What Is The Surface Area Of A Cloud?

Or what is the surface area of any fractal solid?

This is strongly related to the Coastline Paradox:


Just with the added dimension of a solid.

Clouds are ‘self similar’ in many cases, yet also can have very different forms too. Watching clouds form, they grow, shrink, shift, stretch and connect, or dissipate a connection. So there is a dynamic aspect too. By the time you figure out what the surface area might be, it is different.

Now further consider that the “surface” does not, in fact, exist. Clouds form from water VAPOR transparently dissolved in air. As that vapor finds a “condensation nuclei” it starts to collect and make a droplet. The droplets grow and continue to coalesce. So what we see from the ground as a cloud is, in fact, “Billions and Billions” of water droplets. Each with a surface area and an edge; but each distinct from the next (or surface tension would form them into one bigger drop). So we can see (in a fuzzy way) the boundary where water droplets are big enough to interact with light and look like a cloud; but that is NOT the surface of a cloud. The cloud has no surface, only the droplets doo.

As the droplets coalesce into larger drops, there are more of them but with less surface area. Held up by Brownian Motion of air molecules. Eventually the drops get big enough that random air motion can’t hold them up, and we get rain. After enough rain, what is left of the cloud dissipates back to water vapor again. Along the way the cloud moved from zero mass / surface area, to some clear mass (measured by total precipitation if nothing else) and large surface area visable, then back to zero mass and surface area again. So if density is mass / volume, and we don’t (can’t?) know the mass or the surface area (and from surface area the volume); if we can’t know those basics, how can we compute the density of the cloud?

I started this ponder in the middle of the Arizona Desert, watching the sun poke though bits of cloud in the rain. How much sun gets to the ground? So what is the density and optical opacity / reflectivity of the clouds? How to compute it? One spot was bright sun. Next to that a patch of solid dark. Some gray in between and around edges. What is the albedo of that? Even the average albedo requires some idea how much is clear and how much “solid” cloud. No surface area. No volume. No density. No mass. How to model that? How to calculate it? How to even measure it? What cell size could even start to capture that? A meter? Maybe 100 meters? A cm?

In the end, it all comes down to parameters. Picking “plug numbers” that you think or guess are close enough to what you think you observed. It is not possible to calculate the surface area of a fractal from first principles. It is not possible to measure it. You must “make a good guess”. Use some kind of “rule of thumb” to shrink the problem (like sailing 200 m off the coastline).

But if all your basic model paraneters for core properties like albedo, solar absorption in clouds, transmission to ground, precipitation, and thermal mass are all essentially “plug numbers” then your model is disconnected from reality. It is a dream (or nightmare) embodied in software guesses.

All this leads me to conclude that any hope of a representative Climate Model is folly. Simply because you can not accurately compute the basics of the water cycle and clouds.

Even the ocean is a fractal surface. What is the surface area of the ocean? First compute all the coastlines of all the land masses and remove that area from the computed surface of the earth… oh, yeah, the coastline problem… Then figure out the ‘roughness’ of the ocean. It changes with the wind. Waves from a few inches to 100 meters high. With swells and ripples on them. With wind blown spray and crashing crests. What is the surface area of the ocean? A “plug number”. Guess well… So what is the heat and water vapor transmission through that surface? W/m^2 with unknown m? Kg/m^2 with unknown m?

It all comes down to the interaction of a bunch of surfaces and volumes with fractal geometry. Good luck with that…

So I’m now trying to figure out some way past this conundrum. How do you weigh a cloud? Without mass, volume, and surface area; how do you compute thermo properties and effects?

I think I see why they say “modeling clouds is hard”. It may be impossible.

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About E.M.Smith

A technical managerial sort interested in things from Stonehenge to computer science. My present "hot buttons' are the mythology of Climate Change and ancient metrology; but things change...
This entry was posted in AGW Science and Background, Earth Sciences, GCM, Global Warming General and tagged , , . Bookmark the permalink.

19 Responses to What Is The Surface Area Of A Cloud?

  1. ossqss says:

    The word stocastic comes to mind. Don’t forget possible Nucleation from Svensmarks cosmic rays aside from Earth based processes. So simple to model really /sarc ;-)

  2. ossqss says:

    Oh, why not provide a supplimental video update from March. Here ya go for consumption, evaluation, and thoughts.

  3. E.M.Smith says:

    Stochastic, eh? How many nucleation events / km^2 of cloud? (Or is that km^3?) So how many rolls of the dice to model them? Are there that many computes on the planet?

  4. ossqss says:

    My Commodore 64 could handle it just as well as anything we have now days! Ain’t happening no matter the computing power at hand EM. Somebody has to write the code and that always follows with preference and inherent bias, even if unintentional. I recall reading several years ago (Dr. Ball I think) of how climate models are developed over time through grad students adding supplimental layers of code. Dang mobile keyboard got me again!

  5. erl happ says:

    Well, the cloud comes and goes according to the temperature of the air in which it forms. The higher the air temperature the more moisture can be accommodated and the less cloud there will be.

    Cloud can form at any elevation below the tropopause, and even above it.

    The upper half of the atmospheric column in mid to high latitudes contains appreciable amounts of ozone, and especially in winter. Ozone is excited (and is an agent of warming) by infrared energy from the Earth itself, available day and night. For this reason the diurnal range of temperature diminishes with elevation. Plainly the temperature of the upper air is not dependent on the amount of ultra violet radiation from the sun that impinges only during daylight hours.

    It is observed that when the temperature of the air at the surface rises or falls the temperature of the upper air does not always vary in unison. Air is constantly moving and the wind at the surface is often different to the wind at elevation..

    When the temperature of the near surface air changes in unison with the temperature of the upper air, as it tends to do on a monthly basis, the amplitude of the movement in the temperature of the upper air is frequently several times greater than the temperature of the movement at the surface.

    I surmise that the temperature of the surface is driven by the more substantial change aloft that changes the cloud cover so as to allow or exclude the passage of solar radiation..

    It can be observed that the gyrations in surface temperature that occur from year to year are greater than the increase and decrease in surface temperature over the last 70 years.

    The amplitude of change in surface temperature from one year to the next is much greater as latitude increases and much greater in winter than in summer. It is in winter that the ozone content of the upper air increases and more so in higher latitudes than low.

    Its also observed that the surface temperature varies with 500 hPa geopotential height. GPH is determined by the temperature of the air column. When GPH increases at 500 hpa it increases to a much greater extent at Jet stream level, about 25 0hPa, where the ozone content of the air is greater than at 500 hpa.

    Its been known for 150 years that surface pressure varies with the ozone content and temperature of the upper part of the atmospheric column, above 500hPa. At 500 hPa half of the atmosphere is above and half below. When surface pressure falls the tropopause can be several kilometres lower.

    So, it appears that the temperature of the surface is primarily driven by the extent of cloud cover in the atmosphere above. This is probably the chief source of natural variation on all time scales. This doesn’t rule out the Svensmark hypothesis as another influence on the extent and density of cloud cover.

    Whats interesting, and yet to be accounted for, is the origins of the variation in ozone aloft. One of the many possible factors involved is the effect of cosmic rays on the composition of the atmosphere in high latitudes in winter.

  6. John F. Hultquist says:

    Perhaps solve the problem by not using shape as the thing of interest.
    One could start with examining water droplets, size, weight, and distribution.
    Then ask how many are in a certain volume, given the cloud’s varying density.
    Not saying this is easy or better. Just musing that there may be another way.
    Because humans see a shape to a cloud doesn’t make that shape important in a physical sense.

  7. tom0mason says:

    And from the weatherman’s perspective ‘How Many Water Droplets Are in a Cloud?’

    Clouds are complex and can be described, categorized and analyzed according to many different characteristics; it all depends on what is being studied. The main ways to measure cloud properties are aircraft and ground stations that directly sample the clouds with instruments, or via remote sensing (ground or satellite based) where the information is gathered from afar.

    Our research, for example, focuses on the liquid component of clouds. From a climate change perspective, the amount of sunlight that is reflected back into space by clouds is very important, since this is energy that could otherwise heat the Earth. Liquid clouds are probably most important for this and their reflectivity is determined by their areal coverage, the amount of liquid water they contain and the number of droplets. We have been using remote sensing techniques to better understand this.


  8. David A says:

    EM says ” How much sun gets to the ground? ”
    Earl says words to the effect that warmer air allows more water vapor before condensation ( water vapor is invisible clouds as they still prevent significant TSI from getting to the surface.)
    So expand E.M s question; what surface and what Sun? Ok, now let us define the
    W/L of the solar spectrums no longer reaching the surface of the ocean from both atmospheric water vapor and condensed water vapor, aka – clouds. Ok, now let us quantify the WsqM ( total energy) and the variable ocean residence time ( total change in accumulated energy due to a change in materials encountered) of that disparate solar insulation no longer entering various ocean depths.

    It appears very possible that while water vapor and clouds increase residence time of upwelling LWIR radiation from the surface, they decrease residence time of insolation that would have reached the surface and penetrated the ocean surface.

    Adding this to the EM post already demonstrating the difficulty of quantifying clouds, and we must admit we do not know. Leaif S admitted to me he has no idea how much energy is gained or lost to the oceans due to decades of low solar insolation compared to high active solar decades. He also admitted that the ocean residence time of disparate solar insolation has not been quantified.

    It is also obvious that the longer the residence time of specific energy input, the greater total energy accumulation or loss can occur. Atmospheric residence times are miniscule compared to ocean residence times. Thus energy can be gained or lost for decades depending on total solar variation and solar W/L variation.

  9. cdquarles says:

    Now supplement that cloud with ongoing dynamic chemical changes and that the cloud isn’t the only aerosol present. It may be the most visible one, but not the only one. And ;), they’re all dynamic. So, your plug-in numbers are all going to be steady state estimates. Oh yeah, ‘equilibrium’ isn’t necessarily static either. Estimates with various errors (‘random’ and systematic) that themselves may have to be estimated.

    This has come to be one of my pet peeves as a grumpy grandpa. People quoting estimates, which if properly done have uncertainty ranges attached to them, as if they are not estimates.

    /rhetorical question. How old is the Earth? Honest answer: “Since we weren’t there at the time of formation, we don’t know. We do have estimates based on formation models and age models. Best guess currently is 4.5 billion years +/- 1 billion.”

    I have a similar peeve with the background “steady state” concentration of carbon dioxide in our atmosphere. No one seems to do the error analysis and propagation, and never seem to quote the uncertainty ranges.

  10. p.g.sharrow says:

    cdquarles says: “one of my pet peeves as a grumpy grandpa.”

    After all that time and effort of acquiring the experience and knowledge to make an informed opinion, some damn 20 something thinks their opinions should rule because of their new found training.
    It is Enough to make any Mature person grumpy!
    Hell they don’t even know enough to understand the question, let alone opine the answer. …pg

  11. Dan_Kurt says:

    Check out EZ Water: https://www.youtube.com/watch?v=i-T7tCMUDXU.

    Dan Kurt

  12. David Walker says:

    “I think I see why they say “modeling clouds is hard”. It may be impossible.”

    If it is a cloudy day, the temperature is usually lower than on a clear day, and yet a cloudy night is warmer than a clear night.

    Hence the feedback has changed sign twice in 24 hours.

    So we effectively can’t even know the sign of the feedback with any degree of accuracy…

  13. cdquarles says:

    He he, pg. I resemble that remark. I have become the grumpy grandpa my grandpa was. Now I understand why he kept putting me in my place. :)

  14. cdquarles says:

    @ David Walker,
    Well, my own experience says that a cloudy day’s daytime high will be clipped. A cloudy night’s overnight low will also be clipped. How much that affects the ‘average’ depends on the shape of the actual diurnal curve determined by the actual readings.

    One thing that I do know is that the dew point temperature isn’t fixed. There is a diurnal range to it, too. That range is changed by bulk transport modified by local conditions. Your overnight low is almost always within 1 degree (F I know, C I’m not sure of) of the actual local dew point.

  15. Svend Ferdinandsen says:

    Most clouds have the same water content as the surrounding air. Only difference is that in the cloud some of the water vapor has condenced.
    The exception is the ugly thunder clouds, that can have much more water.

  16. ossqss says:

    Cloud types are very important and that needs to be part of the analysis too ;-)

    One wonders how the atmosphere and albedo responds to the different cloud types at different levels or multiple levels of the atmosphere simultaneously….


  17. erl happ says:

    ‘If it is a cloudy day, the temperature is usually lower than on a clear day, and yet a cloudy night is warmer than a clear night’

    Here is my take on that phenomenon.

    In the mid and high latitudes moist air comes from the tropics. Hence night time temperatures are warmer. The warmer night is frequently attributed to back radiation from cloud. That’s an error.. The air is warmer because it comes from a warm place and is moving into a cooler place.

    In the day time the cloud shields the surface from the sun and despite the fact that the air is already warm because of its origin its cooler on a cloudy day than a sunny day. What happened to the back radiation?.

    Cloud cools. The global maximum in cloud cover occurs in January when the Earth is closest to the sun. Irradiance is 6% stronger at this time and yet this is the time when the global average temperature reaches its minimum.

    In July, when irradiance from the sun is weakest the vast landmasses of the northern hemisphere heat the air, reducing cloud cover to its annual minimum allowing the Earth to reach its annual maximum temperature.

    The evolution of near surface temperature can not be understood or explained without reference to cloud or the evolution of surface atmospheric pressure.that drives the winds. The global sink for the atmosphere is on the margins of Antarctica. Here surface pressure has declined by about 10hPa over the last seventy years. The planetary winds are evolving. The rate of transfer of energy from the tropics to high latitudes is changing. Change is endemic and natural. The Earth is not a closed system.

    The strongest winds are found at the tropopause. To understand the evolution of the winds we need to understand the influence of ozone on local air density and surface pressure.

  18. Bruce Ryan says:

    volume isn’t as important as density and 2d area. So you have a scale of 1 to 3 that interprets the opaqueness of the cloud. Nearly see through clouds equal low volume over the height plane.

  19. chrism56 says:

    There was some interesting work done by people like Jonas on the condensation of water droplets in supercooled steam. It migh be a tangent, but It is all a similar process working around the Willans zone. The properties of droplets vary with size and it is recognizing those break points that is critical. For the situation you want to model, could not the minimum and maximum sizes be done, then that would give you the working range. Lets you know if it was orders of magnitude or something quite tight

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