The role of gravity in the greenhouse effect

There could be no planetary atmosphere without gravity, but gravity also plays a fundamental role in the greenhouse effect thereby determining surface temperatures. To see why this is the case lets imagine that gravity has somehow been switched off and the atmosphere is held in place on the earth by an infinitely thin membrane at height d. Let’s also assume that the atmosphere is 100% composed of CO2 absorbing IR in the 15 micron band.

Fig 1: Zero gravity CO2 atmosphere held in place by thin membrane over surface at temperature Ts

Fig 1: Zero gravity CO2 atmosphere held in place by thin membrane over surface at temperature Ts

The atmosphere will behave as a perfect gas of temperature Ts. The pressure will be P = RTs/d and CO2 will absorb all 15 micron IR from the surface while emitting exactly the same amount to space at the membrane. Viewed from afar the IR spectrum will appear to be a perfect black body at temperature Ts. There is no greenhouse effect at all. Effectively the atmosphere can be viewed as part of the surface. There would be no net  difference if the gas was replaced by Argon.

Conclusion: There can be no greenhouse effect without a gravitational field. CO2 has no greenhouse effect parallel to a gravitational field.

Now switch on gravity and remove the membrane. The atmosphere expands and a density/pressure gradient is setup as it quickly reaches hydrostatic equilibrium and the atmosphere extends upwards. The surface pressure equals the weight of the atmosphere per unit area – 15 psi or 101000 pascal falling exponentially with height approximately  as

P = P_0 \exp{-\frac{Mgz}{RT_s}}

which assumes constant T, which as we will see is not exactly what occurs.

Gravity generates an exponential pressure gradient

Fig 2: Gravity generates an exponential pressure gradient

The density of CO2 molecules now diminishes exponentially with height. Therefore the IR radiative flux emitted by CO2 is no longer homogenous because gravity has broken the symmetry. Each layer has a different emissivity that depends on the density of CO2 molecules in that layer. Despite this  radiative emission within a thin horizontal layer is still homogeneous in 2 dimensions and we call this ‘local thermodynamic equilibrium’ LTE for a given height h. However each height has a different emissivity ( or absorption) for 15 micron photons.

The net flux of radiation through the atmosphere from the surface at height h is then the integral of the (emission – absorption)  from all lower levels  minus the integral of the (emission – absorption) from all higher levels. There is no longer vertical thermodynamic equilibrium and temperature can vary with height.

Figure 1: Model schematic of radiation transfer from surface at 288K through 100m wide slices of atmosphere. Each slice is a grey  body absorbing and emitting IR. A lapse rate of 6.5K/km and a hydrostatic scale height of 8.6km is assumed.

Figure 3: Model schematic of radiation transfer from surface at 288K through 100m wide slices of atmosphere. Each slice is a grey body absorbing and emitting IR. A lapse rate of 6.5K/km and a hydrostatic scale height of 8.6km is assumed.

How does the flow of radiative energy through the atmosphere change the energy balance? Since density falls exponentially there exists an effective emission height for each wavelength above which >50% of IR photons escape to space.  I calculated this height for the 15 micron CO2 band using HITRAN cross-section data for 2 different concentrations of CO2 on earth..

Fig 5b: The CO2 emission height profile for 300ppm and for 600ppm smoothed with a resolution of 20 lines.

Fig 4: The CO2 emission height profile for 300ppm and for 600ppm smoothed with a resolution of 20 lines.

Without convection the atmosphere would reach a radiative equilibrium whereby at all heights below this an equal flux of radiation would flow. This can only be achieved by the surface warming up significantly. Well before this can happen convection starts and stabilizes the temperature profile of the troposphere at the adiabatic lapse rate.

\frac{DT}{DZ} = - \frac{g}{C_p}

Here again gravity plays the crucial role because at the adiabatic lapse rate there is a perfect balance matching  buoyancy against  gravity. Such stable atmospheric condition are  rare and this is what drives weather systems. Convection and the lapse rate both halt where the radiative transfer to thin upper layers stops and IR photons escape directly to space. This is  the tropopause.  Note that it is radiative transfer by GHGs through the troposphere that  drives convection towards the lapse rate. The energy to power this atmospheric heat engine comes from the sun radiating energy directly onto the surface.

Conclusion: You need greenhouse gasses to generate a lapse rate. You  need a lapse rate  for greenhouse effect to work because radiation to space from higher altitudes reduces net upwelling IR. Gravity sets the scale of the lapse rate.  (thanks tallbloke)

Blogger HockeySchtick and others (Stephen Wilde etc.) propose a purely gravitational/Mass theory of the atmospheric greenhouse effect seemingly independent of GHG. HockeySchtick writes  :

The “effective radiating level” or ERL of planetary atmospheres is located at the approximate center of mass of the atmosphere where the temperature is equal to the equilibrium temperature with the Sun.

He then  derives a formula for planetary temperature which works really quite well. However they all assume a pre-existing lapse rate generated only by gravity even in the absence of any greenhouse gasses. This is wrong because you need the sun’s energy plus both gravity and greenhouse gasses to power the convective heat engine maintaining the lapse rate. Radiative transfer of surface heat through the atmosphere tries to steepen the lapse rate towards radiative equilibrium. This instability drives convection (and evaporation on earth) resulting in the approximately observed adiabatic lapse rate. Gravity just defines the thermodynamic scale.

The centre of Mass of the atmosphere corresponds to a height with a pressure of half that of the surface pressure. This is also exactly where the number of CO2 molecules below and above are equal. Therefore you would expect this to approximately coincide with the effective emission height – but for a different reason. It is not the  gravitational energy that is ‘warming’  lower levels due to compression – like in a bicycle pump . It is because above this level the IR ‘fog’ clears and photons can escape freely to space. Greenhouse warming is a subtle effect ’caused’  both by gravity and GHGs  choking surface warming directly to space. You need both. A pure argon atmosphere would have no greenhouse effect and no real lapse rate.

How much warming results from  CO2 on earth and how does that change with increased concentration? I previously calculated these emission spectra for different CO2 concentrations.

Fig 2. Change in outgoing IR  spectra for a range of CO2 concentrations. Each increasing spectra has been offset by 5 mmW/m2sr-1cm-1 to better visualise the differences.

Fig 5. Change in outgoing IR spectra for a range of CO2 concentrations. Each increasing spectra has been offset by 5 mmW/m2sr-1cm-1 to better visualise the differences.

Resulting in a CO2 surface warming effect as follows

Fig 3: Surface temperature change induced by a gradual increase in CO2 concentrations from a starting temperature of 284K

Fig 6: Surface temperature change induced by a gradual increase in CO2 concentrations from a starting temperature of 284K

You can see how the surface temperature follows a T_{lim} \times (1 - \exp{CO_2}) . Direct CO2 forcing converges on a limiting GHE temperature at 100% concentration of about 11C for the 15 micron band. This is because the central  lines saturate , and it is only the smaller side lines that continue to grow with concentration increase. So called ‘runaway greenhouse effects’ are not caused by CO2 but depend on assumptions about H2O feedbacks for hotter climates like that on Venus due to higher solar radiation.

The way the greenhouse effect on earth works is not obvious.

Conclusions:

  1. There can be no greenhouse effect without gravity.
  2. Atmospheric pressure gradient is caused by gravity.
  3. The lapse rate scale is defined by gravity but is generated by convection.
  4. Convection is induced by Radiative transfer of heat through the atmosphere
  5. Radiative transfer is due to greenhouse gasses.
  6. There can be no greenhouse effect without greenhouse gases. Gravity alone will not work.
Posted in AGW, Climate Change, climate science, Physics, Science | Tagged , , | 65 Comments

Tides and the Jan 5th storm 2014

In this post I look at how exceptionally strong tides over the first few days of January 2014 could have played a role in the severe storm that hit the UK on the 5-6 January.

Meteociel.fr provide twice daily (midnight and midday) pressure maps of the polar regions which show how the polar Jet Stream changes rather well. The Atlantic storms last winter were all spawned in a region near off Nova Scotia where warm tropical air meets cold polar air creating instability. Did high spring tides play a role in triggering these storms? The video below shows an animation of the horizontal tractional forces acting on the Jet Stream as spring tides sweep through the Atlantic. Maximum spring tides were experienced 3-6 January which also led to coastal flooding on UK shores.

Early january saw the strongest tides of 2014. The figure below shows the relative magnitude of the combined solar/lunar gravitational tides. At the equinoxes spring tides at new moon and full moon  tend to be roughly equal, whereas in winter it is new moon tides that dominate. The chart below was prepared by Roberto Madrigali
TIDES-STORM-AND-RAIN2014

If we look in more detail at the January storm we see that large tides sweeping across the Atlantic may have affected the unstable convergence of warm tropical air and cold polar air east of Canada. This was where the very low pressure January storm was spawned.

frame51

A tongue of warm air enters from the Gulf
frame62
Low pressure begins to form as air rises
frame79
A very intense low is forming
frame85

This low merges with a pre-existing low pressure system
frame102

The storm is born and moves westward following the Jet Stream towards the UK.

frame114

The storm hits the UK in coincidence with high spring tides along western coasts. Severe damage and coastal flooding results.  The Met Office describe the winter storms

 5 January

In early January, the focus of concern again shifted to coastal flooding, particularly affecting exposed locations in South West England and South Wales. A large area of low pressure in the north Atlantic, driving strong winds and coinciding with high spring tides resulted in exceptionally high waves affecting coastal communities along the South Coast of England and west coast of Wales. In estuaries, the potential flood risk was exacerbated by high runoff from rivers.

Synoptic situation at 1200 UTC 5 January 2014, with a deep area of low pressure in mid-Atlantic driving very large waves towards western and southern coasts.

Met-office-map

The position and undulations of the Jet Stream determine the winter weather over Western Europe and the US. I estimate the horizontal tidal forces acting on on the Jet flow can reach the equivalent of about 5 metric tons per km and tweak the flow every 12 hours as each tidal bulge passes through. Is this enough to trigger winter storms?

Posted in climate science, Physics, Science | Tagged , , | 6 Comments

Something Fishy in the air?

I have noticed that wind power delivered to the Grid is always less than 6 GW, no matter how windy it gets. This was clearly demonstrated  on October 21st when wind speeds across the country reached around 50 mph for most of the day. The  wind output was simply bumping along continuously below 6 GW. Something fishy is going on – What is it?

Winds-21Oct

Power-21Oct

The heart of the problem becomes clearer once  you start looking at  the constraint payments made to  wind farms under the Grid’s ‘balancing mechanism’ (see: ref.org.uk). Large wind farms were paid a staggering £2 million on 21st October to disconnect from the Grid. These payments are priced at over £90 for each MWh of ‘generated’ wind energy which is then simply thrown away !

REF

Nor is this an isolated incident. Over the past year constraint payments have been increasing continuously as more capacity has been added. We can see similar periods over weekends last August and April. All these hidden costs for wind are passed on to the consumer through their monthly bills.

6GW-limit

The UK installed wind capacity is 11.2 GW but the effective load capacity on a perfect day of wind is apparently only around a maximum of 60 %.  The Grid simply cannot handle more than 6GW of instantaneous wind power, whereas it has no problem with 30GW of Coal or Gas. I think the problem lies in the Grid topology which is based on large power lines to central generators. The high voltage connections to dispersed wind farms cannot handle large power, and this is made worse by unpredictability. There is really no point adding any new wind capacity until the underlying infrastructure is upgraded. But how much would it cost to completely redesign the National Grid, and is it really worth it when we could simply build large modern gas and nuclear plants compatible with the existing Grid?

This message of course is not what the green Wind lobby want to hear. They want to instal as much as possible because they can’t lose. They get paid whatever happens reaping handsome profits from ‘phantom’ energy. Why are they not also charged for the extra expense to upgrade the Grid?

Finally lets look at the headline wind energy statistics that are often quoted. Renewable Energy UK quote that the UK fleet of wind farms generate 27,263,077 MWh of Energy each year. This is based on DECCs own DUKES review of on-shore and off-shore capacity factors (27.82%). So let’s now look at the actual electrical energy supplied to the Grid over a full year of operations. I have integrated the total energy supplied to the grid over the last 13 months based on hourly monitoring.

Power delivery by Fuel type to meet Peak demand every day since September 2013. Weekdays peak demand occurs around 18:00 and fat weekdays around 20:00.

Power delivery by Fuel type to meet Peak demand every day since September 2013. Weekdays peak demand occurs around 18:00 and at weekdays around 20:00.

The total electrical energy  supplied to the Grid by Wind farms between  1st September 2013 and 1st October 2014 was 22,833,000 MWh. The total energy generated in a 12 month period September to September was 20,217,523,383 MWh.  This demonstrates that up to 26% of the reported energy paid out to wind farms is simply  thrown away. This fact is well hidden from public scrutiny because we all pay for such wastage through our electricity bills. Wind drives energy prices up. DECC and the Wind industry would prefer you not to know because it undermines their economic case for green energy.

Similarly the real ‘savings’ of CO2 emissions from wind were 3 million tonnes less than the official DECC figures of 11.7 million tonnes, and which also ignores the  increased emissions of Gas plants to balance Wind.  The real capacity load factor of Wind Farms was 20.6% and not the quoted 28.7%, once you take into account the discarded excess wind energy.

The real costs of Wind electricity should  be revised upwards by  35%. Only if and when the Grid gets upgraded to handle multiple power lines to such a dispersed energy source as wind can the current DECC and wind industry figures be believed. The costs of upgrading the Grid are enormous and must be factored into the real costs of expanding wind energy. Until the Grid is upgraded  it makes hardly any sense at all to add any new UK wind capacity. That is unless you are a wind operator with  guaranteed 20% return on investment underwritten by the UK government.

Posted in Energy, renewables, Science, Technology, wind farms | Tagged | 35 Comments