From Boundary Layer Climates, T.R. OKE

1. CHAPTER 1
Pabitra Gurung
ENERGY AND MASS
EXCHANGES

2. Contents
1. Atmospheric scales
2. A systems view of energy and mass exchanges and balances
3. Energy balances
(a) Radiation characteristics
(b) Energy balances of the total Earth-Atmosphere system
(c) Diurnal energy balance at an ‘ideal’ site
(d) Atmospheric motion
4. Mass balances
(a) Properties of water
(b) Water balance
(c) Other mass balances

3. 1. Atmospheric Scales
 Atmospheric features:
characterized by space
and time (associated
with motion)
 Small-scale turbulence
to Jet stream
 Micro to Local scale
categories (focused by
boundary layer)

4. 1. Atmospheric Scales
 The vertical structure of the atmosphere (Ideal picture)
o Influence of surface
(troposphere)
o Daily heating/solar cycle
o Rough and rigid surface
o Frictional drag
o Turbulence movement
o Height and Time (day and
night)
o Boundary layer (BL)
o Heat transfer
(day ↑, & night ↓)
o BL Depth (day: 1-2 km ↑, &
night: 100 m ↓)
o Turbulent surface layer
10 km
1 km (0.1 km – 2 km)
≈ 50 m at day time
≈ 1 to 3 times the ht./sp.
o Roughness layer and laminar boundary layer
o V, H, T : ≈1 km, ≈50 km, ≈1 day
o Large scale weather phenomena (wind and cloud patterns)

5. 2. A systems view of energy and mass
exchanges Earth-Atmospheric (EA) System
o Principal climatological parameters (air
temperature and humidity) for the fundamental
energy and water cycles
o Radiant, Thermal, Kinetic, and Potential energy
o Energy exchange (Conduction, convection and
radiation)
o First law of thermodynamics (Conservation of
energy): neither created nor destroyed
o Energy storage and temperature change
(process-response system: energy flow and
temperature change)
o General energy or mass balance equation
𝐸𝑛𝑒𝑟𝑔𝑦 𝐼𝑛𝑝𝑢𝑡 𝑄𝑖 = 𝐸𝑛𝑒𝑟𝑔𝑦 𝑂𝑢𝑡𝑝𝑢𝑡(𝑄 𝑜)
𝑄𝑖 = 𝑄 𝑜 + 𝐸𝑛𝑒𝑟𝑔𝑦 𝑆𝑡𝑜𝑟𝑎𝑔𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 (∆𝑄)
𝐼𝑛𝑝𝑢𝑡 − 𝑂𝑢𝑡𝑝𝑢𝑡 − 𝑆𝑡𝑜𝑟𝑎𝑔𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = 0

6. 3. Energy balances
(a) Radiation characteristics
o Radiation is transferred by photons
(bundles of energy), which have
properties similar to particles and
waves
o The electromagnetic fields and
spectrum
o Energy/photon energy and wave length
o Atmospheric application: 0.1 to 100
μm
o Visible portion of the spectrum
o Black body or full radiator (surface
emissivity, ε = 1)

7. 3. Energy balances
(a) Radiation characteristics
o Planck’s Law (relation between the amount
of radiation emitted by a black body, and
the wavelength of that radiation)
o Stefan-Boltzmann Law (total energy emitted
≈ area under the Planck’s curve)
𝐸𝑛𝑒𝑟𝑔𝑦 𝑒𝑚𝑖𝑡𝑡𝑒𝑑 = 𝜀𝜎𝑇0
4
Where,
𝜀 = Emissivity (0 – 1)
𝜎 = Stefan-Bolzmann proportionality constant
(5.67× 10−8
𝑊𝑚−2
𝐾−4
)
𝑇0 = Surface temperature of the body (K)
o Short-wave (0.15 – 3.0 μ𝑚) and Long-wave
(3.0 – 100 μ𝑚)
Approx. avg. temp. of the Sun (6000 K) and the E-A system (300
K)
0.48 μm
10 μm

8. 3. Energy balances
(a) Radiation characteristics
o Planck’s Law (relation between the amount
of radiation emitted by a black body, and
the wavelength of that radiation)
o Stefan-Boltzmann Law (total energy emitted
≈ area under the Planck’s curve)
𝐸𝑛𝑒𝑟𝑔𝑦 𝑒𝑚𝑖𝑡𝑡𝑒𝑑 = 𝜀𝜎𝑇0
4
Where,
𝜀 = Emissivity (0 – 1)
𝜎 = Stefan-Bolzmann proportionality constant
(5.67× 10−8
𝑊𝑚−2
𝐾−4
)
𝑇0 = Surface temperature of the body (K)
o Short-wave (0.15 – 3.0 μ𝑚) and Long-wave
(3.0 – 100 μ𝑚)
o The wavelength of peak emission (λ 𝑚𝑎𝑥)
λ 𝑚𝑎𝑥 𝑇0 = 2.88 × 10−3
𝑚𝐾
Approx. avg. temp. of the Sun (6000 K) and the E-A system (300
K)

9. 3. Energy balances
(a) Radiation characteristics
o Radiation of wavelength (λ) or Incident energy
𝐼𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑒𝑛𝑒𝑟𝑔𝑦 = 𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑒𝑛𝑒𝑟𝑔𝑦 +
𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑒𝑛𝑒𝑟𝑔𝑦 + 𝐴𝑏𝑠𝑜𝑟𝑝𝑒𝑑 𝑒𝑛𝑒𝑟𝑔𝑦
o For single wavelength
𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑣𝑖𝑡𝑦(ψλ) + 𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑣𝑖𝑡𝑦(𝛼λ) + 𝐴𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑣𝑖𝑡𝑦(ζλ) = 1
o Kirchhoff’s Law of thermal radiation (at the same temperature and wavelength, good
absorbers are good emitters)
For a full radiator; ζλ = ελ = 1, 𝑎𝑛𝑑 ψλ = 𝛼λ = 0
For an opaque non-black body; ψλ ≈ 0, 𝑎𝑛𝑑 𝛼λ = 1 − ζλ = 1 − ελ
o Very helpful in long-wave exchange considerations between bodies at typical E-A system
temperatures
Surface albedo for solar radiation Emissivity (ελ) for the same radiation

10. 3. Energy balances
(a) Radiation characteristics
o Absorption at various wavelengths by constituents of the Atmosphere

11. 3. Energy balances
(b) Energy balance of the total Earth-Atmosphere system
o The annual energy balance of E-A system
o Energy exchanges between the earth, the
atmosphere and space
o Most of natural surfaces: 𝜀 ≈ 1
o Earth mean annual temp. ≈ 288 K
𝐸𝑛𝑒𝑟𝑔𝑦 𝑒𝑚𝑖𝑡𝑡𝑒𝑑 𝑏𝑦 𝑒𝑎𝑟𝑡ℎ 𝑠𝑢𝑟𝑓𝑎𝑐𝑒
= 𝜀𝜎𝑇0
4
≤ 390 𝑊𝑚−2
o Radiation budget of E-A system
𝑆𝑜𝑙𝑎𝑟 𝑖𝑛𝑝𝑢𝑡(100%)
= 𝑆ℎ𝑜𝑟𝑡𝑊𝑎𝑣𝑒 𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑(28%)
+ 𝐿𝑜𝑛𝑔𝑊𝑎𝑣𝑒 𝐸𝑚𝑖𝑠𝑠𝑖𝑜𝑛(72%)
o Equilibrium: the E-A system and the E-A sub-
system
o Annual net sub-surface storage is zero
o Net 𝑄 𝐺 in annual balance is also zero
𝐾 𝐸𝑥 = 𝐾 ↑(𝐴𝑐)+ 𝐾 ↑(𝐴𝑎)+𝐾
∗
(𝐴𝑐)+𝐾
∗
(𝐴𝑎) +𝐾 ↑(𝐸) +𝐾
∗
(𝐴𝐸)
100% = 19% + 6% + 5% + 20% + 3% + 47%
𝐾 𝐸𝑥 = Spatial mean energy input ≈ 338 W m-2
(Values are in %)

12. 3. Energy balances
(c) Diurnal energy balance at an ‘ideal’ site
o Diurnal variation of the important radiation
budget components
o Diffusion of radiation (Cloud, water vapour
haze, smoggy areas, distance between sun
and atmosphere)
o Net radiation budget
𝑁𝑒𝑡 𝑠ℎ𝑜𝑟𝑡𝑤𝑎𝑣𝑒 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛(𝐾∗) = 𝐾 ↓ −𝐾 ↑
𝑁𝑒𝑡 𝑙𝑜𝑛𝑔𝑤𝑎𝑣𝑒 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛(𝐿∗
) = 𝐿 ↓ −𝐿 ↑
o Total net radiation budget on the earth
surface (𝑄∗)
𝐴𝑡 𝑑𝑎𝑦 𝑡𝑖𝑚𝑒, 𝑄∗
= 𝐾∗
+ 𝐿∗
𝐴𝑡 𝑛𝑖𝑔ℎ𝑡 𝑡𝑖𝑚𝑒, 𝑄∗
= 𝐿∗
Radiation budget components for 30July1971, at Matador,
Saskatchewan over a 0.2 m stand of native grass in cloudless
[𝐾 ↑= 𝛼𝐾 ↓]
[𝐿 ↑= 𝜀𝜎𝑇0
4
+ 1 − 𝜀 𝐿 ↓]

13. 3. Energy balances
(c) Diurnal energy balance at an ‘ideal’ site
o Convective heat exchange to or from
atmosphere (sensible or latent heat), and
conduction to or from the underlying soil
𝑄∗ = 𝑄 𝐻 + 𝑄 𝐸 + 𝑄 𝐺
(a) Energy balance component, (b) temperatures (Surface,
air, and soil). On 30July1971, at Agassiz, BC with cloudless

14. 3. Energy balances
(c) Diurnal energy balance at an ‘ideal’ site
o Effects of cloud and non-uniform surface properties
o Direct beam (S) and diffuse radiation (D)
Variation of incoming solar radiation on a very hazy day (10August1975) in central Illinois

15. 3. Energy balances
(d) Atmospheric motion
o Air Movement: Horizontal temperature
difference and horizontal pressure
differences
o Thermal energy of the solar cycle to the
kinetic energy of wind systems
o The kinetic energy dissipation
o In annual scale, balance between the
kinetic energy production and dissipation
o Concerned of the boundary layer; (a) wind
system generated by horizontal thermal
differences, (b) role of surface roughness
in shaping the variation of wind speed
with height

16. 4. Mass balances
(a) Properties of water
o An importance climatological substance
o The high heat capacity (4.18 × 106
𝐽𝑚−3
𝐾−1
)
o More energy input and energy storage
o States of water in the E-A system: ice, water and water vapour based on the
temperature
o Latent heat of fusion (𝑳 𝒇): The energy required for the melting or freezing
(𝟎. 𝟑𝟑𝟒 𝑀𝐽𝑘𝑔−1
at O°C)
o Latent heat of vaporization (𝑳 𝒗): The energy required for the evaporation or
condensation (𝟐. 𝟓 𝑀𝐽𝑘𝑔−1
at O°C)
o Latent heat of sublimation (𝑳 𝒔): The energy required to effect a change directly
between the ice and vapour phases () (𝐿 𝑠 = 𝐿 𝑓 + 𝐿 𝑣 = 𝟐. 𝟖𝟑𝟒 𝑀𝐽𝑘𝑔−1
at O°C)

17. 4. Mass balances
(b) Water balance
o Annual average hydrologic cycle
o Mean annual global precipitation (p) ≈ 1040 mm
o Evaporation (from water surface and soil), and transpiration (from vegetation)
o Evapotranspiration (E): The composite loss of water to the air from all sources
o Net runoff (∆𝒓): The net change in runoff over a distance
(Values are in %)
(P < E)
(E < P)
In annual,
o For E-A sub-systems
𝑝 = 𝐸 ± ∆𝑟
o For total E-A system
𝑝 = 𝐸
o Net storage change is
zero

18. 4. Mass balances
(b) Water balance
o Small-scale interaction over short time:
(a) Natural surface
𝑝 = 𝐸 + 𝑓 + ∆𝑟
Where, 𝑓 = Infiltration
(b) Soil-plant column
𝑝 = 𝐸 + ∆𝑟 + ∆𝑆
Where, ∆𝑆= Net change in soil
moisture content
o ∆𝑆 is non-zero on the short time scale

19. 4. Mass balances
(b) Water balance
o Soil moisture is significant in surface
energy balance because it affects radiative,
conductive and convective partitioning
o Importance: addition of soil moisture;
• Will alter the surface albedo
• Will change thermal properties of soil
• Will affect heat transfer and storage
o The water and energy balance equation
Energy for evaporation, 𝑄 𝐸 = 𝐿 𝑣 𝐸
o For melting or freezing (≤ 0℃)
Energy flux density, ∆𝑄 𝑀= 𝐿 𝑓 𝑀
Where,𝐸 and 𝑀 = Mass flux density
(𝑘𝑔 𝑚−2
𝑠−1
)

20. 4. Mass balances
(c) Other mass balances
o Carbon cycle
(The biogeochemical cycle by which carbon
is exchanged among the biosphere,
pedosphere, geosphere, hydrosphere, and
atmosphere)
o Nitrogen cycle
(i. Nitrogen fixation, Assimilation,
Ammonification, and Nitrification; and ii.
Denitrification)
𝐶𝑂2 + 𝐻2 𝑂 + 𝐸𝑛𝑒𝑟𝑔𝑦 → 𝐶6 𝐻12 𝑂6 + 𝑂2
𝐶𝐻4 𝑜𝑟 𝐶6 𝐻12 𝑂6 + 𝑂2 → 𝐶𝑂2 + 𝐻2 𝑂 + 𝐸𝑛𝑒𝑟𝑔𝑦
[𝑁2 → 𝑁𝐻4
+
→ 𝑁𝑂2
−
→ 𝑁𝑂3
−
→ 𝑁2]
𝑁2 + 3 𝐻2 → 2 𝑁𝐻3
2 𝑁𝐻3 + 3 𝑂2 → 2 𝑁𝑂2 + 2 𝐻+
+ 2 𝐻2 𝑂
2 𝑁𝑂2
−
+ 𝑂2 → 2 𝑁𝑂3
−
𝑁𝑂3
−
+ 𝐶𝐻2 𝑂 + 𝐻+
→ 1
2 𝑁2 𝑂 + 𝐶𝑂2 + 1 1
2 𝐻2 𝑂

21. 4. Mass balances
(c) Other mass balances
o Oxygen cycle
(Process of photosynthesizing, cycled between biosphere and lithosphere
(limestone sedimentary rock), lithosphere consumes free oxygen (rust: iron oxide))
𝐶𝑎𝐶𝑂3 → 𝐶𝑎𝑂 + 𝐶𝑂2
4 𝐹𝑒𝑂 + 𝑂2 → 2 𝐹𝑒2 𝑂3
o Sulphur cycle
𝑆𝑂4 + 𝑂𝐻 ∙ → 𝐻𝑂𝑆𝑂2 ∙
𝐻𝑂𝑆𝑂2 ∙ +𝑂2 → 𝐻𝑂2 ∙ +𝑆𝑂3
𝑆𝑂3 + 𝐻2 𝑂 → 𝐻2 𝑆𝑂4

22. THANK YOU