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?
Soil Physics 2010
Heitman’s soil E method
Key concept #1:
q = 0.01 is small relative
to measurement error,
but LE for q = 0.01 is big
S (heating the soil)
Soil Physics 2010
Key concept #2:
LE in the soil is
about E, not ET
LE (evaporation
from the soil)
Sensible heat balance can be used to estimate the
latent heat (LE) used for evaporation.
LE = (H1 – H2) – DS
<0 Condensation
=0 No net change
>0 Evaporation
Upper sensible
heat flux H1
Sensible heat
storage DS
Lower sensible
heat flux H2
Soil Physics 2010
LE
Components of heat flow into
/ out of this thin layer:
e, mm/day
Heitman’s soil E method
Stage
I
Stage
II
Stage
III
time
Negligible in
Stages II & III
Liquid water flow
up/down
Soil temperature
warming/cooling
Phase change
water evaporating /
condensing
Given by
Fourier’s law
Calculate by
difference
Soil Physics 2010
Heat Pulse (HP) sensors
a heat-pulse sensor
0 mm
C 1, k 1
T1
dT/dz1 H1
3 mm
6 mm
C 2, k 2
1
2
T2
9 mm
12 mm
DS
dT/dz2 H2
3
T3
LE = (H1 – H2) – DS
Soil heat flux:
H = -k(dT/dz)
Change in soil heat storage: DS = C (Dz) (dT/dt)
Soil Physics 2010
Measuring heat flow into tiny layers
T
 
T 
Fourier: C
  k

t
z 
z 
Active
C1
C2
k1
k2
Passive
Dz1
Dz2
T1
Radiation
Conduction
T2
Convection
Latent heat
T3
LE = (H1 – H2) – DS
Soil Physics 2010


T

T


→ LE    k
C
z 
z 
t
HP probes installed in top 6 cm of bare field
6 cm
In 2007 Summer
Soil Physics 2010
In 2008 Summer
Improved Heat Pulse probe (“Model T”)
First used summer 2009
mm
Side view
0
6
12
18
24
30
36
42
48
10 mm
Soil Physics 2010
T (˚C)
Temperature (T ,
°C) 80
0 mm
6 mm
12 mm
60
40
20
0
174
175
176
177
178
Day of year 2007
Soil Physics 2010
179
180
Temperature, Heat capacity, & Thermal conductivity
T (˚C)
80
60
40
0 mm
6 mm
12 mm
0
3
1.2
C. (3-9 mm)
. (3-9 mm)
k
2
175
176
177
178
Day of year 2007
Soil Physics 2010
0.8
0.4
1
0
174
k (W m -1 ˚C -1)
C (MJ m-3 ˚C -1)
20
179
0
180
Evaporation (mm/hr)
Evaporation within soil layers
0.8
0.6
3-9 mm
1st depth
9-15 mm
2nd
This is the “drying front”
we’ve mentioned earlier
– now actually observed.
15-21 mm 3rd
0.4
21-27 mm 4th
0.2
0
-0.2
174
175
176
177
178
179
180
Day of year 2007
Soil Physics 2010
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
Daily Evaporation (mm)
Comparison of methods
4
Micro-lysimeter
3
Bowen ratio
2
y = 1.02 x - 0.05
2
R = 0.94
1
0
0
Soil Physics 2010
1
2
3
Daily Evaporation by HP (mm)
4
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
Solute Transport
Flow
Diffusion
Convection
Dispersion
Soil Physics 2010
Steady-State Diffusion
Under steady-state conditions
we get a straight line, just as
we did with Darcy’s law.
C1  C0
Q  D
A
L
C1
C0
Soil Physics 2010
L
just like Q = -KiA
Transient diffusion
For transient diffusion, we need to know the
initial and boundary conditions.
C
C
 D 2
t
x
2
Soil Physics 2010
C/C0
Suppose we have
Ci = 0
x > 0, t = 0
C0 = 1
x = 0, t = 0
Ci = 0
x = ∞, t > 0
t0
Constant area
t1 under curve
(constant mass)
t2
t3
x
Breakthrough
So, 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,
C/C0
we’d see
Soil Physics 2010
Constant
concentration
C0 = 1
Ci = 0
Solute mass increases
with time
This is
called a
Breakthrough
Curve
t
Another breakthrough curve
C/C0
x
t0
t
t1
t2
t3
Soil Physics 2010
Diffusion with Convection
Sir Geoffrey Taylor examined a “slug” of dye
traveling in a tube of flowing water (early 1950s).
t0
t1
t2
v
The slug moved at the mean water velocity,
and it spread out but remained symmetrical.
This seemed remarkable to Taylor.
Soil Physics 2010
t3
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