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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 much 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/and accumulated and IR emitted.

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

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.

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 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).

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 ≤ 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 cooperating term.

So Φ and Albedo are always bounded together. The Φ(1 - a) term is a coupled physical term.

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.

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.

(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)

Φ = 1; Albedo 0 ≤ a ≤ 1

There are planets which reflect only diffusely (heavy cratered and gaseous planets)

Φ = 0,47; Albedo 0 ≤ a ≤ 1

For smooth surface without-atmosphere planets

Φ = 0,47 is an exact number

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March Hare

02.05.2021 02:05

“BRDF”

https://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function

Christos Vournas

02.05.2021 11:17

When the (energy in) is being correctly estimated:

Φ(1 - a)S πr² (W)

The ROTATIONAL WARMING is the next major parameter being implemented for planet mean surface temperature theoretical calculation

March Hare

02.05.2021 02:02

“BRDF defines the sun-angle dependence of surface albedo, one of the key parameters included in climate and weather forecasting models that constrain the surface energy budget.”

https://earth.gsfc.

Christos Vournas

02.05.2021 11:06

Since the "absorbed" fraction is based on the Planet cross-section (flat) disk SW absorption (1-a)Sπr^2 there is no room being initially left for the specular reflection to consider in energy budget

March Hare

02.05.2021 01:14

This study of specular reflection on earths’ a energy budget is almost 20 years old.

https://repository.arizona.edu/bitstream/handle/10150/27879

Christos Vournas

02.05.2021 11:05

The Earth's Albedo a=0,3 is unchanged from 1971

The T=288 K is unchanged from 1981

March Hare

02.05.2021 00:46

“Sun glint is a common phenomenon in satellite images – it essentially refers to the specular reflection of the sun on water surfaces.”

http://blog.imagico.de/sun-glint/

Christos Vournas

02.05.2021 10:20

Sun glint is what satellites only randomly capture. Never satellite going after specular reflection measurements. What satellites measure is Albedo = diffuse reflection.

March Hare

02.05.2021 00:30

“glint”, not glitter. “The specular reflection over the ocean is a feature widely observed in satellite imagery..”

https://agupubs.onlinelibrary.wiley.com/doi/pdfdirect/10.1029/2005JC003343

March Hare

01.05.2021 23:27

There is a ton of research regarding the issue of specular reflection (often called “glitter”) and satellite measurements. For example:

https://core.ac.uk/download/pdf/71326774.pdf

Christos Vournas

02.05.2021 10:11

Thank you March. What they do is to adjust the measurements so they are not getting disturbed by glint.

Tim Folkerts

01.05.2021 13:12

The same fractions get absorbed, diffusely reflected, and specularly reflected whether you work with totals or averages. So this is not a problem with the 'greenhouse theory'.

Christos Vournas

02.05.2021 10:00

Thank you Tim. The "absorbed" fraction is not emitted on average. The vast amount of emitting occurs day-time. The slow rotation leads to stronger emission. So less is accumulated for the night-time e

Tim Folkerts

01.05.2021 13:03

1) If you think the energy measurements from CERES have such a serious flaw, you should contact them. I suspect someone would answer, and they would tell you you are mistaken.

Christos Vournas

02.05.2021 10:07

I know they have omitted the specular reflection in the every planet energy budget estimation, not only Earth's. Also, the very definition of Planet Albedo is the diffusely reflected fraction of the i