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- Review sessions this week:
- Noon today, Agronomy 1581
- Another one later?

- Homework due Wednesday
- Quiz?

Soil Physics 2010

Key concept #1:

q = 0.01 is small relative to measurement error,

but LE for q = 0.01 is big

Key concept #2:

LE in the soil is about E, not ET

LE(evaporation from the soil)

S(heating the soil)

Soil Physics 2010

Sensible heat balance can be used to estimate the latent heat (LE) used for evaporation.

<0 Condensation

=0 No net change

>0 Evaporation

LE = (H1 – H2) –DS

Upper sensible

heat flux H1

LE

Sensible heat storage DS

Lower sensible heat flux H2

Soil Physics 2010

Components of heat flow into / out of this thin layer:

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

1

T1

0 mm

H1

dT/dz1

C1,k1

3 mm

2

T2

DS

6 mm

H2

dT/dz2

C2,k2

9 mm

3

T3

12 mm

Soil heat flux:H = -k(dT/dz)

Change in soil heatstorage:DS = C (Dz) (dT/dt)

a heat-pulse sensor

LE = (H1 – H2) –DS

Soil Physics 2010

Measuring heat flow into tiny layers

Active

Passive

T1

C1

k 1

Dz1

T2

Dz2

C2

k2

T3

Fourier:

Radiation

Conduction

Convection

Latent heat

LE = (H1 – H2) –DS →

Soil Physics 2010

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

Temperature, Heat capacity, & Thermal conductivity

T (˚C)

k (W m -1 ˚C -1)

C (MJ m-3 ˚C -1)

3

.

1.2

.

C (3-9 mm)

2

0.8

k (3-9 mm)

1

0.4

0

0

174

175

176

177

178

179

180

Day of year 2007

Soil Physics 2010

Evaporation within soil layers

Evaporation (mm/hr)

3-9 mm 1st depth

9-15 mm 2nd

15-21 mm 3rd

21-27 mm 4th

Day of year 2007

This is the “drying front” we’ve mentioned earlier – now actually observed.

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 Research44, W00D05

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 Research44, W00D05

Soil Physics 2010

C1

C0

Under steady-state conditions we get a straight line, just as we did with Darcy’s law.

just likeQ = -KiA

L

Soil Physics 2010

For transient diffusion, we need to know the initial and boundary conditions.

t0

Constant area under curve (constant mass)

t1

Suppose we have

Ci = 0 x > 0, t = 0

C0 = 1 x = 0, t = 0

Ci = 0 x = ∞, t > 0

C/C0

t2

t3

x

Soil Physics 2010

concentration

C0 = 1

Ci = 0

Breakthrough

C/C0

t

So, what if we had

Ci = 0 x > 0, t = 0

C0 = 1 x = 0, t≥ 0

Ci = 0 x = ∞, t > 0

Solute mass increases with time

This is

called a Breakthrough Curve

Then at some distance x, we’d see

Soil Physics 2010

t1

t0

t3

t2

Diffusion with Convection

v

Sir Geoffrey Taylor examined a “slug” of dye traveling in a tube of flowing water (early 1950s).

The slug moved at the mean water velocity, and it spread out but remained symmetrical.

This seemed remarkable to Taylor.

Soil Physics 2010

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

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