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A numerical model for simulating the temperature and moisture regimes of soil under various mulches
Agricultural and Forest Meteorology, 61 (1992) 281-299
281
Elsevier Science Publishers B.V., Amsterdam
A numerical model for simulating the temperature and moisture regimes of soil under various mulches Hong-jian Sui", De-chao Zeng b and Fa-zu Chen c ~Research Centre of Environment, Beijing Institute of Management, University of Science and Technology of China, Beijing, People's Republic of China bLaboratory of Tillage Technology, Beijing Agricultural Engineering University, Beijing, People's Republic of China Clnstitute of Geography, Chinese Academy of Sciences, People's Republic of China (Received 2 July 1991; revision accepted 6 April 1992)
ABSTRACT Sui, H., Zeng, D. and Chen, F., 1992. A numerical model for simulating the temperature and moisture regimes of soil under various mulches. Agric. For. Meteorol., 61: 281-299. A two-dimensional numerical model for simulation of the effects of mulches was developed, and the governing equations were solved by the finite element approach of Galerkin-type together with the Douglas-Dupout prediction-correction method. A simulation program to predict the influence of porous and film mulches on heat and vapour transport under conditions of evaporation was developed and validated by field experiment. Preliminary application of the program showed that clear polyethylene film increased soil temperature the most effectively. However, there was little difference in the conservation of soil moisture for the three types of mulch, and paper coated with oil could significantly improve the soil microclimate for seed germination.
INTRODUCTION
Mulching is very effective in modifying the soil microclimatic conditions for plant growth. In the last 20 years, the mulching effects of various kinds of plastic and natural materials have been tested in field experiments, especially for the effect on soil temperature (Katan, 1979; Maurya and Lal, 1981; Gurnah, 1987). Computer modelling can provide a means of predicting the effects of mulching and, in many circumstances, can cut down drastically the amount of field test required. A one-dimensional numerical model for the prediction of soil temperature beneath clear polyethylene (PE) film was presented by Mahrer (1979), and a two-dimensional numerical model for the same predicCorrespondence to: H. Sui, Research Centre of Environment, Beijing Institute of Management, University of Science and Technology of China, Beijing, People's Republic of China.
0168-1923/92/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
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H. S U I E T AL.
tion was presented later by Mahrer and Katan (1981). A one-dimensional model for both soil water and heat behaviour was presented by Mahrer (1984). The results in his study showed that the moisture content of the mulched soil strongly affected the soil temperature, and soil temperature was much lower at the edges of the mulch than at the middle. A one-dimensional model for soil temperature regime under an asphalt emulsio~ film was developed by Chen (1980), with the assumption that the film is in close contact with the soil surface. A one-dimensional model suitable for describing both heat and moisture transfer through a surface residue-soil system was also developed by Bristow and Campbell (1986). However, in that model the effect of the density and the arrangement of the porous mulch was not considered. In the present work, the effects of various mulches on soil moisture and temperature regimes were investigated. Mulches were classified into two categories: porous mulches (e.g. straw, gravel, sand, etc.) and film mulches (e.g. oiled paper, asphalt emulsion film, etc.). Porous mulches were treated as porous materials similar to soil. The primary functional factors of a porous mulch that can affect soil moisture and temperature regimes are its heat and vapour transport parameters, such as heat capacity, heat conductivity and vapour transport resistance, whereas the primary functional factors of a film mulch are its optical properties such as albedo, transmissivity and emissivity of short- and long-wave radiation. A two-dimensional model was established to predict the heat and moisture regimes of soil under a strip mulch. THE MODEL
The numerical model consists of two parts: one for the soil layer and one for the mulch layer. A schematic description of the mulched soil column is given in Fig. 1.
The soil layer The moisture transfer equation given by Philip and De Vries (1957) is
~t -
Oz D° ~z
+ ~x D o E
+ ~z
Dtv~z +~xx Dtv~x
~?z (1)
where 0 is the volumetric moisture content (m 3m-3), t is the time (in seconds), x and z are the horizontal and vertical coordinates (m), respectively. Do is the isothermal moisture diffusivity (m 2s-l), Dt~ is the thermal vapour diffusivity (m 2 s-I K - I ) , and can be calculated by the formula given by Philip and De Vries (1957) and T is the soil temperature (K). K is the isothermal liquid water conductivity (m s- L), which is calculated from the formula K = CwD, where D is the soil liquid water diffusivity (m 2 s-I), and Cw = -~0/0~J is the volu-
283
S I M U L A T I O N OF MULCH EFFECTS ON SOIL MICROCL1MATE
_
.
_
Fig. 1. Schematic description of the mulched soil column under investigation.
metric water capacity (m ~), with ~, the matric potential (m-'). Cw can be calculated by graphic differentiation of the soil moisture characteristic curve. By applying the expressions
a0
a0
at - Cw~
and
a~
Do = Kw-~O eqn. (1) can be deduced as
+N
DtvN + ~
D~v~
az
(2)
Kw = K + Kv, is the isothermal moisture conductivity (m s-l). The soil heat transfer equation was given by Philip and De Vries (1957) as Ch at
az
~XX
~zz
~xx
(3) where Ch is the volumetric heat capacity (J m -3 K - ' ), 2 is the thermal conductivity (Jm -~ s -~ K -1), both Ch and 2 are evaluated according to De Vries (1963), p~ is the density of liquid water (kg m -3), L is the heat of vaporization (J kg -l) and Kv is the isothermal vapour conductivity (m s-~), which is calculated by the formula given by Philip and De Vries (1957).
284
H. SUI ET AL.
Soil boundary conditions At the soil-mulch interface, z = 0, 0 <~ x <<. D/2; -Kw
c~z
Dtv ~ z + K =
~T ~ --2-~z - p'LKV Oz -
Es, (t, x)
S,(t,x)
(4) (5)
where Es~ (t, x) is the soil-mulch moisture flux, which is equal to the mulch evaporation rate ( m s -t), and St(t, x) is the heat flux ( J m I s - t ) at the soil-mulch interface. At the soil-atmosphere interface, z = 0, D/2 < x <~ Dt/2; - K w ~3ff OT + K (~-7 -- sty -~z
=
- 2 ~OT z - plLKv ~~z
S(t, x)
-
Es(t, x)
(6) (7)
where Es(t, x) and S(t, x) are the evaporation rate and heat flux at the soil-atmosphere interface respectively. At the soil lateral boundaries, x = 0, x = D/2, 0 <~ z <~ H, the heat and moisture flux are equal to zero, because the two sides of each b o u n d a r y line are symmetrical, that is, --Kw ~63~ ' -- sty ~OT x + X OT 0~ - - 2 - ~ x -- p, L X v ~
=
=
0
0
(8)
(9)
The above equations of soil b o u n d a r y condition (eqns. (4)-(9)) can be derived from the moisture and heat transfer eqns. (2) and (3). At the base of the soil profile, 0 ~< x ~< Dj/2, z = H; =
~h(H)
T = T(H)
(10) (11)
Initial condition, t = 0 =
~0(x, z)
(12)
T =
To(x, z)
(13)
The soil surface temperature, conductive heat flux and evaporation rate at the soil-atmosphere interface are calculated by the aerodynamic approach (Van Bavel and Hillel, 1976).
SIMULATION OF MULCH EFFECTS ON SOIL MICROCLIMATE
285
The mulch layer Porous mulch
The porous mulch was simplified as a layer of porous materials for heat transfer. As the mulching width and length is much greater than the thickness, and the boundary conditions are homogeneous, the one-dimensional diffusion equation is applied: •T
Cm~t
-
~(
~z
~3T) 2m-~z
(14)
where Cm is the mulch volumetric heat capacity (J m -3 K-~ ) and ~'mis the heat conductivity of mulch (W m - 1K ' ). Both Cm and 2m are evaluated according to De Vries (1963). Mulch surface temperature is computed from the soil-air interface heat balance equation using the modified Newton iteration method which is called the secant method (Atkinson, 1978). Because the mulch is made of porous materials, the approach of Van Bavel and Hillel (1976) was applied to calculate the sensible heat flux. The heat balance equation is Rn -
LEsl -
A -
Sml
=
0
(15)
where R n is the net radiation (Wm-2), S m , and A are the mulch heat and sensible heat fluxes (W m-Z), respectively, and Es~ is the mulch evaporation rate. Mulch evaporation rate is calculated, according to Van Bavel and Hillel (1976), as Esl = ( H s -
Ha)/(Re, n + rs +
rm)
where H s and H a are the absolute humidity of the air at the soil surface and at a reference elevation (2 m)(kg m-3), respectively, Rcm is the aerodynamic resistance between the mulch surface and the reference elevation ( s m - ' ) , which is calculated by the formula of Van Bavel and Hillel (1976), rs is the transport resistance at the soil surface (sm -~), r m is the vapour transport resistance of the mulch (s m - ~) which is dependent upon its density, arrangement and material, r s and r m are determined by the method of Camillo and Robert (1986). The net radiation is expressed as follows: Rn
=
(1
--
0¢)Rg
+
R I --
~m~yTm 4
where Rg is the total short-wave irradiance (W m-Z), R~ is the long-wave sky irradiance (Wm-2), 0¢is the mulch albedo, em is the mulch emissivity, T m is the mulch surface temperature (K) and a is the Stefan-Boltzmann constant.
286
H. SUI ET AL.
The mulch heat flux is given by Sm I =
- ).m(Tml -
Tm)/Zm t
where T m l is the mulch temperature at the depth Zm~ (K). The sensible heat flux is given by A
=
C(Ta-
(16)
Tm)/Rcm
where C is the volumetric specific heat of the air (J m 3 K-1 ) and Ta is the air temperature at the reference elevation (K). At the mulch-soil interface Tm,
=
(17)
Ts
where T m , and Ts are the mulch bottom and soil surface temperature (K), respectively. Soil surface temperature at the soil-mulch interface is computed from the heat balance equation after the mulch temperature regime is calculated. At the soil-mulch interface, the net radiation is considered to be negligible. Thus the heat balance equation can be given by Sl
-
=
Sm
0
(18)
where S~ and S m are the soil and mulch heat flux (Wm-2), respectively. The expression for the mulch heat flux is Sm
=
)~m(Tmn_l -
Ts)/h -
gmn_l)
where T m , _ ~ is the mulch temperature at the depth Z m , _ ~ (K), Z m , _ ~ is the depth of mulch at the layer n - l(m) and h is the mulch thickness (m). The expression for the soil heat flux is S,
=
-21(T,
-
Ts)/Z,
where 21 is the soil heat conductivity of the layer from the soil surface to the depth Z~ (W m-~ K-~ ) and T~ is the soil temperature at depth ZI (K). Film mulch
Much work has been done in simulating the effect of transparent PE film on the soil temperature and moisture regimes. Here the Mahrer method (1984) is modified to determine the surface temperature of soil mulched with film, such as oiled paper or asphalt emulsion film. The characteristics of the films are their optical properties, such as long- and short-wave transmissivities, albedo and emissivity. The mulched soil surface energy balance equation is expressed as follows: R n -- S I -
E 0 - A0 =
0
(19)
where E0 and A0 are the latent and sensible heat fluxes (W m-2), respectively. The expression for net radiation R n is given by Rn
=
(1 -- a)flsR ~ + ~fljR I
+
~emaTm 4 -- ~aTs 4
SIMULATION OF MULCH EFFECTS ON SOIL M1CROCLIMATE
287
where fls, fl~ are the transmissive coefficients of the film to short- and longwave radiation, respectively, and e is the soil emissivity. The expressions for the sensible and latent fluxes are (Mahrer, 1984) Ao =
pC(Ts-
Tin) 4/3
Eo =
p L ( T s -- Trn)l/3(qs -- q m )
where p is the air density ( k g m -3) and qs and q m are the saturated specific humidities at the temperature of soil surface and mulch, respectively. Thus, eqn. (19) is rewritten as follows: FTs
=
R n ( T s , Tin) -- A o ( T s , T m ) -
E o ( T s , T m ) -- S ( T s )
=
0
(20)
The energy balance equation for the film mulch is Rn~ + A 0 + E 0 -
A = 0
(21)
where A is the film's sensible heat flux (W m-2), and its expression is the same as eqn. (16) instead of that of Mahrer (1984). Rn~ is the net radiation, and is expressed as Rn 1 =
gmRl +
t~Rg -k- g m e o ' ( T m ) 4
where 6 = 1 - fls - em is the absorptive coefficient for the solar radiation. In the same way, eqn. (21) is rewritten as follows: FTm
=
R n l ( T s , Tin) -
A(Tm)
+ Ao(Ts , Tm) + Eo(Ts , Tm)
(22)
The soil and mulch temperature can be determined from (20) and (22) by combining the secant and the iteration approach. The steady convergence of the computation of the two equations requires an initial condition Ts ~ T m . SOLUTION P R O C E D U R E
The flow chart of the computer program M S M T R F - I is given in Fig. 2. The required input and the initial data are the photometric and physical properties of the mulch, soil characteristics (texture and hydraulic parameters), finite element profiles of initial water content and temperature for both the mulch and soil. The atmospheric boundary conditions needed at each step are the global radiative fluxes, air temperature, relative humidity and wind speed. The numerical experiments were run on an IBM personal microcomputer. For a time interval, At, of 15min, a 24h simulation requires about 4 h on an IBM-XT computer and 40 min on an IBM-386 microcomputer. EXPERIMENTAL PROCEDURE
The performance of the model in correctly predicting temperature and
H. SUI ET AL.
288
(1) /~!
INPUT
o i l and mulch c h a r a c t e r i s t i c s / nitial moisture & temperature/ egimes / initeelement profiles / imulation control parameters/
/
1 and s o i l
Compute s o i l
IInitiallzol / I n p u t Net . . . .
logical
s u r f a c e Temp. Ts(x) Temp. Equ. p a r a m e t e r s ~ - ~
I S o l v e s o i l Temp. p r e d i c t i o n o r ] c o r r e c t i o n Equ. (32). (33) /
d a t a / ~ - (2)
Compute s o i l
Mois. Equ. p a r a m e t e r s ~ - ~
/
Yes Solve soil [correction
Mois. p r e d i c t i o n
Equ. (30), (31)
or]
]
]
e v a p o r a t i o n and mulch s u r f a c e Temp.
[ Solve ~nlch Temp. Equ. I
No
1 (1)
Yes (2)
/Print .... It V
Fig. 2. Simplified flow chart of the computer program.
moisture regimes of a seedbed mulched with porous or film mulches was tested at the Yucheng Experimental Station, Institute of Geography, Chinese Academy of Sciences, in April 1989. The soil at this location is a clay loam, composed of 41% sand, 31% silt and 22% clay. The water table is at about 2 m depth. Cotton seed had been sown on 17 April and the soil was mulched immediately after sowing. Three kinds of strip mulching, i.e. wheat straw (with a straw length of about 5 cm and a mulching thickness of about 5 cm), clear PE film (of 0.015 mm thickness) and oiled paper (newspaper coated with lubrication oil), as well as a bare soil plot (control), were tested. Each mulching treatment consisted of two strips, to eliminate the edge effect of the mulch. Wind speed, air temperature and humidity were recorded at 2h intervals, at 2 m elevation on the same plot. The temperature profiles in soil were recorded at 06:00h, 10:00 h, 14:00h, 18:00h each day with thermistor probes at depths of 5, 10, 15 and 20 cm beneath the centre line of the mulch, and at a depth of 5 cm at 5, 10 and 20 cm horizontally both outside and inside the strip mulch. The surface temperature of soil and mulches were measured with an IR thermometer at 06:00h, 08:00h, 10:00h, 12:00h, 14:00h, 16:00h and 18:00 h each day. The soil moisture contents were measured by gravimetric
289
S I M U L A T I O N O F M U L C H E F F E C T S O N SOIL M I C R O C L I M A T E
ch
on
~;,'::~d 1 i n g
ion of soJ] ~rat u r e m e a s u r e m e n t
2ion o f s o l ] :ure m e a s u r e m e n t
I
0.8m Fig. 3. Layout of strip mulch pattern and the soil moisture and temperature measurements. The circle at the mulch centre represents the layout point of the collimated neutron probe. The solid triangle at the centre line of the mulch represents the layout points of the thermistor probes, at depths of 5, 10, 15 and 20cm.
analysis at depths of 1, 5, 10 and 20 cm and by collimated neutron probe at depths o f 30, 50, 70, 90 and 120 cm beneath the mulch centre line. Meanwhile, the soil moisture contents were also measured by gravimetric analysis at a depth of 5 cm at 0, 10 and 20 cm horizontally both outside and inside the strip mulch. The experimental arrangement of the strip mulching is shown in Fig. 3. The soil moisture characteristic curve was measured by a pressure plate apparatus, at pressures o f 0 to - 15 bar. The soil liquid water diffusivity was measured by a horizontal soil cylinder m e t h o d (Lei et al., 1988). The soil texture and hydraulic parameters are listed in Table 1. The measurements of photometric properties of soil and mulches were carried out before and during the field experiment. The transmissive coefficient fl~ of film mulches to short-wave radiation was measured by a DU-7 spectrometer. The albedoes e and 0~m of soil and mulch surfaces were measured five times a day by an albedometer at the same plot at the Yucheng Experimental Station. The average daily m e a n albedo for 3 days for soil and mulches was adopted. The transmissive coefficient 13, o f film mulches to the long-wave radiation was determined using two grey sources with different temperatures to eliminate the influence of IR radiation from the film itself (Zhang and Niu,
290
H. SUI ET AL.
TABLE 1
Soil texture and hydraulic parameters for experimental plot at Yucheng Experimental Station Depth
Bulk density
Moisture characteristic
Water conductivity
(m)
(kgm
curve
K = al(O/OJ bi ( m s
3)
1)
¢ = - ae b ' ( m )
a~ a
0-0.05
1.2E3
0.05-0.10
1.3E3
0.10-0.80
1.4E3
bi
b 5602.3I
- 31.40
8
4.75
0 ~< 0.15 444.73
0 ~< 0.15 - 15.28
2.65E -
0 ~< 0.28 8.88E - 6
0 ~< 0.28 12.60
0 > 0.15
0 > 0.15
0 > 0.28
0 > 0.28
3587.26
- 26.20
8
5.78
0 ~< 0.15 403.99 0 > 0.15
0 ~< 0.15 - 14.15 0 > 0.15
4.22E -
0 ~< 0.28 1.19E - 5 0 > 0.28
0 ~< 0.28 11.70 0 > 0.28
3370.71 0 ~< 0.15 423.47
- 24.03 0 ~< 0.15 - 13.28
3.33E - 9 0 ~< 0.28 4.20E - 5
4.62 0 ~< 0.28 11.76
0 > 0.15
0 > 0.15
0 > 0.28
0 > 0.28
1981). The emissivities e and em of soil and mulches were also determined by the method of Zhang and Niu (1981). The photometric properties of the soil and mulches are listed in Table 2. RESULTS
AND
DISCUSSION
Figures 4 and 5 show the diurnal observed and simulated variations in soil moisture and temperature respectively at depths of 5 cm and 20 cm, on 22-26 April for a bare plot and plots mulched with clear PE film, oil-coated paper and wheat straw. Figures 6 and 7 show the horizontal variations of daily mean soil temperatures and moisture contents at a depth of 5 cm from the outside to the inside of the mulch strip. The maximum of the relative differences between the predicted and observed values was less than 15%. The residual variances of the observed values with the corresponding predicted values at soil depths of 5 and 20 cm are used to judge the performance of the model. The TABLE 2
Photometric properties of soil and mulches
Soil P E film
Oiled paper Straw
0.84 0.08
0.75 0.07
0.23 0.32 0.21 0.32
0.95 0.15 0.79 0.84
SIMULATION OF MULCH EFFECTS ON SOIL M1CROCLIMATE
291
35 I
(a) •
0
C~
10
G)
25-
Obs. Sim. + PE film o ---- Oiled paper • --Straw Control .
(b) .
4"~
20
i0 Ap
I
I
14 22 22th
]
6
I
I
14 22 23th
I
6
I
'
14 22 24th
I
6
,
l
14 22 25th
I
6
,
14 2 26th
,
Hour Day
Fig. 4. Simulated and observed soil temperature variations for 22-26 April 1989 beneath the strip mulch centre. (a) A t a depth of 5 c m . (b) A t a depth of 20cm. - - - , Simulation of PE film; oil-coated paper; - - - , wheat straw; - . . , control. Observed values are represented as follows: + , P E film; O, oil-coated paper; e , straw; A, control.
residual variances of soil temperatures are 0.2269°C 2, 0.3451°C 2, 0.4805°C 2 and 0.1874°C 2 for PE film, oiled paper, straw and the bare plot, respectively. These show that the average errors of soil temperatures between the predicted and observed values are less than 0.7°C. The residual variances of soil moisture contents are 0 . 2 7 9 4 E - 3(m3m 3)2 0 . 3 4 5 1 E - 3(m3m 3)2, 0.3385E - 3(m3m-3) 2 and 0.4461E - 3(m3m-3) 2 for PE film, oiled paper, straw and the bare plot, respectively. These show that the average errors of soil moisture contents between the predicted and observed values are not more than 0.02 m 3 m - 3 . These results suggest that the predicted values of soil temperatures and moisture contents under conditions of evaporation are in good agreement with the corresponding observed values. Mulching with PE sheet gave the highest soil temperatures, those for the
292
H, su1
~'~
.20
¢¢3
.15
i
Obs. + o • •
./"
"~
ET AL,
•
~..~.~"~"~.
Sim. ~ ~--
PE f i l m Oiled paper Straw Control
~~--
.I0
(b)
o
~r/l .4
"
30 .
.25
.201'
.15 Apr.
i i 14 22 22th
| 6
I 14 23th
I. 22
I 6
. 14 24th
, 22
I 6
i 14 25th
i 22
I 6
~ 14 2 2 26th
Hour Da-y
Fig. 5. Simulated and observed soil moisture variations for 22-26 April 1989 beneath the strip mulch centre. (a) At a depth of 5 cm. (b) At a depth of 20 cm. (Symbols as in Fig. 4.)
oiled paper were slightly lower than those for the PE film, and the straw mulch showed the lowest temperature of the four treatments. The soil moisture levels were similar for all the mulched treatments. All of the mulches have a good ability to conserve water in the soil, and, on average, mulched treatments had about 25% more soil moisture than the unmulched plot at 5cm depth. Although the PE film gave the largest increase in soil temperature, it is difficult to dispose of, as it does not degrade easily. The paper coated with oil significantly increased the soil temperature and conserved soil moisture. It remained intact for 10 days, was degraded and caused only minimal pollution of the soil. For the germinating period, oiled paper appears to be a better mulch than the PE film, in terms of both increasing soil temperature and conserving soil wetness. The straw mulch reduced the soil temperature. It is not suitable for mulching during the germination period. However, it can conserve soil moisture as effectively as PE film and oiled paper. Moreover, the
SIMULATION OF MULCH EFFECTS ON SOIL MICROCLIMATE
293
Temperature Obs.
$im.
24
-
0
o¢
o
PE film ---- O i l e d paper
•
---
Straw
20 o
18
.14
I
~
I
-20
,
i
-i0
0
I
i
I
I0 O u t s J de
Inside
20
..
Distance
cm
Fig. 6. A v e r a g e daily m e a n soil t e m p e r a t u r e for 3 days, in a horizontal direction at a d e p t h o f 5 cm. (Symbols as in Fig. 4.)
3 -3
Moisture content m Obs.
• ~-_~.
,24
~
SJm.
+
PE
o
Oiled
fJ lm paper
•
• +
m
~
.
.
---
Straw
!
" ~ . ' 2 2~
~...
"---._... ~
•
.20
.18
I -20
I
I -i0 Inside
I
i 0
I i0 Outside
i
i 20
__ Distance
cm
Fig. 7. A v e r a g e daily m e a n soil m o i s t u r e for 3 days, in a horizontal direction at a d e p t h o f 5 c m ( S y m b o l s as in Fig. 4.)
294
H. SUl ET AL.
straw mulch also has the advantage of improving soil structure and increasing its humus content. The effects of the edge of the strip mulch on soil moisture and temperature are shown in Figs. 6 and 7. The horizontal gradients of the daily mean soil temperatures and soil moisture contents at 5 cm depth away from the edge of the mulch were approximately I°C in 10cm and 0.02cm3cm 3 in 10cm, respectively. The horizontal gradient of the daily mean soil temperatures is consistent with the result obtained by Mahrer and Katan (1981), who found an average gradient of daily maximum and daily minimum soil temperatures of about 1.25°C in 10 cm. These results suggest that a two-dimensional model for simulating the effect of a strip mulch on soil temperature and moisture is necessary.
The results are similar to the experimentally observed values of Maurya and Lal (1981). In their study, clear PE film, rice straw and an unmulched soil plot were tested. The differences in soil moisture reserve at 5 cm depth for the two mulching treatments were small, and the mulched treatments had 2030% more soil moisture than the unmulched plot. The PE film increased the maximum soil temperature at 5 cm depth by 5°C and the straw reduced it about 5°C compared with the bare plot. CONCLUSION
A numerical two-dimensional model to predict mulched soil moisture and temperature regimes under conditions of evaporation has been developed, tested and verified. The model can be used in decision-making on the most appropriate time for mulching and sowing, and the best mulch material, and especially on the selection of mulching characteristics, such as mulching thickness, width and density, for particular agricultural and plant requirements. Oil-coated paper mulch is highly efficient in conserving soil moisture and increasing soil temperature during the germination period. It is cheap, and decomposes in situ. REFERENCES Atkinson, K.E., 1978. An Introduction to Numerical Analysis. Wiley, New York, 587 pp. Bristow, K.L. and Campbell, G.S., 1986. Simulation of heat and moisture transfer through a surface-residue-soil system. Agric. For. Meteorol., 136: 193-214. Camillo, P.J. and Robert, J.G., 1986. A resistance parameter for bare soil evaporation models. Soil Sci., 141: 225-232. Chen, F., 1980. A micrometeorological study on the thermal effect of soil mulching. Acta Qeogr. Sin., 35: 68-75. De Vries, D.A., 1963. Thermal properties of soils. In: W.R. van Wijk (Editor)~ Physics of Plant Environment. North-Holland, Amsterdam, pp. 210-235. Gurnah, A.M., 1987. Effect of mulches on soil temperature under Arabica coffee at Kebete, Kenya. Agric. Meteorol., 25: 234-244.
SIMULATIONOF MULCHEFFECTSON SOILMICROCLIMATE
295
Katan, J., 1979. Solar heating of the soil by polyethylene mulching for the control of plant diseases and weeds. ASAE Paper 79-46. Lei, Z., Yang, S. and Hui, S., 1988. Soil Water Dynamics. Chinese Science Publishing Co., Beijing, 282 pp. Mahrer, Y., 1979. Prediction of soil temperature of a soil mulched with transparent polyethylene. J. Appl. Meteorol., 18: 1263-1267. Mahrer, Y. and Katan, J., 1981. Spatial soil temperature regime under transparent polyethylene mulch: numerical and experimental studies. Soil Sci., 131: 82-87. M ahrer, Y., 1984. Temperature and moisture regimes in soils mulched with transparent polyethylene. Soil Sci. Soc. Am. J., 48: 362-367. Maurya, P.R. and Lal, R., 1981. Effects of different mulch materials on soil properties and on the root growth and yield of maize and cowpea. Field Crops Res., 4: 33-45. Philip, J.R. and de Vries, D.A., 1957. Moisture movement in porous materials under temperature gradients. Trans. Am. Geophys. Union, 38: 222-232. Pinder, G.F., 1982. Numerical Solution of Partial Differential Equations Science and Engineering. Wiley, New York, 677 pp. Van Bavel, C.H.M. and Hillel, D.I., 1976. Calculating potential and actual evaporation from bare soil surface by simulation of concurrent flow of water and heat. Agric. Meteorol., 17: 453-476. Zhang, Y. and Niu, W., 1981. Principle and Application for Asphalt Emulsion Mulch. Chinese Science Publishing Co., Beijing, 107 pp. APPENDIX A: LIST OF SYMBOLS
A mulch sensible heat flux (W m -2) Ao mulched soil sensible heat flux ( W m -2) C volumetric heat of the air (J m 3 K - t ) soil volumetric heat capacity (J m -3 K -I ) mulch volumetric heat capacity (J m - 3K - t ) C soil volumetric water capacity (m -~ ) soil thermal vapour diffusivity (m 2 s- t K - t ) Do soil isothermal moisture diffusivity (m 2 s - t ) Dt sum of mulch and unmulched soil width of tile strip mulch (m) Eo mulched soil latent heat flux (W m - 2 ) Es(t, x) soil evaporation rate at the soil-atmosphere interface (m s -t) Est (t, x) mulch evaporation rate equal to soil-mulch water flux (m s -t ) h mulching thickness (m) H depth of the domain fl (m) Ha absolute humidity of the air at 2 m elevation (kg m -3) Hs absolute humidity of the soil surface (kgm -3) K soil isothermal liquid water conductivity (m s - t ) Kv soil isothermal vapour conductivity (m s -~ ) Kw soil isothermal moisture conductivity (m s - t ) L heat of vaporization (J kg- t ) qrn saturated specific humidities at mulch surface qs saturated specific humidities at soil surface vapour transport resistance of mulch (s m -t) rrn vapour transport resistance at soil surface (s m - t ) rs
296
H. SUI ET AL.
Rc Rcm Rg
Ri Rn Rn~
S(t, x) S1 (t, x) Sin(t, x) Sm I (t, x) t T
To(x, z) TL Ta Tm Tm n Tm~ Trn._ i Ts X, Z
Z1 Zm I Zmn- I 0~, O~m
6 g', f'rn
0
Os 2 2m 21
aerodynamic resistance between soil surface and 2m elevation (sm ') aerodynamic resistance between mulch surface and 2 m elevation (sm-') total short-wave irradiance (W m -2) long-wave sky irradiance (W m -2) net radiation (Wm z) net radiation of the film mulch (Wm -2) soil heat flux at the soil-atmosphere interface (J m ' s-' ) soil heat flux at the soil-mulch interface (J m - ' s - ' ) mulch heat flux at the soil-mulch interface (J m - ' s ') mulch heat flux at mulch-atmosphere interface (J m - ' s- ' ) time (s) soil temperature (K) initial soil temperature (K) soil temperature at the depth z, (K) air temperature at the reference elevation (K) mulch surface temperature (K) mulch bottom temperature (K) mulch temperature at depth Zm, (K) mulch temperature at depth Z m . _ , (K) soil surface temperature (K) horizontal and vertical coordinates, respectively (m) soil depth of layer 1 (m) mulch depth of layer 1 (m) mulch depth of layer n - 1 (m) soil and mulch albedoes, respectively transmissive coefficient of the film for the long-wave radiation transmissive coefficient of the film for the short-wave radiation absorptive coefficient for the solar radiation soil and mulch emissivities, respectively soil volumetric moisture c o n t e n t (m 3 m -3) saturated soil volumetric moisture content (m 3m -3) soil thermal conductivity (J cm-I s-I K - l ) mulch thermal conductivity (J cm-~ s- ~K ~) soil thermal conductivity of the layer from depth 0 to z~ (Jcm -I s -I K -l)
P density of air (kg m - 3) Pl density of liquid water (kg m 3) o" Stefan-Boltzmann constant 0 soil matric potential (m) Oo(X, z) initial soil matric potential (m)
297
SIMULATION OF MULCH EFFECTS ON SOIL MICROCLIMATE
APPENDIX
B: N U M E R I C A L
APPROACH
First, the governing eqns. (2) and (3) are rewritten as follows: ~K ~$ V-(KWV~b) + V'(DtvVT) + 0--7- cw ~t -- 0
L($)
=
L(T)
~T = V " ( ) V T ) + p, LV'(KvV~O) - Ch Ot -- 0
(A1) (A2)
Discretization o f plane domain The region fl as shown in Fig. 1 for soil heat and moisture transfer investigation is subdivided into N triangular elements. For the element e, according to the Galerkin method, the approximate solutions to the problem at any given time t are expressed as follows: T =
~ Ni(x, z)Ti = [U]{T(t)} i=1
~O =
~ N,.(x, z)~Oi =
[N]{~(t)}
i=1
where N,.(x, z) is the shape function of the node i on element e, m is the total number of nodes on element e, and $i and T,. are respectively the soil matric potential and temperature at node i. According to the weighted residual method, in the domain ~, the values of T and $ must be determined so as to satisfy the initial and boundary conditions of the problem together with the orthogonality requirements IIn W~. L ( O d n
=
0
(A3)
where Wi is the weighted residual function and L(~) represents eqns. (A1) and (A2). By combining eqns. (A1)-(A3) and applying Green's first identity, a set of quasilinear differential equations is obtained: [Kl 1 ]{I/1} + [Ku]{T} + [C,] t3~ _
{P1} + {/2}
(A4)
[&,]{T} + [K=]{q,} + [G] aT ~t -
{P3}
(A5)
t~t
where {~}
= [~,, ~ , - - .
{T}
=
[Kll ]
=
~',]~
[T,, T ~ , . . . T,] ~ (~[U] ~ a[U]
a[U] ~
Y~if~, ~x K~'--~ + - ~ z e
~[U]~
Kw Oz /dxdz
298
H. S U I E T AL.
r Dtv 8[N] 8[N]r 8[N]'] ffo \( 8[N] ax "-~-x + ~ D t " - - ~ f - z J dxdz
[K12]
(0IN] r
[K~,]
~[N]
8[N] r
8[N]~
e
[K22 ] =
(~[N] r
0IN] ~[N] r
~[N]']
P~L ~ ffne --J-Z-x Kv--5-Z + --E-z KV Oz / dx dz e
[c,]
fI~ [N]r Cw[N] dx dz
= e
[cd
~f~ [N]rCh[N] dx dz
= e
{/'1}
=
- ~ Ir~ [N]TEsdF e
{P2}
=
0K ~ ff~e[N]T-~g dx d2 e
{P3} -
•;r,[U] TSdF e
where f~e and 1-'eare the plane domain and boundary of the element e.
Discretization of time domain and linearization procedure Equations (A4) and (A5) are non-linear, because the coefficients Kw, Cw, Dtv, Kv and 2 are dependent on the soil moisture and temperature. The Douglas-Dupout prediction-correction method (Pinder, 1982) is employed; this has the advantage of requiring less computer time than the iteration procedure. The method has two classes of time accuracy. First, eqns. (A4) and (A5) are rewritten as follows:
a~ [c,]-b7 + [K,,]{~,}
=
{PA}
(A6)
~T [(721--~ + [Kz,]{T}
=
{P,}
(A7)
where
{PA } =
{P,} + {P2} - {K,2}{T}
{P,} =
(P3} - {K=}{~}
By applying the prediction-correlation approach, finally we obtain the differential schemes for calculating soil moisture and temperature. For the moisture regime:
SIMULATION OF MULCH EFFECTS ON SOIL MICROCLIMATE
299
Prediction:
[Ci] r -t- (1 -I-2 og)At [Ki']r } {I//}r* : + {[C~]~
AT{PA}r
(1-2co)At [K~]~} [~O]r
(A8)
Correction: [Ct]* + (1 + og)At } = 2 [KI,]* {~k},+, f + {[C,]r* (
(1
og)mt 2
) [Ki 1]*}j - {~s}, -
For the temperature regime: Prediction: ) (1 + og)Al [C2] r -I-[K21lr~ { T } * ) 2
f
(1
-'t- ~ [ C 2 ] r
t
og)mt 2
At{PA}.
=
(A9)
At{PB},
)
[K21]r} {T}r J
(A10)
Correction:
[c:]* + (1 + og)At [/21]r*} {T}r+I = AI{PB}r* 2 + {[c~]*
(1 - og)at 2 [K21 ]r~ } {T}r
(All)
The coefficient matrices and the right-hand terms can then be expressed as follows:
[X]r = [X(U,)] [x]~* :
[x((l+
o 9 ) ~ +2 (1 - og)Ur)]
where the matrix [X] represents [CI], [C2], [K,I], [K21], [PA] and [Ps], U represents the temperature T and matric potential ~k, the subscripts r and r + 1 represent the time step t and t + At respectively, the superscript * represents the predicted value, and o9 is the differential scheme coefficient (o9 = 1 represents the backward scheme, o9 = 0.5 the time-centred scheme and o9 = 0.667 the Galerkin scheme). For the mulch temperature differential scheme, eqns. (A10) and ( A l l ) are also used but {Ps} = {P3}.
281
Elsevier Science Publishers B.V., Amsterdam
A numerical model for simulating the temperature and moisture regimes of soil under various mulches Hong-jian Sui", De-chao Zeng b and Fa-zu Chen c ~Research Centre of Environment, Beijing Institute of Management, University of Science and Technology of China, Beijing, People's Republic of China bLaboratory of Tillage Technology, Beijing Agricultural Engineering University, Beijing, People's Republic of China Clnstitute of Geography, Chinese Academy of Sciences, People's Republic of China (Received 2 July 1991; revision accepted 6 April 1992)
ABSTRACT Sui, H., Zeng, D. and Chen, F., 1992. A numerical model for simulating the temperature and moisture regimes of soil under various mulches. Agric. For. Meteorol., 61: 281-299. A two-dimensional numerical model for simulation of the effects of mulches was developed, and the governing equations were solved by the finite element approach of Galerkin-type together with the Douglas-Dupout prediction-correction method. A simulation program to predict the influence of porous and film mulches on heat and vapour transport under conditions of evaporation was developed and validated by field experiment. Preliminary application of the program showed that clear polyethylene film increased soil temperature the most effectively. However, there was little difference in the conservation of soil moisture for the three types of mulch, and paper coated with oil could significantly improve the soil microclimate for seed germination.
INTRODUCTION
Mulching is very effective in modifying the soil microclimatic conditions for plant growth. In the last 20 years, the mulching effects of various kinds of plastic and natural materials have been tested in field experiments, especially for the effect on soil temperature (Katan, 1979; Maurya and Lal, 1981; Gurnah, 1987). Computer modelling can provide a means of predicting the effects of mulching and, in many circumstances, can cut down drastically the amount of field test required. A one-dimensional numerical model for the prediction of soil temperature beneath clear polyethylene (PE) film was presented by Mahrer (1979), and a two-dimensional numerical model for the same predicCorrespondence to: H. Sui, Research Centre of Environment, Beijing Institute of Management, University of Science and Technology of China, Beijing, People's Republic of China.
0168-1923/92/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
282
H. S U I E T AL.
tion was presented later by Mahrer and Katan (1981). A one-dimensional model for both soil water and heat behaviour was presented by Mahrer (1984). The results in his study showed that the moisture content of the mulched soil strongly affected the soil temperature, and soil temperature was much lower at the edges of the mulch than at the middle. A one-dimensional model for soil temperature regime under an asphalt emulsio~ film was developed by Chen (1980), with the assumption that the film is in close contact with the soil surface. A one-dimensional model suitable for describing both heat and moisture transfer through a surface residue-soil system was also developed by Bristow and Campbell (1986). However, in that model the effect of the density and the arrangement of the porous mulch was not considered. In the present work, the effects of various mulches on soil moisture and temperature regimes were investigated. Mulches were classified into two categories: porous mulches (e.g. straw, gravel, sand, etc.) and film mulches (e.g. oiled paper, asphalt emulsion film, etc.). Porous mulches were treated as porous materials similar to soil. The primary functional factors of a porous mulch that can affect soil moisture and temperature regimes are its heat and vapour transport parameters, such as heat capacity, heat conductivity and vapour transport resistance, whereas the primary functional factors of a film mulch are its optical properties such as albedo, transmissivity and emissivity of short- and long-wave radiation. A two-dimensional model was established to predict the heat and moisture regimes of soil under a strip mulch. THE MODEL
The numerical model consists of two parts: one for the soil layer and one for the mulch layer. A schematic description of the mulched soil column is given in Fig. 1.
The soil layer The moisture transfer equation given by Philip and De Vries (1957) is
~t -
Oz D° ~z
+ ~x D o E
+ ~z
Dtv~z +~xx Dtv~x
~?z (1)
where 0 is the volumetric moisture content (m 3m-3), t is the time (in seconds), x and z are the horizontal and vertical coordinates (m), respectively. Do is the isothermal moisture diffusivity (m 2s-l), Dt~ is the thermal vapour diffusivity (m 2 s-I K - I ) , and can be calculated by the formula given by Philip and De Vries (1957) and T is the soil temperature (K). K is the isothermal liquid water conductivity (m s- L), which is calculated from the formula K = CwD, where D is the soil liquid water diffusivity (m 2 s-I), and Cw = -~0/0~J is the volu-
283
S I M U L A T I O N OF MULCH EFFECTS ON SOIL MICROCL1MATE
_
.
_
Fig. 1. Schematic description of the mulched soil column under investigation.
metric water capacity (m ~), with ~, the matric potential (m-'). Cw can be calculated by graphic differentiation of the soil moisture characteristic curve. By applying the expressions
a0
a0
at - Cw~
and
a~
Do = Kw-~O eqn. (1) can be deduced as
+N
DtvN + ~
D~v~
az
(2)
Kw = K + Kv, is the isothermal moisture conductivity (m s-l). The soil heat transfer equation was given by Philip and De Vries (1957) as Ch at
az
~XX
~zz
~xx
(3) where Ch is the volumetric heat capacity (J m -3 K - ' ), 2 is the thermal conductivity (Jm -~ s -~ K -1), both Ch and 2 are evaluated according to De Vries (1963), p~ is the density of liquid water (kg m -3), L is the heat of vaporization (J kg -l) and Kv is the isothermal vapour conductivity (m s-~), which is calculated by the formula given by Philip and De Vries (1957).
284
H. SUI ET AL.
Soil boundary conditions At the soil-mulch interface, z = 0, 0 <~ x <<. D/2; -Kw
c~z
Dtv ~ z + K =
~T ~ --2-~z - p'LKV Oz -
Es, (t, x)
S,(t,x)
(4) (5)
where Es~ (t, x) is the soil-mulch moisture flux, which is equal to the mulch evaporation rate ( m s -t), and St(t, x) is the heat flux ( J m I s - t ) at the soil-mulch interface. At the soil-atmosphere interface, z = 0, D/2 < x <~ Dt/2; - K w ~3ff OT + K (~-7 -- sty -~z
=
- 2 ~OT z - plLKv ~~z
S(t, x)
-
Es(t, x)
(6) (7)
where Es(t, x) and S(t, x) are the evaporation rate and heat flux at the soil-atmosphere interface respectively. At the soil lateral boundaries, x = 0, x = D/2, 0 <~ z <~ H, the heat and moisture flux are equal to zero, because the two sides of each b o u n d a r y line are symmetrical, that is, --Kw ~63~ ' -- sty ~OT x + X OT 0~ - - 2 - ~ x -- p, L X v ~
=
=
0
0
(8)
(9)
The above equations of soil b o u n d a r y condition (eqns. (4)-(9)) can be derived from the moisture and heat transfer eqns. (2) and (3). At the base of the soil profile, 0 ~< x ~< Dj/2, z = H; =
~h(H)
T = T(H)
(10) (11)
Initial condition, t = 0 =
~0(x, z)
(12)
T =
To(x, z)
(13)
The soil surface temperature, conductive heat flux and evaporation rate at the soil-atmosphere interface are calculated by the aerodynamic approach (Van Bavel and Hillel, 1976).
SIMULATION OF MULCH EFFECTS ON SOIL MICROCLIMATE
285
The mulch layer Porous mulch
The porous mulch was simplified as a layer of porous materials for heat transfer. As the mulching width and length is much greater than the thickness, and the boundary conditions are homogeneous, the one-dimensional diffusion equation is applied: •T
Cm~t
-
~(
~z
~3T) 2m-~z
(14)
where Cm is the mulch volumetric heat capacity (J m -3 K-~ ) and ~'mis the heat conductivity of mulch (W m - 1K ' ). Both Cm and 2m are evaluated according to De Vries (1963). Mulch surface temperature is computed from the soil-air interface heat balance equation using the modified Newton iteration method which is called the secant method (Atkinson, 1978). Because the mulch is made of porous materials, the approach of Van Bavel and Hillel (1976) was applied to calculate the sensible heat flux. The heat balance equation is Rn -
LEsl -
A -
Sml
=
0
(15)
where R n is the net radiation (Wm-2), S m , and A are the mulch heat and sensible heat fluxes (W m-Z), respectively, and Es~ is the mulch evaporation rate. Mulch evaporation rate is calculated, according to Van Bavel and Hillel (1976), as Esl = ( H s -
Ha)/(Re, n + rs +
rm)
where H s and H a are the absolute humidity of the air at the soil surface and at a reference elevation (2 m)(kg m-3), respectively, Rcm is the aerodynamic resistance between the mulch surface and the reference elevation ( s m - ' ) , which is calculated by the formula of Van Bavel and Hillel (1976), rs is the transport resistance at the soil surface (sm -~), r m is the vapour transport resistance of the mulch (s m - ~) which is dependent upon its density, arrangement and material, r s and r m are determined by the method of Camillo and Robert (1986). The net radiation is expressed as follows: Rn
=
(1
--
0¢)Rg
+
R I --
~m~yTm 4
where Rg is the total short-wave irradiance (W m-Z), R~ is the long-wave sky irradiance (Wm-2), 0¢is the mulch albedo, em is the mulch emissivity, T m is the mulch surface temperature (K) and a is the Stefan-Boltzmann constant.
286
H. SUI ET AL.
The mulch heat flux is given by Sm I =
- ).m(Tml -
Tm)/Zm t
where T m l is the mulch temperature at the depth Zm~ (K). The sensible heat flux is given by A
=
C(Ta-
(16)
Tm)/Rcm
where C is the volumetric specific heat of the air (J m 3 K-1 ) and Ta is the air temperature at the reference elevation (K). At the mulch-soil interface Tm,
=
(17)
Ts
where T m , and Ts are the mulch bottom and soil surface temperature (K), respectively. Soil surface temperature at the soil-mulch interface is computed from the heat balance equation after the mulch temperature regime is calculated. At the soil-mulch interface, the net radiation is considered to be negligible. Thus the heat balance equation can be given by Sl
-
=
Sm
0
(18)
where S~ and S m are the soil and mulch heat flux (Wm-2), respectively. The expression for the mulch heat flux is Sm
=
)~m(Tmn_l -
Ts)/h -
gmn_l)
where T m , _ ~ is the mulch temperature at the depth Z m , _ ~ (K), Z m , _ ~ is the depth of mulch at the layer n - l(m) and h is the mulch thickness (m). The expression for the soil heat flux is S,
=
-21(T,
-
Ts)/Z,
where 21 is the soil heat conductivity of the layer from the soil surface to the depth Z~ (W m-~ K-~ ) and T~ is the soil temperature at depth ZI (K). Film mulch
Much work has been done in simulating the effect of transparent PE film on the soil temperature and moisture regimes. Here the Mahrer method (1984) is modified to determine the surface temperature of soil mulched with film, such as oiled paper or asphalt emulsion film. The characteristics of the films are their optical properties, such as long- and short-wave transmissivities, albedo and emissivity. The mulched soil surface energy balance equation is expressed as follows: R n -- S I -
E 0 - A0 =
0
(19)
where E0 and A0 are the latent and sensible heat fluxes (W m-2), respectively. The expression for net radiation R n is given by Rn
=
(1 -- a)flsR ~ + ~fljR I
+
~emaTm 4 -- ~aTs 4
SIMULATION OF MULCH EFFECTS ON SOIL M1CROCLIMATE
287
where fls, fl~ are the transmissive coefficients of the film to short- and longwave radiation, respectively, and e is the soil emissivity. The expressions for the sensible and latent fluxes are (Mahrer, 1984) Ao =
pC(Ts-
Tin) 4/3
Eo =
p L ( T s -- Trn)l/3(qs -- q m )
where p is the air density ( k g m -3) and qs and q m are the saturated specific humidities at the temperature of soil surface and mulch, respectively. Thus, eqn. (19) is rewritten as follows: FTs
=
R n ( T s , Tin) -- A o ( T s , T m ) -
E o ( T s , T m ) -- S ( T s )
=
0
(20)
The energy balance equation for the film mulch is Rn~ + A 0 + E 0 -
A = 0
(21)
where A is the film's sensible heat flux (W m-2), and its expression is the same as eqn. (16) instead of that of Mahrer (1984). Rn~ is the net radiation, and is expressed as Rn 1 =
gmRl +
t~Rg -k- g m e o ' ( T m ) 4
where 6 = 1 - fls - em is the absorptive coefficient for the solar radiation. In the same way, eqn. (21) is rewritten as follows: FTm
=
R n l ( T s , Tin) -
A(Tm)
+ Ao(Ts , Tm) + Eo(Ts , Tm)
(22)
The soil and mulch temperature can be determined from (20) and (22) by combining the secant and the iteration approach. The steady convergence of the computation of the two equations requires an initial condition Ts ~ T m . SOLUTION P R O C E D U R E
The flow chart of the computer program M S M T R F - I is given in Fig. 2. The required input and the initial data are the photometric and physical properties of the mulch, soil characteristics (texture and hydraulic parameters), finite element profiles of initial water content and temperature for both the mulch and soil. The atmospheric boundary conditions needed at each step are the global radiative fluxes, air temperature, relative humidity and wind speed. The numerical experiments were run on an IBM personal microcomputer. For a time interval, At, of 15min, a 24h simulation requires about 4 h on an IBM-XT computer and 40 min on an IBM-386 microcomputer. EXPERIMENTAL PROCEDURE
The performance of the model in correctly predicting temperature and
H. SUI ET AL.
288
(1) /~!
INPUT
o i l and mulch c h a r a c t e r i s t i c s / nitial moisture & temperature/ egimes / initeelement profiles / imulation control parameters/
/
1 and s o i l
Compute s o i l
IInitiallzol / I n p u t Net . . . .
logical
s u r f a c e Temp. Ts(x) Temp. Equ. p a r a m e t e r s ~ - ~
I S o l v e s o i l Temp. p r e d i c t i o n o r ] c o r r e c t i o n Equ. (32). (33) /
d a t a / ~ - (2)
Compute s o i l
Mois. Equ. p a r a m e t e r s ~ - ~
/
Yes Solve soil [correction
Mois. p r e d i c t i o n
Equ. (30), (31)
or]
]
]
e v a p o r a t i o n and mulch s u r f a c e Temp.
[ Solve ~nlch Temp. Equ. I
No
1 (1)
Yes (2)
/Print .... It V
Fig. 2. Simplified flow chart of the computer program.
moisture regimes of a seedbed mulched with porous or film mulches was tested at the Yucheng Experimental Station, Institute of Geography, Chinese Academy of Sciences, in April 1989. The soil at this location is a clay loam, composed of 41% sand, 31% silt and 22% clay. The water table is at about 2 m depth. Cotton seed had been sown on 17 April and the soil was mulched immediately after sowing. Three kinds of strip mulching, i.e. wheat straw (with a straw length of about 5 cm and a mulching thickness of about 5 cm), clear PE film (of 0.015 mm thickness) and oiled paper (newspaper coated with lubrication oil), as well as a bare soil plot (control), were tested. Each mulching treatment consisted of two strips, to eliminate the edge effect of the mulch. Wind speed, air temperature and humidity were recorded at 2h intervals, at 2 m elevation on the same plot. The temperature profiles in soil were recorded at 06:00h, 10:00 h, 14:00h, 18:00h each day with thermistor probes at depths of 5, 10, 15 and 20 cm beneath the centre line of the mulch, and at a depth of 5 cm at 5, 10 and 20 cm horizontally both outside and inside the strip mulch. The surface temperature of soil and mulches were measured with an IR thermometer at 06:00h, 08:00h, 10:00h, 12:00h, 14:00h, 16:00h and 18:00 h each day. The soil moisture contents were measured by gravimetric
289
S I M U L A T I O N O F M U L C H E F F E C T S O N SOIL M I C R O C L I M A T E
ch
on
~;,'::~d 1 i n g
ion of soJ] ~rat u r e m e a s u r e m e n t
2ion o f s o l ] :ure m e a s u r e m e n t
I
0.8m Fig. 3. Layout of strip mulch pattern and the soil moisture and temperature measurements. The circle at the mulch centre represents the layout point of the collimated neutron probe. The solid triangle at the centre line of the mulch represents the layout points of the thermistor probes, at depths of 5, 10, 15 and 20cm.
analysis at depths of 1, 5, 10 and 20 cm and by collimated neutron probe at depths o f 30, 50, 70, 90 and 120 cm beneath the mulch centre line. Meanwhile, the soil moisture contents were also measured by gravimetric analysis at a depth of 5 cm at 0, 10 and 20 cm horizontally both outside and inside the strip mulch. The experimental arrangement of the strip mulching is shown in Fig. 3. The soil moisture characteristic curve was measured by a pressure plate apparatus, at pressures o f 0 to - 15 bar. The soil liquid water diffusivity was measured by a horizontal soil cylinder m e t h o d (Lei et al., 1988). The soil texture and hydraulic parameters are listed in Table 1. The measurements of photometric properties of soil and mulches were carried out before and during the field experiment. The transmissive coefficient fl~ of film mulches to short-wave radiation was measured by a DU-7 spectrometer. The albedoes e and 0~m of soil and mulch surfaces were measured five times a day by an albedometer at the same plot at the Yucheng Experimental Station. The average daily m e a n albedo for 3 days for soil and mulches was adopted. The transmissive coefficient 13, o f film mulches to the long-wave radiation was determined using two grey sources with different temperatures to eliminate the influence of IR radiation from the film itself (Zhang and Niu,
290
H. SUI ET AL.
TABLE 1
Soil texture and hydraulic parameters for experimental plot at Yucheng Experimental Station Depth
Bulk density
Moisture characteristic
Water conductivity
(m)
(kgm
curve
K = al(O/OJ bi ( m s
3)
1)
¢ = - ae b ' ( m )
a~ a
0-0.05
1.2E3
0.05-0.10
1.3E3
0.10-0.80
1.4E3
bi
b 5602.3I
- 31.40
8
4.75
0 ~< 0.15 444.73
0 ~< 0.15 - 15.28
2.65E -
0 ~< 0.28 8.88E - 6
0 ~< 0.28 12.60
0 > 0.15
0 > 0.15
0 > 0.28
0 > 0.28
3587.26
- 26.20
8
5.78
0 ~< 0.15 403.99 0 > 0.15
0 ~< 0.15 - 14.15 0 > 0.15
4.22E -
0 ~< 0.28 1.19E - 5 0 > 0.28
0 ~< 0.28 11.70 0 > 0.28
3370.71 0 ~< 0.15 423.47
- 24.03 0 ~< 0.15 - 13.28
3.33E - 9 0 ~< 0.28 4.20E - 5
4.62 0 ~< 0.28 11.76
0 > 0.15
0 > 0.15
0 > 0.28
0 > 0.28
1981). The emissivities e and em of soil and mulches were also determined by the method of Zhang and Niu (1981). The photometric properties of the soil and mulches are listed in Table 2. RESULTS
AND
DISCUSSION
Figures 4 and 5 show the diurnal observed and simulated variations in soil moisture and temperature respectively at depths of 5 cm and 20 cm, on 22-26 April for a bare plot and plots mulched with clear PE film, oil-coated paper and wheat straw. Figures 6 and 7 show the horizontal variations of daily mean soil temperatures and moisture contents at a depth of 5 cm from the outside to the inside of the mulch strip. The maximum of the relative differences between the predicted and observed values was less than 15%. The residual variances of the observed values with the corresponding predicted values at soil depths of 5 and 20 cm are used to judge the performance of the model. The TABLE 2
Photometric properties of soil and mulches
Soil P E film
Oiled paper Straw
0.84 0.08
0.75 0.07
0.23 0.32 0.21 0.32
0.95 0.15 0.79 0.84
SIMULATION OF MULCH EFFECTS ON SOIL M1CROCLIMATE
291
35 I
(a) •
0
C~
10
G)
25-
Obs. Sim. + PE film o ---- Oiled paper • --Straw Control .
(b) .
4"~
20
i0 Ap
I
I
14 22 22th
]
6
I
I
14 22 23th
I
6
I
'
14 22 24th
I
6
,
l
14 22 25th
I
6
,
14 2 26th
,
Hour Day
Fig. 4. Simulated and observed soil temperature variations for 22-26 April 1989 beneath the strip mulch centre. (a) A t a depth of 5 c m . (b) A t a depth of 20cm. - - - , Simulation of PE film; oil-coated paper; - - - , wheat straw; - . . , control. Observed values are represented as follows: + , P E film; O, oil-coated paper; e , straw; A, control.
residual variances of soil temperatures are 0.2269°C 2, 0.3451°C 2, 0.4805°C 2 and 0.1874°C 2 for PE film, oiled paper, straw and the bare plot, respectively. These show that the average errors of soil temperatures between the predicted and observed values are less than 0.7°C. The residual variances of soil moisture contents are 0 . 2 7 9 4 E - 3(m3m 3)2 0 . 3 4 5 1 E - 3(m3m 3)2, 0.3385E - 3(m3m-3) 2 and 0.4461E - 3(m3m-3) 2 for PE film, oiled paper, straw and the bare plot, respectively. These show that the average errors of soil moisture contents between the predicted and observed values are not more than 0.02 m 3 m - 3 . These results suggest that the predicted values of soil temperatures and moisture contents under conditions of evaporation are in good agreement with the corresponding observed values. Mulching with PE sheet gave the highest soil temperatures, those for the
292
H, su1
~'~
.20
¢¢3
.15
i
Obs. + o • •
./"
"~
ET AL,
•
~..~.~"~"~.
Sim. ~ ~--
PE f i l m Oiled paper Straw Control
~~--
.I0
(b)
o
~r/l .4
"
30 .
.25
.201'
.15 Apr.
i i 14 22 22th
| 6
I 14 23th
I. 22
I 6
. 14 24th
, 22
I 6
i 14 25th
i 22
I 6
~ 14 2 2 26th
Hour Da-y
Fig. 5. Simulated and observed soil moisture variations for 22-26 April 1989 beneath the strip mulch centre. (a) At a depth of 5 cm. (b) At a depth of 20 cm. (Symbols as in Fig. 4.)
oiled paper were slightly lower than those for the PE film, and the straw mulch showed the lowest temperature of the four treatments. The soil moisture levels were similar for all the mulched treatments. All of the mulches have a good ability to conserve water in the soil, and, on average, mulched treatments had about 25% more soil moisture than the unmulched plot at 5cm depth. Although the PE film gave the largest increase in soil temperature, it is difficult to dispose of, as it does not degrade easily. The paper coated with oil significantly increased the soil temperature and conserved soil moisture. It remained intact for 10 days, was degraded and caused only minimal pollution of the soil. For the germinating period, oiled paper appears to be a better mulch than the PE film, in terms of both increasing soil temperature and conserving soil wetness. The straw mulch reduced the soil temperature. It is not suitable for mulching during the germination period. However, it can conserve soil moisture as effectively as PE film and oiled paper. Moreover, the
SIMULATION OF MULCH EFFECTS ON SOIL MICROCLIMATE
293
Temperature Obs.
$im.
24
-
0
o¢
o
PE film ---- O i l e d paper
•
---
Straw
20 o
18
.14
I
~
I
-20
,
i
-i0
0
I
i
I
I0 O u t s J de
Inside
20
..
Distance
cm
Fig. 6. A v e r a g e daily m e a n soil t e m p e r a t u r e for 3 days, in a horizontal direction at a d e p t h o f 5 cm. (Symbols as in Fig. 4.)
3 -3
Moisture content m Obs.
• ~-_~.
,24
~
SJm.
+
PE
o
Oiled
fJ lm paper
•
• +
m
~
.
.
---
Straw
!
" ~ . ' 2 2~
~...
"---._... ~
•
.20
.18
I -20
I
I -i0 Inside
I
i 0
I i0 Outside
i
i 20
__ Distance
cm
Fig. 7. A v e r a g e daily m e a n soil m o i s t u r e for 3 days, in a horizontal direction at a d e p t h o f 5 c m ( S y m b o l s as in Fig. 4.)
294
H. SUl ET AL.
straw mulch also has the advantage of improving soil structure and increasing its humus content. The effects of the edge of the strip mulch on soil moisture and temperature are shown in Figs. 6 and 7. The horizontal gradients of the daily mean soil temperatures and soil moisture contents at 5 cm depth away from the edge of the mulch were approximately I°C in 10cm and 0.02cm3cm 3 in 10cm, respectively. The horizontal gradient of the daily mean soil temperatures is consistent with the result obtained by Mahrer and Katan (1981), who found an average gradient of daily maximum and daily minimum soil temperatures of about 1.25°C in 10 cm. These results suggest that a two-dimensional model for simulating the effect of a strip mulch on soil temperature and moisture is necessary.
The results are similar to the experimentally observed values of Maurya and Lal (1981). In their study, clear PE film, rice straw and an unmulched soil plot were tested. The differences in soil moisture reserve at 5 cm depth for the two mulching treatments were small, and the mulched treatments had 2030% more soil moisture than the unmulched plot. The PE film increased the maximum soil temperature at 5 cm depth by 5°C and the straw reduced it about 5°C compared with the bare plot. CONCLUSION
A numerical two-dimensional model to predict mulched soil moisture and temperature regimes under conditions of evaporation has been developed, tested and verified. The model can be used in decision-making on the most appropriate time for mulching and sowing, and the best mulch material, and especially on the selection of mulching characteristics, such as mulching thickness, width and density, for particular agricultural and plant requirements. Oil-coated paper mulch is highly efficient in conserving soil moisture and increasing soil temperature during the germination period. It is cheap, and decomposes in situ. REFERENCES Atkinson, K.E., 1978. An Introduction to Numerical Analysis. Wiley, New York, 587 pp. Bristow, K.L. and Campbell, G.S., 1986. Simulation of heat and moisture transfer through a surface-residue-soil system. Agric. For. Meteorol., 136: 193-214. Camillo, P.J. and Robert, J.G., 1986. A resistance parameter for bare soil evaporation models. Soil Sci., 141: 225-232. Chen, F., 1980. A micrometeorological study on the thermal effect of soil mulching. Acta Qeogr. Sin., 35: 68-75. De Vries, D.A., 1963. Thermal properties of soils. In: W.R. van Wijk (Editor)~ Physics of Plant Environment. North-Holland, Amsterdam, pp. 210-235. Gurnah, A.M., 1987. Effect of mulches on soil temperature under Arabica coffee at Kebete, Kenya. Agric. Meteorol., 25: 234-244.
SIMULATIONOF MULCHEFFECTSON SOILMICROCLIMATE
295
Katan, J., 1979. Solar heating of the soil by polyethylene mulching for the control of plant diseases and weeds. ASAE Paper 79-46. Lei, Z., Yang, S. and Hui, S., 1988. Soil Water Dynamics. Chinese Science Publishing Co., Beijing, 282 pp. Mahrer, Y., 1979. Prediction of soil temperature of a soil mulched with transparent polyethylene. J. Appl. Meteorol., 18: 1263-1267. Mahrer, Y. and Katan, J., 1981. Spatial soil temperature regime under transparent polyethylene mulch: numerical and experimental studies. Soil Sci., 131: 82-87. M ahrer, Y., 1984. Temperature and moisture regimes in soils mulched with transparent polyethylene. Soil Sci. Soc. Am. J., 48: 362-367. Maurya, P.R. and Lal, R., 1981. Effects of different mulch materials on soil properties and on the root growth and yield of maize and cowpea. Field Crops Res., 4: 33-45. Philip, J.R. and de Vries, D.A., 1957. Moisture movement in porous materials under temperature gradients. Trans. Am. Geophys. Union, 38: 222-232. Pinder, G.F., 1982. Numerical Solution of Partial Differential Equations Science and Engineering. Wiley, New York, 677 pp. Van Bavel, C.H.M. and Hillel, D.I., 1976. Calculating potential and actual evaporation from bare soil surface by simulation of concurrent flow of water and heat. Agric. Meteorol., 17: 453-476. Zhang, Y. and Niu, W., 1981. Principle and Application for Asphalt Emulsion Mulch. Chinese Science Publishing Co., Beijing, 107 pp. APPENDIX A: LIST OF SYMBOLS
A mulch sensible heat flux (W m -2) Ao mulched soil sensible heat flux ( W m -2) C volumetric heat of the air (J m 3 K - t ) soil volumetric heat capacity (J m -3 K -I ) mulch volumetric heat capacity (J m - 3K - t ) C soil volumetric water capacity (m -~ ) soil thermal vapour diffusivity (m 2 s- t K - t ) Do soil isothermal moisture diffusivity (m 2 s - t ) Dt sum of mulch and unmulched soil width of tile strip mulch (m) Eo mulched soil latent heat flux (W m - 2 ) Es(t, x) soil evaporation rate at the soil-atmosphere interface (m s -t) Est (t, x) mulch evaporation rate equal to soil-mulch water flux (m s -t ) h mulching thickness (m) H depth of the domain fl (m) Ha absolute humidity of the air at 2 m elevation (kg m -3) Hs absolute humidity of the soil surface (kgm -3) K soil isothermal liquid water conductivity (m s - t ) Kv soil isothermal vapour conductivity (m s -~ ) Kw soil isothermal moisture conductivity (m s - t ) L heat of vaporization (J kg- t ) qrn saturated specific humidities at mulch surface qs saturated specific humidities at soil surface vapour transport resistance of mulch (s m -t) rrn vapour transport resistance at soil surface (s m - t ) rs
296
H. SUI ET AL.
Rc Rcm Rg
Ri Rn Rn~
S(t, x) S1 (t, x) Sin(t, x) Sm I (t, x) t T
To(x, z) TL Ta Tm Tm n Tm~ Trn._ i Ts X, Z
Z1 Zm I Zmn- I 0~, O~m
6 g', f'rn
0
Os 2 2m 21
aerodynamic resistance between soil surface and 2m elevation (sm ') aerodynamic resistance between mulch surface and 2 m elevation (sm-') total short-wave irradiance (W m -2) long-wave sky irradiance (W m -2) net radiation (Wm z) net radiation of the film mulch (Wm -2) soil heat flux at the soil-atmosphere interface (J m ' s-' ) soil heat flux at the soil-mulch interface (J m - ' s - ' ) mulch heat flux at the soil-mulch interface (J m - ' s ') mulch heat flux at mulch-atmosphere interface (J m - ' s- ' ) time (s) soil temperature (K) initial soil temperature (K) soil temperature at the depth z, (K) air temperature at the reference elevation (K) mulch surface temperature (K) mulch bottom temperature (K) mulch temperature at depth Zm, (K) mulch temperature at depth Z m . _ , (K) soil surface temperature (K) horizontal and vertical coordinates, respectively (m) soil depth of layer 1 (m) mulch depth of layer 1 (m) mulch depth of layer n - 1 (m) soil and mulch albedoes, respectively transmissive coefficient of the film for the long-wave radiation transmissive coefficient of the film for the short-wave radiation absorptive coefficient for the solar radiation soil and mulch emissivities, respectively soil volumetric moisture c o n t e n t (m 3 m -3) saturated soil volumetric moisture content (m 3m -3) soil thermal conductivity (J cm-I s-I K - l ) mulch thermal conductivity (J cm-~ s- ~K ~) soil thermal conductivity of the layer from depth 0 to z~ (Jcm -I s -I K -l)
P density of air (kg m - 3) Pl density of liquid water (kg m 3) o" Stefan-Boltzmann constant 0 soil matric potential (m) Oo(X, z) initial soil matric potential (m)
297
SIMULATION OF MULCH EFFECTS ON SOIL MICROCLIMATE
APPENDIX
B: N U M E R I C A L
APPROACH
First, the governing eqns. (2) and (3) are rewritten as follows: ~K ~$ V-(KWV~b) + V'(DtvVT) + 0--7- cw ~t -- 0
L($)
=
L(T)
~T = V " ( ) V T ) + p, LV'(KvV~O) - Ch Ot -- 0
(A1) (A2)
Discretization o f plane domain The region fl as shown in Fig. 1 for soil heat and moisture transfer investigation is subdivided into N triangular elements. For the element e, according to the Galerkin method, the approximate solutions to the problem at any given time t are expressed as follows: T =
~ Ni(x, z)Ti = [U]{T(t)} i=1
~O =
~ N,.(x, z)~Oi =
[N]{~(t)}
i=1
where N,.(x, z) is the shape function of the node i on element e, m is the total number of nodes on element e, and $i and T,. are respectively the soil matric potential and temperature at node i. According to the weighted residual method, in the domain ~, the values of T and $ must be determined so as to satisfy the initial and boundary conditions of the problem together with the orthogonality requirements IIn W~. L ( O d n
=
0
(A3)
where Wi is the weighted residual function and L(~) represents eqns. (A1) and (A2). By combining eqns. (A1)-(A3) and applying Green's first identity, a set of quasilinear differential equations is obtained: [Kl 1 ]{I/1} + [Ku]{T} + [C,] t3~ _
{P1} + {/2}
(A4)
[&,]{T} + [K=]{q,} + [G] aT ~t -
{P3}
(A5)
t~t
where {~}
= [~,, ~ , - - .
{T}
=
[Kll ]
=
~',]~
[T,, T ~ , . . . T,] ~ (~[U] ~ a[U]
a[U] ~
Y~if~, ~x K~'--~ + - ~ z e
~[U]~
Kw Oz /dxdz
298
H. S U I E T AL.
r Dtv 8[N] 8[N]r 8[N]'] ffo \( 8[N] ax "-~-x + ~ D t " - - ~ f - z J dxdz
[K12]
(0IN] r
[K~,]
~[N]
8[N] r
8[N]~
e
[K22 ] =
(~[N] r
0IN] ~[N] r
~[N]']
P~L ~ ffne --J-Z-x Kv--5-Z + --E-z KV Oz / dx dz e
[c,]
fI~ [N]r Cw[N] dx dz
= e
[cd
~f~ [N]rCh[N] dx dz
= e
{/'1}
=
- ~ Ir~ [N]TEsdF e
{P2}
=
0K ~ ff~e[N]T-~g dx d2 e
{P3} -
•;r,[U] TSdF e
where f~e and 1-'eare the plane domain and boundary of the element e.
Discretization of time domain and linearization procedure Equations (A4) and (A5) are non-linear, because the coefficients Kw, Cw, Dtv, Kv and 2 are dependent on the soil moisture and temperature. The Douglas-Dupout prediction-correction method (Pinder, 1982) is employed; this has the advantage of requiring less computer time than the iteration procedure. The method has two classes of time accuracy. First, eqns. (A4) and (A5) are rewritten as follows:
a~ [c,]-b7 + [K,,]{~,}
=
{PA}
(A6)
~T [(721--~ + [Kz,]{T}
=
{P,}
(A7)
where
{PA } =
{P,} + {P2} - {K,2}{T}
{P,} =
(P3} - {K=}{~}
By applying the prediction-correlation approach, finally we obtain the differential schemes for calculating soil moisture and temperature. For the moisture regime:
SIMULATION OF MULCH EFFECTS ON SOIL MICROCLIMATE
299
Prediction:
[Ci] r -t- (1 -I-2 og)At [Ki']r } {I//}r* : + {[C~]~
AT{PA}r
(1-2co)At [K~]~} [~O]r
(A8)
Correction: [Ct]* + (1 + og)At } = 2 [KI,]* {~k},+, f + {[C,]r* (
(1
og)mt 2
) [Ki 1]*}j - {~s}, -
For the temperature regime: Prediction: ) (1 + og)Al [C2] r -I-[K21lr~ { T } * ) 2
f
(1
-'t- ~ [ C 2 ] r
t
og)mt 2
At{PA}.
=
(A9)
At{PB},
)
[K21]r} {T}r J
(A10)
Correction:
[c:]* + (1 + og)At [/21]r*} {T}r+I = AI{PB}r* 2 + {[c~]*
(1 - og)at 2 [K21 ]r~ } {T}r
(All)
The coefficient matrices and the right-hand terms can then be expressed as follows:
[X]r = [X(U,)] [x]~* :
[x((l+
o 9 ) ~ +2 (1 - og)Ur)]
where the matrix [X] represents [CI], [C2], [K,I], [K21], [PA] and [Ps], U represents the temperature T and matric potential ~k, the subscripts r and r + 1 represent the time step t and t + At respectively, the superscript * represents the predicted value, and o9 is the differential scheme coefficient (o9 = 1 represents the backward scheme, o9 = 0.5 the time-centred scheme and o9 = 0.667 the Galerkin scheme). For the mulch temperature differential scheme, eqns. (A10) and ( A l l ) are also used but {Ps} = {P3}.