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PPT – Energy Balance Energy in = Energy out ? Storage PowerPoint presentation | free to view - id: 40ff13-ODA0M

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Energy Balance Energy in Energy out

? Storage

- Bio 164/264
- January 11, 2007
- C. Field

Radiation Reminders from last time

- Energy of a photon depends on 1/wavelength
- E hc/l
- h is Plancks constant (6.6310-34 Js), c is the

speed of light (3108m s-1), and l is wavelength

(m). - Thermal radiation depends on T4 Stefan-Boltzmann

law - s 5.67 10-8 W m-2 K-4
- Wavelength of maximum energy depends on

1/temperature (Wien Law) - Solar constant 1360 W m-2, over sphere 342

W m-2

Energy balance

- Conservation of energy
- Energy in Energy out ? Storage
- Energy transport
- Radiation
- Conduction
- Convection Sensible heat
- Evaporation Latent heat
- ? Storage
- Change in temperature
- Change in the energy stored in chemical bonds
- Change in potential energy

Radiation balance

SS 600 W m-2, q 20

- Thermal
- In IR down IR up
- Out IR down IR up
- 461 346 397 397 63
- SW
- In directcosqa
- diffuse downa diffuse up a 282

120 50 W m-2 - Out reflected up
- reflected down
- transmitted down transmitted

up already included in in

Sd 100 W m-2

T 10, e 1.0

ST 426 W m-2

ST 365 W m-2

T 25, e .95, a 0.5

ST 426 W m-2

ST 486 W m-2

a 0.6

T 35, e .95

Conduction

- Not very important in this class.

Convection

- Rate of transport driving force

proportionality factor - Ficks law diffusion Fj -Dj (drj/dz)
- D molecular diffusivity
- Fouriers law heat transport H -k (dT/dz)
- k thermal conductivity (m2 s-1)
- Darcys law water flow in a porous medium
- Jw -K(y) (dy/dz)
- K(y) hydraulic conductivity

Keeping units straight - Moles

- Most of the mass fluxes in this class will be in

moles, where 1 mole m.w. in g - N2 1 mole 28.01 g
- O2 1 mole 32.00 g
- CO2 1 mole 44.01 g
- H2O 1 mole
- Molar density (mol m-3) rj/Mj is the same for

all gases - Ideal gas law pjV njRT
- 44.6 mol m-3 _at_ 0C and 101.3 kPa (STP)
- rj/Mj

First get mass flux in molar units

- Convert Ficks law to molar units
- diffusion Fj -Dj (drj/dz)
- Fj Fj/Mj - Dj (dCj/dz)
- D molecular diffusivity
- Cj mole fraction of substance j

Convection moving heat in air

- Start with Fouriers law
- Heat transport H -k (dT/dz)
- k thermal conductivity
- cp molar specific heat of air 29.3 J mol-1 C-1
- k/cp DH thermal diffusivity
- Heat transport H - cpDH(dT/dz)
- In discrete form
- Mass Fj gj (Cjs Cja) (Cjs Cja)/rj
- Heat H gHcp(Ts-Ta) cp(Ts-Ta)/rH

Conductances and resistances?

- Ohms law
- V IR
- I V/R
- Conductances mol m-2 s-1
- Resistances -- m2 s mol-1

series

parallel

Physics of the conductance gH

- Dimensionless groups
- Re ratio of inertial to viscous forces
- Pr ratio of kinematic viscosity to thermal

diffusivity - Gr ratio of bouyantinertial to viscous2
- Forced convection
- gH (.664DHRe1/2Pr1/3)/d
- gHa 0.135 v(u/d) (mol m-2

s-1) - Free convection
- gH (.54DH(GrPr)1/4/d
- gHa .05((Ts-Ta)/d)1/4 (mol m-2 s-1)

Heat transport by convection

- If
- Ta 20,Tl 25, u 2, d .2
- Then
- gHa .135(3.16) .427
- H gHa2cp(Tl-Ta) .427229.35 125 W m-2

Latent heat Energy carried by water

- Latent heat of vaporization (l) energy required

to convert one mol of liquid water to a mol of

water vapor - l is a slight function of temp, but is about

44103 J mol-1 at normal ambient - (this is 585 cal/g!)
- Latent heat of fusion energy required to

convert one mol of solid water to a mol of liquid

water 6.0103 J mol-1 - Latent heat plays a dramatic role in temperature

control. - Water temperature wont rise above boiling
- Frozen soil or snow wont rise above zero
- Evaporating water requires a large amount of

energy. - 1 mm/day 1kg/m2day, requires 2.45106 J/m2
- since a day is 86,400 s and a Watt is a J/s, this

amounts to 2.45106/8.64104 28.3 W/m2 - when the atmosphere is dry, evaporation can be 6

mm/day, or even more

Evaporation

- Here, we can return directly to Ficks law
- Fj Fj/Mj - Dj (dCj/dz)
- Fj gj (Cjs Cja) (Cjs Cja)/rj
- Where the driving gradient (Cjs Cja) is the

difference between the water vapor inside and

outside the leaf (mol mol-1) - And gw is a theme for another lecture

Water vapor concentration

- The amount of water vapor the air can hold is a

function of temperature saturation vapor

pressure - Relative humidity ratio of actual vapor

pressure to saturation vapor pressure

Saturation vapor pressure

- where t 1 - (373.16/T)
- T absolute temperature T (ºC) 273.16
- Vsat is in Pascals 101325 Pascals 1 atm
- Vapor pressure of the air V VsatRH
- Vapor pressure deficit Vsat V
- Mol fraction (wi) V/P where P atmospheric

pressure

Evaporation and Latent heat

- E gw(wl wa)
- Latent heat lE
- Example
- If gw .5 mol m-2 s-1, wl 0.03 mol mol-1, wa

0.01 mol mol-1 - Then E .5.02 .01 mol m-2 s-1
- lE .0144103 440 W m-2

Energy balance

- Net radiation Convection Latent heat

D storage 0 - Or
- Rn H lE D storage 0

Functional role of energy balance

- Ehleringer, J., O. Björkman, and H. A. Mooney.

1976. Leaf pubescence effects on absorptance and

photosynthesis in a desert shrub. Science

192376-377.

Energy balance classics leaf scale

- Parkhurst, D. F., and O. L. Loucks, 1972 Optimal

leaf size in relation to environment. Journal of

Ecology, 60, 505-537. - Mooney, H. A., J. A. Ehleringer, and O. Björkman,

1977 The energy balance of leaves of the

evergreen desert shrub Atriplex hymenelytra.

Oecologia, 29, 301-310. - Gates, D. M., W. M. Heisey, H. W. Milner, and M.

A. Nobs, 1964 Temperatures of Mimulus leaves in

natural environments and in a controlled chamber.

Carnegie Inst. Washington Ybk., 63, 418-426.

Energy balance classics large scale

- Charney, J., P. H. Stone, and W. J. Quirk. 1975.

Drought in the Sahara A biogeophysical feedback.

Science 187434-435. - Shukla, J., and Y. Mintz. 1982. Influence of

land-surface evapotranspiration on the earth's

climate. Science 2151498-1501. - Bonan, G. B., D. B. Pollard, and S. L. Thompson.

1992. Effects of boreal forest vegetation on

global climate. Nature 359716-718. - Sellers, P. J., L. Bounoua, G. J. Collatz, D. A.

Randall, D. A. Dazlich, S. Los, J. A. Berry, I.

Fung, C. J. Tucker, C. B. Field, and T. G.

Jenson. 1996. A comparison of the radiative and

physiological effects of doubled CO2 on the

global climate. Science 2711402-1405.