Let’s take two cases:

sm

Lsm

a) the soil is dry, b) the soil is very moist.

Ta

RwTa2

L K s'

0

s sm

T, P

z

R1 cos t tm

cp K

c * * Km

In the case (a)

ˆ

sm

z

Lsm

sm Ta

Lsm

Ta

const

For 24 h

In the case (b):

z

RwTa2

T

z

R T 2 z

a

w

a

sm

sm

Lsm

Ta Ta

z

z

R T 2 z

w a

ˆ

Lsm

R1 cos t

tm

cp K

L K

c * * Km

z

2

z

z 0

RwTa

At t,0 t,0

2

ˆ

L sm

z

c * * Km

R1 cos t tm cp R T 2

K

12

w

a

2

ˆ

L sm

cos

R T 2

z

c * * Km

R1

t tm cp

K

w a

2

c

*

L sm

p

c

p

R T 2

w a

ˆ

cos t tm

*

R1

cp K

z

c * * Km

ˆ

cos t tm

cp K

c * * Km

R1

z

Solution of these equations with respect to soil temperature are: For the moist surface

					ˆ			COS t tm 8
0,t 0,t					R1
			c*p		c * *
				k		km
						13

For the very dry surface

ˆ

COS t tm 8

0,t 0,t

R1

cp

c * *

k

km

2

2

7.29 10 5 s 1

86400

Scrutinizing these formulas suggests:

1. Amplitude of the soil temperature diurnal variation is proportional to the amplitude of the radiation budget diurnal variation.

2. Amplitude of the soil temperature variation decreases as eddy

coefficient increases, soil temperature conductivity coefficient Km increases, and soil volume heat capacity c*ρ* increases.

3. Significant impact on the surface temperature variation is made by

the soil moisture.

14

Dry soil				No evaporation				Larger amplitude

Very moist soil						Evaporation			Much smaller
									amplitude
						Not significant soil			(more than 3
						porosity			times)

4. The value Π/8 suggests that maximal temperature occurs 3 hours later than .R Rmax

That is all! Good luck!

15