Published online 14 April 2008
Published in Vadose Zone J 7:420-425 (2008)
DOI: 10.2136/vzj2007.0103
© 2008 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH
Influence of Plant, Soil, and Water on the Leaching Fraction
Lynn M. Dudleya,*,
Alon Ben-Galb and
Uri Shanic
a Dep. of Geological Science, Florida State Univ., Tallahassee, FL 32306-4100
b Environmental Physics and Irrigation, Agricultural Research Organization, Gilat Research Center, D.N. Negev 85280, Israel
c Dep. of Soil and Water Sciences, Faculty of Agricultural, Food and Environmental Sciences, Hebrew Univ. of Jerusalem, P.O. Box 12, Rehovot 76100, Israel
* Corresponding author (dudley{at}gly.fsu.edu).
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Received 31 May 2007.
 |
ABSTRACT
|
|---|
Reducing the amount of drainage water that contains salts, nutrients, and trace elements may reduce environmental contamination to groundwater by reducing the dissolution of trace-element-containing minerals, maximizing chemical precipitation of salts, and improving nutrient uptake efficiency. If salt accumulates, transpiration and yield will decrease and some fraction of the irrigation water will not be extracted by roots, subsequently becoming drainage. We modeled yield and salt and water budgets under conditions of extended irrigation with poor quality water in amounts ranging from 0.6 to 1.6 times the ratio of irrigation (I) to reference evaporation (E0). The surface boundary conditions were taken from a field experiment where melon (Cucumis melo ssp. melo cv. Galia) was irrigated with waters of electrical conductivities of 1.2, 3, 6, and 9 dS/m at I/E0 = 1.0 for a growing season (1152 h). The model contained one-dimensional solutions to Richards' equation with a root-sink term and the equation of continuity for salt transport. Solutes were treated conservatively. For any given salinity value, the leaching fraction had a minimum value corresponding to the irrigation level where a minimum amount of water was used to control salinity and those minimum values were 0.11, 0.24, 0.44, and 0.54 for salinity levels 1.2, 3, 6, and 9 dS/m. Yield reduction for these irrigation levels were 80, 70, 60, and 40% of maximum possible yields, suggesting an economic price to minimizing drainage and further suggesting that plant–irrigation–drainage relationships are highly self-regulating.
Abbreviations: EC, electrical conductivity • LF, leaching fraction
|
INTRODUCTION
|
|---|
DEFICIT IRRIGATION is a strategy for coping with water shortages that might result from temporary conditions such as drought or from a permanent reduction in supply due to reallocation of water resources to urban and industrial users, and principles for maximizing yield under deficit irrigation are emerging. For example, field studies of strategies for cotton (Gossypium hirsutum L., Jalota et al., 2006) and wheat (Triticum aestivum L., Panda et al., 2003) production have been recently published and models of crop production under deficit irrigation have also appeared in recent literature (Tayfur et al., 1995; Ganji et al., 2006). Deficit irrigation, the deliberate and systematic underirrigation of crops, is often defined as an agricultural water management system in which <100% of the potential evapotranspiration is provided by a combination of stored soil water, rainfall, and irrigation during the growing season (English et al., 1990; English and Raja, 1996). Of course, deficit irrigation with poor quality water results in salt accumulation in the root zone. Therefore, we suggest that a more appropriate definition of deficit irrigation would be any irrigation less than the amount of water required to remove salt left by the previous irrigation added to the amount required to refill the soil profile. While considerable salt may be stored in the root zone without causing significant yield loss in the short term (Francois, 1981), it has been suggested that prolonged deficit irrigation with poor quality water eventually causes "secondary salinization," progressively decreasing yield and compromising the soil resource (Beltrán, 1999).
Management of saline water for irrigation is often based on application of excess water designed to maintain a root-zone salinity that avoids salinity-induced yield reduction. The amount of additional water required to maintain a target salinity level, the leaching requirement (LR), is a function of crop sensitivity and irrigation water salinity (Ayers and Westcot, 1985). Traditional irrigation management strategy under conditions where water is not limiting is to provide water such that the ratio of the actual depth of drainage to the depth of irrigation, the leaching fraction (LF), satisfies the LR. Due to the complexities of interactions between water, soil, and plant uptake, reaching such matching of LF with LR is not simple.
In a well-drained system, salt accumulates at the bottom of the root zone (Meiri et al., 1977; Francois, 1981; Meiri and Plaut, 1985), where uptake may be lower than in the upper portion due to decreased root density and resistance to flow within the root (Feddes and Raats, 2004). The accumulation of saline water in the lower portion of the root zone reduces the osmotic potential, which, combined with the soil water matric potential, decreases the potential gradient for water flow from soil to roots and thus further reduces uptake. Accumulation of salt in the lower root zone effectively eliminates a portion of the root zone from being involved in uptake. Meiri and Plaut (1985) concluded that uptake in the lower root zone ceased when the salinity level reached a value corresponding to zero yield on the crop response curve. To meet climatic demand, more water would have to be extracted from the low-salinity, upper portion of the root zone. Eventually, a condition would be reached in which some fraction of the irrigation water could not be extracted due to decreasing transpiration and yield, and the unused water would become drainage. Yield decrements are limited because drainage would occur with some roots in the upper root zone still actively extracting water. We hypothesize, therefore, that for any given irrigation amount, the accumulation of salt (secondary salinization) is limited and does not progressively decrease yield beyond the limiting value, as has been suggested (Beltrán, 1999).
Our objectives were to investigate the consequences of deficit irrigation with poor quality water and to evaluate the effect of plant response on the leaching fraction. Such an investigation might produce a better understanding of the system-imposed limits on yield and salt accumulation in the root zone under deficit irrigation and enhance our ability to manage crop production and soil and water resources under suboptimal conditions. Because it would require several irrigation seasons to produce the steady-state water flow and salt transport condition required to clearly elucidate system behavior, we modeled yield and salt and water budgets under conditions of extended irrigation with poor quality water in amounts ranging from 0.6 to 1.6 times I/E0.
|
Materials and Methods
|
|---|
The Model
The model contains one-dimensional, second-order, time-centered solutions to Richards' equation with a root-sink term and the equation of continuity for salt transport with subroutines that simulate crop and root growth and water flux through the upper boundary as transpiration and evaporation. In this version of the model, solutes are conservative (Hanks and Cui, 1990). The model computes yield (Y) as a linear function of transpiration (T):
 | [1] |
where subscript r denotes relative and max the maximum value. The algorithm used to compute transpiration from the sum of root uptake within each depth node (root sink) as a function of matric, h, and osmotic, 
, potentials was developed by Dudley and Shani (2003). The root-sink term was computed in an iterative procedure in which a potential-flux equation (Childs and Hanks, 1975) accounted for the influence of the matric potential:
 | [2] |
where S(z,t) is the extraction rate of water at soil depth z and time t, RDF(z) is the fraction of roots at z, K(
) is the bulk-soil hydraulic conductivity, 
x and z are the distance from the root to where water is extracted, Hroot is the root water head bounded by minimum value Hmin (e.g., –150 m [Nimah and Hanks, 1973] or –90 m [Bresler, 1987]), Rr is a root resistance term, and h(z,t) is the matric head. The influence of soil salinity on transpiration was computed from a transpiration apportioning equation (van Genuchten, 1987) multiplied by the root uptake in response to the matric potential (Homaee et al., 2002):
 | [3] |
where is the osmotic head, the subscript 50 denotes the osmotic head that causes a 50% yield loss, and p is a constant that is usually taken as 3 (van Genuchten, 1987).
Boundary Conditions and Model Parameters
In addition to the plant response parameters Hmin and 50 described above, the model requires upper and lower boundary conditions for water and salt, the initial water content and salt profile, and parameters for soil permeability–saturation–matric potential functions. The surface boundary conditions were taken from a field experiment where melon was irrigated with waters of electrical conductivity (EC) = 1.2, 3, 6, and 9 dS/m at I/E0 = 1.0 (Shani and Dudley, 2001) for a growing season (1152 h). The EC levels reflect those caused by Cl– salts with Na and Ca cations only. Salinity from other salts and added fertilizer added approximately 0.8 dS/m to all irrigation water treatments.
Deficit irrigation may be accomplished by at least three methods: (i) reducing the amount of each irrigation event, (ii) keeping the amount of each irrigation event the same and increasing the time between irrigation events, or (iii) decreasing specific irrigation events at less sensitive growth stages (Tayfur et al., 1995). The first method was used for simulations in this study. A model control parameter allows the user to apply a uniform scaling factor to the irrigation surface boundary condition as a ratio of I/E0. Scaling factors of 0.6, 0.8, 1.0, 1.2, 1.4, and 1.6 were used in the simulations. Pan evaporation was used as the reference for treatments because it has historically produced useful estimates of evapotranspiration by well-watered crops. The range of scaling factors was obtained from the leaching requirement computed as recommended by Ayers and Westcot (1985):
 | [4] |
where the subscript iw denotes irrigation water and EC10% is the EC producing a 10% yield loss. The leaching requirement for salinity levels EC = 1.2, 3, 6, and 9 dS/m were 0.06, 0.16, 0.4, and 0.72, respectively. These leaching requirements correspond to irrigation levels, given as I/E0, of 1.06, 1.2, 1.6, and 3.6 so the amounts of irrigation in the simulations ranged from deficit to at least that required for salinity control for all salinity levels except 9 dS/m.
An initial water content (0.2) and soil solution salinity (4 dS/m), approximately the values at the beginning of the experiment, were used as model input for a simulation of the first season of salinity and irrigation level combinations. The simulated water content and salinity profile at the end of that season were used as the initial conditions for simulation of the subsequent season and this procedure was repeated until the water content and salinity profiles and yield were the same at the end of two successive simulations, i.e., steady state was achieved. To prevent upward flux of moisture in the deficit simulations, a fixed and low water content was used as the bottom boundary condition.
Dudley and Shani (2003) recommended a crop coefficient for transpiration of 0.95, 50 = –45 m and Hmin = –15 m based on the best fit of the model to the data. The value of 50 = –45 m was computed from a Maas–Hoffman response function using a threshold EC of 4.3 dS/m and a slope of 0.5 for the decreasing linear portion of the response function (Dudley and Shani, 2003). To investigate the influence of crop tolerance to salinity values of 50 = –60 m and Hmin = –60 m were used in a separate set of simulations. Brooks–Corey parameters (Brooks and Corey, 1964) for Arava sandy loam and Millville silt loam were used to simulate saturation–potential–permeability relationships (Table 1).
|
Results and Discussion
|
|---|
Steady-State Yield
As expected, total dry matter production (yield) and transpiration decreased with increasing salinity and decreasing irrigation (Fig. 1
) and yield values reached a steady state for each salinity and irrigation combination after several simulated irrigation seasons. Even at the lowest irrigation and greatest salinity level, yields were greater than zero although relative yields were reduced to about 0.3. Moreover, Fig. 1 shows that the relationship between irrigation and yield was nonlinear, thus the increment in yield loss decreased as the increment in irrigation water increased. This suggests that yield would be greater than zero for even greater salinity levels than those simulated. Visual comparison of Fig. 1a and 1b reveals that soil texture produced only a small difference in predicted relative yield for any given irrigation and salinity combination. The influence of soil texture is discussed in greater detail below.
View larger version (31K):
[in this window]
[in a new window]
|
FIG. 1. Predicted relative yield (yield/yieldmax) as influenced by the ratio of irrigation to pan evaporation (I/E0) and electrical conductivity for the (a) Arava soil and (b) Millville soil with osmotic head that causes a 50% yield loss (50) = –45 m and matric head that causes a 50% yield loss (h50) = –15 m.
|
|
Increasing plant tolerance to salinity (decreasing 50) had the expected effect of increasing yield for any given salinity and irrigation that produced a crop response (Fig. 2
). The combinations of salinity and irrigation that did not result in relative yield values <1.0 were also increased.
View larger version (40K):
[in this window]
[in a new window]
|
FIG. 2. Predicted relative yield (yield/yieldmax) as influenced by the ratio of irrigation to pan evaporation (I/E0) and electrical conductivity for the Arava soil with osmotic head that causes a 50% yield loss (50) = –60 m and matric head that causes a 50% yield loss (h50) = –60 m.
|
|
Leaching Fraction
The number of simulated irrigation seasons required to produce steady-state salt and water content profiles varied among the irrigation and salinity treatments. Generally, simulations producing the greatest leaching fractions reached steady state after fewer than five seasons. The steady-state distributions of water and salt in the simulated soil profiles are presented as matric and osmotic head values because they are the parameters for the plant response functions. The matric head profiles at steady state were most strongly determined by the irrigation level and were almost independent of the irrigation water salinity. Soil texture also had an influence on the matric head profiles and, for a given irrigation level, they were greater for the sandy loam simulation than the silt loam simulation (Fig. 3
).
View larger version (15K):
[in this window]
[in a new window]
|
FIG. 3. Predicted steady-state matric head profiles for the sandy loam (SaL) and silt loam (SiL) soils from simulations of the electrical conductivity (EC) = 1.2 and 9 dS/m for ratios of irrigation to pan evaporation (I/E0) = (A) 1.6, (B) 1.0, and (C) 0.6.
|
|
The osmotic head values presented in Fig. 4
were computed from the steady-state salt concentrations as = –RTC, where R is the universal gas constant, T is the temperature in Kelvin, and C is the molar salt concentration; salt concentration and osmotic head values differ only by multiplication by a constant and are used interchangeably here. The amount of salt stored in the soil profile was a function of the irrigation water salinity, irrigation level, and soil texture. As might be expected, the salt concentrations increased (osmotic potential more negative) in all depths but the surface as a function of increasing irrigation water salinity for a given irrigation level and soil texture (Fig. 4). Salt concentration values throughout the profile also increased with decreasing irrigation level for a given irrigation level, salinity, and soil texture (Fig. 4). At the greatest irrigation level, I/E0 = 1.6, salt profiles for the two soil textures were similar throughout, but differences between the profiles were observed as irrigation decreased (Fig. 4). At the other two irrigation levels and for a given salinity treatment level, the osmotic head values were similar near the surface and diverged with depth. Salt concentrations at a given soil depth, irrigation level, and irrigation water salinity were generally smaller (osmotic head less negative) for the sandy loam soil than the silt loam soil. The reason for the difference in salt accumulation was that the model predicted the onset of drainage in the sandy-textured soil in fewer irrigation seasons than for the silt-textured soil. While matric head values were similar for the two soils for a given salinity and irrigation level, the water content was much lower in the sandy soil than the silt soil. Thus, the sandy-textured soil stored less salt than the silt-textured soil.
View larger version (16K):
[in this window]
[in a new window]
|
FIG. 4. Predicted steady-state osmotic head (potential in kilopascals = 9.81 x head in meters) profiles for the sandy loam (SaL) and silt loam (SiL) soils from simulations of the electrical conductivity (EC) = 1.2 and 9 dS/m for ratios of irrigation to pan evaporation (I/E0) = (A) 1.6, (B) 1.0, and (C) 0.6.
|
|
Because of the similarities in matric head profiles discussed above and the fact that the osmotic head profiles differed, the discussion of results for the osmotic head profiles applies to the hydraulic head profiles. One might have expected more similarity in the hydraulic head profiles between the two soils for a given treatment since the steady-state drainage and transpiration were dictated by plant response to both matric and osmotic potentials. Differences in hydraulic conductivity in the two soils would result in different water velocities in the two soils that would be reflected in water uptake, as reported in lysimeter studies by Meiri et al. (1977).
Accumulation of saline water in the lower profile resulting from salinity-induced reduction in transpiration for a given irrigation level resulted in drainage for all simulations. For any given salinity value (a leaching fraction—I/E0 cross-section of the surface in Fig. 5
), the leaching fraction had a minimum value corresponding to the irrigation level where the least amount of water was used to control salinity. The curves obtained from a plot of the leaching fraction as a function of I/E0 for each salinity level (not shown) were fit to a cubic equation and the resulting functions had minimum values of I/E0 = 0.83, 0.81, 0.71, and 0.5 for salinity levels 1.2, 3, 6, and 9 dS/m, respectively, for plant response parameters of Hmin = –15 and 50 = –45 m. These I/E0 values correspond to leaching fractions of 0.11, 0.24, 0.44, and 0.54, respectively. As might be expected, the minimum value of the leaching fraction was achieved at an irrigation level less than pan evaporation and the minimum value of the leaching fraction increased with increasing salinity. Less intuitive might be the decrease in irrigation with increased salinity that was required to produce a minimum value of the leaching fraction. Thus, the model predicted greater yield penalty to achieve a minimum leaching fraction with increasing salinity. The minimum values of the leaching fraction compare with the leaching requirements computed from Eq. [4]; however, the relative yield values for these leaching fractions were 0.8, 0.7, 0.6, and 0.4, respectively, different from the 0.9 value used to obtain the EC10% for Eq. [4]. At irrigation less than the curve minimum, the leaching fraction is increased by yield loss due to water and salt stress. At irrigation levels greater than the minimum, the leaching fraction is increased by yield loss from salt accumulation and overirrigation.
View larger version (45K):
[in this window]
[in a new window]
|
FIG. 5. The leaching fraction as a function of salinity and the ratio of irrigation to pan evaporation (I/E0) for the Arava soil (sandy loam texture) computed with osmotic head that causes a 50% yield loss (50) = –45 m and matric head that causes a 50% yield loss (h50) = –15 m.
|
|
Decreasing the plant response parameters (increasing tolerance to salt and water stress) to Hmin = –60 and 50 = –60 m resulted in minimum leaching fraction values of 0.09, 0.19, 0.32, and 0.44 for the 1.2, 3, 6, and 9 dS/m salinity levels, respectively. Thus, one should choose a crop with the greatest possible salt tolerance to minimize the quantity of drainage water and maintain an economic yield.
Leaching fractions computed for the two soils were compared for each salinity treatment across the range of I/E0 values. As might be expected, the salinity profiles for the two textures are similar at the greatest irrigation level (Fig. 4a). As the irrigation was decreased, salinity differences between the two soil textures increased with a greater salt concentration at any given depth in the silt loam compared with the sandy loam soil. Both soils maintained similar salinity values at the soil surface for any given irrigation level. The values of the leaching fraction for the two soils fell near the 1:1 line (LF silt loam = 1.0217LF sandy loam, r2 = 0.9833) indicating that soil texture had little effect on the leaching fraction. Even though the salt concentrations in the profiles for a given treatment varied between the soils, the leaching fraction was similar for the EC and I/E0 combinations.
|
Conclusions
|
|---|
The model predicted that water too saline to be used by plants accumulated in the lower soil profile and that such accumulation of saline water effectively shortened the root zone. Eventually, the combination of salt accumulation and reduced transpiration caused leaching. Thus, there is a maximum amount of salt that can be stored in the root zone under deficit irrigation. Once the maximum amount of salt accumulates, leaching begins and more extensive yield loss does not result from repeating the irrigation schedule. The leaching fraction increased as transpiration decreased due to salinity, making the plant–irrigation–drainage relationships self-regulating.
Limitations to yield loss and salt storage have implications for managing crop production and salt under conditions of deficit irrigation. Implications for crop management are that when external factors reduce water availability and quality, yields greater than zero will still be expected even under conditions of severe stress. Moreover, the relative yield loss with increasing salinity is not linear and the yield loss increment decreases with increasing increments in irrigation water salinity, with the caveat that drainage is not limiting. Implications to salt management by deficit irrigation might be less obvious. Deficit irrigation has been proposed as a means of increasing salt storage and decreasing the salt load in drainage waters. For example, South Australia has an irrigation efficiency target of 15% maximum LF to allow productive agriculture while minimizing salt loading from agricultural lands to the River Murray (National Water Commission, 2006). Such a strategy might result in salt storage in the short term for systems where the initial salinity in the soil profile is low. Our results suggest that there is a minimum leaching fraction for each plant–soil–irrigation level–irrigation water quality combination that limits both salt storage and the amount of drainage.
|
ACKNOWLEDGMENTS
|
|---|
This work was supported by CSREES award no. 2005-345552 and the Utah Agricultural Experiment Station, Utah State University, Logan, under Project no. UTA00298. Approved as Journal Paper no. 7889.
|
REFERENCES
|
|---|
- Ayers, R.S., and D.W. Westcot. 1985. Water quality for agriculture. FAO Irrig. Drain. Pap. 29. FAO, Rome.
- Beltrán, J.M. 1999. Irrigation with saline water: Benefits and environmental impact. Agric. Water Manage. 40:183–194.[CrossRef]
- Bresler, E. 1987. Application of conceptual model to irrigation water requirement and salt tolerance of crops. Soil Sci. Soc. Am. J. 51:788–793.[Abstract/Free Full Text]
- Brooks, R.H., and A.T. Corey. 1964. Hydraulic properties of porous media. Hydrol. Pap. 3. Colorado State Univ., Fort Collins.
- Childs, S.W., and R.J. Hanks. 1975. Model of soil salinity effects on crop growth. Soil Sci. Soc. Am. Proc. 39:617–622.
- Dudley, L., and U. Shani. 2003. Modeling plant response to drought and salt stress: Reformulation of the root-sink term. Vadose Zone J. 2:751–758.[Abstract/Free Full Text]
- English, M., J.T. Musick, and V.V.N. Murty. 1990. Deficit irrigation. p. 631–663. In G.J. Hoffman et al. (ed.) Management of farm irrigation systems. ASAE, St. Joseph, MI.
- English, M., and S.N. Raja. 1996. Perspectives on deficit irrigation. Agric. Water Manage. 32:1–14.[CrossRef]
- Feddes, R.A., and P.A.C. Raats. 2004. Parameterizing the soil–water–plant root system. In R.A. Feddes et al. (ed.) Unsaturated zone modeling: Progress, challenges, and applications. Springer, New York.
- Francois, L.E. 1981. Alfalfa management under saline conditions with zero leaching. Agron. J. 73:1042–1046.[Abstract/Free Full Text]
- Ganji, A., K. Ponnambalam, D. Khalili, and M. Karmouz. 2006. A new stochastic optimization model for deficit irrigation. Irrig. Sci. 25:63–73.[CrossRef]
- Hanks, R.J., and J.K. Cui. 1990. Model SOWATSAL: Soil–plant–atmosphere–salinity management model. Users' manual. Utah State Univ., Logan.
- Homaee, M., R.A. Feddes, and C. Dirksen. 2002. A macroscopic water extraction model for nonuniform transient salinity and water stress. Soil Sci. Soc. Am. J. 66:1764–1772.[Abstract/Free Full Text]
- Jalota, S.K., A. Sood, G.B.S. Chahal, and B.U. Choudhury. 2006. Crop water productivity of cotton (Gossypium hirsutum L.)–wheat (Triticum aestivum L.) system as influenced by deficit irrigation, soil texture and precipitation. Agric. Water Manage. 84:137–146.[CrossRef]
- Meiri, A., and Z. Plaut. 1985. Crop production and management under saline conditions. Plant Soil 89:253–271.[CrossRef][Web of Science]
- Meiri, A., J. Kamburov, and J. Shalhevet. 1977. Transpiration effects on leaching fractions. Agron. J. 69:779–782.[Abstract/Free Full Text]
- National Water Commission. 2006. Investing in irrigation: Achieving efficiency and sustainability case studies. Natl. Water Commiss., Canberra, NSW, Australia.
- Nimah, M.N., and R.J. Hanks. 1973. Model for estimating soil, water, plant and atmospheric interrelations: I. Description and sensitivity. Soil Sci. Soc. Am. Proc. 37:522–527.
- Panda, R.K., S.K. Behera, and P.S. Kashyap. 2003. Effective management of irrigation water for wheat under stressed conditions. Agric. Water Manage. 63:37–56.[CrossRef]
- Shani, U., and L.M. Dudley. 2001. Field studies of crop response to drought and salt stress. Soil Sci. Soc. Am. J. 65:1516–1522.[Abstract/Free Full Text]
- Tayfur, G., K.K. Tanji, B. House, F. Robinson, L. Teuber, and G. Kruse. 1995. Modeling deficit irrigation in alfalfa production. J. Irrig. Drain. Eng. 121:442–451.[CrossRef]
- van Genuchten, M.Th. 1987. A numerical model for water and solute movement in and below the root zone. Res. Rep. 121. U.S. Salinity Lab., Riverside, CA.
This article has been cited by other articles:
|
|
|
|
 
A. Ben-Gal, U. Yermiyahu, and S. Cohen
Fertilization and Blending Alternatives for Irrigation with Desalinated Water
J. Environ. Qual.,
February 6, 2009;
38(2):
529 - 536.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
L. M. Dudley, A. Ben-Gal, and N. Lazarovitch
Drainage Water Reuse: Biological, Physical, and Technological Considerations for System Management
J. Environ. Qual.,
September 2, 2008;
37(5_Supplement):
S-25 - S-35.
[Abstract]
[Full Text]
[PDF]
|
|
|
TOP
ABSTRACT
INTRODUCTION
and β are empirical soil characteristic parameters, 
e is the air-entry matric potential.