Measurement of Near-Surface Soil Heat Storage in Energy

Balance Studies

T.E. Ochsner1

T.J. Sauer2

R. Horton3

1 USDA-ARS St. Paul, MN2 USDA-ARS Ames, IA

3 Iowa State University

Soil heat storage in the energy balance

LEHGRn 0

SGG r 0

Gr = heat flux at the reference depth zr

S = rate of change of heat storage in the soil above the reference depth

G0 = heat flux at the soil surface

Is S negligible?

Neglecting S causes underestimates of the magnitude of G.

Neglecting S delays peaks in G.

Ar / A0

0.2 0.4 0.6 0.8 1.0

Ref

eren

ce d

epth

(cm

)

0

2

4

6

8

10

2 x 10-7

5 x 10-7

8 x 10-7

(m2 s-1)

tr - t0 (hours)

0 1 2 3 4 5 6R

efer

ence

dep

th (

cm)

0

2

4

6

8

10

2 x 10-7

5 x 10-7

8 x 10-7

(m2 s-1)

Why not make zr shallow?

• Potential LE error up to 100 W m-2 (Buchan)

• Obstruction of water and heat transfer D

aily

ra

infa

ll (m

m)

0

5

10

15

20

25

30

35

Diff

ere

nce

in w

ate

r co

nte

nt (

kg k

g-1)

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

RainfallAcross plateAmbient

Day

192 193 194 195 196 197 198 199 200 201 202 203 204

Diff

ere

nce

in te

mp

era

ture

(K

) -6

-5

-4

-3

-2

-1

0

– Plastic disks buried at 2 cm increased water content and temperature gradients 200 to 300%.

• Greater risk of poor thermal contact due to soil drying or freezing

S depends on C and T

• C = soil volumetric heat capacity

• T = soil temperature

• A diversity of ways to determine C in current practice

• Objective to compare methods– Estimation by soil sampling (CSS)– Estimation by Theta Probe (CTP)– Direct measurement by heat pulse sensors (CHP)

rz

dzTCt

S0

Simultaneous C measurements

When C was determined using all three techniques simultaneously, the results agreed to within 6% on average.

x = CHP

1.0 1.5 2.0

y =

CSS

1.0

1.5

2.0

2.5Bare soil siteSoybean siteCorn site

x = CHP

1.0 1.5 2.0y

= C

TP

x = CSS

1.0 1.5 2.0 2.5

y =

CTP

Heat capacity (MJ m-3 K-1)

Hea

t ca

paci

ty (

MJ

m-3

K-1

)

(a) (b) (c)

Temporal variability in C

• Temporal variability of C was best recorded with the heat pulse sensors

• Sampling three times per week was not frequent enough to consistently record the temporal variations in C of the near-surface soil.

Calendar date

1 Jul 15 Jul 29 Jul 12 Aug

Dai

ly r

ainf

all (

mm

)

0

25

50

75

Hea

t cap

acity

(M

J m

-3 K

-1)

1.0

1.5

2.0

Hea

t cap

acity

(M

J m

-3 K

-1)

1.0

1.5

2.0

Dai

ly r

ainf

all (

mm

)0

25

50

75

Hea

t cap

acity

(M

J m

-3 K

-1)

1.0

1.5

2.0

2.5

Dai

ly r

ainf

all (

mm

)

0

25

50

75

100

CHPCSSCTPRainfall

2001Bare soil site

2002Soybean site

2002Corn site

Spatial variability in C

0 20 40 60

-6

0

0 20 40 60

D istance from north row (cm )

-6

0

0 20 40 60

-6

0

1.2 1.4 1.6 1.8 2.0 2.2 2.4

(a)

(c)

(b)

Heat capacity (M J m-3

K-1

)

Dep

th (

cm)

Both soil sampling and heat pulse sensors are suitable for describing variations of C with depth in the top few centimeters of the soil.

rr zz

dzt

CTdz

t

TCS

00Simplification:

Calculating S

Definition:

rz

dzTCt

S0

X 1

1 1

1,,1,

1

2

ii

N

i jj

jijiji

jj zztt

TTC

ttSDiscretization:

11 1

1,1,,,1

2

ii

N

i jj

jijijijijj zztt

TCTCttSIncluding

dC/dt:

The neglect or inclusion of dC/dt had larger effects on S than did the measurement technique used to determine C.

Hourly S values

-100 0 100 200

-100

0

100

200

300Bare soil siteSoybean siteCorn site

S (W m-2)

HP

SS

S (

W m

-2)

S (W m-2)

TP

S (W m-2)

HP w/o dC/dt

(a) (b) (c)

-100 0 100 200 300-100 0 100 200

Effects of neglecting dC/dt

Calendar date

24 Jul 26 Jul 28 Jul 30 Jul 1 Aug 3 Aug

Dai

ly r

ainf

all (

mm

)

0

5

10

15

20

25C

umul

ativ

e S

(M

J m

-2)

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

RainfallSS - HPSS

S (

W m

-2)

0

100

200HP SS

(a)

(b)

• Large underestimates of S during infiltration– 246 W m-2 at the

bare soil site– 282 W m-2 at the

soybean site– 90 W m-2 at the

corn site

• Small persistent overestimates of S during drying

Recommendations

• In long-term surface energy balance studies C determinations should be automated and frequent.

• Heat pulse sensors or dielectric sensors should be used to perform these frequent, automated C determinations.

• In short-term studies where frequent site visits are acceptable, determination of C by soil sampling or by use of the Theta Probe should be considered.

• S should be measured in all surface energy balance studies.