Sentences with phrase «as t ^»

To put it another way, while he surface itself radiates approx as T ^ 4, the almost balancing back radiation also increases as T ^ 4.

Not exact matches

Your first reply ^ seems to convey that you don't endorse Mike Mahler's T supplement, and then your latter reply does seem to tout Aggressive Strength T formula as beneficial.

Also, I once computed the derivative (calculus stuff) of the compound interest equation (basically a = pr ^ t, using t as the variable) and it's compound interest equations all the way down... unlike most equations that eventually reach 0.

A note for the technically minded: The quadratic fit to the sea - level curve can be written as: SL (t) = a t ^ 2 + b t + c, where t = time and a, b and c are constants.

Since the energy emitted goes like T ^ 4 power, the earth thus emits less energy back into space, which is why it has to warm (until it reaches a temperature when the earth is again emitting as much energy back out into space as it receives from the sun and so is back in equilibrium).

So the surface is warmer than the air immediately above it, with T ^ 4 larger by the same amount as it is smaller at a unit optical depth above the surface.

But is sure ain't increasing in proportion to T ^ 4, as Planck radiation would.

This is much simpler than what Michael proposes as an alternative, if for no other reason that the emissivity is balanced by the absorption, which is not proportional to T ^ 4.

Each layer must transport the same energy as the layer below and its emissivity is perfect (optically thick) so it transports according to R ^ 2T ^ 4 where R is the radius from the center of the planet and T is absolute temperature.

If you do the calculations as the formula is written, you get a T of over 300K The formula should be (So / 4) * (1 - A) = sigma * T ^ 4 That will give a T of 255K

That makes some intuitive sense to me (as allowed by optical thickness, photons moving out of a region in proportion to concentration; constant photon concentration gradient can be sustained with constant T ^ 4 gradient, etc.), though then I have to correct something I said earlier — within the region where T ^ 4 varies linearly (over optical distance), the radiation will be anisotropic.

Thus, for a well - coupled convecting troposphere, one defines the climate sensitivity (in the absence of feedback) as 1 / [d (SB) / dT] = 1 / (4 * sigma * T ^ 3), where T in this case is actually the emission temperature of the planet where infrared radiation leaks out to space (analogous to the photosphere of the sun, where eventually the outer layers of the sun become optically thin to visible radiation, and allow that energy to escape to space), not the surface temperature.

«As an object radiates energy at a rate given by Equation 20.18 [P = o A e T ^ 4], it also absorbs electromagnetic radiation.

He seems to use - as you say - Delta T = lambda Delta RF and calls lambda the climate sensitivity, which has units of K / W m ^ 2.

If an object is at temperature T and its surroundings are at a temperature T [0], then the net energy gained or lost each second by the object as a result of radiation is P [net] = o A e (T ^ 4 - T [0] ^ 4).

Total net feedbacks are usually estimated as negative because the Planck feedback ~ T ^ 4 is the strongest.

Indeed, one way you can think of this is that the flux is sigma T ^ 4, but if dT is small, then you can expand this as dF = 4 sigma T ^ 3 dT, so — for small changes in dT — the response is approximately linear in dT.

When the inter-methodological (+ / --RRB- 2 C noted by Bemis, et al., is added as the rms to the average (+ / --RRB- 1.25 C measurement error from the work of McCrae 1950 and Bemis 1998, the combined 1 - sigma error in determined T = (+ / --RRB- sqrt (1.25 ^ 2 +2 ^ 2) = (+ / --RRB- 2.4 C.

-- When you use T ^ 4 as part of the transport equations, you are basing that on the Stefan - Boltzmann law, which is about the radiant power integrated over all frequencies.

Figure 1 gives the measured relationship between temperature and dO18 in calcium, strontium, and barium carbonates, over the range 0 - 500 C. Focusing on the calcium data as paleoproxy relevant, the replotted data yielded the fitted equation: 1000 * ln - alpha = 2.78 * (10 ^ 6 / T)-3.35, r ^ 2 = 0.9996, where alpha is a dO18 fractionation factor.

Moreover; a sensitivity metric expressed as degrees per W / m ^ 2 has a non linear 1 / T ^ 3 dependence as T (the temperature) increases.

dT = dForcing / 4 * sigma * T ^ 3 where sigma = Stefan Boltzmann constant (0.0000000567) T = temperature in degrees K, (defined as 255.1 K)

And before anyone starts screaming about the ice caps melting, let's keep in mind that T ^ 4 applies by latitude as well as season.

If the atmosphere contained no IR - absorbing substances, then all the IR emitted by the earth's surface would escape into space and radiative balance would dictate that the earth's average surface temperature (or really the average of emissivity * T ^ 4 where T is the absolute temperature and the emissivity of most terrestrial materials in the wavelength range of interest is very close to 1) is set by the condition that the earth must radiate as much energy as it absorbs from the sun.

If we want to do any kind of averaging we should be averaging T ^ 4 as it provides a measure of radiated power.

For example if instead of each observation x (t) being represented as that, you can represent each observation as a vector, say — v (t) = (x (t), x (t) ^ 2, x (t) ^ 3), and then a MIMO model for linear evolution of v (t) ends up capturing some nonlinear parts of the evolution.

Turbulent kinematic viscosities scale as ~ ν ~ u» L' or L' ^ 2 / T» where u is a characteristic velocity, L is an integral time scale (usually) and T» is an integral time scale (usually).

Again, the correct procedure is as follows: Q / m ^ 2 = e * (s)(T) ^ 4 = 0.82 (5.6697 x 10 ^ -8 W / m ^ 2 K ^ 4)(293 K) ^ 4 = 342.62 W / m ^ 2 Q / m ^ 2 = a * (s)(T) ^ 4 = 0.82 (5.6697 x 10 ^ -8 W / m ^ 2 K ^ 4)(293 K) ^ 4 = 342.62 W / m ^ 2»

Just as a demonstration of this look at the units of the equation: Q = e (A)(σ)(T ^ 4) e: dimensionless quantity A: m ^ 2 σ: J / -LRB-(K ^ 4)(m ^ 2) s) T: K Put that all together and we get: Q = (m ^ 2) * (J / (K ^ 4 * m ^ 2 * s)-RRB- * (K ^ 4) Q = J * (K ^ 4) * (m ^ 2) / -LRB-(K ^ 4) * (m ^ 2) * s) Q = J (K ^ 4)(m ^ 2) / -LRB-(K ^ 4)(m ^ 2) s) And that leaves us with: Q = J / s Which is simply a Watt (W).

That is not the same as saying absorption is dependent on T ^ 4.

In the context of «changes», tossing (H, H, H, H, H, H, H, H, H, H, H, H, H, H) is just as likely as tossing (H, T, H, T, T, T, H, H, T, T, H, H, T, T) or any other sequence of realizations, the probability of that particular realization being 0.5 ^ 14.