# The Planet Surface Rotational Warming Phenomenon

## The Planet Mean Surface Temperature Equation Tmean = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

### The Budget considers the planet's energy balance in Total, and not in average as the Greenhouse warming theory very mistakenly does. The Planet Radiative Energy Budget can be applied to all planets.We have Φ for different planets' surfaces varying 0,47 ≤ Φ ≤ 1 And we have surface average Albedo "a" for different planets' varying 0 ≤ a ≤ 1Notice: Φ is never less than 0,47 for planets (spherical shape).Also, the coefficient Φ is "bounded" in a product with (1 - a) term, forming the Φ(1 - a) product cooperating term. So Φ and Albedo are always bounded together. The Φ(1 - a) term is a coupled physical term.

Planet Surface Radiative Energy Budget: Albedo a = 1

### In the diagram the horizontal and the vertical lines are crossing somewhere inside of the orthogonal. So, when Albedo "a" varies from 0 to 1, the Vertical line moves from the right to the left, till the diffuse reflection area covers the entire orthogonal.

Plane Surface Radiative Energy Budget: Φ = 1; Albedo a = 0

### And, there is a case when Albedo a = 0, so, when Φ varies from 0,47 to 1, the Horizontal line moves upward, till the (not reflected) area covers the entire orthogonal.

Planet Surface Radiative Energy Budget: Φ = 0,47; Albedo a = 0

### (a non diffusely reflecting (Albedo a = 0), but only specularly reflecting dark planet) In this case a planet is very dark, so it doesn't reflect diffusely (a = 0 ) but Φ may vary (0,47 ≤ Φ ≤ 1)

Planet Surface Radiative Energy Budget: Φ = 1

### Φ = 1; Albedo 0 ≤ a ≤ 1There are planets which reflect only diffusely (heavy cratered and gaseous planets)

Planet Surface Radiative Energy Budget: Φ = 0,47; Albedo 0 ≤ a ≤ 1

### The division into “smooth” vs “heavily cratered” planet surfaces

The division into “smooth” vs “heavily cratered” planet surfaces seems arbitrary. Just looking at images of the moons and planets, of the “smooth” ones seem rougher than some of the “heavily cratered” ones. At first it seems there should be some objective standard. Also, it seems there should be a continuous scale from 0.47 to 1.00 based on just how cratered it is.

Planet surface roughness is a criteria which comes from the surface roughness to the planet's diameter very huge dimensions comparison.

So, the smooth surface planet (Φ = 0,47) is not necessarily a microscopically smooth surface. There is a big interval in planet surface roughness, from the perfect microscopical smooth surface to the boundary of the planet being still considered a smooth surface planet (Φ = 0,47).

The rough enough state, for the solar irradiation 100 % capturing ( Φ = 1 ) example is a dense urban area. When solar rays hit the walls of the buildings the rays are multiply specularly reflected with a general direction towards the bottom, and till the energy is completely diffusely reflected or “absorbed” and IR emitted.

Also, it seems there should be a continuous scale from 0.47 to 1.00 based on just how cratered it is.

Yes, I thought about it a lot. What I came with is that when surface is at a Φ = 0,47 state, it cannot become even more smooth.

For a planet surface to reflect specularly more than 0,53*S is not possible, because of the planet's spherical shape.

And like-wise, when the surface is at the rough Φ = 1 state, it cannot capture even more solar light (even more higher buildings urban areas cannot capture even more solar energy).

The states in between could not been conserved, because of the multibillion years planet-surface-shaping HISTORY, which was shaping surface towards one Φ = 0,47 (the smooth version), or towards the another, the Φ = 1 (the heavy cratered, the rough version).

### A spherical planet covered with sand and gravel

On a spherical planet covered with sand and gravel what kind of reflection would prevail?

A planet shaped like a cube, but covered with smooth glass, would have mostly spectral reflection.

But the 0,47 in equation comes a chart of various shapes, and nothing to do with surface material. it seems like making no sense.

Yes, a planet shaped like a cube, but covered with smooth glass, would have mostly specular reflection...

Now, let's imagine a spherical planet covered with smooth glass... For smooth sphere Φ = 0,47

So the not reflected portion of the incident solar flux S would be:

not reflected = IR emitted = Φ(1 - a)S πr²

a glass covered planet resemblances the case of the Earth (Φ = 0,47)

Let's now imagine a planet covered with glass cubes...

The sizes of the cubes compared to the spherical planet size is what determines the Φ (the planet surface shape and roughness coefficient).

A spherical planet covered with sand and gravel would have mostly diffuse reflection.

So, sand and gravel covered planet is like being covered with small-size cubes.

A planet covered with sand and gravel resemblances the general case of smooth surface planets without-atmosphere Φ = 0,47.

But if the sizes of cubes are 10-20 stores high buildings, the planet surface shape and roughness coefficient Φ will approach very much close to the Φ = 1.

We have Φ for different planets' surfaces varying 0,47 ≤ Φ ≤ 1

And we have surface average Albedo "a" for different planets' varying 0 ≤ a ≤ 1

Notice:

Φ is never less than 0,47 for planets (spherical shape). Also, the coefficient Φ is "bounded" in a product with (1 - a) term, forming the Φ(1 - a) product coupled term.

### We should have correctly estimated the planet radiative energy budget

CERES omits planet specular reflection.

Specular reflection from a parallel solar rays hitting planet spherical surface cannot be “seen” by spacecraft’s SW radiation measuring sensor.

Specular reflection from sphere never gets onto the sensor’s plate. Therefore planet specular reflection is not taken into account not only for Earth, but also for other smooth surface planets without atmosphere (Mercury, Moon, Mars, Europa, Ganymede).

Why it is a problem?

It is a problem, because by omitting the planet specular reflected portion of the incident on the planet surface solar flux the planet effective temperature (equilibrium temperature) Te is calculated wrongly.

To calculate planet's Te we should know the exact "absorbed" (not reflected) portion of the incident on the planet solar energy flux.

Te - planet effective temperature:

Te = [ (1-a) S /4σ ] ¹∕ ⁴

Te.correct - the planet corrected effective temperature:

Te.correct = [ Φ (1 - a) S /4σ ] ¹∕ ⁴

Φ - is the solar irradiation accepting factor (it is the planet surface spherical shape, and planet surface roughness coefficient)

Φ = 0,47 - for smooth surface planets without atmosphere

Φ = 1 - for heavy cratered without atmosphere planets

Φ = 1 - for gases planets

In the Table we have the planet effective Te and the planet corrected Te.correct (which are calculated with the Te.correct equation) comparison.

Planet.......Te......Te.correct

Mercury....439,6 K.....364 K

Earth..........255 K.......210 K

Moon.......270,4 Κ......224 K

Mars........209,91 K.....174 K

When comparing the Te and Te.correct it becomes obvious how important is the planet surface specular reflection portion for the correct calculation of the planet theoretical equilibrium temperatures.

To have calculated the planet equilibrium temperature we should have correctly estimated the planet radiative energy budget:

Energy in = energy out

Φ(1 - a)S πr² (W) is the correctly estimated planet's energy in (the "absorbed" not reflected portion of the incident solar energy).