carbon dioxide (CO2) in the atmosphere Carbon dioxide dissolved in water Carbonate (CaCO3) rocks (limestones and corals) Fossil fuels - deposits of coal, petroleum, and natural gas derived from once-living things Living plants Dead organic matter - e.g. harvested wood and wood products, plant litter, humus in the soil Carbon is continuously cycled between these reservoirs in the ocean, on the land, and in the atmosphere. This carbon cycle has been continuing naturally since plant life took hold on land about 400 million years ago.

Greenhouseworld – carbon balance
Redrawn from NASA's Earth Observatory and Cooperative Research Centre for Greenhouse Accounting

Greenhouseworld – carbon balance
Redrawn from NASA's Earth Observatory and Cooperative Research Centre for Greenhouse Accounting

Cooperative Research Centre for Greenhouse Accounting
Greenhouse effect The blanket of gases covering the Earth traps some of this radiation while the rest is re-radiated towards space. This absorption of heat maintains the Earth's surface temperature at a level necessary to support life. This natural process is called the greenhouse effect. Without heat-trapping greenhouse gases, the surface of the Earth would have an average temperature of -18°C rather than our current average of 15°C. Unfortunately, human actions such as burning fossil fuels and land clearing are increasing the concentration of greenhouse gases in the atmosphere, resulting in an increase in the heat trapped. This is called the enhanced greenhouse effect. The major consequence of this is an increase in temperature on the Earth's surface resulting in climate changes. Cooperative Research Centre for Greenhouse Accounting

Wimovac Windows Intuitive Model Of Vegetation response to Atmospheric & Climate change University of Essex and Brookhaven National Laboratory Free Air Carbon dioxide Enrichment (FACE) experiments.

Wimovac Plant in Wimovac model

1/2 scheme of Wimovac model

2/2 scheme of Wimovac model

GCM / MOSES MOSES I. MOSES II. (2.2)
(Cox et al (1999)) MOSES II. (2.2) (Richard Essery, Martin Best and Peter Cox (2001)) Tiled model of subgrid heterogenity The set of equations represented by 126 ones is solved by a two-sweep algorithm (subroutine GAUSS). Hadley Centre, Met Office, London Road, Bracknell, Berks R12 2SY, UK

Princip of 3D Global Climate Model
GCM / MOSES II. Princip of 3D Global Climate Model

GCM / MOSES II. + TRIFFID => HadCM3

GCM / MOSES II. + TRIFFID Albedos of snow free vegetated and unvegetated tiles

GCM / MOSES II. + TRIFFID

Basic equation for carbon cycle
GCM / MOSES II. + TRIFFID Basic equation for carbon cycle

Global climate modeling and prediction
Input data

Global climate modeling and prediction
Input data

Global climate modeling and prediction
Output data (without men influence)

Global climate modeling and prediction
Output data (with men influence)

Global climate modeling and prediction
BOINC – Climate prediction experiment

Global climate modeling and prediction
BOINC – Climate prediction experiment

Processes with the influence on Earth’s temperature and their modelling
Special thanks to all from which I took their science info and pictures

Thank you very much for your attention
Published on conference The man in his earth and space environment Upice Observatory / Czech Republic At (1. revision for web pages at )

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