KVA Talar till Barnen

Kungliga Vetenskapsakademien KVA har givit ut skriften Vetenskapen säger: Om Klimatet författad av bland andra Deliang Chen, professor i fysikalisk meteorologi vid Göteborgs universitet, med syfte att upplysa svenska folket: 

• Syftet är att nå ut med vetenskapssamhällets samlade syn på en fråga som berör oss alla.
• Att forskningen på senare år nått fram till en samsyn om klimatförändringarna tror Delian Chen inte alltid att allmänheten är fullt medveten om. 
• Istället sprids ibland missuppfattningar om att det fortfarande råder oenighet inom vetenskapssamhället om hur det faktiskt förhåller sig.
• Det är viktigt att känna till att det kapitlet är avslutat nu. 
• Det är också viktigt att veta att det inte är för sent att agera och att allt vi gör påverkar klimatet. Ibland hör man att det inte spelar någon roll vad vi gör i Sverige, men det är inte sant. 
• Varje ton koldioxid vi släpper ut har en påverkan.

Skriften stödjer detta budskap på följande sätt: 

1. Det är obestridligt att människans påverkan, främst genom utsläpp av växthusgaser, har orsakat en global uppvärmning och andra förändringar i klimatsystemet.
2. Klimatsystemet tar emot energi från solen genom att fånga upp solstrålningen, och blir av med nästan lika mycket energi igen genom att sända ut infraröd strålning (värmestrålning) till rymden. För närvarande är den infraröda utstrålningen runt 0,8 W/m2 mindre än solinstrålningen. Det är denna strålningsobalans som leder till den pågående globala uppvärmningen.
3. De senaste 160 åren har den globala medeltemperaturen stigit med 1,1 grader. Det finns ingen annan vetenskapligt förankrad förklaring till detta än de ökande halterna av växthusgaser, främst koldioxid.
4. Ofta beskrivs växthuseffekten, väldigt förenklat, som ett växthus där solstrålning lätt kan ta sig in medan värmen inne i växthuset har svårt att ta sig ut igen. Det medför en ökad temperatur i växthuset, se följande förklarande figur:

 

Kommentar: 

1. Att påstå att något är obestridligt är inte ett vetenskapligs argument. I vetenskap kan allt bestridas och ändras om nya fakta tillkommer, till skillnad från religion eller juridik.
2. Noggrannheten i mätning av in och utstrålning är inte tillräcklig för att avgöra en skillnad på 0.8 W/m2 när maximal instrålning är ca 1366 W/m2. 
3. Noggrannheten av mätning av global medeltemperatur är inte mindre än 1 C (avläs en typisk termometer) varför påståendet om 1.1 C höjning saknar mening. Höjningen kan lika gärna vara 0.5 C eller 0.1 C dvs utan signifikans. Att säga att koldioxiden är orsaken till den eventuella höjningen, eftersom man inte vet någon annan förklaring, är inte heller något vetenskapligt argument eftersom säkerheten i påståendet verkat öka ju mindre man vet. Och vad är egentligen innebörden av global medeltemperatur?
4. Bilden som ser ut som en barnteckning med sin eviga sol i övre hörnet ger en helt felaktig bild av jorden + atmosfären som ett växthus med tak som verkar reflektera (återstråla) både högfrekvent solstrålning och lågfrekvent infraröd strålning från jorden. Varför ger KVA en fysikaliskt helt felaktig missvisande beskrivning av den s k växthuseffekten? 

Sammantaget ger skriften intryck av att ha skrivits för förskolan. Varför riktar sig KVA till barnen med sin ovetenskapliga skrämselpropaganda? Jag har bett KVA om svar, som kommer att rapporteras.

Här kan vi jämföra KVAs teckning med en riktig barnteckning som illustrerar Solen, det Svenska Samhället samt Hotet från Koldioxidutsläpp:

Back Radiation: Algebraic Fiction or Physical Reality? 2

This is a continuation of the previous post with focus on the unphysical nature of back radiation as expressed in Schwarzschild's two-stream model of radiative heat transfer taking the following form in a setting of a horisontal atmospheric layer connecting the Earth surface to outer space with $z$ a vertical coordinate representing optical distance:

• $\frac{dU}{dz}=-U+B,$
• $\frac{dD}{dz}= D-B,$

where $U$ is upwelling radiation and $D$ is downwelling radiation and $B(T)$ is upward/downward emission of radiation according Stefan-Boltzmann's law with $T$ temperature depending on $z$. Subtracting the equations, we have

• $\frac{d(D-U)}{dz}=D-2B+U.$  (0)

We see a balance at a certain level $z$ between U as incoming radiation from below, D as incoming radiation from above and -2B as emission upward and downward. Discretizing $z$ into discrete levels/nodes $z_i=i*h$ with $h$ a mesh size and $i=0,1,2...$, the balance of upward and downward radiation involves  

• $B_{i+1}-2B_i+B_{i-1}$    (1)

with $B_i=B(T(z_i))$, if we set $B_{i+1}=D(z_{i+1})$ and $B_{i-1}=U(z_{i-1})$. 

We will now compare (0)-(1) with the following discretised heat equation for a temperature $T(z,t)$ with $t$ a time coordinate:

• $dT_i/dt = (T_{i+1}-2T_i+T_{i-1})*\frac{1}{pow(h,2)}$   (2)

where $T_i=T(z_i,t)$, which is a discretisation of $\frac{\partial T}{\partial t}=\frac{\partial^2 T}{\partial x^2}$. We know that the heat equation is a stable physical model subject to perturbations $p$ of (2) of the form

• $dT_i/dt = (T_{i+1}-2T_i+T_{i-1})*\frac{1}{pow(h,2)}+p$.    (3)

while perturbations $P$ of (1) would have the form

• $B_{i+1}-2B_i+B_{i-1}+P$.    (4)

We see that introducing a perturbation $P$ of the form (4) in (2) would correspond to a perturbation $p=\frac{P}{pow(h,2)}$ which would be big since $h$ is small. We thus see a fundamental difference as concerns stability between a heat equation of the form (2), which is stable, and a two-stream model of radiative transfer of the form (0). 

Note that the idea of two-stream radiative heat transfer with upwelling/outgoing (longwave) radiation OLR and downwelling (long wave) DLR is firmly implanted in the discussion of the GHE through the two-stream Schwarzschild model. In particular, the existence of DLR is supposedly being demonstrated experimentally with the help of a pyrgeometer, which however is a ghost detector. 

Back Radiation: Algebraic Fiction or Physical Reality?

The physics of a "greenhouse effect" (GHE) resulting from "back radiation" from a colder atmosphere with "greenhouse gases" (GH-gases) to a warmer Earth surface, is still a subject of active discussion. A recent contribution is Verification of the Greenhouse Effect in the Laboratory by Hermann Harde and Michael Schnell published in Science of Climate Change, presenting the following main points:

• The impact of the different greenhouse gases (GH-gases) on our climate is not really well understood and even under experts this repeatedly leads to doubts about its existence and its influence on our climate.
• This article summarizes the theoretical background of the GHE and presents first quantitative measurements of this effect with an advanced experimental set-up. 
• For our studies we use an experimental set-up, which consists of two plates in a closed housing, one plate heated to 30 C, the other cooled to -11.4 C. 
• ...the set-up...uses a heated plate as radiation source and simultaneously as sensitive detector for the back-radiation from GH-gases. We measure the increasing temperature of this plate or, alternatively at stabilized temperature, the energy saving due to the back-radiation.
• We measure the additional warming of a pre-heated plate due to back-radiation of the greenhouse gases carbon dioxide, methane and nitrous oxide as a function of the gas concentration, and we derive from the observed warming the radiative forcing of these gases.
• Our studies also demonstrate that contrary to the often-misinterpreted 2nd law of thermodynamics a warmer body can further be heated by absorbing the radiation from a colder body, here the radiation from the cooled plate and a GH-gas.
• In addition and independent of the temperature measurements is the back radiations of the GH gases directly recorded as reduced electrical heating of the upper plate.
• These measurements clearly demonstrate that contrary to the often misinterpreted 2nd law of thermodynamics a warmer body can further be heated by absorbing the radiation from a colder body, here the radiation from the cooled plate and a GH-gas.
• The presented measurements and calculations clearly confirm the existence of an atmospheric GHE, but they also demonstrate the only small impact on global warming with increasing GH-gas concentrations, which in any way are apperently dominated by natural emissions. So, there is no reason for panic and climate emergency.

The article claims to give the first verification of GHE in a laboratory setting with measurements supported by theory in the form of Schwarzschild's two-stream equation for radiative heat transfer. GHE is viewed to be an effect of back radiation with a warmer plate absorbing radiation from a colder plate, yet without violation of the 2nd law of thermodynamics. 

I have agued (see also video) that back radiation with two-way radiative heat transfer is unphysical and should be replaced by one-way transfer from warm to cold, with recent detailed follow up by Joseph Reynen. The presence of back radiation is directly connected to Schwarzschild two-stream model, which is described as follows in standard treatise Atmospheric Radiation: Theoretical Basis by Goody and Yung: 

• While it sets the pattern of the formalism used in radiative transfer problems, its physical content is very slight.
• The Schwarzschild-Schuster approximation is now of historical interest only.

The key issue concerning back radiation and Schwarzschild's two-stream equation is as follows: Stefan-Boltzmann's equation (SB) for one-way radiative heat transfer $Q$ between two bodies $B_1$ and $B_2$ of temperatures $T_1$ and $T_2$ with $T_2>T_1$ takes the form

• $Q =\epsilon\sigma (T_2^4-T_1^4)$      (1)

with $\sigma$ Stefan-Boltzmann's constant and $0<\epsilon \le1$ a coefficient depending on the nature of the bodies with $\epsilon =1$ for black bodies. Algebraically the SB equation can formally be written 

•  $Q = \epsilon\sigma T_2^4 - \epsilon\sigma T_1^4$    (2)

expressing two-way transfer with $\epsilon\sigma T_2^4$ heat transfer from $B_2$ to $B_1$ and $\epsilon\sigma T_1^4$ heat transfer from $B_1$ to $B_2$.  We see that (1) expresses $Q$ as net transfer from warm to cold, which in (2) is formally written as the difference between two gross transfers back and forth between warm and cold. 

Implicit in (2) is Kirchhoff's Law expressing that absorptivity is equal to emissivity since in (2) the coefficient $\epsilon$ has both the role of emissivity and absorptivity depending on the interpretation of (2) as both heat balance for $B_1$ absorbing heat from $B_2$ while emitting heat to $B_2$, and heat balance for $B_2$ absorbing heat from $B_1$ while emitting heat to $B_1$. 

Algebraically (1) and (2) are formally the same but the physics is different with one-way net heat transfer in (1) and two-way difference of gross heat transfer in (2). Now comes the key observation: From stability point of view (1) and (2) are not the same: A percentagewise small perturbation of net transfer will result in a small change of net transfer, while a small percentagewise perturbation of gross flow may result in a big perturbation of net transfer. 

One can now argue that physics must be stable to persist over time and so two-way radiative heat transfer as expressed by Schwarzschild's two-stream equations is unphysical and that is also what Goody and Yung says. 

It thus remains to find a mathematical model for one-way radiative heat transfer and here the stack model studied by Reynen is a first step. In a next post I will exhibit the crucial aspect of stability in a simple example comparing from stability point of view Schwarzschild's unphysical two-stream equations with a physical heat equation.