Another simple summary of the cause of global warming

Posted: November 11, 2010 by tallbloke in solar system dynamics

Scientist .of .Doom says:
You don’t seem to have a handle on the type of complexity we are dealing with here. Hint, check out where the heat comes from.

It only seems to be complex from the point of view of proponents of the co2 driven global warming hypothesis because they have to do complex contortions to try to make it seem like the energy is coming from the atmosphere and heating the ocean.

It’s actually pretty simple and the other way round. the energy is coming from the sun, into the ocean which then emits energy into the atmosphere which causes the atmosphere to warm.

During the global warming period ~1980-2003 cloud cover was reduced, according to ISCCP data, and the sun was well above average activity levels, as the sunspot number records show. There was no tropospheric hotspot as predicted by the co2 driven model, as the radiosonde records show, so the extra heat must be due to excess energy coming from the ocean. This thesis is backed up by the OHC records and the SST records and the fact that changes in atmospheric temperature lag behind changes in SST.

All the empirical evidence points to the sun and lowered albedo being responsible for global warming.

That’s where the extra energy came from.

I don’t know how to make it any clearer than that.

Here is tropical cloud cover vs air temperature 1983-2008
isccp-temp

Comments
  1. Bryan says:

    I followed your dialog on Science of Doom, however you must be disappointed by SoDs inability to comprehend your points.

    It seems that anything that contradicts his AGW theory is simply ignored.

    I have asked him to comment on the experiment by Wood in your thread “John Nicol: Greenhouse Effect re-examined” and in SoDs own site.

    He refuses to engage.

    Further I have asked him to solve a simple equation on heat transfer – he refuses.

    He is preoccupied by Gerlich & Tscheuschner.

    This is shown by the number of oblique attacks he makes on them.

    I think he fears that they may be correct.

    This is indicated by a large number of posts where apparently he shows how heat moves from a colder to a hotter body despite the second law.

    I describe SoD as “he” because “he” or “she” or “them” refuse to give the slightest details of who they are.
    Most sites(like you own) give some details of the proprietors.
    Its not very brave to mount attacks on named individuals like Gerlich & Tscheuschner from behind a clock of anonymity.

  2. tallbloke says:

    Hi Bryan,
    The more S.o.D. talks around the substantive issue istead of dealing with it directly, and the more S.o.D. pretends not to get the point, the more I get the opportunity to repeat the facts over and over again in different ways.

  3. Dear “Magister Ludi” Remember the original Magister Ludi played with a Glass Bead Game, with beads of all colors of the rainbow. Thus energy it is ALL THE SPECTRUM and its interactions with the different media.
    I know you know that, I just remark it for the uninitiated, who must not forget electric, magnetic and gravity interactions. (and our friend Vukcevic, who is currently involved in melting the north pole with his induction furnace 🙂 )

  4. j ferguson says:

    Glasperlenspiel. I always wondered what the book was about. Maybe I read it when I was too young. Thank you for reminding me of it.

    john

  5. j ferguson says:
    November 11, 2010 at 4:10 pm
    It was all about the Unified Field traditional symbols “speak” (which, BTW., are actual blueprints of how forces act on nature)
    http://www.scribd.com/doc/42018959/Unified-Field-Explained-9

    [for further discussion visit https://tallbloke.wordpress.com/2010/10/30/adolfo-giurfa-unified-field-explained/ ]

  6. Tenuc says:

    Scientist .of .Doom says:
    “You don’t seem to have a handle on the type of complexity we are dealing with here. Hint, check out where the heat comes from.”

    LOL… :)) SoD sounds like a member of a strange cult trying to defend the “faith”. He is keen to push the evangelical message of CAGW, but seems unable to listen to evidence which contradicts his belief.

    Like the rest of the cult followers, he seems only willing to consider thermal energy being important to climate, rather than the full spectrum of energy which impacts climate systems. Vuk’s brilliant discovery of the link between magnetic field and Arctic temperature is a good example of this:-

    http://www.vukcevic.talktalk.net/NFC1.htm

    Here’s my take on how our marvellous planet maintains its energy balance sufficiently well to keep the biosphere happy (except for ‘black swan’ events like ice-ages)…

    It has been known since the 1960’s that climate acts very much like a forced pendulum, and exhibits deterministic chaos. This is responsible for the many different quasi-cycles which can be observed which happen over different time periods. It also leads to an effect called maximum entropy production (MEP), which means that a complex non-linear system will select the trajectory (or assemblage of trajectories) out of those available which maximise the dissipation of energy.

    So as climate warms due to the myriad of observed over-lapping quasi-cycles, the total system changes to become more efficient at losing energy (mainly through turbulence and changes to boundary conditions). The reverse happens when cooling occurs, but it is important to remember that there will be over-shoot (like the 1998 temperature peak), and undershoot, as this dynamic system seeks to find a balance.

    Current climate science fails to recognise how this complex, highly interlinked turbulent system oscillates around it’s strange attractor(s) and chooses to treat it as if it were a simple linear one instead. It makes too many invalid assumptions and makes unfalsifiable conjectures. Because of this situation it will continue flounder, with no real worthwhile progress made.

  7. tallbloke says:

    “I just remark it for the uninitiated, who must not forget electric, magnetic and gravity interactions”

    Here you go Adolfo, get your teeth into this:

    Click to access Atmos_060302.pdf

    Atmospheric Ionization and Clouds as Links Between Solar Activity
    and Climate
    Brian A. Tinsley1 and Fangqun Yu2
    1University of Texas at Dallas, Richardson, TX (Tinsley@UTDallas.edu)
    2State University of New York at Albany, NY (yfq@asrc.cestm.albany.edu)
    Observations of changes in cloud properties that correlate with the 11-year cycles in space
    particle fluxes are reviewed. The correlations can be understood in terms of one or both of
    two microphysical processes; ion mediated nucleation (IMN) and electroscavenging. IMN
    relies on the presence of ions to provide the condensation sites for sulfuric acid and water
    vapors to produce new aerosol particles, which, under certain conditions, might grow into
    sizes that can be activated as cloud condensation nuclei (CCN). Electroscavenging depends
    on the buildup of space charge at the tops and bottoms of clouds as the vertical current
    density (Jz) in the global electric circuit encounters the increased electrical resistivity of the
    clouds. Space charge is electrostatic charge density due to a difference between the
    concentrations of positive and negative ions. Calculations indicate that this electrostatic
    charge on aerosol particles can enhance the rate at which they are scavenged by cloud
    droplets. The aerosol particles for which scavenging is important are those that act as insitu
    ice forming nuclei (IFN) and CCN. Both IMN and electroscavenging depend on the
    presence of atmospheric ions that are generated, in regions of the atmosphere relevant for
    effects on clouds, by galactic cosmic rays (GCR). The space charge depends, in addition,
    on the magnitude of Jz. The magnitude of Jz depends not only on the GCR flux, but also on
    the fluxes of MeV electrons from the radiation belts, and the ionospheric potentials
    generated by the solar wind, that can vary independently of the GCR flux. The roles of
    GCR and Jz in cloud processes are the speculative links in a series connecting solar
    activity, the solar wind, GCR, clouds and climate. This article reviews the correlated cloud
    variations and the two mechanisms proposed as possible explanations for these links.

  8. tallbloke says:

    And this from Palle et al

    Click to access palle1266.pdf

    Our simulations suggest a surface average
    forcing at the top of the atmosphere, coming only from
    changes in the albedo from 1994/1995 to 1999/2001, of
    2.7+/-1.4 W/m2 (Palle et al., 2003), while observations
    give 7.5+/-2.4 W/m2. The Intergovernmental Panel on
    Climate Change (IPCC, 1995) argues for a comparably
    sized 2.4 W/m2 increase in forcing, which is attributed to
    greenhouse gas forcing since 1850.
    Still,whether the Earth’s reflectance varies with the
    solar cycle is a matter of controversy, but regardless of
    its origin, if it were real, such a change in the net sunlight
    reaching the Earth would be very significant for the
    climate system.

  9. David says:

    Thank you for the simple post and graphic showing tropical clouds and global temperatures. I would like to see the graph extended to current. Can anyone here discuss and help quantify the following if the basic premise is correct? Can high thin clouds cause a short term warming but a long term cooling due to reduced SWR impacting the oceans?” If the answer is in the affirmative, can it be quantified?

    Is the orthodox view that the increased residence time of LWIR within the atmosphere due to increased GHG overwhelms the decrease in SWR reaching the ocean surface when compared on a WM/2 basis, and somehow this increased atmosphere temperature and LWIR somehow warms the ocean, creating an additional warming over a decade or longer lag effect and that feedbacks such as high clouds amplify this warming further?

    On the other hand your presentation appears more intuitive to me. However I have seen neither scenario quantified on a WM/2 basis along with an analysis of the radiative spectrum effects that appear critical to me. So, (please forget the inaccuracy of my any numbers, they are illustrative only) the high thin clouds that “climate scientist” consider to have a net warming on the planet, atmosphere, earth and ocean, change the incoming TSI from what spectrum and WM/2 to what spectrum and WM/2 at the OCEAN surface, and further how does this DECREASE in SWR affect the ocean LONG TERM even though there is a rapid increase in atmospheric temperature due to LWIR scattering all around before finally leaving?

    My questions are awkwardly formatted because I am not a scientist so please understand the poorly worded structure. Perhaps a more simple assertion would be something like this. High thin clouds which produce an ocean surface REDUCTION of 5 WM2 SWR in these spectral WL, has greater long term cooling of the planets heat content then the increase in LWIR in the atmosphere which achieves a temporarily higher atmospheric radiative balance until the oceans radiative balance equalizes to a cooler temperature, which then reduces the LWIR from the surface, counteracting the temperature rise from the increased residence time of LWIR due to increased GHGs.

    Or to really shorten the assertion” Over X time a reduction of 5 WM/2 of SWR at the ocean surface negates 10 WM/2 increase in LWIR in the atmosphere. (Again the numbers are merely illustrative.)

    Now I know there are many other factors, the ones you mention, an increase in all clouds, the speeding of the hydrologic cycle, the increased biomass which has a CO2 reducing lag effect via absorbing more CO2 as the biomass increases, latitude shifts in jet streams and therefore cloud cover, etc, but the different long term effects of changes in the radiative spectrum is what I am trying to understand and I think the oceans and how they absorb radiation have everything to do with this.

    Or to really simplfy my question, is it valid to paraphrase “A SW photon in the ocean is worth two IR photons in the atmosphere?

    Thanks in advance for any feed back and apologies for the length, but due to my non science background I am not confident in either my assertions or the formatting of my questions.

  10. tallbloke says:

    Hi David,
    great post, you have opened up the issue nicely.
    The calculations I did show that the excess energy which must have entered the oceans in the 1993-2003 decade to account for the steric sea level rise would have required a 4W/m^2 forcing at the surface. This is pretty much in line with what Palle et al found, and is greater than the co2 forcing in the atmosphere.

    Those extra watts raised SST by 0.3C and the OHC by around 8×10^23J in the top 700m.

    If this was due to reduced cloud cover, and the low cloud cover varies fairly consistently with the solar cycle as Tinsley and Yu confirmed, then the longer term trend in tropical cloud cover shown by the ISCCP data means high cloud cover fell, but temperatures increased due to the ocean moving the atosphere to a higher temperature equilibrium, and the larger amount of solar energy absorbed directly in the atmosphere.

    The co2 driven model has the whole thing exactly backasswards.

  11. gnomish says:

    Aye. SciD has a co2 fetish that won’t let go.
    Remember the term ‘pretzel logic’?
    I’ve previously posted there the detailed calculations of heat capacities of the various components of the atmosphere and proven that h2o in any given volume of it carries more than 50 thousand times the heat. Hadley cells are massive convection engines – and poor old SciD won’t touch convection. The atmossphere + ocean makes a heat pump. Radiation physics is inadequate to explain the physics of that. Radiation physics really has no significance except at the boiling end and the infinite heat sink of space end.
    It’s modern phlogiston theory, T.B.
    He’s got religion – and that’s not something that can be treated with reason. In fact, it is inappropriate to attempt to apply that remedy – it can not work where it’s not a valid currency for his vending machine.
    Facts are facts. Dan Pearly thought sweet reason could prevail where it wan’t acceptable currency. Watch that vid to see what it takes for a liberal to become apostate. It’s a great lesson to learn and can save one so much misdirected effort and deserved frustration.
    Your’e right. it’s simple. You just have to know what matters. For some it’s the pride of being right. For others it’s the vanity of appearing authoritative.
    Repetition is incantation of a magickal thinker. He’s lost.

  12. gnomish says:
    November 12, 2010 at 4:58 pm
    What you don’t see also exists:

    Since Earth is electrically charged, it maintains an electric field at its surface of between 50 and 200 volts per meter. In other words, for every meter of altitude the voltage increases by that measure.
    Electromagnetic fields beneath thunderstorms increase to 10,000 volts per meter because the storms and the Earth act like the plates of a capacitor, storing electrical energy from the surrounding environment. A “wind” of charged particles blows toward the developing storm, which could be construed as an electric current flowing into the base of the clouds. The surrounding air is pulled along with the current flow, creating powerful updrafts that can occasionally rise into the stratosphere

    http://www.thunderbolts.info/tpod/2010/arch10/101111capacitors.htm
    Read also:
    http://www.scribd.com/doc/42018959/Unified-Field-Explained-9

    Adolfo Giurfa: Unified Field explained

  13. David says:

    Response to tallbloke says:
    November 12, 2010 at 2:12 pm

    “The calculations I did show that the excess energy which must have entered the oceans in the 1993-2003 decade to account for the steric sea level rise would have required a 4W/m^2 forcing at the surface. This is pretty much in line with what Palle et al found, and is greater than the co2 forcing in the atmosphere.”

    “Those extra watts raised SST by 0.3C and the OHC by around 8×10^23J in the top 700m. If this was due to reduced cloud cover, and the low cloud cover varies fairly consistently with the solar cycle as Tinsley and Yu confirmed, then the longer term trend in tropical cloud cover shown by the ISCCP data means high cloud cover fell, but temperatures increased due to the ocean moving the atmosphere to a higher temperature equilibrium, and the larger amount of solar energy absorbed directly in the atmosphere.”

    Thank you, and this further clarifies my thinking, but (there is always a but) several more questions come to mind…
    Has the IPCC acknowledged the veracity of the change in cloud cover over this period and explained its cogency to their view?

    Certainly the IPCC must account for the different effects on ocean warming of various WL from IR to UV. They cannot consider only the WM/2 entering the atmosphere, and not the various absorption depths and ocean residence times of different SW insolation.
    What is their take on this? Is the limited inability of LWIR to heat the oceans accepted?

    Can this be tested in a large pool for instance; specifically in regard to high clouds we must know the albedo effect on tropical TSI as well as any change in the spectrum as it reaches the ocean surface as this should be easy to measure? Knowing this could we not test the warming effect of these two different surface insolation levels (one with no clouds, one with high clouds) in a controlled experiment? Could we not also compare this with increased LWIR induced by additional CO2 and verify the water warming potential of CO2 as well as changes in TSI?

    I believe NASA has a 40’ plus deep pool used for their astronaut program. I know this cannot test the real world ocean effects due to different level of penetration of various SW insolation beyond the pool depth, currents, difficulty in isolating the pool from outside conduction contamination, etc, yet if some of the different effects in a controlled environment were realized it could may some clarity to the debate, or does the IPCC think this is all understood and accounted for in their models?

  14. David says:

    I am long winded due to my limiited recent two years of very part time research into the CAGW issue and my non science background. What I am hoping science can quantify with real numbers is this paraphrased assertion, “A SW photon in the ocean is worth two IR photons in the atmosphere?

  15. tallbloke says:

    Putting together the ISCCP data from all the different weather satellites was not an easy job, and there are difficulties and problems with the process. However I see no fundamental reason why we should doubt the main direction of the results, which are supported by other methods such as Palle et al’s Earthshine Project.

    Proponents of the AGW theory have tried to cast doubt on evidence which conflicts with their hypothesis. ISCCP data, radiosonde data too. I think the radiosonde data is probably ok though, otherwise we wouldn’t see such a neat correlation between specific humidity at the altitude of the tropopause, and solar activity levels.

    Practical experiments are difficult, the small difference to temperature made by slight changes in the fluxes of various WL’s are hard to measure ‘in the wild’ and tanks have problems of heat conduction through their sides.

    Keep researching!

  16. David says:

    Thanks, and I understand the problems with control, however a large deep indoor, inground pool should be somewhat isolated, and at the very least pure LWIR could be tested verses pure SW radiation where the WM/2 influx is the same. (When I am elected president I will have this done) (-;

  17. tallbloke says:

    Hi David,
    it would have to be a deep pool, SW penetrates over 100m!
    But the other problem is that the question of the mixing down of heat from the surface by eddy currents couldn’t be adequately settled in a limited size of tank.

    Have you read the realclimate ‘experiment’ done to try to validate Minnetts hypothesis in the open ocean?

    http://www.realclimate.org/index.php/archives/2006/09/why-greenhouse-gases-heat-the-ocean/

  18. E.M.Smith says:

    FWIW, I got to do a trivial “experiment” along the lines of an “IR in the air vs a SW in the water” on my recent trip to Florida…

    Along the way I stopped to have a “bath” in the Gulf. Wading into the water was an enlightening experience. The air temperatures were a reasonably warm about 70F or so. The water at the surface was cool / a little cold to the skin. Where the sun was on my skin was quite warm. The shade not so much. But that top of the water caused “Goose Bumps”. Why? A modest wind (10 mph?) blowing ashore evaporating water. As I waded out, I discovered a Very Odd Thing.

    My feet were quite warm.

    The sunshine was making it through the (modestly turbulent and a bit silty) top meter and into the darkish mud-sand at the bottom and warming it very nicely.

    Between the mud and the surface the water was of intermediate temperature.

    This effect continued to my limit of immersion (which was about my armpits…) where I finished cleaning off 2 days of road time, dunked under the cool top layer, and then headed back to shore.

    The point?

    1) Measuring Sea Surface Temperature doesn’t tell you much about the heat gain of a body of water.

    2) Sea Surface Temperature tells you a great deal about sea surface conditions such as wind and humidity.

    3) Sunshine acts in large part at some depth. The clearer the water, the deeper. And it can be very deep.

    4) The deep effects are significantly decoupled from the surface effects.

    5) Nothing beats a direct observation of the conditions of the data collection space…

    6) As near as I can tell, the CO2 advocates ignore things like the tendency for the perimeter of water bodies to have the bottom warm a great deal under solar heating while the surface does not. They just look at SST and call it gospel.

    So much from one ‘wade in the pool’…

    Oh, and don’t forget that SW radiation has higher energy per photon than IR. So depending on how high you make that wavelength, you automatically get more energy in the SW than the LW…

  19. tallbloke says:

    Hi E.M. thanks for dropping by.
    Indeed solar shortwave penetrates up to 100 metres or more in clear water, though most of the energy is absorbed in the top ten metres or so.

    My logical deduction from the fact that the sun spend a large part of the C20th at above ocean equilibrium levels of activity is that some of the excess energy must somehow get taken further down into the ocean by various tidal, meridional and other natural overturning processes, otherwie we’d have observed bigger changes in shape of the temperature curve from the bottom of the well mixed layer down to the thermocline. However, the depth the thermocline forms at varies tremendously over the oceans and seasons anyway, so the best we can say is the ocean is highly mobile and active in the way it moves energy around.

    I’m trying to think of ways we can determine the sorts of timescales and magnitudes the ocean sequesters and releases energy at, because that may have a good deal of explanatory power regarding multi-decadal warming and cooling of surface temperatures.

    In general, the sunspot number integrated at a departure from the equilibrium value, which aslo happens to coincide with the long term average sunspot number as far as I can tell, seems to be a reasonable proxy for ocean heat content.

  20. NOAA agrees – the oceans heat the atmosphere, not the other way around

    Click to access CompoSardeshmukh2007a.pdf

  21. Also, even if increased GHGs could heat the oceans, ocean heat capacity is so immense that there would be no significant change in ocean temperature

    http://hockeyschtick.blogspot.com/2010/08/why-greenhouse-gases-wont-heat-oceans.html

  22. tallbloke says:

    Heh, from the link at NOAA:

    “the degree to which the oceans themselves have recently warmed due
    to increased GHG, other anthropogenic, natural solar and volcanic forcings, or internal multi-decadal climate variations is a matter of active investigation (Stott et al. 2006; Knutson et al. 2006; Pierce et al. 2006). Reliable assessments of these contributing factors depend critically on reliable estimations of natural climate variability, either from the observational record or from coupled climate model simulations without anthropogenic forcings.”

    Active investigation eh? settled science my ar$e.

  23. tallbloke says:

    “Also, even if increased GHGs could heat the oceans, ocean heat capacity is so immense that there would be no significant change in ocean temperature.”

    Over on the realclimate experiment thread, Frank reckons he shows that the co2 effect amounts to 0.008C for a doubling.

    So much for “heat in the pipeline”.

  24. David says:

    Iallbloke says, Have you read the realclimate ‘experiment’ done to try to validate Minnetts hypothesis in the open ocean?

    http://www.realclimate.org/index.php/archives/2006/09/why-greenhouse-gases-heat-the-ocean/

    Thanks just starting to look, so far more questions then answers as I am not certain yet of the details but it is only logical that if you add more energy to the “skin” although still cooler then the water just below, will heat up some, but the potential for that additional energy to go straight into laten heat via evaporation and accelration of the hydrologic cycle is , as far as I can tell,not discussed, I will read it again. Also the fact that during the day at most laditudes the oceans are gaining heat as the atmoshere is typically 5F to 15 f higher then the surface, so the reduced gradiant flow is reversed, does not appear to be considered.

  25. David says:

    Re tallbloke says:
    November 14, 2010 at 4:49 pm

    “I’m trying to think of ways we can determine the sorts of timescales and magnitudes the ocean sequesters and releases energy at, because that may have a good deal of explanatory power regarding multi-decadal warming and cooling of surface temperatures.”

    In my view this subject is as poorly understood as cloud formation and the “residence time” (total time spent from the bottom of the ocean to the top of the atmosphere) of various WL TSI is critical. Hence my paraphrase of an old maxim, ” A SW photon in the ocean is worth two long wave photons in the atmosphere” I understand that 5% of sunlight reaches about 80 meters and UVWL penetrates close to 300m. I also think UVL variies with TSI more then lpnger WLs over the sun cycle.

    The critical fact is that the energy is CUMLITIVE for everyday of “residence” and some of this energy may increase DAILY for as many days, months, years or decades that a change in TSI or cloud cover continues. Hence my paraphrase of an old maxim, ” A SW photon in the ocean is worth two LWIR photons in the atmosphere,” Of course it could be 30 to one for all I know.

    After all CAGW is predicated on the understanding that CO2 increases the “residence time” of LWIR in the atmosphere, sort of like a freeway where the red cars (LWIR) all suddenly decide to change lanes constantly, thus staying on the freeway (atmosphere) longer and so there are now more red cars on the freeway. However, and this is critical, in the ocean the speed limit is far slower and so any change can accumulate for far longer.

  26. It would be really a weird world where breakfasts were prepared with Hairdryers….
    Have you realized that even hairdryers work with electricity?

  27. tallbloke says:

    “The critical fact is that the energy is CUMULITIVE for everyday of “residence” and some of this energy may increase DAILY for as many days, months, years or decades that a change in TSI or cloud cover continues.”

    David, some more useful thoughts there, thanks. I agree SW is cumulative, that’s why I integrate the sunspot number departing from the ocean equilibrium value and use it as a proxy fro ocean heat content. Have a look at these two threads when you have time:

    Nailing the solar activity – global temperature divergence lie

    My simple solar-planetary energy model

  28. Tenuc says:

    Adolfo Giurfa says:
    November 15, 2010 at 2:50 pm
    “It would be really a weird world where breakfasts were prepared with Hairdryers….
    Have you realized that even hairdryers work with electricity?”

    Interesting to see where the energy to turn the generators which create the electricity came from in the first place:-

    Coal/oil/natural gas – Solar energy stored as chemical energy.
    Nuclear power – ???
    Hydro – Solar energy creates mechanical potential energy from hydrological cycle.
    Wind – Mechanical power from the air molecules being driven by Earth’s spin / lunar&solar tides / hydrological cycle.
    Solar cells – caused by solar photon bombardment of certain metal/rare earth wafers/films
    Tidal power – Mechanical power by lunar&solar tides/wind.

    It is easy to convert energy from one form to another with varying degrees of eficiency – perhaps no surprise that by concentrating on thermal energy alone wisdom about climate is very, very, low.

  29. Tenuc says:
    November 18, 2010 at 7:35 pm

    Right!. And those who divide nature in totally separated compartments, are absolutely wrong. They are the stubborn survivors of the Kali Yuga era 🙂

  30. Those who eat “junk food” irradiate too much LWR 🙂

  31. For sure “Magister Ludi” will lead us to higher energetic levels (each time of a shorter wavelength).