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Values from Table
m-3
Other values….
Thermal admittance of dry soil ~ 102 J m-2 s-1/2 K-1
Thermal admittance of wet saturated soil ~ 103 J m-2 s-1/2 K-1
Water content
Sandy
Clay
Peat
Elevated % of quartz and clay minerals
Elevated % of organic matter
Soil density, thermal conductivity, thermal admittance.
(this is only qualitative the relations are non linear)
Low values
High values
Water content
Sandy
Clay
Peat
Elevated % of quartz and clay minerals
Elevated % of organic matter
Amplitude of the temperature wave at the surface T.
(this is only qualitative the relations are non linear)
Low values
High values
Water content
Sandy
Clay
Peat
Elevated % of quartz and clay minerals
Elevated % of organic matter
Specific heat
(this is only qualitative the relations are non linear)
High values
Low values
Water content
Sandy
Clay
Peat
Elevated % of quartz and clay minerals
Elevated % of organic matter
Thermal diffusivity.
(this is only qualitative the relations are non linear)
Low values Low values
High values
Examples:
Dry Sandy Soil (40% pore space)
1-1-
1-s
-3s
K m W .ktyconductivi thermal
K kg J.cheat pecifics
m kg.density soil
30
1080
106113
3
CoGQ T
isday and night between variatione temperatur
the 200W/m2of Flux Heat Ground maximuma For
m .Dzcycle) (annual depth Damping
m 0.08Dzcycle)(daily depth Damping
1-K 1/2-s 2-m JksC admittance Thermal
1-s 2m .scs
kydiffusivit Thermal
1-K 3-m J.scssC Capacity Heat
38
512
2
620
610240
610281
Saturated Sandy Soil (40% pore space)
1-1-
1-s
-3s
K m W .ktyconductivi thermal
K kg J.cheat pecifics
m kg.density soil
22
10481
100213
3
CoGQ T
isday and night between variatione temperatur
the 200W/m2of Flux Heat Ground maximuma For
m .Dzcycle) (annual depth Damping
m0.14 Dzcycle)(daily depth Damping
1-K 1/2-s 2-m JksCadmittance Thermal
1-s 2m .scs
kydiffusivit Thermal
1-K 3-m J.scssC Capacity Heat
9
722
2
2550
610740
610962
Limitations of the previous approach:•Measurements show that the ground heat flux is not sinusoidal in time. In particular during night-time is more uniform and much flatter.•The assumed sinusoidal variation of the surface temperature may be not realistic.•The simplifying assumption of the homogeneity of the submedium is often not realized.
min
max
9 hrs
1st approach:Statistical parameterizations
Reasonable expectation that QG is a fraction of Q* forcing. The surface QG leads the Q* forcing by about 3 hours. Therefore a daily plot of QG vs Q* results in a hysteresis loop
This loop can be modeled as
ct
*Qb*aQGQ
Where a, b, c are deduced from measurements. Ex. For bare soil (Novak, 1981):a=0.38,b=0.56 hrs, and c=-27.3 W m-2
This approach ignores the role of wind (Convection) in heat sharing at the surface
They take into account net radiation, latent and sensible heat fluxes at the surface
The Force-Restore method (Deardorff, 1978)
Two layer approximation
A shallow thermally active layer near the surface, and a thicker layer below.
2nd approach: physically based models
Energy budget of the shallow layer
Q*=net radiationQE=Latent Heat FluxQH=Sensible Heat FluxQG =Ground Heat FluxTG=ground temperature of the shallow layer= depth of the shallow layerC= specific heatsoil density
GQEQHQ*Qct
GT 1
*Q HQ EQ
)(QG
N.B. Non radiative positive fluxes are directed away from the surface. QH and QE are positive when upward, QG
when downward. Q*
(radiative flux) is positive when downward.
zmTGT
sC
kEQHQ*Q
sCtGT
layer thick
the of etemperatur mT withz
GTmTk)(GQ
thatAssuming
1
2
222
212
sCDzk
sC
kDz
sC
k,
/
Dz
ydiffusivit thermal and
depthdamping of definitionthe from
z
c=Cs is the heat capacity of the soil, function of the water content.
layer soil ground nearthe of
area unit percapacity heatthe issCGC
mTGTEQHQ*QGCt
GT
Dzz and Dzassuming
zmTGTDz
EQHQ*QGCt
GT
12
2
21
If the surface forcing term is removed, the restoring term will cause TG to move exponentially towards Tm
Surface forcing term Restoring term
To estimate Tm two possibilities:•Constant (equal to the mean air temperature of the previous 24hrs)•Computed assuming that the ground heat flux at the bottom of the thicker layer is zero.
mgm TTt
T
Multi-Layer Soil Models (Tremback and Kessler, 1985)
*Q HQ EQ
)z(Q iG
Compute the soil temperature in several layers in the soil solving numerically:
zGT
ztGT
The thermal diffusivity is computed as a function of the soil heat capacity and soil moisture potential
(Pa).pressure negative a ofthose are Units
matrix. soilthe from waterextract tonecessary
energy the is It content. waterofmeasure
indirect an is potentialmoisture soilThe
The forces which bind soil water are related to the soil porosity and the soil water content (S, volume of water per volume of soil). The forces are weakest for open
textured, wet soils and greatest for a clay soil
For a given soil, the potential increases as S decreases. It is relatively easy to extract moisture from a wet soil but as it dries out it becomes increasingly difficult to remove additional units
Vertical flux of liquid water in soil (in absence of percolating rain) is result of:• Gravity•Vertical water potential gradient (flux gradient relationship as for heat). Darcy’s Law
tyconductivihydraulic fKzfKJ
g
The effect of evapotranspiration is to create a vertical positive potential gradient which becomes greater than the opposing gravitational gradient and encourage the upward movement of water.
Soil heat flux measurements (Oke, 374-5)
In theory QG can be calculated from TG profiles and knowledge of k or – in practice this is not really possible, since the values of k and are variable and very difficult to measure.
Most use soil heat flux plats (similar idea to net radiometer thermopile)
Plates should be inserted in un-disturbed soil (few cm depth), and not right at the surface. The depth depends on the nature of the soil and the presence of roots.
Need to consider energy budget between plate and surface
zSCt
T)z(GQ)(GQ
)z(GQ)(GQzSCt
T
0
01
z
measured measured
Soil heat capacity estimated from volume fraction of mineral, organic matters and waterCS =Cm m + Co o + Cw w + Ca a
Plate
