Post on 03-Feb-2016
description
Soil Physics 2010
Outline
• Announcements
• Heitman’s soil E method
• Solute movement
Soil Physics 2010
Announcements
• Review sessions this week:
• Noon today, Agronomy 1581
• Another one later?
• Homework due Wednesday
• Quiz?
Heitman’s soil E method
LELE (evaporation from the soil)
Soil Physics 2010
Key concept #1: = 0.01 is small relative to measurement error, but LE for = 0.01 is big Key concept #2:
LE in the soil is about E, not ET
SS (heating the soil)
LE = (H1 – H2) – S
Sensible heat balance can be used to estimate the latent heat (LE) used for evaporation.
<0 Condensation=0 No net change>0 Evaporation
Upper sensible
heat flux H1
Sensible heat
storage S
Lower sensible
heat flux H2
LE
Soil Physics 2010
Heitman’s soil E method
Soil Physics 2010
Components of heat flow into / out of this thin layer:
Liquid water flow up/down
Soil temperature warming/cooling
Phase change water evaporating /condensing
Negligible in Stages II & III
Given by Fourier’s law
Calculate by difference
time
e, m
m/d
ay Stage I
Stage II
Stage III
time
e, m
m/d
ay
time
e, m
m/d
ay Stage I
Stage II
Stage III
Stage I
Stage II
Stage III
Heat Pulse (HP) sensorsa heat-pulse sensor
0 mm
3 mm
6 mm
9 mm
12 mm
2
1
3
T1
T3
T2
LE = (H1 – H2) – S
dT/dz1
dT/dz2
C1,1
C2,2
Change in soil heat storage: S = C (z) (dT/dt)
S
H1
H2
Soil heat flux: H = -(dT/dz)
Soil Physics 2010
Soil Physics 2010
T1
T2
T3
z1
z2
Passive
Measuring heat flow into tiny layers
Active
1
2
C1
C2
z
T
zt
TC
t
TC
z
T
zLE
Fourier:
LE = (H1 – H2) – S →
Radiation
ConductionConvection
Latent heat
6 cm
In 2007 Summer In 2008 Summer
HP probes installed in top 6 cm of bare field
Soil Physics 2010
Improved Heat Pulse probe (“Model T”)
First used summer 2009
Side view
10 mm
0
6
12
18
24
30
36
42
48
mm
Soil Physics 2010
Temperature (T , °C)T
(˚C
)
0
20
40
60
800 mm6 mm12 mm
Day of year 2007
174 175 176 177 178 179 180
Soil Physics 2010
Temperature, Heat capacity, & Thermal conductivity
T (
˚C)
0
20
40
60
800 mm6 mm12 mm
Day of year 2007
174 175 176 177 178 179 180
C (
MJ
m-3
˚C -
1)
0
1
2
3 C (3-9 mm) (3-9 mm)
0
0.4
0.8
1.2.
.
(W
m -1
˚C -1
)
Soil Physics 2010
Evaporation within soil layers
Heitman, J.L., X. Xiao, R. Horton, and T. J. Sauer (2008), Sensible heat measurements indicating depth and magnitude of subsurface soil water evaporation, Water Resource Research 44, W00D05
Eva
po
rati
on
(m
m/h
r)
Day of year 2007
-0.2
0
0.2
0.4
0.6
0.8
174 175 176 177 178 179 180
3-9 mm 1st depth
9-15 mm 2nd
15-21 mm 3rd
21-27 mm 4th
Soil Physics 2010
This is the “drying front” we’ve mentioned earlier – now actually observed.
Comparison of methods
Heitman, J.L., X. Xiao, R. Horton, and T. J. Sauer (2008), Sensible heat measurements indicating depth and magnitude of subsurface soil water evaporation, Water Resource Research 44, W00D05Soil Physics 2010
Solute Transport
Soil Physics 2010
Flow
Diffusion
Convection
Dispersion
Steady-State Diffusion
L
C1
C0
Under steady-state conditions we get a straight line, just as we did with Darcy’s law.
AL
CCDQ 01
just like Q = -KiA
Soil Physics 2010
Transient diffusion
For transient diffusion, we need to know the initial and boundary conditions.
2
2
x
CD
t
C
Suppose we have
Ci = 0 x > 0, t = 0
C0 = 1 x = 0, t = 0
Ci = 0 x = ∞, t > 0
x
C/C
0
t0
t1
t2
t3
Constant area under curve
(constant mass)
Soil Physics 2010
BreakthroughSo, what if we had
Ci = 0 x > 0, t = 0
C0 = 1 x = 0, t ≥ 0
Ci = 0 x = ∞, t > 0
Then at some distance x, we’d see
C/C0
t
This is called a
Breakthrough Curve
Ci = 0
Constantconcentration
C0 = 1
Solute mass increases with time
Soil Physics 2010
Another breakthrough curve
t0
t1
t2
C/C0
tx
t3
Soil Physics 2010
Diffusion with Convection
Sir Geoffrey Taylor examined a “slug” of dye traveling in a tube of flowing water (early 1950s).
vThe slug moved at the mean water velocity, and it spread out but remained symmetrical.
This seemed remarkable to Taylor.
t0 t1 t2 t3
Soil Physics 2010
Why was this remarkable?
Taylor knew that water flowing through a tube has a parabolic velocity profile. Water in the center flows at twice the mean water velocity.
The velocity profile is not symmetrical, but the dye slug was symmetrical.
Soil Physics 2010