Physical aspects of soil solarization

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Diego Gutkowski¹ and Salvatore Terranova²

¹Dipartimento di Fisica dell Universita di Catania, Corso ltalia 57, 95129 Catania, Italy
²Istituto di Fisiologia Umana dell Universita di Catania, Viale Andrea Doria 6, 95125 Catania, Italy

Abstract

The usual physical theory of soil solarization is based on an energy balance equation and on coupled differential equations for heat and moisture diffusion. These equations are explicitly given, and the involved parameters, related to physical properties of soil and mulch, are illustrated. The theoretical predictions of the temperature regime are compared to the experimental results. Some of the assumptions of the usual theory are critically examined. Results are presented concerning the dependence of soil temperature on the shape of the exposed soil surface on the mulching film. Such results indicate that one can obtain soil temperatures which are higher than those obtained by means of the usual technique.

Introduction

The population densities of soilborne pathogens and weeds at a given instant strongly depend on previous soil physical conditions (temperature, moisture, etc.), so the control of the latter for a convenient time interval before planting will be important in order to prevent subsequent plant disease, to increase the yield and to improve the quality.

This paper deals with the control of soil physical conditions by means of soil solarization. To make clear the scope of such a study we shall classify the involved physical conditions and shall explain some expressions we need to formulate the general problem of a control theory of soil solarization. Such explanations are not formal definitions, but have a heuristic value.

When soil solarization is implemented in a given plot, the physical and biological results depend on several conditions, e.g.:

a) the physical properties of the soil (heat capacity, thermal conductivity, and emissivity);
b) the climatic conditions (air temperature, sky transparency);
c) the solar radiation;
d) the duration of the treatment;
e) the total amount and the time distribution of the water supplied to the soil;
f) the material and thickness of the mulching film;
g) others, among which chemical and biological conditions we will not consider in this paper.

It is convenient to give a short name to those conditions one assumes to be independent of the operator's will or choice; they will be called "exterior conditions". Typical exterior conditions could be those quoted under a), b), c) in the above list. Other conditions can be chosen by the operator among a certain set of possibilities; this set will be called the "set of possible choices". Typical conditions belonging to the set of possible choices could be those related to the items e) and f) of the above list.

The thermodynamical non-equilibrium state of the layer of soil subject to solarization (the system) depends on the exterior conditions and on the choice of the human operator. There is experimental evidence [ 11 ] that a satisfactory control of weeds and pathogens can be obtained if the evolution of the thermodynamical state of the system satisfies certain conditions which will be call "effective physical conditions". Obviously effective physical conditions can be obtained by means of methods different from soil solarization.

Suppose that a target in terms of prevention of plant disease, yields and quality of crops, has been assigned for a not yet treated plot prior to planting, and that some method has been used to control the evolution of the thermodynamical state of the system (e.g. by supplying energy into the soil through soil solarization); we shall say that the control is effective if effective physical conditions are obtained. The main problem of control theory of soil physical conditions in soil solarization is the following: for given exterior conditions and for a given set of possible choices determine whether there are choices which produce an effective control of soil physical conditions, and if there are, find them.

In small-scale cultivations there is no problem to get an effective control of physical soil conditions, since a small amount of energy can be easily supplied to the soil through various methods, but in large-scale cultivations, which are typical of commercial production, to get an effective control one is faced with the problem of supplying to the soil and storing in it, a great amount of energy.

Soil solarization exploits a "cheap" source of energy (essentially the energy of the radiation field of the sun) and its effectiveness has been experimentally proved in many circumstances. However, as far as the usual method of soil solarization is concerned, the exterior conditions (especially the climatic ones) for which soil solarization is effective are subject to restrictions. This is in part due to the fact that in the usual method the set of possible choices is too "small". For this reason the attempt to get a proper control theory of soil physical conditions for soil solarization will be worthwhile. Indeed such a control theory would allow one to use the most suitable soil solarization techniques depending on the climatic conditions, on the soil properties, and on the purposes of plant conditions. Thus, one needs a physical description of the evolution of soil or the state of an open system [2] (the layer of soil to be heated) interacting with the surroundings.

As a physical process soil solarization is a very complicated one, since it depends on thermodynamical, optical, radiative, diffusive, and stochastic phenomena which cannot be studied separately. In spite of the great amount of experimental results in soil solarization a satisfactory physical knowledge of the process suitable to improve the control of soil physical conditions is still a far target. This is mainly due to the following facts:

a) in most experiments many relevant physical data (such as the energy spectrum and the polarization state of the incoming and outgoing radiation, the complex refractive index of the mulching film, the thermal conductivity and heat capacity of the soil, etc.) have not been measured. It is impossible to test whether a physical theory fits the existing experimental data on the measured physical quantities such as the soil temperatures at various depths and to explain the differences observed in different experiments.

b) the usual physical theory of soil solarization (and the corresponding experimental applications described by the theory) is not suitable to formulate a control theory, since only few choices at the disposal of the operator are considered; they concern the material and the thickness of the mulching film and the use of a single or a double layer mulch [5, 6].

c) in the usual physical theory of soil solarization only few global properties of the incoming and outgoing radiation field are taken into account, the theory does not consider either a quantum or a classical radiation field in interaction with matter.

A sketch of the usual theory and a comparison with experimental results are given in the next section. An example of a method having a set of possible choices greater than the usual one is given in Section 3. Some conclusions are drawn in Section 4.

Usual Theory

The usual physical theory of soil solarization is based on an energy balance equation and on coupled differential equations for the heat and the moisture diffusion [9, 10].

The equation for the energy balance in a fixed layer of mulched soil is:

(1)

where E is the energy, t is the time, a is the albedo, ß_s and ß_L are the transmissivity coefficients of the plastic cover to short- and long-wave radiation, respectively. R_s is the power of long-wave radiation, R_L is the latent heat flux, F_s is the sensible heat flux, F_c is the conductive heat flux, e and e P are the emissivities of the soil and the cover, respectively. s is the Stefan-Boltzmann constant, T_M, and T_s are the absolute temperatures of the mulch and of the soil surface, respectively.

The scalar fields of soil temperature T and moisture q are obtained by solving the following equations with suitable boundary conditions:

(2)

(3)

where z is the depth, C is the heat capacity per unit volume, l is the soil thermal conductivity, Dq is the soil moisture diffusivity, D_T is the soil moisture thermal diffusivity, Kq , is the hydraulic conductivity. C is the convex combination of the heat capacities per unit volume of the soil constituents [3], i.e.:

(4)

where x_k is the volume fraction of soil material of heat capacity C_k per unit volume.

Average values of the heat capacities per unit volume are about 2 x 10s Jm^-3 K^-1 for quartz and clay minerals and about 2.5 x 10s 1 m^-3K^-1 for organic matter [3]; they vary slightly with the temperature in the considered range.

Equation (4) shows that C depends on q , since C increases as water content in soil increases (and correspondingly air content decreases) due to the fact that C is about 3 500 times C₂, the heat capacity per unit volume of air.

The soil thermal conductivity l depends on q and on T. This dependence, which is quite complicated, was studied by De Vries (3) for various soil constituents. For fixed T ? [293 K, 333 K], 0 is a monontonic increasing function of q ; for T=348 K = 75°C (a temperature value which at present is not reached in soil solarization) this is no more the case.

Equations (2), and (3) are coupled since C and l depend both on T and q ; therefore, for suitable boundary conditions they can be solved only numerically.

The results of calculations based on equations (1), (2), (3) or on similar ones were compared to the experimental results for soil mulched with transparent polyethylene (7, 8, 9). The agreement between measured and calculated soil temperatures was good for the wettest soil and bad for the driest one (9).

For a bare soil, Equations (2) and (3) are not to be changed, but the energy balance equation is:

(5)

instead of Eq. (1). Results of numerical computations based on Equations (5), (2), (3) were compared to experimental results for bare soils; the agreement between measured and calculated soil temperatures was good [(9)].

A criticism should be made to the usual theory concerning the term -d s T⁴ _S in Equation (1). For a black body at temperature T. expressed in K, the energy radiated per unit area per unit time in the wave-length interval is [l ,l +dl ] is

(6)

where:

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By integrating e( l ) one gets for the energy per unit area per unit time radiated by a black body at temperature T:

(7)

where s = 5.66 x I^-10 Jm^-2s^-1K^-4 is the Stefan-Boltzmann constant.

For a grey body of emissivity e (O=< e = <1), independent on l one obtains in a similar fashion that the radiation energy emitted per unit area per unit time is:

(8)

but when the spectral distribution of the emitted radiation is not proportional to e(l ) defined by Eq. (6) then in general the emitted energy is not proportional to T⁴as in Eq. (8). The thermal radiation of a bare soil is not very different from a grey body radiation; in such a case Eq. (5) describes with sufficient accuracy the energy balance. The thermal radiation emitted by a mulched soil is composed of two parts, namely the thermal radiation R^T emitted by the soil surface and transmitted through the mulching film and the thermal radiation R^M emitted by the upper surface of the mulch. The spectral distribution of R_T depends on the thermal radiation of the bare soil and on the transmittance of the mulch as a function of l . If the transmittance varies slightly with l in the region where the emitted energy is not negligible, then Eq. (1) fairly describes the energy balance, whereas if the transmittance varies quickly with l , then Eq. (1) provides a poor description of the energy balance. For a polyethylene mulch the variations of transmittance with l are much smaller than for an EVA mulch, which in the region 2 m =< l =< 40 m has very sharp and narrow resonances. So one would expect a better agreement between the usual theory and the experimental results in the case of a polyethylene mulch, than in the case on an EVA one. As far as we know the usual theory has only been compared with the experimental results for polyethylene mulches.

Solarization of Pierced Soil

The subiect.- This section deals with a series of physical experiments carried out in 1987, 1988 and 1989 on solarization of soils having holes on their surfaces under the mulch. Several choices concerning the size of the holes, the number of holes per unit area and the mulching film were tested on the same type of sandy soil, as described in the next section on materials and methods. Soil temperatures at various depths were measured and recorded every hour in different specimens with holes and in control specimens without holes. The comparison of the data recorded at the same instant, at the same depth, in different specimens which were solarized under the same exterior conditions (such as solar radiation air temperature, etc.), during the same time, shows a dependence of the soil temperatures on the set of chosen conditions (such as the size of the holes, the number of holes per unit area and the mulching film).

Materials and methods.- The experiments E₁, E₂, E₃, E₄, described below took place near Catania (latitude 37°25' N. longitude 15° E). The specimens were contained in boxes (parallelepipeds having square horizontal faces 2 m x 2 m and height 35 cm) filled with sandy soil (sand 92.4 percent, silt 4.7 percent, clay 2,9 percents water capacity in weight 26.3 percent). The boxes having neither cover nor bottom were placed on the ground, their walls were thermally isolated. For any experiment E_j (j =1, 2, 3, 4) there were n_j specimens ^Pj,1, ^Pj,2,....,P_j, n_j prepared as follows: first they were irrigated at field capacity, so at the beginning of the experiment the water content was equal to the water capacity. Then N_j,k holes/m² were made on the surface of the specimen P_j.k (j=1, 2, 3, 4; k =1, 2,...,n_j). The holes had the shape of cylinders having vertical axis, diameter f _j,k and height h_j'k (in other words h_j'k is also the depth of the holes in the specimen P_j,k). The numbers n_j, N_j,k and the lengths ( f _j,k,h_j,k are given below for each experiment E_j (j =1,2,3,4; k =1,2,...,n_j). Lastly the exposed soil surfaces of the n_j specimens P_j,1,P_i,2...,P_j,n_j were mulched with a transparent plastic film. The characteristic of the mulching films are given below for each experiment. There could be two types of control specimens in any experiment E_j (j=1,2,3,4):C_j were prepared as the specimens P_j,k except for the holes, the specimens of type C_j were neither mulched nor irrigated. In each experiment E_j the measured physical quantities were: the air temperature in the shade, the energy of the incident solar radiation per unit time per unit area of horizontal surface and the soil temperatures in the specimens at various depths d_j'1,d_j'2,...,d_j,m_j which are given below for each experiment. The measured physical quantities were automatically recorded by a computer every hour throughout the run of the experiment. The specific conditions characterizing each experiment are given below.

1. Experiment E_i. Period: August 1987; and n₁ =1 (number of mulched specimens with holes). Mulching film: polyethylene B25/07 100 percept., thickness 29 ?m, haze 5 percent, clarity 13 percent, gloss 61 percent.

f _1,1 = 1 cm (hole diameter in the specimen P_1,1),
h_1,1 = 8 cm (hole depth in the specimen P_1,1),
N_1,1 = 1200 (number of holes/m² in the specimen P_1,1).
Control: C₁ (smooth soil surface mulched as P_1,1).

Depths at which soil temperatures were measured: d_1,1=5cm,d_1,2 =25 cm.

2. Experiment E₂. Period: August 1987; n₂ =1 (number of mulched specimens with holes). Mulching film: EVA, 12 percent VA, 75 percent Riblene D DV2735, 13 percent LLDPEth BF2221; thickness 30 m m, haze 6 percent, clarity 30 percent, gloss 55 percent.

f _2,1 = 1 cm (holes diameter in the specimen P_2,1),
h_2,1 = 8 cm (holes depth in the specimen P_2,1),
N_2,1 = 1 200 (number of holes/m2 in the specimen P_2,1).
Control: C₂ (smooth soil surface mulched as P_2,1).

Depths at which soil temperatures were measured: d_2,1 = 5 cm, d_2,2 = 25 cm.

3. Experiment E₃. Period: August 8 to 25, 1988; n₃ =3 (number of mulched specimens with holes). Mulching film: EVA, 14 percent VA, thickness 32mm, haze 5 percent, clarity 32 percent, gloss 62 percent.

f _3,1 =8mm, f _3,2 = 10mm, f _3,3 = 16mm (hole diameters in the specimens P_3,1,,P_3,2,P_3,3, respectively),

h_3,1 =72mm, h_3,2 = 90mm, h_3,3 = 144mm (hole depths in the specimens P_3,1, P_3,2, P_3,3 respectively).

N_3,1 =1 736, N_3,2 = 1111, N_3,3 = 434 (number of holes per m² in the specimens P_3,1, P_3,2, P_3,3, respectively).

Remark: h_3,k = 9f _3,k the distance between the centres of nearest holes was 3f _3,k and for the chosen geometrical pattern (Fig.1), N_3,k = (1 m²)/(3 f _3,k)², k=1,2,3.

Control: C₃ (smooth, bare soil surface).
Depths at which soil temperatures were measured: d_3,1 = 5 cm, d_3,2 = 15 cm, d_3,3 = 25 cm.

4. Experiment E₄. Period: from July 30 to August 31, 1989; n⁴ =2 (number of mulched specimens with holes). Mulching film: EVA.

f _4,1 = 6mm, f _4,2 = 10mm (hole diameters in the specimens P_4,1, P_4,2, respectively),

h_4,1 = 54mm, h_4,2 = 90mm (hole depths in the specimens P_4,1, P_4,2 respectively),

N_4,1 = 3086, N_4,2 = 1111 (number of holes per m² in the specimens P_4,1, P_4,2 respectively).

Remark: h_4.k = 9f _4,k the distance between the centres of nearest holes was 3f _4,k and for the chosen geometrical pattern (Fig. 1), N_4,k = (1 m²)/(3f _4k)², K= 1 ,2.

Control:
C₄ (smooth soil surface mulched as P_4,1 , and P_4,2)
and
C₄ (smooth, bare soil surface).

Depths at which soil temperatures were measured:
d_4,1=5cm, d_4,2= 15cm, d_4,3=25cm.

Results

Experiment E₁- Some results on soil temperatures are given in Table 1. Corresponding air temperatures varied between 26.8°C and 28.8°C between days 9 and 15, while solar radiation energy kjm^-2) varied from 21956 to 25 794; they are the same as the exterior conditions of the experiment E₂, since the period was the same and the distance between the specimens in the two experiments was in the order of few metres.

Further results and more details are given by Cartia et al. (1).

Experiment E₂.- Some results on soil temperatures are given in Table 2. The corresponding exterior conditions are the same as the exterior conditions of the experiment E₁, since the period was the same and the distance between the specimens in the two experiments was in the order of few metres.

Further results and more details are given by Cartia et al. (1).

Experiment E₃.- Some results on soil temperatures are given in Fig. 2, A-C. The corresponding exterior conditions are given in Fig. 3.

Experiment E₄.- Some results on soil temperatures are given in Table 3 and in Fig. 4, A-C. The corresponding exterior conditions are given in Fig. 5.

Discussion

The experiments E₁ and E₂, verify the following statements concerning mulched soils which were under the same conditions but for the ones explicitly mentioned:

(i) soil temperatures in pierced soils are higher than those in soils having a smooth surface (not pierced);

(ii) the rise in soil temperatures due to the holes is higher with an EVA mulch than with a polyethylene one;

(iii) temperatures in soils mulched with EVA films are higher than temperatures in soils mulched with polyethylene films;

(iv) the combination of soil piercing and EVA mulching produces a synergistical effect in raising soil temperatures with respect to the case of a polyethylene mulching on a smooth soil surface.

Due to the above statements (ii) and (iv), in subsequent experiments on thermal effects of soil piercing we limited ourselves to testing EVA mulches. Statement (i) was verified in experiments E₄ too (Table 3, Fig. 4 A-C, and all the recorded data we do not produce) in experiment E₃ there was no proper control to verify it (lack of a control C₃).

The experiments E₃ and E₄ had a common feature; the surface of all the pierced specimens were connected by a local scale transformation (see remarks for experimental results for E₃ and E₄). The pierced soil surfaces beneath the mulch were geometrically similar. The scale transformation was local since the specimens were not scaled in their whole size (which was 2 m x 2 m x 0.35 m for every specimen). To specify the geometrical shape of the soil surface there is only one degree of freedom, that can be chosen as the hole diameter f (since if f is given then the hole depth and the distance between nearest holes is determined). The experiments E₃ (Fig. 2, A-C, and all the recorded data we do not produce) and E₄ (Table 3, Fig. 4. A-C, and all the recorded data we no not produce) verify the following statement:

(v) for the hole pattern and hole diameters specified in experimental results for E3 and E4, soil temperature is a decreasing function of hole diameter. Statements (i), (ii), (iii), (iv), (v) have been, in our opinion, the most significant results that we have obtained in solarization of pierced soils.

One could ask why there is such a scale dependence as described in statement (v). At present we do not know the answer, but several are possible. A first one will sound brighter in Feynman's words than in ours: "Suppose that we ask: are the physical laws symmetrical under a change of scale? Suppose we build a certain piece of apparatus and then build another apparatus five times bigger in every part, will it work exactly the same way? The answer is, in this case, no! The wavelength of light emitted, for example, by the atoms inside one box of sodium atoms and the wavelength of light emitted by a gas of sodium atoms five times in volume is not five times longer, but is in fact exactly the same as the other. So the ratio of the wavelength to the size of the emitter will change." [Feynman et al. (4)]. Other possible explanations may lie in the fact that the size of soil particles in the specimens P_3,1,P_3,3,P_4,1 ,P_4,2 is not scale transformed, or in the fact that heat transfer by convection is scale dependent We will be inquiring experimentally and theoretically the question raised by statement (v).

Conclusions

The main reasons of our interest in physical research on soil solarization were not to provide a satisfactory theory for the physicist in order to explain the existing data and to describe the physical process as it develops under the conditions so far used. Our purpose is rather to provide the user with the knowledge of the best choices to make in order to reach, if possible, a given target under given exterior conditions. We do not conceive soil solarization as a recipe consisting of only one list of prescriptions to be followed independently on the target and on the exterior conditions. In the preceding section we have given the example of a method which produces higher soil temperatures than those obtained by the usual method. This is only a first step; to apply the piercing of soil on a large scale one needs to improve both the physical and the technological knowledge, for the method of piercing soil may have commercial application only if suitable machinery exists to implement it.

References

1. Cartia, G., Gutkowski, D., and S. Terranova. 1988. Effetti termici del lipo di pacciamatura e della foratura della superficie del terreno net processo di solarizzazione. Atti Giornate Fitopathologiche 1988 1: 449-458.

2. Davies, E. B. 1976. Quantum Theory of Open Systems. pp. 26, 149. Academic Press, London.

3. De Vries, D. A. 1963. Thermal properties of soils, p. 210-235. In W.R. Van Wijk (Ed.), Physics of Plant Environment. North Holland, Amsterdam.

4. Feynman, R. P., Leighton, R. B., and M. Sands. 1969. The Feynman Lectures on Physics, Volume I - Part 2, Ch. 52, p.3 Addison-Wesley, London.

5. Garibaldi, A. 1990. Use of solarization in marginally suitable climates. Proceedings of this Conference.

6. Garibaldi, A. and G. Tamietti. 1989. Solar heating: recent results obtained in northern Italy. Acta Horticulturae 255: 125-130.

7. Mahrer, Y. 1979. Prediction of soil temperature of a soil mulched with transparent polyethylene. J. Appl. Meterol. 18:1263-1267.

8. Mahrer, Y., and J. Katan. 1981. Spatial soil temperature regime under transparent polyethylene mulch: Numerical and experimental studies. Soil Sci. 131: 82-87.

9. Mahrer, Y., Naot, O., Rawitz, E., and J. Katan. 1984. Temperature and moisture regimes in soils mulched with transparent polyethylene. Soil Sci. Soc. Am. J. 48:362-367.

10. Philip, J. R., and D. A. De Vries. 1957. Moisture movement in porous materials under temperature gradients. Trans Am. Geophys. Union 38: 222-232.

11. Pullman, G. S., DeVay, J. E., and R. H. Garber. 1981. Soil solarization and thermal death: a logarithmic relationship between time and temperature for four soilborne plant pathogens. Phytopathology 71: 959-964.

Table 1. Mean daily values of soil temperatures at 5 cm and 25 cm depth in the pierced specimen P_1,1 and in the control specimen C₁ (mulch without holes) from August 9 to 15, 1987

Table 2. Mean daily values of soil temperatures at 5 cm and 25 cm depth in the pierced specimen P_2,1 and in the control specimen C₂ (mulch without holes) from August 9 to 15, 1987

Table 3. Mean daily values of soil temperatures at 5 cm and 25 cm depth in the pierced specimen P_4,1, P_4,2 and in the control specimen C₄ (mulch without holes) and C4 (smooth, bare soil surface) from August 5 to 11, 1989

Figure 1. The diagram was implemented on various scales in experiments E₃ and E₄. A and B are on the soil surface, the shaded area represents the soil.

Figure 2. (A) Experiment E₃. Soil temperatures on August 17, 1988 at 5 cm depth; Specimens P_3,k (k=1, 2, 3) and C₃. (B) Soil temperatures at 15 cm depth; Specimens P_3,k (k=1, 2, 3) and C₃. (C) Soil temperatures at 25 cm depth; Specimens P_3,k (k=1, 2, 3) and C₃.

Figure 3. Experiment E₃. Air temperature t and solar radiation R on August 17, 1988.

Figure 4. (A) Experiment E₄ Soil temperatures on August 10, 1989 at 5 cm depth; Specimens P_4,k (k=1, 2), C4 and C4. (B) Soil temperatures at 15 cm depth; Specimens P_4,k (k=1, 2 and C4 and C4. (C) Soil temperatures at 25 cm depth; Specimens P_4,k (k=1, 2), C4 and C4.

Figure 5. Experiment E₄. Air temperature t and solar radiation R on August 10, 1989.

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