Soil temperature and energy balance
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Transcript of Soil temperature and energy balance
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Soil temperature and energy balance
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Temperature• a measure of the average kinetic energy of the
molecules of a substance
• that physical property which determines the direction of heat flow between two substances in thermal contact
• not a measure of heat content
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RAICH, J.W., and W.H. SCHLESINGER. 1992. The global carbon dioxide flux in soil respiration and its relationship to vegetation and climate. Tellus B 44:81-99.
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Modes of energy transfer• radiation: emission of energy in the form of
electromagnetic waves
• conduction: transfer of heat by molecular motion
• convection: heat transfer by bulk fluid motion
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• Stefan-Boltzmann law
Jt = total radiant fluxe = emissivity = 1 for a “black body”; 0.9 to 1.0 for soil = Stefan-Boltzmann constant = 5.67 x 10-8 W m-2 K-4 T = temperature of the emitter (K)
Radiation
4TJ t e
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• Wien’s law
m = wavelength of maximum radiation intensity
Radiation
TKm
m
2900
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http://www.atmos.washington.edu/~hakim/301/handouts.html
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• short-wave radiation: the incoming solar spectrum
• long-wave radiation: the spectrum emitted by the earth
Radiation
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• Net radiation = the sum of all incoming minus outgoing radiant energy fluxes
Net radiation at the soil surface
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Net radiation at the soil surface
loliasn JJJJJ 1
Jn = net radiation (W m-2, J s-1 m-2)Js = direct beam incoming short-waveJa = diffuse incoming short-wave = albedo = the fraction of incoming short-wave
radiation reflected by the surfaceJli = incoming long-waveJlo = outgoing long-wave
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Albedo• for soil it varies from 0.1 to 0.4 (unitless)• depends on:
– soil color– surface roughness– sun angle– soil moisture
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Surface energy balance• For the soil surface layer (infinitely thin), energy
in = energy out
Jn = net radiation at the surfaceS = heat flux into the soilA = sensible heat flux to the atmosphereL = latent heat of vaporization (J kg-1)
– temperature dependent, 2.4 x 106 J kg-1 @ 25C
E = rate of evaporation (mm d-1, kg m-2 d-1)
LEASJ n
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Surface energy balance
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Energy balance components measured above a corn residue covered soil surface in 1994 at a site near Ames, Iowa. Net radiation (Rn) is positive toward the surface. The other terms are positive away from the soil surface. Adapted from Sauer et al. (1998).
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Calculate the direction and magnitude of the soil heat flux:
• Incoming shortwave = 300 W m-2
• Albedo = 0.15• Surface temperature = 25C• Sensible heat flux = 0• Evaporation rate = 2 mm d-1
• Surface emissivity = 0.9• Atmosphere returns 60% of outgoing
longwave
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Heat conduction• Fourier’s Law: the heat flux is proportional to
the temperature gradient
qh = heat flux by conduction (W m-2) = thermal conductivity (W m-1 K-1)T = temperature (K or C)z = position (m)
dzdTqh
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Calculate the soil heat flux (W m-2)soil thermal conductivity = 1.2 W m-1 K-1
temperature at 5 cm = 30 Ctemperature at 10 cm = 28 C
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• Change in energy storage equals energy in minus energy out
C = volumetric heat capacity (J m-3 K-1)DT = thermal diffusivity = /C
zq
tTC h
Continuity equation
zT
zzq
tTC h
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• Soil thermal properties, p. 218-225
Reading assignment
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• Three primary thermal properties of soil– volumetric heat capacity– thermal conductivity– thermal diffusivity
• Applications– used to predict soil temperatures– used for measurement of soil moisture– used for remote sensing applications
Soil thermal properties
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• the amount of energy required to raise the temperature of a unit volume of soil by 1 degree (J m-3 K-1)
• a linear function of soil water content and bulk density
• cs = specific heat of the soil solids (kJ kg-1 K-1)
• cw = specific heat of water (4.18 kJ kg-1 K-1)
Volumetric heat capacity
wccC wsb
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Table 1. Density, specific heat, and thermal conductivity of common soil constituents at 10
C (after de Vries, 1963, Table 7.1).
Soil constituent Density () Specific heat (c) Thermal
conductivity ()
Mg m 3 kJ kg 1 K 1 W m 1 K 1
Quartz 2.66 0.75 8.8
Clay minerals 2.65 0.76 3
Soil organic matter 1.3 1.9 0.3
Water 1.00 4.18 0.57
Ice (0 C) 0.92 2.0 2.2
Air 0.00125 1.0 0.025
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Calculate the volumetric heat capacitybulk density = 1300 kg m-3
gravimetric water content = 0.20 kg kg-1 specific heat of the soil solids = 0.85 kJ kg-1 K-1
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Thermal properties of clay loam soil as functions of volumetric water content. Reprinted from Ren et al. (1999).
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• the ratio of the magnitude of the heat flux through the soil to the magnitude of the temperature gradient (W m-1 K-1)
• a measure of the soil's ability to conduct heat
• influenced by:– texture, mineralogy, organic matter, density,
water content, air-content, structure, water vapor in the pores, temperature
Thermal conductivity
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Table 1. Density, specific heat, and thermal conductivity of common soil constituents at 10
C (after de Vries, 1963, Table 7.1).
Soil constituent Density () Specific heat (c) Thermal
conductivity ()
Mg m 3 kJ kg 1 K 1 W m 1 K 1
Quartz 2.66 0.75 8.8
Clay minerals 2.65 0.76 3
Soil organic matter 1.3 1.9 0.3
Water 1.00 4.18 0.57
Ice (0 C) 0.92 2.0 2.2
Air 0.00125 1.0 0.025
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Thermal properties of clay loam soil as functions of volumetric water content. Reprinted from Ren et al. (1999).
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Thermal properties of silica sand as functions of volumetric water content. Reprinted from Ren et al. (1999).
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• the ratio of the thermal conductivity to the volumetric heat capacity (m2 s-1) ; DT = /C
• a measure of the rate of transmission of a temperature change through the soil
• influenced by:– all that influences and C
Thermal diffusivity
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Thermal properties of clay loam soil as functions of volumetric water content. Reprinted from Ren et al. (1999).
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• Soil thermal regime, p. 227-233
Reading assignment
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• oscillations driven by the daily and yearly cycles
• irregularities from: clouds, precipitation, cold fronts, warm fronts, etc…
• highest and lowest temperatures can occur at the surface– near 700C under an intense forest fire– below -20 C in Arctic winter
Soil surface temperature
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15
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30Below RowsA
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3525 cm From West Row
B
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Rows
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152025303540
0 cm 5 cm20 cm
25 cm From East Row
D
0 4 8 12 16 20 24Time (hours)
Tem
pera
ture
(°C
)
Soil temperature with time at 0, 5, and 20 cm below the soil surface as measured between two NE-SW oriented rows of 60 cm high chile (Capsicum annuum L.) plants. The rows were 100 cm apart. Reprinted from Horton et al. (1984).
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• sine wave can serve as a first approximation
Tave = average temperature of the surfaceA0 = amplitude of the wave at the surface = angular frequency = 2/period
Modeling surface temperature
tATtT ave sin,0 0
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Fri Sat Sun Mon Tue Wed Thu Fri15
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Tem
pera
ture
(C)
Diurnal fluctuations of soil temperature at 6 cm depth in a silt loam soil in southeast Minnesota under perennial vegetation.
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• assuming that:– surface temperature is (and has been)
oscillating as a sine wave– Tave is the same for all depths– deep in the soil T is constant at Tave
• then soil temperature at any depth is:
Modeling soil temperature
dzteATtzT dzave sin, 0
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• the soil temperature is described by:
z = depth (m)d = damping depth = (2DT/)1/2
= phase constant
Modeling soil temperature
dzteATtzT dzave sin, 0
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01/23 03/14 05/03 06/22 08/11 09/30 11/19 01/080
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Tem
pera
ture
(C)
MeasuredSine wave
Annual cycle of soil temperature at 1 m depth in a silt loam soil in southeast Minnesota under perennial vegetation.
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• the soil depth at which the temperature wave amplitude is 1/e (1/2.718 = 0.37) of that at the surface
• d = damping depth = (2DT/)1/2
Damping depth
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• Thermal diffusivity, DT = 0.5 x 10-6 m2 s-1
• What is the damping depth for the diurnal temperature wave?
• What is the damping depth for the annual temperature wave?
• At what depth is the amplitude of the annual temperature wave only 5% of the amplitude of the annual wave at the surface?
Damping depth
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• if the soil temperature is described by:
• then the time lag between two depths is
Time lag
dzteATtzT dzave sin, 0
TDzztt
212
12
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• Thermal diffusivity, DT = 0.5 x 10-6 m2 s-1
• What is the time lag between the occurrence of the daily maximum temperature at the surface and at 30 cm depth?
Time lag
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