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