For instance, the Fibonacci spiral, a geometry generated
by a logarithmic series of numbers, appears in the spirals of shells, sunflowers, pine cones and even in non-visual progressions like the «bee ancestry code»!
-- NATURAL temperature (atmospheric) variations are given
by LOGARITHMIC functions (time - derivatives)-- the Arrhenius expressions.
No the need to use less resources is set
by the logarithmic growth law.
Second, his exponential for 1962 - 2050, linearized
by the logarithmic y - axis, is simply Manacker's old argument for a 0.5 % CAGR, which is completely unphysical.
Inspired
by the logarithmic spiral of a nautilus shell, this graceful example of organic architecture imparts a sense of peaceful harmony.
Not exact matches
mozRank — A
logarithmic ranking provided
by SEOmoz from 0 - 10.0 of the number and quality of inbound links pointing to a certain website or page on that website.
The scatter plot below charts the amount of venture and debt capital raised
by companies on a
logarithmic scale, and their corresponding valuations at the time of the IPO or acquisition.
Surveyors counted 324,592 individual trees and shrubs, and sorted them
by species — ranking these in turn according to their abundance The above graph shows relative abundance on a
logarithmic scale and arrayed from commonest to rarest.
An extravagance is a positive number that can't be arrived at
by performing finitely many algebraic,
logarithmic, or exponential operations on earlier numbers.
It provides practice in calculating the derivatives of trigonometric, exponential and
logarithmic functions
by the definition.
Its worth thinking about the shape of a rising or falling market line, it usually isnt linear, but tends to roll off in a
logarithmic way, so you can get a good idea of momentum
by just looking at the shape of the curve.
Most elegantly, if the natural logarithm is used, yielding the neper as
logarithmic units, scaling
by 100 to obtain the centineper yields units that are infinitesimally equal to percentage change (hence approximately equal for small values), and for which the linear equations hold for all values.
Since the CO2 forcing is
logarithmic, it appears that it may be close to the point where it will be overwhelmed
by the current intensity of the «natural» forcing; if so, then anyone could work out implications for future rise in the GLT.
Oh, and we've increased CO2
by 100 ppm already (it doesn't quite have the punch of the other 100 ppm because of
logarithmic effects, yadda yadda, but the court can be assured we're going to warm up
by about an ice age
by 2100).
However, it is important to keep in mind that we might easily more than double it if we really don't make much effort to cut back (I think the current estimated reserves of fossil fuels would increase CO2
by a factor of like 5 or 10, which would mean a warming of roughly 2 - 3 times the climate sensitivity for doubling CO2 [because of the
logarithmic dependence of the resulting warming to CO2 levels]-RRB-... and CO2 levels may be able to fall short of doubling if we really make a very strong effort to reduce emissions.
Radiative forcing is
logarithmic in concentration, but the concentration increases faster than linearly with emissions, since the more you emit, the less is taken up
by the oceans and the more remains in the atmosphere.
The decibel scale is
logarithmic, with every ten dB meaning a doubling of noise and vice versa, so a reduction of ten dB means it is reducing the noise level
by 50 percent.
Using the IPCC model - based estimate for climate sensitivity and the same
logarithmic calculation as for the UK alone, we will have averted 1.2 °C of warming
by 2100
by shutting down the world carbon - based economy.
The
logarithmic relationship was first posited
by Svante Arrhenius in 1896, based on measurements of infrared radiation from the full moon obtained with the Langley bolometer.
It was therefore easily rebutted when I wrote your «totally unsuitable» is contradicted
by three papers: Arrhenius's 1896 paper proposing a
logarithmic dependence of surface temperature on CO2, Hansen et al's 1985 paper pointing out that the time needed to warm the oceanic mixed layer would delay the impact of global warming, and Hofmann et al's 2009 paper modeling the dependence of CO2 on time as a raised exponential.
Any increase could be at most
logarithmic, and this is also generally agreed
by all sides.»
@manacker: So we have a rate of temperature increase that is linear in the most pessimistic case and
logarithmic in the most optimistic case — and this will not get us to the alarming temperature increases projected
by IPCC (or
by Vaughan Pratt's exponential curve).
I should also have given a more complete list of the problems with your objections: in this case your «totally unsuitable» is contradicted
by three papers: Arrhenius's 1896 paper proposing a
logarithmic dependence of surface temperature on CO2, Hansen et al's 1985 paper pointing out that the time needed to warm the oceanic mixed layer would delay the impact of global warming, and Hofmann et al's 2009 paper modeling the dependence of CO2 on time as a raised exponential.
AGW is «driven»
by the change in concentration of GHGs, supposedly in a
logarithmic relation at the sort of levels we might see.
Although Callendar did not characterize the curve in this figure as
logarithmic, it obviously can be closely approximated
by a log curve, as shown
by the red overplot which shows a log curve fitted to the Callendar graphic.
For intermediate values it's slightly more complicated as pointed out
by Andreas, since the relation is
logarithmic rather than linear.
His conclusion was that the CO2 forcing is unquestionably
logarithmic, so that each additional molecule we emit has less forcing and warming effect than its predecessors; that the precise value of the coefficient in the CO2 forcing function, which the IPCC has already reduced
by 15 %, can not be determined; and that, all things considered, 1 K per doubling was probably in the right ball - park.
My point is that since the response is
logarithmic you can't answer the question
by just eyeballing the graph of CO2 emissions.
Using the
logarithmic relation and IPCC's model - derived 2xCO2 climate sensitivity of 3 °C, we have a net reduction in global warming
by 2100 of 0.045 °C.
BTW, I have found one experiment performed
by Herr Koch in 1901 that proved the
logarithmic properties.
Research presented here and at other credible locations has shown CO2's effect to be
logarithmic with possible offsetting
by negative feedbacks rather than amplified greatly
by positive feedback mechanisms.
The
logarithmic relationship between CO2 levels and global temperature was first presented way back in the 1930s
by a scientist named Guy Callendar, and it is now widely accepted as science fact.
If the modern fraction error is normally distributed, then the error distribution of the RC age is log normal — since the activity level over time is dictated
by the well known «exponential decay» formula and the transform from modern fraction to time is
logarithmic.
There is NOT a «
logarithmic input of effect»
by «water» as the energy inputted to Kinetic Induction is also powering Turbulence, such energy NOT being measurable as «temperature» of the mass being «moved» and this is in precedence to any measure of «temperature» especially in a Gas, but also in a liquid.
Though he is willing to confirm that the the equation is indeed
logarithmic, so that each additional molecule of CO2 has less forcing effect than its predecessors, he is less sure about the coefficient, which the IPCC has already reduced
by 15 % (it was 6.3 in the 1990 and 1995 reports).
By default, it uses a Lorentz function integrator that utilizes
logarithmic time steps (a much slower linear integrator is optional and used only for cross checking calculations).
Yes at the line center the absorption of CO2 is «saturated: — surface emission totally replaced
by emission from the top of the ghg column but as the conc of the ghg increases, the line width increases so the ghg starts to absorb over a greater and greater range of wavelengths — this is the cause of the
logarithmic relationship between concentration and absorption.
Even for an increase in CO2
by a factor of 10, the temperature increase does not exceed 2.5 ° K.» Even the IPCC acknowledges radiative gases» inverse
logarithmic influence on temperature.
Between this shortcut / mistake (which violates the Stephan - Boltzmann equations and was copied
by all the following climate scientists) and through the climate model's assumption of a constant linear lapse rate of 6C / kilometre when it is probably not constant), they have changed all the
logarithmic radiation equations into linear ones.
This progressive
logarithmic diminution effect, acknowledged
by warmists and us alike, punctures Global Warming fright nights and so is seldom if ever discussed.
However the underlying
logarithmic term shows that the actual enhanced warming was more like the 1940 - 2008 value of 0.45 C. Therefore climate models are likely over-estimating AGW
by about 50 %.
Logarithmic or not, one should not overlook the massive differences between the puny amount of CO2 emitted
by humans (or even the relatively tiny amount of total carbon contained in all fossil fuels on this planet) as compared with the gigantic carbon sink contained in the carbonate / bicarbonate of the ocean.
I actually think this comment
by our host deserves more discussion: «We are already a very long way towards doubling CO2 (esp if effect is
logarithmic).
Not evenly of course, I suppose the curve (absorbed energy vs depth) would have
logarithmic shape, more or less where bulk of the energy is absorbed
by the first few centimeters of water.
It follows from this that the
logarithmic dependence of the outgoing longwave radiation (which
by the way, has to do the the exponential decay of the absorption coefficient away from the center of the absorption line) can still lead to significant temperature changes, particularly since water vapor enhances the value of λ and smoothes out a plot of the outgoing radiation vs. temperature (making it more linear than T ** 4).
This «S» shape goes away at night not because evaporation is less powerful, but rather because the input (solar) has gone away and the natural rising takes on a more
logarithmic shape
by depth where output is the only variable.
Regardless, climate models are made interesting
by the inclusion of «positive feedbacks» (multiplier effects) so that a small temperature increment expected from increasing atmospheric carbon dioxide invokes large increases in water vapor, which seem to produce exponential rather than
logarithmic temperature response in the models.
But it's important to note that potential tenants do not decide on which property they are going to rent
by plugging the amenities and specs into a spreadsheet and running a
logarithmic, covariate algorithm that takes the least - squares regression of the hypotenuse to determine the best value.