Copyrights Prof Marko Popovic 2021 Atmosphere The Aeronauts follows the adventures of James Glaisher, a scientist, and Amelia Wren, a flamboyant aeronaut who lost her husband in a balloon accident. The pair, fighting against thunderstorms, wind, hailstones and rain as they ascend higher and higher, achieve something phenomenal: they travel to heights no man or woman has ever reached before. In The Aeronauts, meteorologist James Glaisher (Redmayne) presents his theories of how a gas balloon expedition could be key to predicting the weather—a science still in its infancy in the 1860s—and asks for funding for the expedition. His peers respond emphatically: “We are scientists, not fortune tellers.” But Glaisher doesn’t give in.

In the movie, the pair breaks the world record for altitude after reaching a height of 36,000 feet. https://www.imdb.com/title/tt6141246/?ref_=vp_vi_tt Glaisher did in fact exist, and he did break the record for traveling higher than any person, but he did so with fellow scientist Henry Tracy Coxwell rather than the fictional character of Amelia Wren. On Sept. 5, 1862, the two men, equipped with pigeons (as in the film), a compass and thermometers, took to the skies and broke the world record for the highest any human had been in a balloon. Gleisher passed out around at 8,800 meters (28,900 feet) before a reading could be taken.

Estimates suggest that he rose to more than 9,500 metres (31,200 feet) and as much as 10,900 metres (35,800 feet) above sea level. Coxwell lost all sensation in his hands. The valve-line had become entangled so he was unable to release the mechanism; with great effort, he climbed onto the rigging and was finally able to release the vent before losing consciousness. This allowed the balloon to descend to a lower altitude. In real life, Glaisher was indeed an influential scientist—he made 28 ascents between 1862 and 1866, recording observations that were crucial to our understanding of weather. Among his discoveries were the fact that wind changes speed at different altitudes, and the way raindrops form and gather moisture.

Science has, of course, advanced significantly since Glaisher’s time. The kinds of scientific measurements he performed using thermometers, barometers and hygrometers are now made in unmanned meteorological balloons.

Modern balloons generally contain electronic equipment such as radio transmitters, cameras, or satellite navigation systems, such as GPS receivers. In 2002, a balloon named BU60-1 reached a record altitude of 53.0 km (32.9 mi; 173,900 ft). How Planes Measure Altitude? How Planes Measure Altitude?

Altimeter displays indicated altitude and this is what is currently used for all traffic separation in US and Canada. Indicated altitude is pressure altitude corrected for local atmospheric conditions. The correction is done by entering the altimeter setting given by Air Traffic Control or on an Automated Weather Observing System (AWOS). All aircrafts in a given area should be on the same altimeter setting so relative (altitude) separation is maintained. A GPS, on the other hand, measures absolute altitude off several ≥ 4 satellites. While potentially more accurate than pressure altitude, it does not provide the same relative separation from other aircrafts (since all aircrafts are using indicated altitude) PRESSURE ALTITUDE (typically from an aneroid barometer) (as a check, GPS and/or radio altimeter are also used) while monitoring temperature

Atmospheric Constituents

Dry air

uniform composition in Homosphere (0 ~ 90 푘푚)

푚 푁푁22 × 14 푚푝 + 푁푂22 × 16 푚푝 + 푁퐴푟40 푚푝 𝜌 = ≅ 푉 푉 푁 푚푝 proton mass = 0.781 × 28 + 0.210 × 32 + 0.009 × 40 푚 푉 푝 푛푚 number of moles 푁 푛 푁 푛 푀 푁퐴 Avogadro’s number = 28.948 푚 = 푚 퐴 28.948 푚 ≅ 푚 푉 푝 푉 푝 푉 푀 molar mass Recall the ideal gas law

The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas.

푝푉 = 푁푘푇 = 푛푚푅푇

푅 = 8,314.472 퐽 푘푚표푙−1 퐾−1 universal gas constant −23 2 −2 −1 푘 also 푘퐵 = Boltzmann constant = 1.38064852 × 10 푚 푘푔 푠 퐾

푁푘 = 푛푚푅 hence 푅 = 푁퐴푘

− 27 푚푝 proton mass 1.67262 × 10 푘푔 푛푚 number of moles 23 −1 푁퐴 Avogadro’s number 6.0221409 × 10 푚표푙 푀 molar mass (air) 2.91 × 10−2 푘푔 푚표푙−1 Variations with altitude

퐴 흆 풉 퐀 ∆풉 품 = 풑 풉 − ∆풉/ퟐ 푨 − 풑 풉 + ∆풉/ퟐ 푨

density , pressure , temperature 𝜌 ℎ + ∆ℎ , 푝 ℎ + ∆ℎ , 푇 ℎ + ∆ℎ 푑푝 𝜌g = − 𝜌 ℎ , 푝 ℎ , 푇 ℎ 푑ℎ 𝜌 ℎ − ∆ℎ , 푝 ℎ − ∆ℎ , 푇 ℎ − ∆ℎ

푁 𝜌 푚 푁푁2 2 × 14 푚푝 + 푁푂2 2 × 16 푚푝 + 푁퐴푟 40 푚푝 𝜌 = ≅ ≅ 푉 푉 푉 28.948 푚푝 푁 = 0.781 × 28 + 0.210 × 32 + 0.009 × 40 푚 푉 푝 푑푝 푁 𝜌 푑ℎ 푑 ln 푝 28.948 푚푝푔 푀푔 푝 = 푘푇 ≅ 푘푇 = − 푘푇 = − = − 푉 28.948 푚푝 28.948 푚푝푔 1 푑ℎ 푘푇 푅푇 푑푝 = d ln 푝 푝 Variations with altitude – constant T approximation ℎ 1 1 1 1 푀푔 푝1 푀푔 න 푑 ln 푝 = − න 푑ℎ ln푝1 − ln푝0 = ln = − න 푑ℎ 0 0 푅푇 푝0 0 푅푇

1 푀푔 ׬ 푑ℎ − 0 푝1 = 푝0푒 0 푅푇

In the zeroth order (constant) approximation assume 푇 ℎ = 푇0 = 푐표푛푠푡 .

푀𝑔 푀푔 − ℎ −ℎ − ℎ1−ℎ0 푅푇 1 0 푝 − 푝 = 푝 [푒 푅푇0 − 1] Then 푝1 = 푝0푒 0 and 1 0 0

∆ℎ 푅푇0 Scale − 퐻 where 퐻 = ∆푝 = 푝0 푒 − 1 푀푔 Height Variations with altitude – constant T approximation

If one sets ℎ0 = 0, 푝0 = 푝 0 and renames 푝1 → 푝 as well as ℎ1 → ℎ then

ℎ 푅푇0 − with scale factor 퐻 = 푝 ℎ = 푝0푒 퐻 푀푔

1 푑푝 푝 푝0 ℎ ℎ From here it also follows that 𝜌 = − = and 𝜌 = 푒− 퐻 = 𝜌 푒− 퐻 푔 푑ℎ 푔퐻 푔퐻 0

However, temperature is not constant with altitude; scale factor varies with altitude

For typical temperature distribution 퐻 0 ≅ 8.5 푘푚 퐻 5 푘푚 ≅ 7.5 푘푚 퐻 10 푘푚 ≅ 6.5 푘푚 Apparently barometric altimeters in planes use relationship that we just obtained to relate pressure and altitude.

ℎ ℎ 푝0 푅푇0 푝0 푝0 푝 ℎ = 푝 푒− 퐻 → = ln → ℎ = ln = 푐푇 ln 0 퐻 푝 푀푔 푝 푝

Pilot uses airport’s altitude and current pressure (and temperature?) to calibrate altimeter which essentially translates to setting correct local value of scale factor.

Points of concern: this formula is the result of simplest (wrong) model assuming constant temperature for the entire air column (hence changes in temperature alone may easily introduce 20-30% errors), value of 푔 is changing (<1%) with latitude, molar mass is changing depending on water vapor concentration (up to ~3% in tropics), also, air is entering barometric altimeter from an external port – hence the exact location of the port, plane’s geometry, and plane speed may introduce additional variability in estimating the plane’s altitude. Mess! 푣Ԧ 퐴 A 푣Ԧ 퐵 Pressure 1 B Pressure 2

Pressure 3

How accurate is the pressure reading? Important for air traffic separation. Any dependence on sensor placement (convention) and aircraft speed? For example, consider Bernoulli’s equation ? for adiabatic flow at less than Mach 0.3 풗 ? ? 𝜌푣2 푝 + + 𝜌푔ℎ = 푐표푛푠푡 ? ? 2 Variations with altitude – linear approximation

In the first order (linear) approximation assume 푇 ℎ = 푇0 1 + 푎 ℎ − ℎ0 . ℎ 1 1 1 1 푑ℎ 1 푑ℎ 1 푑ℎ 1 푑 푏 + 푐ℎ 푏 + 푐ℎ 푐 න = න = න = න 푐 = ln 1 0 푇 0 푇0 1 + 푎 ℎ − ℎ0 0 푏 + 푐ℎ 0 푏 + 푐ℎ 푏 + 푐ℎ0

0 1 1 푑ℎ that is ׬ = ln 1 + 푎 ℎ − ℎ 푇0푎 . Hence 0 푇 1 0

푀𝑔 1 푀푔 푅푇 푎 ׬ 푑ℎ − ln 1+푎 ℎ1−ℎ0 0 − 푝1 = 푝0푒 0 푅푇 = 푝0푒

푀푔 − 푅푇 푎 푝1 = 푝0 1 + 푎 ℎ1 − ℎ0 0 Variations with altitude – linear approximation

Again, if one sets ℎ0 = 0, 푝0 = 푝 0 and renames 푝1 → 푝 as well as ℎ1 → ℎ then 1 − 푀푔 1 푇 퐻푎 − 푅푇 푎 − 푝 = 푝0 1 + 푎ℎ 0 = 푝0 1 + 푎ℎ 퐻푎 = 푝0 푇0 It is easy to verify that this goes to our zeroth order result when 푎 → 0

1 1 푑푝 푝0 Similarly as before 𝜌 = − = 1 + 푎ℎ − 퐻푎−1 푔 푑ℎ 푔퐻

1 − −1 푝 1 푇 퐻푎 − 퐻푎−1 푝0 𝜌 = = 𝜌0 1 + 푎ℎ = 𝜌0 with 𝜌0 = 1 + 푎ℎ 푔퐻 푇0 푔퐻 Let’s plot results for linear assumption in troposphere

150 퐾 200 퐾 250 퐾 300 퐾

Mean value for tropopause Lapse rate (9 푘푚 @ poles and 푑푇 − = −푎푇 = ퟕ. ퟕ 푲 풌풎−ퟏ 17 푘푚 @ equator; 푑ℎ 0 Temp.= −ퟖퟎ풐푪) assumed −ퟏퟏퟐ풐푭 assumed Temperature

5 Density 푝0 = 1.01235 × 10 푃푎 3 Pressure 𝜌0 = 1.225 푘푔/푚

푇0 = 293 퐾 20표퐶 68표퐹 note sensitivity on boundary condition (temperature @ tropopause)

150 퐾 200 퐾 250 퐾 300 퐾

Mean value for tropopause Lapse rate (9 푘푚 poles and 푑푇 −ퟏ − = −푎푇0 = ퟔ. ퟐ 푲 풌풎 17 푘푚 equator; 푑ℎ Temp.= −ퟔퟎ풐푪) assumed −ퟕퟔ풐푭 assumed Temperature

5 Density 푝0 = 1.01235 × 10 푃푎 3 Pressure 𝜌0 = 1.225 푘푔/푚

푇0 = 293 퐾 20표퐶 68표퐹 푑푇 휌 ℎ 푝 ℎ For smaller temperature change, = 푎 → 0, pressure and density vs altitude are more similar, → 푑ℎ 휌0 푝0 150 퐾 200 퐾 250 퐾 300 퐾

Mean value for tropopause Lapse rate 푑푇 (9 푘푚 poles and −ퟏ − = −푎푇0 = ퟒ. ퟔ 푲 풌풎 17 푘푚 equator; 푑ℎ Temp.= −ퟒퟎ풐푪) assumed −ퟒퟎ풐푭 assumed Temperature

5 Density 푝0 = 1.01235 × 10 푃푎 3 Pressure 𝜌0 = 1.225 푘푔/푚

푇0 = 293 퐾 20표퐶 68표퐹 How much estimated height varies if lapse rate is changing, i.e. ∆퐿 ≠ 0 , while ground pressure 푝0 and ground temperature 푇0 are both constant?

푀푔 푀푔 − 1 푝 푅푇0푎 푥 푅푇 푎 Recall 푝 = 푝0 1 + 푎ℎ 0 ℎ 푝, 푥 = − 1 푎 푥 푝0

What is the change of altitude while following same isobar (constant pressure surface) and moving say in x direction?

푀푔 푀푔 휕ℎ 1 푝 푅푇0푎 푥 1 푝 푝 푅푇0푎 푥 푀푔 1 푑푎 푥 ∆ℎ|푝=푐표푛푠푡. = ∆푥 = − 2 − 1 + ln − 2 ∆푥 휕푥 푎 푥 푝0 푎 푥 푝0 푝0 푅푇0 푎 푥 푑푥

Or focus just on change in lapse rate (∆퐿 = −푇0∆푎)

1 ∆퐿 Next slide ∆ℎ|푝=푐표푛푠푡. = − 2 푎ℎ + 푎ℎ + 1 ln 푎ℎ + 1 ∆푎 with ∆푎 = − 푎 푇0 Change of altitude vs altitude for relative change of lapse rate (based on nominal value ퟔ. ퟓ 푲 풌풎−ퟏ)

±1% ±5% ±10%

Indicated Altitude as explained by pilot (Flying Magazine)

Indicated altitude is what the altimeter reads when the local pressure (altimeter setting) is set in the Kollsman window. On the ground, set the altimeter to the airport elevation (at that point on the airport); indicated altitude should be the same as the true altitude, and the setting in the Kollsman window (see opposite) should match the current altimeter setting. In the air, as you fly along and encounter nonstandard temperatures, indicated altitude can differ from true altitude. The colder the temperature, the more significant (and possibly dangerous) this difference can be. When the temperature is colder than standard, you are at an altitude lower than your altimeter indicates. When the temperature is warmer than standard, you are higher than your altimeter indicates. When you are flying above a location for which you obtained a local current altimeter setting in extremely cold temperatures, the true altitude of the aircraft can be significantly lower than indicated. Of course, when you reach the runway, a perfectly set altimeter should be exactly correct no matter the temperature. The Venturi effect of a howling wind blowing through a mountain pass can create an isolated low-pressure area that may cause the altimeter to indicate as much as 1,000 feet higher than actual altitude (in other words, the aircraft could be 1,000 feet lower than indicated). Troposphere Troposphere is the densest layer, containing about 75% - 80% mass of the entire atmosphere.

The majority (99%) of the atmospheric water vapor or moisture is found in the troposphere.

Most of the phenomena associated with day-to-day weather occur in the troposphere.

The troposphere is mostly heated through energy transfer from the surface.

Lapse rate is positive (about 6.5 퐾 푘푚−1). Negative lapse rate (temperature inversion) may limit or prevent convection and diffusion from lower levels leading to air pollution.

Characterized by turbulent vertical mixing through convection and diffusion. 휔 푠푙표푤 휔 푠푙표푤 Atmospheric circulation for slowly rotating planet like Venus COLD

HOT HOT

COLD

Atmospheric circulation 휔 푓푎푠푡 휔 푓푎푠푡 for rapidly rotating planet like Earth COLD

HOT HOT

COLD Hadley Circulation

Air heated near the equator rises and flows towards poles.

Instead of having a single “donut” circulation for each hemisphere, Coriolis forces introduce 3 “donut” circulations, also called the Hadley circulation model.

Btw, George Hadley was an 18th century English lawyer (and amateur meteorologist). Jet Stream

Jet streams are fast flowing, narrow, meandering air currents located near the altitude of the tropopause and are westerly winds (flowing west to east).

The strongest jet streams are the polar jets, at 9–12 km (30,000–39,000 ft) above sea The width of a jet stream is typically a few hundred level, and the higher altitude kilometers or miles and its vertical thickness often less and somewhat weaker than five kilometers (16,000 feet). subtropical jets at 10–16 km (33,000–52,000 ft).

Jet Stream

The path of the jet typically has a meandering shape, and these meanders themselves propagate eastward, at lower speeds than that of the actual wind within the flow. Each large meander, or wave, within the jet stream is known as a Rossby wave (planetary wave). Rossby waves are caused by changes in the Coriolis effect with latitude.

The wind speeds are greatest where temperature differences between air masses are greatest, and often exceed 92 km/h (50 kn; 57 mph). Speeds of 400 km/h (220 kn; 250 mph) have been measured. Rossby Waves Fluid vorticity is 훻 × 푢 with 푢 being 휕 휕 휕 휕푥 휕푦 휕푧 fluid speed. 훻 × 푢 = 푢푥 푢푦 푢푧 푖Ƹ 푗Ƹ 푘෠ The vorticity caused by rotating sphere (e.g. Earth) is maximal at the poles and goes to zero at the equator. As an air parcel moves northward or southward over different latitudes, it experiences change in Earth vorticity. In order to conserve the absolute vorticity, the air has to rotate to produce relative vorticity.

Tropopause The tropopause is the boundary between the troposphere and the stratosphere. The tropopause is defined as the lowest level at which the lapse rate is 2 표퐶 푘푚−1or less provided that the average lapse rate between this level and all higher levels within 2 푘푚 does not exceed 2 표퐶 푘푚−1. Occasionally, a second tropopause may be found if the lapse rate above the first tropopause exceeds 3 표퐶 푘푚−1. Tropopause

(A)Temperature stops decreasing (and temperature inversion starts) (B)Static stability metric, the square of the Brunt‐Väisälä frequency, 푁2, increases sharply (C)Ozone concentration increases (D)Water vapor stops decreasing

ℎ

t = 0 t = 1/푁 The square of the Brunt‐Väisälä frequency, 푁2 푐 If air parcel satisfies adiabatic approximation ∆푄 ≈ 0 and 푝푉훾 = 푐표푛푠푡. with 훾 = 푝 푐푉 7 being ratio of isobaric and isochoric specific heats. In case of diatomic gas 훾 = . 5 When parcel moves ℎ → ℎ + 훿ℎ the pressure changes as 푝 ℎ → 푝 ℎ + 훿ℎ and that 1 푝 ℎ indicates change of parcel’s volume 푉 → 훾 푉 corresponding to change in 푝 ℎ+훿ℎ 1 푝 ℎ − density of parcel 𝜌 → 훾 𝜌. Hence, buoyancy equation becomes 푝 ℎ+훿ℎ

1 1 − − 푝 ℎ 훾 푑2훿ℎ 푝 ℎ 훾 𝜌 ℎ = −푔 𝜌 ℎ − 𝜌 ℎ + 훿ℎ 푝 ℎ + 훿ℎ 푑푡2 푝 ℎ + 훿ℎ

1 푑2훿ℎ 푔 푝 ℎ 훾 = − 𝜌 ℎ − 𝜌 ℎ + 훿ℎ = 푁2훿ℎ 푑푡2 𝜌 ℎ 푝 ℎ + 훿ℎ

Stratosphere The stratosphere, 13 푘푚 ≤ ℎ ≤ 50 푘푚 (8 to 31 miles), is stratified (layered) in temperature, with warmer layers higher and cooler layers closer to the Earth; this increase of temperature with altitude is a result of the absorption of the Sun's ultraviolet radiation (shortened UV) by the ozone layer.

Temperatures range from an average of −51 °C (−60 °F; 220 K) near the tropopause to an average of −15 °C (5.0 °F; 260 K) near the mesosphere. This temperature inversion makes the stratosphere dynamically stable; there is no regular convection and associated turbulence.

The mechanism addressing the formation of the ozone layer was described by British mathematician Sydney Chapman in 1930. Paul J. Crutzen, Mario J. Molina and F. Sherwood Rowland were awarded the Nobel Prize in Chemistry in 1995 for their work describing the formation and decomposition of stratospheric ozone. The ozone layer helps protect living things from harmful ultraviolet rays from the sun. Concerns about its depletion and subsequent harmful radiation date back to the 1970s. Scientists later discovered a “hole” in the ozone layer over the Antarctic in the 1980s, catalyzing the global community to ratify the Vienna Convention and its Montreal Protocol (16 September 1987) to reduce and eliminate chemicals that harm the ozone layer.

Nobel prize winner Mario Molina hails the Montreal Rowland and Molina in a scientific article Protocol as “a unique, planet-saving agreement. And it published in the journal Nature in 1974 warn is still getting stronger, playing a critical role that human-generated Chlorofluorocarbons safeguarding the global commons of the planetary (CFCs) are harming the ozone layer. system.” The largest Antarctic More than 99 percent of ozone depleting substances ozone hole, averaging 26.6 have been phased out by the Montreal Protocol over million square kilometres, the last 30 years, and the ozone layer is on track to is recorded in 2005. recovery by mid-century. Ozone is extremely valuable since it absorbs a range of ultraviolet energy. When an ozone molecule absorbs even low-energy ultraviolet radiation, it splits into an ordinary oxygen molecule and a free oxygen atom. Usually, this free oxygen atom quickly re- joins with an oxygen molecule to form another ozone molecule. Because of this "ozone-oxygen cycle," harmful ultraviolet radiation is continuously converted into heat.

푂3 + ℎ휈 → 푂2 + 푂 (+푡ℎ푒𝑖푟 푘𝑖푛푒푡𝑖푐 푒푛푒푟푔푦 ≡ ℎ푒푎푡) 푂2 + 푂 → 푂3

Because ozone and free oxygen atoms are highly unstable, they react very easily with nitrogen, hydrogen, chlorine, and bromine compounds that are found naturally in Earth's atmosphere (released from both land and ocean sources). For example, single chlorine atoms can convert ozone into oxygen molecules and this ozone loss balances the production of ozone by high-energy ultraviolet rays striking oxygen molecules.

푂2 + ℎ휈 → 푂 + 푂 푂2 + 푂 → 푂3 Human production of chlorine-containing chemicals such as chlorofluorocarbons (CFCs) has added an additional factor that destroys ozone. Once in the stratosphere, the CFC molecules are no longer shielded from ultraviolet radiation by the ozone layer. Bombarded by the sun’s ultraviolet energy, CFC molecules break up and release chlorine atoms.

퐶푙 + 푂3 → 퐶푙푂 + 푂2 퐶푙푂 + 푂 → 퐶푙 + 푂2

If each chlorine atom released from a CFC molecule destroyed only one ozone molecule, CFCs would pose very little threat to the ozone layer. However, this reaction happens over and over again, allowing a single atom of chlorine to act as a catalyst, destroying many molecules of ozone. Fortunately, chlorine atoms do not remain in the stratosphere forever. When a free chlorine atom reacts with gases such as methane (CH4), it is bound up into a molecule of hydrogen chloride (HCl), which can be carried downward from the stratosphere into the troposphere, where it can be washed away by rain. Stratosphere explorer  https://www.ted.com/talks/alan_eustace_i_leapt_from_the_stratosphere_here_s_how_i_did_it?language=en#t-851119 (14 minutes 21 seconds) TED2015 | March 2015 On October 24, 2014, Alan Eustace donned a custom- built, 235-pound spacesuit, attached himself to a weather balloon, and rose above 135,000 feet, from which point he dove to Earth, breaking both the sound barrier and previous records for high-altitude jumps. On October 24, 2014, Alan Eustace became the record holder for reaching the altitude record for a manned balloon at 135,890 ft (41,419 m). Eustace also broke the world records for vertical speed skydiving, reached with a peak velocity of 1,321 km/h (822 mph) and total freefall distance of 123,414 ft (37,617 m) – lasting four minutes and 27 seconds. Mesosphere

In the mesosphere, 50 푘푚 ≤ ℎ ≤ 80 푘푚, temperature decreases as altitude increases. This characteristic is used to define its limits: it begins at the top of the stratosphere (sometimes called the stratopause), and ends at the mesopause, which is the coldest part of Earth's atmosphere with temperatures below −143 °C (−225 °F; 130 K).

The mesosphere is cold enough to freeze water vapor in its atmosphere into ice . These ice clouds are blue-white and are called noctilucent clouds or . These clouds are more visible at sunset from the earth's poles.

Most meteors are known to burn and vaporize in this level. As a result, the mesosphere has a relatively high concentration of iron and other metal atoms from meteor materials. There are approximately 40 tons of meteors that fall towards Earth every day. Meteoritics terminology

Meteoroids = typically smaller bodies < 10 푐푚 in the inner solar system (chunks of comets and/or asteroids). Smallest particles from comets tail can be only ~0.5 휇푚 and largest meteoroids can be ~300 푚 (a bit fuzzy boundary between large meteoroid and small asteroid). At 1AU from the Sun their speed can be easily ~40 푘푚/푠 and typically not more than ~70 푘푚/푠.

Meteor = a glowing streak of ionized gas from meteoroid heated to incandescence due to collision with air molecules (typically at about ~90 푘푚 altitude). The typical size of meteoroid that gives rise to naked-eye meteor is less than 1 cm across.

Meteorite = a meteoroid remnant that reaches the Earth’s surface (primarily chunks of asteroids; 95% are stony , i.e. silicate rock meteoroids and 5% are iron , i.e. iron-nickel alloy meteoroids). They need to be larger than at least 3 cm to survive passage through atmosphere. Meteoroids that completely vaporize are typically chunks of comets. What cause meteors to burn in the atmosphere? “Shooting stars” physics

푣Ԧ푠표푢푛푑 A meteor moves very fast and collides with many air particles. These microscopic collisions add to form a macroscopic drag force that slows down the meteor.

In the meteor’s co-moving frame drag force can be related to air pressure in the vicinity of meteor. This pressure is different from atmospheric pressure 푣Ԧ 푚푒푡푒표푟 as air in the vicinity of the meteor is

푣Ԧ푠표푢푛푑 more tightly packed. By application of adiabatic compression, one could relate temperature in the vicinity of the meteor to ambient temperature. Physical quantities in the vicinity of In the meteor’s co-moving frame meteor are labeled with star symbol 퐶퐷 2 퐶퐷 2 퐹푑푟푎푔 = 𝜌푎푡푚푣푚푒푡푒표푟 A → 푝∗ = 𝜌푎푡푚푣푚푒푡푒표푟 For simplicity assume 2 2 meteor is disk 푣Ԧ푠표푢푛푑

푝푎푡푚 𝜌푎푡푚 In the adiabatic approximation 푣Ԧ푠표푢푛푑∗ 푇 훾 푝∗ 푎푡푚 2 훾−1 푝∗ 퐶퐷 𝜌푎푡푚푣푚푒푡푒표푟 푇∗ 𝜌∗ = = 푇∗ 푝푎푡푚 2 푝푎푡푚 푇푎푡푚

푣Ԧ푠표푢푛푑∗ 퐶 7 For 퐷 ≅ 1and 훾 = for diatomic gasses 2 5 푣Ԧ 푚푒푡푒표푟 2 2 7 𝜌푎푡푚푣푚푒푡푒표푟 𝜌푎푡푚 푝 푇∗ = 푇푎푡푚 푎푡푚 푝푎푡푚 푇푎푡푚 푣Ԧ푠표푢푛푑 Let’s check this result in the upper mesosphere, say at ℎ = 70 푘푚, for meteor moving with 푣푚푒푡푒표푟 = 5 푘푚/푠. (compare with 푣푠표푢푛푑 = 0.2971 푘푚/푠 for this altitude)

The conventional values for temperature, density, and pressure may be obtained at http://www.aerospaceweb.org/design/scripts/atmosphere/ For ℎ = 70 푘푚 푘푔 푇 = 219.6퐾 , 𝜌 = 0.000082829 , 푝 = 5.2209 푃푎 푎푡푚 푎푡푚 푚3 푎푡푚

Hence, one obtains for 푣푚푒푡푒표푟 = 5 푘푚/푠

표 푇∗ = 푇푎푡푚5.5256 = 1,213.4 퐾 = 940. 4 퐶

For 푣푚푒푡푒표푟 = 15 푘푚/푠

표 푇∗ = 푇푎푡푚10.352 = 2,273.3 퐾 = 2,000. 3 퐶 Large meteoroid impacts on record

Tunguska, Siberia 1908: Trees flattened for tens of kilometers in all directions, shattered windows hundreds kilometers away, lights seen in London UK

Barringer Crater, Arizona (about 50,000 years ago): crater 1.5 푘푚 in diameter created by the impact of an iron meteorite ~50 푚 across

Btw, Cretaceous-Tertiary extinction (~65 million years ago) most likely caused by nuclear winter caused by an impact of an asteroid or comet with the Earth: dinosaurs' disappearance, death of 99% of all organisms, and the extinction of 75% of all species. Most likely location: Chicxulub Crater on the Yucatan peninsula (180 km diameter, most likely caused by an impacting body ~10 km across). Ionosphere Earth's atmosphere contains a series of regions that have a relatively large number of electrically charged atoms and molecules. As a group, these regions are collectively called the ionosphere. There are three main regions of the ionosphere, called the D layer, the E layer, and the F layer. These regions do not have sharp boundaries, and the altitudes at which they occur vary during the course of a day and from season to season. The ionosphere is very different in the daytime versus night. During the day, X-rays an UV light from the Sun continuously provides the energy that knocks electrons free from atoms and molecules, producing a continuous supply of ions and free electrons. At the same time, some of the ions and electrons collide and re-combine to form normal, electrically neutral atoms and molecules. During the day, more ions are created than are destroyed, so the number of ions in the three regions increases. At night, the recombination process takes over in the absence of sunlight, and the number of ions drops. Over the course of most nights, the D region disappears entirely and the E region weakens as the number of ions in that layer plummets. Ionosphere and radio

Before communication via satellites became common, the operators of radio communication systems often used the ionosphere to extend the range of their transmissions. Radio waves generally travel in straight lines, so unless a tall transmission tower can "see" the top of a receiver tower, the curvature of the Earth limits the range of radio transmissions to stations that are not over the horizon. However, some frequencies of radio waves bounce or reflect off of the electrically charged particles in certain ionosphere layers. Pre-satellite radio communications often took advantage of this phenomenon, bouncing radio waves off of the "sky" to extend the range of the signals. Radio operators had to account for the constant changes in the ionosphere, particularly the shifts or disappearance of the layers between day and night, to effectively take advantage of these mirror-like reflections of radio waves. Thermosphere

Thermosphere: 80 to 700 km (50 to 440 miles). Within this layer of the atmosphere, ultraviolet radiation causes photoionization and photodissociation of molecules, creating ions. Thermospheric temperatures increase with altitude due to absorption of highly energetic solar radiation. Temperatures are highly dependent on solar activity and can rise to 1,700 °C (3,100 °F) or more. The Kármán line is an attempt to define a boundary between Earth's atmosphere and outer space. The Fédération Aéronautique Internationale (FAI) defines the Kármán line as the altitude of 100 kilometres (62 miles; 330,000 feet) above Earth's mean sea level. Clouds

Clouds are classified according to their height above and appearance (texture) from the ground.

The following roots and translations summarize the components of this classification system:

1) Cirro-: curl of hair, high. 2) Alto-: mid. 3) Strato-: layer. 4) Nimbo-: rain, . 5) Cumulo-: heap. From the World Meteorological Organization's (WMO) International Cloud Atlas

High-Level Clouds Cirrus (Ci), Cirrocumulus (Cc), and Cirrostratus (Cs) are high level clouds. They are typically thin and white in appearance, but can appear in a magnificent array of colors when the sun is low on the horizon. Ci: Detached clouds in the form of white, delicate filaments, mostly white patches or narrow bands. They may have a fibrous (hair-like) and/or silky sheen appearance. Composed of ice crystals, and their transparent character depends upon the degree of separation of the crystals.

Cc: Thin, white patch, sheet, or layered of clouds without shading. They are composed of very small elements in the form of more or less regularly arranged grains or ripples. In general, Cirrocumulus represents a degraded state of cirrus and cirrostratus.

Cs: Transparent, whitish veil clouds with a fibrous (hair-like) or smooth appearance. A sheet of cirrostratus which is very extensive, nearly always ends by covering the whole sky typically with halo phenomena produced with the sun or the moon in the background. From the World Meteorological Organization's (WMO) International Cloud Atlas

Mid-Level Clouds Altocumulus (Ac), Altostratus (As), and Nimbostratus (Ns) are mid-level clouds They are composed primarily of water droplets. However, they can also be composed of ice crystals when temperatures are low enough. Ac: White and/or gray patch, sheet or layered clouds, generally composed of laminae (plates), rounded masses or rolls. They may be partly fibrous or diffuse and may or may not be merged. The most common mid cloud, more than one layer of Altocumulus often appears at different levels at the same time. As: Gray or bluish cloud sheets or layers of striated or fibrous clouds that totally or partially covers the sky. They are thin enough to regularly reveal the sun as if seen through ground glass. Do not produce a halo phenomenon. At times may even reach the ground causing very light precipitation.. Ns: Resulting from thickening Altostratus, dark gray cloud layer diffused by falling rain or snow. Thick enough throughout to blot out the sun. The cloud base lowers as precipitation continues. Because of the lowering base it is often erroneously called a low-level cloud. From the World Meteorological Organization's (WMO) International Cloud Atlas

Low-Level Clouds Cumulus (Cu), Stratocumulus (Sc), Stratus (St), and Cumulonimbus (Cb) are low clouds composed of water droplets. Cumulonimbus, with its strong vertical updraft, extends well into the high level of clouds. Cu: Detached, dense clouds with sharp outlines developed vertically in the form of rising mounds, domes or towers with bulging upper parts often resembling a cauliflower. Develops on days of clear skies, and is due diurnal convection; it appears in the morning, grows, and then dissolves again toward evening.

Sc: Gray or whitish patch, sheet, or layered clouds which almost always have dark tessellations (honeycomb appearance), rounded masses or rolls. Except for they are non-fibrous and may or may not be merged.

St: A generally gray cloud layer with a uniform base which may, if thick enough, produce drizzle, ice prisms, or snow grains. When the sun is visible through this cloud, its outline is clearly discernible. Sometimes appearing as ragged sheets Do not produce a halo phenomenon except, rarely at very low temperatures. Cumulonimbus (Cb)

The thunderstorm cloud, this is a heavy and dense cloud in the form of a mountain or huge tower. The upper portion is usually smoothed, fibrous or striated and nearly always flattened in the shape of an anvil or vast plume. Under the base of this cloud which is often very dark, there are often low ragged clouds that may or may not merge with the base. They produce precipitation, which sometimes is in the form of virga. Cumulonimbus clouds also produce hail and tornadoes. What Are the Different Types of Clouds? (2 minutes and 55 seconds) https://www.youtube.com/watch?v=JIkEMBiT6hQ&feature=emb_logo NOAA SciJinks

Beautiful Science - The Science of Clouds (5 minutes and 43 seconds) https://www.youtube.com/watch?v=dnL5LPil77M Beautiful Science Lightning science

This video was recorded at The awesome power of the lightning stroke Left video shows just two main 4000 frames/second. It shows a originates in the thunderstorm cloud where channels of a stepped leader highly branched step leader charges somehow become separated. The approaching ground. The first to make approaching the ground. When one exact mechanism of charge separation is not a connection discharges the entire branch of the stepped leader makes yet fully understood. Although air is normally channel. Right video is the same as left a connection, a very bright return an excellent insulator, when stressed by a video, except played back at an even stroke surges upward through the sufficiently high voltage (an electric field of slower rate to show the apparent 6 channel. about 3 푥 10 푉/푚 or 3 푘푉/푚푚 ), air can movement of the return stroke as the begin to break down, becoming partially two channels are discharged. conductive. (see Paschen's Law) Lightning science

While the exact details of the charging process are still being studied, scientists generally agree on some of the basic concepts of thunderstorm electrification. The main charging area in a thunderstorm occurs in the central part of the storm where air is moving upward rapidly (updraft) and temperatures range from -15 to -25 Celsius. The combination of temperature and rapid upward air movement produces a mixture of super-cooled cloud droplets (small water droplets below freezing), small ice crystals, and soft hail (graupel). The updraft carries the super-cooled cloud droplets and very small ice crystals upward. At the same time, the graupel, which is considerably larger and denser, tends to fall or be suspended in the rising air. The differences in the movement of the precipitation cause collisions to occur. When the rising ice crystals collide with graupel, the ice crystals become positively charged and the graupel becomes negatively charged. Dielectric strength of air around 3 MV/m

When a large enough electric field is applied to any insulating substance, at a certain field strength the concentration of charge carriers in the material suddenly increases by many orders of magnitude, so its resistance drops and it becomes a conductor. This is called electrical breakdown. The field strength at which breakdown occurs is an intrinsic property of the material called its dielectric strength. For gases, dielectric strength increases with pressure according to Paschen's law.

Paschen's law is an equation that gives the breakdown voltage, that is, the voltage necessary to start a discharge or electric arc, between two electrodes in a gas as a function of pressure and gap length. For air, dielectric strength increases slightly as the absolute humidity increases but decreases with an increase in relative humidity.

Absolute humidity is the measure of water vapor (moisture) in the air, regardless of temperature. It is expressed as grams of moisture per cubic meter of air (g/m3). Relative humidity also measures water vapor but RELATIVE to the temperature of the air. It is expressed as the amount of water vapor in the air as a percentage of the total amount that could be held at its current temperature. At breakdown, the electric field frees bound electrons. If the applied electric field is sufficiently high, free electrons from background radiation may be accelerated to velocities that can liberate additional electrons by collisions with neutral atoms or molecules, in a process known as avalanche breakdown. Breakdown occurs quite abruptly (typically in nanoseconds), resulting in the formation of an electrically conductive path and a disruptive discharge through the material. Lightning science

Stepped leader cloud-to-ground stroke refers to motion of electrons toward ground along branched structure with about 50 푚 steps. Each step represents an initial rush of electrons along some direction causing multiple ionizing collisions with air molecules and hence inducing an avalanche of electrons in the same direction. The process of ionization is accompanied with dim light that is visible on high-speed camera. This avalanche step is slowed down to full stop due to slow, inert positive ions that are left behind. As electrons accumulate at the end of the stopped step the conditions for new rush through breakdown air are met again and “stepping” process repeats itself.

The stepped leader takes about 5/1000 of a second, moving at about 240 miles per second, to reach from cloud to ground. Lightning science

Eventually the electric circuit is fully closed when one of the brunches touches the ground and then all the electrons in all brunches rush toward realized brunch or channel. The large amount of light will be emitted from the contact point in the vicinity of ground because there will be many electrons and ionization events in that region. As time progresses new incoming electrons will “slowly” fill the vertical realized path in bottom-top approach and lightning will appear as moving from ground toward cloud. This is however just visual illusion as no particles are actually moving upward.

Even though the negative charges all move from cloud to ground, the bright flash of lightning moves from ground to cloud in a speedy 1/10,000 of a second, moving 푡푒푛푠 표푓 푡ℎ표푢푠푎푛푑 miles per second! Lightning science

The super-heated air expands outward explosively, producing the shock wave we hear as thunder. The bright flash of glowing air is called the return stroke since it moves from ground to cloud, opposite to the moving charges.

The breakdown plasma passage is available for quite some time and hence typically other pockets of separated charge in the cloud will discharge using the same originally realized path or channel. Usually there are 2-3 such lightning flickering and up to 40 has been recorded.

There is quite a lot of energy in a lightning stroke, about 250 kilowatt-hours. With that amount of energy, you could lift a 푚푒푡푟𝑖푐 푡표푛 heavy car 92 푘푚 high! The Greenhouse Effect

The average surface temperature of the moon, which has no atmosphere, is 0°F (-18°C). By contrast, the average surface temperature of the Earth is 59°F (15°C). This heating effect is called the greenhouse effect.

According to the Faint Young Sun Paradox the early Sun was probably only about 70% as bright as it is in modern times and hence early Earth may have had much, much higher concentrations of greenhouse gases in its atmosphere; enough to warm the planet above freezing despite the dimmer Sun. There is a lot of geologic evidence that there was liquid - not frozen - water on Earth even very early in our planet's history.

The Green House effect is all about the balance; the earth-atmosphere energy balance is the balance between incoming energy from the Sun and outgoing energy from the Earth.

Without greenhouse effect, our planet would be a frozen ball of ice. Thanks to the natural greenhouse effect, Earth is a comfortable place for life as we know it. However, too much of a good thing can cause problems. In recent decades, a rise in the amount of so-called greenhouse gases has likely begun to warm Earth a bit too much. There are several different types of greenhouse gases. The major ones are carbon dioxide, water vapor, methane, and nitrous oxide. These gas molecules all are made of three or more atoms. The atoms are held together loosely enough that they vibrate when they absorb heat. Eventually, the vibrating molecules release radiation, which will likely be absorbed by another greenhouse gas molecule. This process keeps heat near the Earth’s surface. Most of the gas in the atmosphere is nitrogen and oxygen, which cannot absorb heat and contribute to the greenhouse effect.

There was about 270 parts per million volume (ppmv) of 퐶푂2 in the atmosphere in the mid-19th century at the start of the Industrial Revolution. The amount is growing as burning fossil fuels releases carbon dioxide into the atmosphere. There is about 400 parts per million volume (ppmv) now. 퐶푂2 accounts for ~76% of global human-caused emissions. Once it’s emitted 40%, 20%, 10% still remains after 100, 1000, 10000 years respectively…

Recommended reading: https://www.nrdc.org/stories/greenhouse-effect-101 푓ℎ표푡

푓푐표푙푑

ퟐ ퟒ 푁푐표푙푑 ퟐ ퟒ 푁 ퟏ ퟏ ℎ표푡

ퟑ ퟑ ퟓ ퟓ

푇푐표푙푑 푇ℎ표푡 Imagine hypothetical planet which was first “cold” and had 푁푐표푙푑 greenhouse molecules in its atmosphere per 푚2. The energy 2 (3) are planet’s blackbody radiated photons outside (inside) window centered at 15 휇푚 corresponding to greenhouse vibrational levels. The planet surface is in thermal equilibrium, i.e. 1+5=2+3 which is equivalent to 1=2+4 as 3=4+5. The number of photons emitted each second per 푚2 with greenhouse compatible energies is 푓푐표푙푑 15 휇푚 ∆휆 푐 ℎ 15 휇푚 Portion of those photons will interact with greenhouse molecules each second 푓푐표푙푑 15 휇푚 ∆휆 푐 푁푐표푙푑𝜎푡표푡푎푙 ℎ 15 휇푚 with 𝜎푡표푡푎푙 being total cross section. And say half will return back to surface as energy 5 1 ퟓ = 푓 15 휇푚 푁 𝜎 ∆휆 2 푐표푙푑 푐표푙푑 푡표푡푎푙 Hence, planet’s surface temperature can be deduced from 1 𝜎푇4 = 푃 + 푓 15 휇푚 푁 𝜎 ∆휆 푐표푙푑 푠푡푎푟 2 푐표푙푑 푐표푙푑 푡표푡푎푙 Now imagine that for some reason the number of greenhouse molecules in its atmosphere increased to 푁ℎ표푡. Hence, following the same reasoning, planet’s surface temperature can be deduced from 1 𝜎푇4 = 푃 + 푓 15 휇푚 푁 𝜎 ∆휆 ℎ표푡 푠푡푎푟 2 ℎ표푡 ℎ표푡 푡표푡푎푙

Quite generally instead of “cold” and “hot” one could parametrize variables with temperature 1 𝜎푇4 = 푃 + 푓 15 휇푚 푁 𝜎 ∆휆 푠푡푎푟 2 푇 푇 푡표푡푎푙

2휋ℎ푐2 Recall, according to Planck radiation law 푓 15 휇푚 = . 푇 15 휇푚 5 푒ℎ푐Τ 15 휇푚 푘푇−1

Therefore, for example, one could easily relate change in temperature with change in number of greenhouse molecules for known total cross section 𝜎푡표푡푎푙 and window width ∆휆. This is very simplified model, but it can be helpful to develop scientific “intuition” regarding greenhouse effect. Till 2012 Till 2019