Theoretical Tropical Meteorology

1. Introduction: Earth’s tropical atmosphere and ocean (Nov. 21)2. Conservation laws and basic equations (Nov. 22)3. Atmospheric vertical structure: Radiative convection equilibrium (Nov. 22)4. Mean zonal and meridional circulations (Nov. 23-24)5. Equatorial waves (Nov. 28-29) 6. Convection: Why can’t we predict rainfall? (Nov. 30-Dec. 1) Open seminar: Tropical coastlines controlling global climate (Dec. 2)

Manabu D. YamanakaSenior Staff, DCOP, JAMSTEC / Professor Emeritus, Kobe University

mdy@jamstec.go.jp, mdy@kobe-u.ac.jp]

Short-term Expert Training Course on Weather Forecasting I, JICA–Sri Lanka Department of Meteorology Improving of Meteorological Observation, Weather Forecasting & Dissemination

Project, 21 November – 1 December 2016http://aoe.scitec.kobe-u.ac.jp/~mdy/srilanka1611/

Additional reading:- Physical climatology of Indonesian maritime continent: An outline to comprehend observational studies, Atmos. Res., Invited Review Section, 178-179, 231-259. http://www.sciencedirect.com/science/article/pii/S0169809516300679

http://www.sciencedirect.com/science/article/pii/S0169809516300679

}→ Chapters 1‐3, 6 → Chapters 3‐5 

}→ Chapters 5‐6 → Seminar 

Yangon

Bangkok HanoiManila

Kuala Lumpur Singapore JakartaJayapura

Dec‐Jan‐Feb monsoon

Monsoons and rainy seasons

Jun‐Jul‐Aug monsoon

Colombo

From large-scale viewpoint

From physical/dynamical viewpoint

Similarity, applicability

Difference from mid/high latitudes

Contents1. Introduction: Earth’s tropical atmosphere and ocean (Nov. 21)2. Conservation laws and basic equations (Nov. 22)3. Atmospheric vertical structure: Radiative-convective equilibrium (Nov. 22)

3.1. Radiative equilibrium3.2. Radiative-convective equilibrium3.3. Moisture effect3.4. Log-pressure coordinate

4. Mean zonal and meridional circulations (Nov. 23-24)4.1. Trade wind (Equatorial easterly)4.2. Potential vorticity conservation and inertial instability4.3. Hadley circulation4.4. Monsoon circulation4.5. Brewer-Dobson circulation

5. Equatorial waves (Nov. 28-29)5.1. Classification of waves in geophysical fluids5.2. Zonal-vertical (Walker) circulation5.3. Atmosphere-ocean interaction: El Nino-southern oscillation (ENSO) and Indian-Ocean dipole mode (IOD) 5.4. Wave-mean flow interaction: Quasi-biennial oscillation (QBO) and semi-annual oscillation (SAO)

6. Convection: Why can't we predict rainfall? (Nov. 30-Dec. 1) 6.1. Sea-land breeze circulation (Horizontal convection)6.2. Conditional instability and clouds (Vertical convection)6.3. Conditional instability of second kind (CISK) and tropical cyclones 6.4. Multiple-scale cloud clusters and intraseasonal variations: Madden-Julian oscillation

Open seminar: Tropical coastlines controlling global climate (Dec. 2)

http://aoe.scitec.kobe-u.ac.jp/~mdy/srilanka1611/

1. Introduction: The earth ’s equatorial region

Two aspects of atmospheric-hydrospheric-oceanic science: 1. “Geography”: locality, descriptive → “Tropical meteorology/hydrology/oceanography”2. “Physics”: Generality, theoretical

Recent development- Technical innovation: Network computers and observational instruments- Sustainability (continuous development without environmental damages) - Other planets (including extra-solar planets) ⇒ General consideration

Change of scientific interests Geography by observation scientists; Physics by theoreticians

⇒ Geography by modelers; Observations by physicists

Common (a few) physical principles for atmospheric/hydrospheric/oceanic phenomena atmosphere＋hydrosphere＋ocean ⇒ climate

Quantitative description and prediction.by mathematics & computers (as tools)⇒ More efficient assessment/operations for environment, disaster , … .

Characteristics of “Equatorial” atmosphere, hydrosphere and oceans- Earth’s rotation axis becomes horizontal → small Coriolis force- Stronger solar heating and weaker annual cycle → hotness and diurnal cycles - Broad ocean → active evaporation, convective cloud generation and latent heating- Wind (around cyclones) makes clouds in extratropics, but clouds make wind in tropics

Universe:  13.7 billion years

Solar System (Planets):4.5 billion years 

Earth with continents, oceans & lives 

Sufficient Oxigen and Landing of lives 400 million years 

Human beings 5 million years 

Both ∝ (distance)－2, but planetary response is different Gravitation

Radiation

（star）

Two major forcings of star on planet

Balanced with planetary IR cooling・Time scale ≫ rotation

⇒Meridional differential heating・Time scale ～ rotation

⇒Zonal diffrential heatingAtmospheric tides

Balanced with revolutional centrifugal force

Revolutional orbit (Kepler’s laws)⇒ Stellar distance ⇒ Stellar radiation,

annual lengthOceanic tides, planetary tides

（star）

planet

planet

Sir Isaac Newton (1642 – 1726/27)

(http://www.newton.ac.uk/about/art-artefacts/newton-portrait)

(Gredenberg, 1995)

1298

Principles of Natural Philosophy(1687, 1713, 1726)

Opticks: Or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light

(1704)

Geometrical opticsLight wave

α → 1/sin α = 1/cos Zenith

→ sin α = cos Zenith

n → n2

→ 1/ n2

Geometry of solar radiationRadiation intensity = Energy flux/area

？ 倍

？ 倍

？

？

(Zenith)

Zenithangle

The distance-2 lawRadiation intensity at a ground with a solar zenith angle α

distance- times times

times

times

times

area

Radiation

zenith area

Radiation

(Integration (area) → Energy flux intensity)Stefan-Boltzmann’s law

≡

( =5.67 10−8 J s − 1 m − 2 K − 4)

(Differentiation (peak) → Maximum mode wavelength)Wien’s law

μm2897 K

(→ Exercise 1-2)

“Energy(-density) flux” (energy per unit time and unit area) for electromagnetic waves radiated (with unit solid angle and unit wavelength interval) from a “black body” with temperature T:

2exp / 1

( : wavelength, : light speed, : Boltzmann constant, : Planck constant).

(Andrews, 2000, Chapter 3

http://www.gahetna.nl/collectie/afbeeldingen/fotocollectie/zoeken/weergave/detail/start/2/tstart/0/q/zoekterm/Planck

Max Planck (1858-1947) Black Body Radiation Law (1900)

Electromagnetic waves

EHF SHF UHF VHF HF MF LF VLF

μm 1mm 1cm 10cm 1m 10m 100m 1km 10km 100km1Å 1nm

vacu

um u

ltrav

iole

t

X-r

ay

γ-ra

y

radi

o w

ave

1THz 100 10 1GHz 100 10 1MHz 100 10 1kHz

Frequency

W Ka KuXCS L

30000 3000 300 30 KTemperature

Sun Earth Radars Profilers Radios

Wavelength Frequency = Light Speed = 300,000 km/s

1 2 5 10 20 50

0

－100

－200

200

Solar Distance (108 km)

100

Earth Mars

Mercury

Venus

Surf

ace

Tem

pera

ture

(ºC

)

Habitable zone with liquid water

UranusSaturn NeptuneJupiter

Titan

· σ · 4 → 4σ ∝ 1

Distance l

radius r

( is the solar constantat the earth at =1 AU)

Parasol effect(Cooling)

Greenhouse effect

(Warming)

(a)(Trenberth et al., 2009)

(b)

Lord RayleighJohn William Strutt

(1842-1919)

Lord KelvinWilliam Thomson

(1824- 1907)

Why sky is blue?Shorter wavelength (violet)

=> Particle (Mie) refraction

Blue color light => Molecule (Rayleigh) refraction

Longer wavelength (green, yellow, red) => Moving straight (sunrise/sunset)

Rainbow by liquid droplets

(Wallace & Hobbs) (Wallace & Hobbs)

(Gedzelman)

(Wallace & Hobbs)

(Gedzelman)

Haloby ice crystals

Lunine (1999)

1904: Doctorate in civil engineering 1909: Professor of applied math at U. Belgrade (Beogradu) 1912: Noted insolation change by earth’s astronomical motion 1920, 30, & 41: Publication on glacial/interglacial cycles 1924: Evaluation (exceptional) by Kӧppen & Wegener 1958 (aged 79): Died of stroke in Belgrade

Milutin Milanković (1879 –1958)

(http://b.static.trunity.net/files/120401_120500/120456/Milankovitch.jpg)

(Milanković, 1941: Kanon der Erdbestrahlung und Seine Anwendung auf das Eiszeitenproblem; Japanese translation by Kshiwaya et al., 1992)

ඉහළ බැමුම්ஒரு சிறந்த ஸ்பின்

spin a top

http://xenon.colorado.edu/spotlight/

Climate-Glacier interaction

(Wallace & Hobbs, 2006)

Glacial isostatic adjustment

Almost linear response at ~20 and ~40 ky cycles.

Too week for the major ~100 ky glacier cycles.

Nonlinear climatic response(ice amount) (subsidence)

(subsidence) (ice amount)

⇓(ice amount) (ice amount) 0⇓

(ice amount) cos

（NASA, 1992)Climate change for recent 1 Myears

Pitecantropes

Toba eruptionLittl

e G

laci

al

Ocean/Continent ~ 7:3 has been conserved for recent 400 Myears

http://www.scotese.com

(Wegener, 1911: Thermodynamik der Atmosphäre; 松野, 1982より孫引き）

1905: Doctorate in astronomy. Work for aeronomy. . 1910: Conceiving of an idea of “continent drift” 1915: Publication of a book on the idea. Marriage. 1919-23: Paleoclimatology with father-in-law Kӧppen 1924: Professor at University of Glaz 1930 (aged 50): Died during Greenland expedition.

(http://www.bildindex.de/bilder/fm426294a.jpg)

Alfred Lothar Wegener (1880 –1930)

Volcano ashes transported by stratospheric zonal flow

(Toba 75,000 year ago; … ; Tambora 1816; Krakatau 1883; …. ; Agung 1964; ……)

Exercise 1 ‐ 1Knowing the solar constant (solar radiation intensity at the top of the atmosphere) as 

1370W/m (where 1 W = 1 J/s) and the sun‐earth distance as  1.5 10 m (called 1 AU, or astronomical unit), calculate the following. (1) Earth’s temperature in the simplest radiative equilibrium as considered in the 

previous slide.   Use the Stefan‐Boltzmann constant:  5.67 10 W m K .(2) Actually about 30% of  should be returned to the space (called albedo).   Then how  

large the equilibrium temperature?    What about the difference from actual earth’s temperature? 

(3) Estimate equivalent temperature on Venus at 0.728 AU and on Mars at 1.524 AU, and compare it with observational evidence in the previous slide.  

(4) Estimate the surface temperature of the sun with the radius 7.0 10 m.    (a little lower than the actual value) 

ANSWERS: (1)  4σ⁄ ≒ 278K   (Note that  is taken by AU. F or earth,  1.(2)  1 0.3 ≒ 0.915. 278K 0.915 254K 19ºC  (too cold!  Green house effect must be considered. → Chap.3)(3) Venus:   1 0.728⁄ ≒ 1.172. 278K 1.172 325K (lower than actual!  Due to greenhouse effect)

Mars:  1 1.524⁄ ≒ 0.729. 278K 0.729 202K  (4) 7.0 10 m/ 1.5 10 m ＝4.7 10 AU.  1 4.7  10⁄ ≒ 10.45278K 10.45 2905K  (lower than actual; due to neglect of radiation from below the solar surface) 

Exercise 1 ‐ 2Integrating and differentiating Planck’s law (for electromagnetic‐wave energy‐density flux per unit solid angle and unit wavelength interval): 

2exp / 1 ,

derive the Stefan‐Boltzmann law (for the total forward radiative energy flux):  

≡

and Wien’s law (for the wavelength with maximum intensity): 2897 [μm K] 

ANSWER: Assuming isotropy, the upward component is obtained by multiplying cos ϛ, where ϛ, is the zenith angle, and thesold‐angle integral with the upward hemisphere is rewritten as small‐circle integral with 2 sin ϛ ϛ.

2 cos ϛ sin ϛ ϛ/

2 cos ϛ sin ϛ ϛ/

·

In the first integral we put  ≡ sin ϛ, and in the second  ≡ / . Then  ≡ cos ϛ ϛ, and  ≡ ⁄ . 

2 ·2

1 ≡

The second integral may be obtained by a complex integral as  1⁄ 15⁄ , and the constant becomes 

2 ·2

1215 5.67 10 Wm K ,

using the Boltzmann (absolute gas) constant  =1.38 10 23 J/K, the Planck constant  =6.63 10 34 J s, and the light speed =3.00 108 m/s.  Finally, the differentiation of the Planck function is solved numerically as 

0 ∴ 5 / 5 ∴ 2857[μm K]