Lal R., Shukla M.K. Principles of Soil Physics
Подождите немного. Документ загружается.
Soil Erosion
Water repellence may exacerbate soil erosion on sloping land by contributing to surface
runoff. In crop or pasture situations it causes an uneven distribution of water through the
surface soil horizons, which may result in patchy growth and reduced yield as seeds fail
to germinate in dry spots. This poor seedling emergence and crop growth exposes the soil
to wind and water, accentuating the risks of soil erosion.
20.5.3 Effect of Wild Fire on Water Repellency
A thin layer of soil at or below the mineral soil surface can become hydrophobic because
of high temperature following an intense heating. The hydrophobic layer is formed as the
result of a waxy substance that is derived from plant material burned during an intense
fire. The waxy substance penetrates into the soil as a gas and solidifies after cooling,
forms a coating around soil particles, and appears similar to nonhydrophobic layers. Plant
leaves, twigs, branches, and needles form a layer of litter and duff on the forest floor and
shrubs accumulating the hydrophobic substances in this layer. During an intense fire,
these substances move into the mineral soil. Some soil fungi also excrete substances,
which render both litter and surface layer water-repellent. However, not all wildfires
create a water-repellent layer. Four factors that commonly influence the formation of this
layer include: (i) a thick layer of plant litter prior to the fire, (ii) high-intensity surface
and crown fires, (iii) prolonged periods of intense heat, and (iv) coarse soil texture.
Very high temperatures are required to produce the gas that penetrates the surface. The
gas is forced into the soil by the heat of the fire. Soils that have large pores, such as sandy
soils, are more susceptible to the formation of hydrophobic layers because they transmit
heat more readily than heavy-textured soils, such as clay. The coarse-textured soils also
have larger pores that allow deeper penetration of the gas. The hydrophobic layer is
generally 2 to 8 cm beneath the soil surface and can be 2 to 3 cm thick. The continuity
and thickness of the layer vary across the landscape (USDA NRCS Soil Quality Institute,
2000).
20.5.4 Management of Water-Repellent Soil
Management options for water-repellent soils can be broadly classified as adaptation
strategies and avoidance strategies (Blackwell, 2003). Some plant species and cultivars
are naturally adapted to water-repellent soils. Conversion to a no-till method of seedbed
preparation can reduce the drying of soil surface under the mulch, increase porosity by
the root network from previous crops, and enhance infiltration of rainwater and water
redistribution in the soil profile. Water repellency in soils can be also be reduced or
masked by the addition of materials with a high surface area, e.g., clay. Dispersed clay
due to wetting exposes a greater surface area of hydrophilic clay surface and the drying
process binds sand and clay particles due to the surface tension masking the hydrophobic
organic coated surfaces and reducing water repellency (Ward and Oats, 1993). Wetting
agents, such as common household detergents or surfactants, can also be used for
Principles of soil physics 604
amelioration and management of soil water repellency. The performance of a wetting
agent is influenced by the degree of water repellency. Wetting agents have a strong
affinity for the hydrophobic soil and are strongly absorbed on the surface of hydrophobic
soil particles, increasing water infiltration and ameliorating the soil (Dekker et al., 2003).
Water-repellent soils can be avoided by either digging up the surface layer and planting
seed on nonrepellent subsoil or totally removing water-repellent topsoil and exporting
them to other areas.
20.6 SCALING METHODS IN SOIL PHYSICS
Knowledge of soil’s physical properties is important to understand and manage soil
resources at scales ranging from pedon to plot to global. Most of the sampling for
measuring soil properties is done using cores and monoliths on a small scale with an
objective to reconstructing soil physical properties across a wider scale such as a field or
watershed. The multiscale characterization of soil physical properties and processes is
useful as a research topic and as a practical tool for data assimilation. Scaling of soil
physical properties is a useful tool to integrate chemical, biological, and physical
properties and processes affecting soil quality and the environment. “Scaling” refers to
developing/formulating/identifying relationships between soil physical properties (data)
at different scales. The term “upscaling” is used when soil properties are integrated at a
larger scale than the one for which data is available, and “downscaling” is the opposite of
upscaling. The scaling theories can be applied using similar media concepts, which imply
that the two or more soil systems are similar and the properties of one can be predicted
from those of the other by using a single scaling factor. The single scale factor describes
either system exactly relative to the other.
20.6.1 Methods
Application of scaling to the characterization of soil properties is done by several
different ways, such as dimensional and similitude analysis, and regression analysis. In
the regression analysis scale factors are obtained by minimizing the sum of squares
between scaled and measured data points (Warrick et al., 1977).
Ed and Bob Miller, who introduced the concepts of scaling during the 1950s, showed
that for constant water content, the matric potential (Φ
m
) and unsaturated hydraulic
conductivities (Kθ) for two similar soil systems (1 and 2) can be explained by a single
scale factor as follows (Miller and Miller, 1956).
λ
1
Φ
m1
=λ
2
Φ
m2
=λ
ave
Φ
mave
(20.36)
K
θ1
/λ
1
=K
θ2
/λ
2
=K
θave
/λ
ave
(20.37)
The similar media concept is often used to scale the field data for soil water characteristic
relationships and unsaturated hydraulic conductivity. Warrick et al. (1977) extended this
concept of Miller and Miller for a single scaling factor and introduced another variable
Freezing and thawing effects 605
known as degree of saturation (s) to scale the volumetric water content. The technique
employed was regression analysis, also known as functional normalization, where scale
factors were obtained by minimizing the sum of squares between scaled and measured
data points. This method is effective in coalescing large sets of data into a very narrow
range. Some of the advantages of the regression method are the possibility to include all
data points without prior smoothing and to approximate the soil heterogeneity in terms of
a single stochastic parameter, i.e., the normalized scaling factor (Russo and Bresler,
1980).
Another method used in soil science to derive scale factors for soil properties is the
“dimensional method” also known as “similitude analysis,” which is based on physical
characteristics of a soil system, and involves reducing the number and complexity of the
physical process or a phenomenon. If a phenomenon depends on n dimensional variables,
dimensional analysis will reduce the problem to only k dimensionless variables where
n−k=1, 2, 3, or 4 depends on the complexity of the problem involved. The similitude
analysis is used in experimental research and design and analysis by the means of a
model or the correlation of field data (Tillotson and Nielsen, 1984; Shukla et al., 2002.)
The physically significant scale factors can be determined by dimensional and
inspectional analysis, and empirical scale factors can be obtained by functional
normalization (Tillotson and Nielsen, 1984; Sposito and Jury, 1985; Shukla et al., 2002).
Scale factors obtained through functional normalization are not necessarily related to
those obtained from dimensional techniques. The scaling parameters and similarity
groups developed in an inspectional analysis also depend on the boundary and initial
conditions imposed, as well as on the special physical hypothesis invoked. Vodel et al.
(1991) proposed that instead of assuming a heterogeneous field to be an ensemble of
mutually similar homogeneous zones, the spatial variability of soil properties can be
assumed to have two components: (i) linear and (ii) nonlinear. Scaling the soil properties
with respect to the dominant component can do the functional normalization for such a
system.
Macroscopic Miller similarity is based on the physical postulate that viscous flow and
capillary forces govern water transport through unsaturated soil. It differs from the
classical Miller similar media concept in which a scaling parameter is required for the
volumetric water content and makes no direct reference to the geometric structure of a
soil at the pore scale. Warrick extended the use of Miller’s single scaling factor,
introduced the degree of saturation, and eliminated the assumption of identical porosity
(Kutilek and Nielsen, 1994). Warrick similarity analysis is formulated independently of
the initial and boundary conditions while adopting three scaling parameters to define
reduced forms of water content, matric potential, and hydraulic conductivity (Warrick et
al., 1977). Nielsen similarity analysis is based on a zero-flux boundary condition and the
analysis develops from the physical assumption that the water diffusivity, hydraulic
conductivity, and matric potential in unsaturated soil are exponential functions of the
volumetric water content (Warrick et al., 1977).
Principles of soil physics 606
20.6.2 Applications of Scaling Theory
Some of the applications of scaling methods are
1. Description of hierarchical heterogeneities over a broad range of scales
2. Reduction of soil water characterization, unsaturated hydraulic conductivities, and
infiltration rates
3. Steady state moisture distribution in heterogeneous fields
4. Diffusion and dispersion in porous media
5. Quantification of variability in hydraulic functions of soils and upscaling
6. Stochastic analysis of soil water regime
7. Water budget modeling
Detailed descriptions on various scaling procedures are given by Simmons et al. (1979),
Hillel and Elrick (1990), Sposito (1998) and Papachepsky et al. (2003) among others.
Example 20.1
Calculate the net annual salt balance in the root zone of soil for an area where total
annual amount of water was 40 cm by rainfall, 80 cm by irrigation, 15 cm by the total
drainage, and 12 cm capillary rise. The concentration of salt was 30 ppm in precipitation,
500 ppm in irrigation, 750 ppm in drainage water, and 900 ppm in capillary water. The
total salt input from fertilizer and amendments was 100gm
−2
, and the salt content
removed by harvested crop was 60gm
−2
. Precipitation and dissolution of salt can be
neglected.
Solution
Assuming a unit field area (1 cm
2
) and bulk density of water as 1 gcm
−3
, the net salt
balance for the soil root zone can be calculated by Eq. (20.30):
∆M=1*(40*30×10
−6
+80*500×10
−6
+12*900×10
−6
)
+100×10
−4
–60×10
−4
–1*15*750×10
−6
=4.48×10
−2
g
Since DM is positive, it indicates that soil is accumulating salts at a rate of 4.48
gcm
−2
yr
−1
.
Example 20.2
Calculate the leaching requirement and depth of leaching for a field where
evapotraspiration is 1000 mm, if EC of irrigation water is 1.2mmhocm
−1
and that of
drainage water can be as high as 4 mmhocm
−1
.
Solution
The leaching requirement (d
i
) can be calculated by Eq. (20.35):
Freezing and thawing effects 607
The leaching depth=d
i
−d
ET
= 1428.6–1000=428.6 mm
Example 20.3
Calculate the total osmotic pressure of a 0.01 M (or 10
−5
molcm
−3
) solution of chloride
and KCl at 27°C.
Solution
The total osmotic potential for chloride solution can be calculated by Eq. (20.23):
Π=10
−5
*8.32*10
7
*300=2.5104 erg cm
−3
=0.25 atm.
For KCl it will be=2*0.25=0.5 atm.
PROBLEMS
1. Calculate the net annual salt balance in the root zone of soil for an area where total
annual amount of water was 50 cm by rainfall, 90 cm by irrigation, 25 cm by the total
drainage, and 15 cm capillary rise. The concentration of salt was 40 ppm in precipitation,
600 ppm in irrigation, 850 ppm in drainage water, and 1000 ppm in capillary water. The
total salt input from fertilizer and amendments was 150gm
−2
, and the salt content
removed by harvested crop was 70gm
−2
. Precipitation and dissolution of salt can be
neglected. Also indicate whether salt accumulation or release is taking place.
2. Calculate the leaching requirement (LR) and depth of leaching for a field where
evapotraspiration is 1200 mm, if EC of irrigation water is 1.5 mmhocm
−1
and that of
drainage water can be as high as 4mmhocm
−1
. If EC of drainage water can be doubled,
calculate the LR.
References
Abrol I.P., Yadav J.S. and Massoud F.I. (1988). Salt effected soils and their management. Food and
Agriculture Organization of the United Nations (FAO), Rome.
Anderson D., Brown K.W. and Green J.1981. Organic Leachate effects on the permeability of clay
liners. In: Land disposal of hazardous waste, (ed. EPA) EPA-600/9–81–0021, 119–130.
Ankeny M.D., Kaspar T.C. and Horton R. (1990). Characterization of tillage and traffic effects on
unconfined infiltration measurements. Soil Sci. Soc. Am. J. 54:837–840.
Bahrani B., Mansell R.S. and Hammond L.C. (1970). Wetting coefficients for water repellent sand.
Soil and Crop Sci. Soc. Florida Proc. 30:270–274.
Benoit G.R. (1973). Effect of freeze-thaw cycles on aggregate stability and hydraulic conductivity
of three soil aggregate sizes. Soil Sci. Soc. Am. J. 37:3–5.
Benoit G.R. and Voorhees W.B. (1990). Effect of freeze-thaw activity on water retension,
hydraulic conductivity, density, and surface strength of two soils frozen at high water content.
Principles of soil physics 608
In: (ed.) Cooley K.R., Proceedings International Symposium on Frozen Soil Impacts on
Agricultural, Range, and Forest Lands. March 21–22, Spokane, US Army Corps of Engineers,
CRREL Special Report 90–1, Washington, pp. 45–53.
Beven K. and Germann P. (1982). Macropores and water flow in soils. Water Resour. Res.
18:1311–1325.
Bisel L.D. and Nielsen K.F. (1964). Soil aggregates do not necessarily breakdown over winter. Soil
Sci. 98:345.
Bisel L.D. and Nielsen K.F. (1967). Effect of frost action on size of soil aggregates. Soil Sci.
104:268–272.
Black P.B. (1990). Three functions that model empirically measured unfrozen water content data
and predict relative hydraulic conductivity. U.S. Army Corps of Engineers, CRREL report 90–
5.
Blackwell P.S. (2003). Management of water repellency in Australia. In: (eds.) Ritsema C.J. and
Dekker L.W., Soil Water Repellency—Occurrence, Consequences, and Amelioration. Elsevier,
Amsterdam, Netherlands, pp. 291–301.
Bond B.D. and Hammond L.C. (1970). Effect of surface roughness and pore shape on water
repellency of sandy soils. Wetting coefficients for water repellent sand. Soil and Crop Sci. Soc.
Florida Proc. 30:308–315.
Bouma J. and Dekker L.W. (1978). A case study on infiltration into dry clay soil, I. Morphological
observations. Geoderma 20:27–40.
Bouma J., Dekker L.W. and Wosten J.H.M. (1978). A case study on infiltration into dry clay soil,
II. Physicsl measurements. Geoderma 20:41–51.
Boynton, A.M. and Daniel D.E. (1985). Hydraulic conductivity tests on compacted clay. Journal of
Geotechnical Engineering 111:465–478.
Briones A.A. and Uehara G. (1977). Soil elastic constants: II. Application to analysis of soil
cracking. Soil Sci. Soc. Am. J. 41:26–29.
Bullock M.S., Kemper W.D. and Nelson S.D. (1988). Soil cohesion as effected by freezing, water
content, time and tillage. Soil Sci. Soc. Am. J. 52(3):770–776.
Burst J.F. (1965). Subaqueously formed shrinkage cracks in clays. Journal of Sedimentary
Petrology 35:891–901. D’Appolonia (1980).
Campbell G.S. (1974). A simple method for determining unsaturated conductivity from moisture
retension data. Soil Sci. 117:311–314.
Carrillo M.L.K., Letey J. and Yates S.R. (2000). Unstable water flow in a layered soil: I. The
effects of stable water repellent layer. Soil Science Soc. Am. J. 64: 456–459.
Cary J.W. and Mayland H.F. (1972). Salt and water movement in unsaturated frozen soil. Soil Sci.
Soc. Am. J. 36:549–555.
Cary J.W., Papendick R.I. and Campbell G.S. (1979). Water and salt movement in unsaturated
frozen soil: principles and field observations. Soil Sci. Soc. Am. J. 43:3–8.
Culley, J.L.B., Larson W.E. and Randall G.W. (1987). Physical properties of a Typic Haplaquoll
under conventional and no tillage. Soil Sci. Soc. Am. J. 51:1587–1593.
D’Appolonia D. (1980). Soil bentonie slurry trench cut-offs. Journal of Geotechnical Engineering
106:399–418.
Dasog G.S. and Shashidhara G.B. (1993). Dimension and volume of cracks in a vertisol under
different crop covers. Soil Science 156:424–428.
DeBano L.F. (2003). Historical overview of soil water repellency. In: (eds.) Ritsema C.J. and
Dekker L.W., Soil Water Repellency—Occurrence, Consequences, and Amelioration. Elsevier,
Amsterdam, Netherlands, pp. 3–24.
Dekker L.W. and Ritsema C.J. (2003). Wetting patterns in water repellent Dutch soils. In: (eds.)
Ritsema C.J. and Dekker L.W., Soil Water Repellency—Occurrence, Consequences, and
Amelioration Elsevier, Amsterdam, Netherlands, pp. 151–166.
Dekker L.W. and Jungerius P.D. (1990). Water repellency in the dunes with special reference to
Netherlands. Catena Suppl. 18:173–183.
Freezing and thawing effects 609
Dekker L.W., Oostindie K., Kostka S.J. and Ritsema C.J. (2003). Treating water repellent surface
layer with surfactant. In: (eds.) Ritsema C.J. and Dekker L.W., Soil Water Repellency—
Occurrence, Consequences, and Amelioration. Elsevier, Amsterdam, Netherlands, pp. 281–289.
Dexter A.R. 1978. Tunnelling in soil by earthworms. Soil Biol. Biochem. 10:447−49.
Edwards et al. (1988). Edwards W.M., Shipitalo M.J. and Norton L.D. (1988). Contribution of
macroporosity to infiltration into a continuous corn no-tilled watersheds: Implications for
contaminant movement. J. Contam. Hydrol. 3: 193–205.
Feng G.L., Letey J. and Wu L. (2001). Water ponding depths affect temporal infiltration rates in a
water repellent sand. Soil Sci. Soc. Am. J. 65:315:320.
Fuller W.H. and Warrick A.W. (1985). Soils in Waste Treatment and Utilization. Volume II, Boca
Raton, CRC Press Inc.
Gardner R. (1945). Some effects of freezing and thawing on aggregation and permeability of
dispersed soils. Soil Sci. 60:437–443.
Gerke H.H. and van Genuchten M.Th. (1993). A dual-porosity model for simulating the
preferential movement of water and solutes in structured porous media. Water Resour. Res.
29(2):305–319.
Gish T.J. and Jury W.A. (1983). Effect of plant roots and root channels on solute transport.
Transactions of the ASAE 26:440–444, 451.
Godwin R.J., Spoor G. and Leeds-Harrison P. (1981). An experimental investigation into the force,
mechanics and resulting soil disturbance of mole ploughs. J. Agr. Eng. Res. 26:477–497.
Granger R.J., Gray D.M. and Dyck G.E. (1984). Snowmelt infiltration to frozen Prairie soils. Can.
J. Earth Sci. 21:669–677.
Harlan R.L. (1973). Analysis of coupled heat-fluid transport in partially frozen soil. Water Resour.
Res. 9(5):1314−1323.
Harris, G.L., Nicholls P.H., Bailey S.W., Howse K.R. and Mason D.J. (1994). Factors influencing
the loss of pesticides in drainage from a cracking clay soil. J. Hydrol. 159:235–253.
Hettiaratchi J.P.A., Hrudey S.E., Smith D.W. and Sego D.C.C. (1988). Shrinkage behavior of clay
liner material exposed to simulated municipal waste landfill leachate. Can. J. Civ. Eng. 15:500–
508.
Hettiaratchi J.P.A., Hrudey S.E., Smith D.W. and Sego D.C.C. (1987). A procedure for evaluating
municipal solid waste leachate components capable of causing volume shrinkage in compacted
clay soils. Envir. Tech. Lett. 9:23–34.
Hillel D. and Elrick D.E. (ed.) (1990). Scaling in Soil Physics: Principles and Applications. SSSA
Spec. Publ. 25. SSSA, Madison, WI.
Hole F.D. (1981). The effects of animals on soil. Geoderma 25:75–112.
Isensee A.R., Nash R.G. and Helling C.S. (1990). Effect of conventional vs. notillage on pesticide
leaching to shallow groundwater. J. Environ. Qual. 19: 434–440.
Iwata S.T.T. and Warkentin B.P. (1988). Soil Water Interactions. M. Dekker, New York and Basel.
Jalalifarahani H.R., Heerman D.F. and Duke H.R. (1993). Physics of surge irrigation II.
Relationship between soil physical and hydraulic parameters. Transactions of the ASAE 36:45–
50.
Johnson W.C. (1962). Controlled soil cracking as a possible means of moisture conservation on
wheatlands of the southwestern Great Plains. Agron. J. 54: 323–325.
Jury A.W., Gardner W.R. and Gardner W.H. (1991). Soil Physics. 5th ed., John Wiley, New York.
Kutilek M. and Nielsen D.R. (1991). Soil Hydrology. Catena Verlag, 38162 Cremlingen-Destedt,
Germany.
Kutilek M. and Nielsen D.R. (1994). Soil hydrology. GeoEcology Textbook. Catena Verlag,
Cremlingen-Destedt, Germany.
Lehrsch G.A., Sojka R.E., Carter D.I. and Jolley P.M. (1990). Effects of freezing on aggregate
stability of soils differing in texture, mineralogy, and organic matter. In: (ed.) Cooley K.R.,
Proceedings International Symposium on Frozen Soil Impacts On Agricultural, Range, and
Principles of soil physics 610
Forest Lands. March 21–22, Spokane, US Army Corps of Engineers, CRREL Special report 90–
1, Washington, pp. 61–69.
Leo M.W.M. (1963). Effect of freezing and thawing on some physical properties of soils as related
to tomato and barley plants. Soil Sci. 96:267–274.
Letey J. (1968). Movement of water through soil as influenced by osmotic pressure and
temperature gradients. Hilgardia 39:405−418.
Low P.F., Hoekstra P. and Anderson D.M. (1968). Some thermodynamic relationships for soils at
or below the freezing point. 2. Effects of temperature and pressure on unfrozen soil water.
Water Resour. Res. 4(3):541–544.
Mailhol J.C. and Gonzalez J.M. 1993. Furrow irrigation model for real-time applications on
cracking soils. Journal of Irrigation and Drainage Engineering 119:768–783.
McCoy E.L., Boast C.W., Stehouwer R.C. and Kladivko E.J. (1994). Macropore hydraulics: Taking
a sledgehammer to classical theory. In: (ed.) Lal R. and Steward B.A., Soil Processes and Water
Quality. Boca Raton, Fla.: Lewis Publishers, pp. 303–348.
McNeal B.L. (1974). Soil salts and their effects on water movement. In: (ed.) van Schilfgaarde J.,
Drainage for Agriculture, Monograph 17 Am. Soc. Agron. Madison, Wisconsin.
Miller E.E. and Miller R.D. (1956). Physical theory for capillary flow phenomenon. J. Appl. Phys.
27:324–332.
Mitchell A.R. and van Genuchten M.Th. (1992). Shrinkage of bare and cultivated soil. Soil Sci.
Soc. Am. J. 56:1036–1042.
Mohanty B.P. Bowman R.S., Hendrickx J.M.H., Simunek J. and van Genuchten M.T. (1998).
Preferential transport of nitrate to a tile drain in an intermittent-flood-irrigated field: Model
development and experimental evaluation. Water Resour. Res. 34(5): 1061–1076.
Mostaghimi S., Young R.A., Wilts A.R. and Kenimer A.L. (1988). Effects of frost action on soil
aggregate stability. Transactions of the ASAE 31:435–439.
Norrish K. (1972). Forces between clat particles. Proc. Intl. Clay Conf., Madrid, pp. 375–383.
Papachepsky Y., Radcliffe D.E. and Selim H.M. (ed.) (2003). Scaling Methods in Soil Physics.
CRC Press, New York.
Philips J.R. (1969). Hydrostatics and hydrodynamics in swelling soils. Water Resour. Res. 5:1070–
1077.
Richards L.A. (ed.) (1954). Diagnosis and Improvement of Saline and Alkali Soils. U.S. Dept. Agr.
Handbook, p. 60.
Richardson S.J. (1976). Effect of artificial weathering cycles on the structural stability of a
dispersed silt soil. J. of Soil Sci. 27(3):287–294.
Ritsema C.J., Nieber J.L., Dekker L.W. and Steenhuis T.S. (1998). Modelling and field evidence of
finger formation and finger recurrence in a water repellent sandy soil. Water Resourc. Res.
34:555–567.
Shukla M.K., Kastanek F. and Nielsen D.R. (2002). Inspectional analysis of convective-dispersion
equation and application on measured BTCs. Soil Sci. Soc. Am. J. 66(4): 1087–1094.
Sillanpaa M. and Webber L.R. (1961). The effect of freezing-thawing and wetting-drying cycles on
soil aggregation. Can. J. Soil Sci. 41:182–187.
Simmons C.S., Nielsen D.R. and Biggar J.W. (1979). Scaling of field-measured soil water
properties. Hilgardia, J. Agri. Sci. UCDAVIS, 47(4):77–173.
Smiles D.E. (1981). Water relations of cracking soils. In: (ed.) McGarity J.W. et al. Proceedings of
Symposium on: The properties and Utilization of Cracking Clay Soils. August 24–28, pp. 143–
149.
Smiles D.E. and Rosenthal M.J. (1968). The movement of water in swelling material. Aust. J. Soil
Res. 6:237–248.
Sposito G. (1998). Scale dependence and scale invariance in hydrology. Cambridge University
Press, Cambridge, New York.
Sposito G. and Jury W.A. (1985). Inspectional analysis in the theory of water flow through
unsaturated soil. SSSAJ, 49(4):791–798.
Freezing and thawing effects 611
Steenhuis, T.S, Staubitz W., Andreni M.S., Surface J., Richard T.L., Paulsen R., Pickering N.B.,
Hagerman J.R. and Geohring L.D. 1990. Preferential movement of pesticides and tracers in
agricultural soils. J. Irrig. Drain. Engg. 116, 50–66
Swartz, G.L. 1966. Modification of the cracking pattern on a black earth of the Darling Downs,
Queensland. Qd. Agr. J. 23:279–285.
Thunholm B. and Ludin L.C. (1990). Infiltration into a seasonally frozen clay soil. In: (ed.) Cooley
K.R., Proceedings International Symposium on Frozen Soil Impacts on Agricultural, Range, and
Forest Lands. March 21–22, Spokane, US Army Corps of Engineers, CRREL Special report 90–
1, Washington, pp. 156–160.
Tillotson P.M. and Nielsen D.R. (1984). Scale factors in soil science. SSSAJ 48(5):953–959.
USDA NRCS Soil Quality Institute (2000). Soil Quality Resource Concerns: Hydrophobicity.
Available at http://www.statlab.iastate.edu/survey/SQI/. The site was visited on 29 July 2003.
Vogel T., Cislerova M. and Hopman J.W. (1991). Porous media with linearly variable hydraulic
properties. Water Res. Res. 27:2735–2741.
Warrick A.W., Mullen G.J. and Nielsen D.R. (1977). Scaling field-measured soil hydraulic
properties using a similar media concept. Water Resources Research, 13(2):355–362.
Watson C.L., Letey J. and Mustafa M.A. (1971). The influence of liquid surface tension and liquid
solid contact angle on liquid entry into porous media. Soil Sci. 178–183.
Yong R.N. and Warkentin B.P., (1975). Soil Properties and Behaviours. Elsevier, Amsterdam.
Principles of soil physics 612
Appendix A
The Greek Alphabet
A α alpha
B β beta
г γ gamma
A δ delta
E ε epsilon
Z ζ zeta
H η eta
Θ θ theta
I τ iota
K κ kappa
A λ lambda
M µ mu
N υ nu
Ξ ξ xi
O O omicron
Π π pi
p ρ rho
Σ a sigma
T τ tau
Y υ upsilon
Φ
phi
X χ chi
Ψ ψ psi
Ω ω omega