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Energy Balance Energy in = Energy out ? Storage

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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 ... – PowerPoint PPT presentation

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Title: Energy Balance Energy in = Energy out ? Storage


1
Energy Balance Energy in Energy out
? Storage
  • Bio 164/264
  • January 11, 2007
  • C. Field

2
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

3
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

4
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
5
Conduction
  • Not very important in this class.

6
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

7
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

8
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

9
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

10
Conductances and resistances?
  • Ohms law
  • V IR
  • I V/R
  • Conductances mol m-2 s-1
  • Resistances -- m2 s mol-1

series
parallel
11
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)

12
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

13
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

14
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

15
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

16
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

17
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

18
Energy balance
  • Net radiation Convection Latent heat
    D storage 0
  • Or
  • Rn H lE D storage 0

19
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.

20
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.

21
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.
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