Processes with the influence on Earth’s temperature and their modelling Keywords: TSI (total solar...

Processes with the influence on Earth’s temperature and their modelling

Keywords:TSI (total solar irradiation), black and grey body, albedo,

greenhouse effekt ,effektive temperature,climate modeling,

Daisyworld, Greenhouseworld , Wimovac,Moses radiometers, spectroradiometers, satellites

Ing. Pavel Oupicky

Institute of Plasma Physics AV ČR ,v.v.i.

Department of Optical DiagnosticTurnov

Procesy ovliňující teplotu Zeměa jejich modelování

Klíčová slova:TSI (total solar irradiation), černé a šedé těleso, albedo,

skleníkový efekt ,efektivní teplota, klimatické modely,Daisyworld, Greenhouseworld , Wimovac,Moses

radiometry, spektroradiometry, satelity

Ing. Pavel OupickýÚstav fyziky plazmatu AV ČR ,v.v.i.

Oddělení optické diagnostiky Turnov

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 PredictionProfessor 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 νl=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 radiationThe 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 bodyBlack 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) :

Sun <=> Earth Radiation Balance

(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

Sun <=> Earth Radiance Balance

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) = 0.707 => 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 December1961 - 1990

TSI data from NASA

Next data wereobtained from the NASA Langley

Research Center AtmosphericScience Data Center.

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 0.014 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

Solar irradiation measuring

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

Solar irradiation measuring

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

Incoming Solar radiation

342 = 1368 / 4 [ W/m2]

Reflected solar radiation

Picture from NASA / Satellite Terra/Modis measuring

Earth and atmosphere irradiation

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

Earth and atmosphere irradiation

Satellite measuring (Modis)

(Data from NASA, Earth Observatory)

Total Sun <-> Earth radiation balance

Radiation - all in W/m2

Total Sun <-> Earth radiation balance

Picture from NASA / Earth Observatory

Total Sun <-> Earth radiation balance

Earth incoming <-> outgoing energy balanceall 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/m2The 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) = 519The 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 modelsThe 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 3.14159 • 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

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

Earth Balance Radiation Experiment (ERBE)

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

Earth Balance Radiation Experiment (ERBE)

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

Earth Balance Radiation Experiment (ERBE)

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

Solarworld, Waterworld

Cloudsworld

Daisyworld, Greenhouseworld,

Wimovac, Stella

Moses (HadSm, HadCm) etc.

Solarworld

Basic counts from the basic equation and constants

Solarworld

T solar ~ 5780ºK

A = 0, G = 0T ef earth ~ 279ºK (6ºC)

A = 0.3, G = 0 T ef earth = 255ºK (-18ºC)

A = 0.3 , 1 – G = 0.612 ( G = 0.388 )

=> Tef earth = 288ºK (15ºC)

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

Fiber coupled solar radiation sensor

Daisyworld ? / tiles and plant

Fiber coupled solar radiation sensor

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 radiationSun / 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-P080510-11.par• Spectrum of Sun and refl. from grass and tile

Time: 2008-05-04,14:40,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| 29.775| 2.648| 0.390| 2.684| -45| reflectance of grass | |13:40:01.75| 27.061| 2.696| 0.409| 2.830| 0| - “ - | |13:39:19.80| 32.589| 3.272| 0.570| 2.954| 45| - “ - | |13:54:39.20|389.953|42.001|11.088| 8.322| -0| Sun direct on Earth | |13:55:01.79|150.208|14.582| 3.457| 2.495| -0| cloudy | |13:55:20.63| 34.223| 3.939| 1.151| 1.644| 0| reflectance of tile | |13:56:04.53| 40.807| 4.657| 1.349| 1.908| -45| - “ - | |13:56:30.54| 38.418| 4.486| 1.326| 1.884| 45| - “ - | --------------------------------------------------------------------------

Measuring in bands – Wide, Green, Red, NIR

Daisyworld ? / leafs and plantsTable nr.2 :Spectrum of Sun and reflection from grass and tile / Malá Skala / 4.5.2008File : Sun-080504-MS-forenoon.ftmInput : 4 (WDB,GREEN,RED,NIR) W/m2 Cas abs. || WDB || GREEN || RED || NIR || Comment |---------------------------------------------------------------------------|| 10:37:29.31 || 49.849 || 8.021 || 3.897 || 4.414 || shadow || 10:37:50.95 || 525.898 || 114.452 || 78.061 || 54.270 || horizont || 10:38:37.39 || 743.284 || 157.980 || 111.348 || 78.812 || perpend. || 10:39:04.62 || 47.412 || 7.741 || 3.805 || 4.202 || shadow || 10:39:20.82 || 37.832 || 6.550 || 3.832 || 11.344 || grass || 10:39:53.47 || 39.146 || 7.915 || 5.702 || 8.551 || tile || 10:40:11.33 || 50.123 || 7.858 || 3.906 || 4.198 || 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-080511-092812.ftm Description: Spectrum of Sun and reflection from grass and tile Parameters: 2,1,1,0 Date and time: 080511*9:27:50*SEC Place: Mala Skala / near of the Turnov, Czech Republic Data: Time * WDB, GREEN, RED, NIR * comment ---------------------------------------------------------- 09:28:40.25 * 276.223, 61.546, 42.187, 29.633 * Sun hor. 09:28:54.72 * 458.327, 101.382, 71.561, 50.773 * Sun perp. 09:29:10.09 * 17.106, 2.726, 1.468, 1.411 * shadow 09:29:50.27 * 26.831, 5.442, 3.730, 6.241 * tile 09:30:12.79 * 27.285, 4.519, 2.330, 9.894 * 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-080517-094140.ftm Description: Radiation of Sun and plants and wood refl. Parameters: 2,1,1,0 Date*Time: 080517*9:41:20*SEC Place: Mala Skala / near of Turnov, Czech Republic Device: USB2000,USB2G13027,Spm-Kal-N-Hal-W4-080510-11.kal Bands: 4*WDB,GREEN,RED,NIR, Data: Time * WDB , GREEN , RED , NIR * comment-------------------------------------------------------- 09:41:43.14* -0.385, -0.012, -0.012, -0.075 * dark 09:41:58.83* 259.607, 57.884, 39.928, 31.020 * horizont. 09:42:22.85* 365.421, 81.802, 57.369, 42.810 * direkt 09:42:44.31* 22.313, 4.152, 2.277, 6.521 * forest 09:43:12.27* 25.948, 5.758, 4.170, 4.456 * wood 09:43:35.12* 19.542, 3.842, 1.924, 8.635 * 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 / ERBEEarth 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 SystemShortwave radiation

CERES / Clouds and Earth Radiation Energy SystemLongwave radiation

Albedo of ecosystems without snow

Satellite/Modis – snow free albedoShortwave reflection

Albedo of ecosystems with snow

Satellite/Modis – albedo with snow

Albedo of ecosystems with snow

Ecosystems that have some vegetative canopy generallyhave a lower albedo. Canopied ecosystems exhibit a peak

around 0.86 μm that suggests contribution by the snow on thecanopy (leaf/needle or otherwise). Evergreen needleleaf forestshave the lowest overall spectral albedo, undoubtedly due to the

relatively lush winter canopy that obscures the ground-levelsnow. The deciduous broadleaf and deciduous needleleaf forests

have nearly identical spectral signatures, as their wintercanopies (of dense branches) are similar. These results are in

accordance with modeling studies that show canopies that coversnow 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 621-30-H4, and to Goddard Space Flight Center (E.G.

Moody, M.D. King, D.K. Hall, S. Platnick) and NASA contract

NAS5-31369 to Boston University (CBS).

Greenhouseworld

Principle of Greenhouseworld

Greenhouseworld ILW = (1- G) σ T4

C ~ CO2

CO2 + light => photosynthesis

dC/dt = - kG N Tmin < T < Tmax

dC/dt = kM N T < Tmin , T > Tmax

G = kGE CEWhere

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 functionof 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 ( ~ 50F ),

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 andCooperative Research Centre for Greenhouse Accounting

Greenhouseworld – carbon balance

Redrawn from NASA's Earth Observatory andCooperative 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 LaboratoryFree Air Carbon dioxide Enrichment (FACE) experiments.

Wimovac

Plant in Wimovac model

Wimovac

1/2 scheme of Wimovac model

Wimovac

2/2 scheme of Wimovac model

GCM / MOSES MOSES I.

(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

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

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 2008-05-22 (1. revision for web pages at 2008-07-10)