Comparison of the Instantaneous Profile Method and inverse modelling for the prediction of effective soil hydraulic properties.Introduction
Investigations into water movement in soils require knowledge of the hydraulic conductivity Hydraulic conductivity, symbolically represented as , is a property of vascular plants, soil or rock, that describes the ease with which water can move through pore spaces or fractures. function K([theta Theta
A measure of the rate of decline in the value of an option due to the passage of time. Theta can also be referred to as the time decay on the value of an option. If everything is held constant, then the option will lose value as time moves closer to the maturity of the option. ]) or K(h) and the soil water retention [theta](h) function, where [theta] is the volumetric volumetric /vol·u·met·ric/ (vol?u-met´rik) pertaining to or accompanied by measurement in volumes.
Of or relating to measurement by volume. soil water content and h is the soil matric n. 1. admission to a group (especially a college or university).
Noun 1. matric - admission to a group (especially a college or university)
matriculation pressure head. Owing to owing to
Because of; on account of: I couldn't attend, owing to illness.
owing to prep → debido a, por causa de their relative importance in many disciplines, including environmental engineering, soil physics (Hopmans et al. 2002), and agricultural and environmental issues (Vachaud and Dane 2002), numerous methods are being developed and improved to effectively determine soil hydraulic properties. These properties are difficult to measure and therefore require the use of both direct and indirect methods to adequately describe the flow and transport processes. Several field and laboratory methods for such determinations exist, each having their own limitations. In-situ determinations of K([theta]) are generally preferred owing to the potential problem of relating K([theta]), determined on undisturbed soil cores in the laboratory, to actual K([theta]) data in the field. Despite the application of various methods, erroneous results are frequently observed (Klute and Dirksen 1986; Dirksen 1991) since there is no single approach that can be generalised for all applications. Problems arise due to the heterogeneity of porous media, the inherent spatial variability Spatial variability is characterized by different values for an observed attribute or property that are measured at different geographic locations in an area. The geographic locations are recorded using GPS (global positioning systems) while the attribute's spatial variability is of soil (Tseng and Jury 1993), and lack of validity in the assumptions used in the various methods. The dynamic nature of the soil physical processes and the strong non-linearity of soil hydraulic functions also pose serious problems. As a result of these limitations, measured and predicted values often disagree strongly. In particular, an understanding of the spatial variability of soil hydraulic properties has become an essential factor for predicting transient water flow in the field. Therefore, comprehensive evaluation of different approaches is necessary before they can be accepted as tools for predicting hydraulic properties in heterogeneous media.
The 1-dimensional flow of water in a porous medium A porous medium or a porous material is a solid (often called frame or matrix) permeated by an interconnected network of pores (voids) filled with a fluid (liquid or gas). Usually both the solid matrix and the pore network (also known as the pore space) are assumed to be can be represented by the following general flow equation (Klute 1973):
(1) C(h) [partial derivative]h / [partial derivative]t = [partial derivative][[KAPPA](h) * ([partial derivative]h / [partial derivative]z + 1)] / [partial derivative]z
where C(h)= [partial derivative][theta]/[partial derivative]h is the water capacity function, t is the time, and z is distance positive above soil surface. The main problem associated with the solution of Eqn 1 is the determination of the soil hydraulic functions for a particular soil. Traditionally, these properties are measured directly in the laboratory or in the field (e.g. instantaneous profile method). Laboratory measurements often lead to hydraulic properties that are not representative of the field (Hopmans et al. 2002). The increasing importance of having accurate and reliable data has also accentuated the need for the development of accurate methods for describing soil hydraulic characteristics (Hopmans et al. 2002). Direct field methods have been extensively used to measure these properties, e.g. plane of zero flux (Arya 2002), constant flux vertical time domain reflectrometry (Parkin parkin
Brit a moist spicy ginger cake usually containing oatmeal [origin unknown] et al. 1995), and the instantaneous profile method (IPM (1) (Impressions Per Minute) Generally refers to document scanners that scan both sides of the page at the same time. Thus, a scanner that scans at 100 ppm (pages per minute) can provide 200 ipm. See ppm and document scanner. ) (Vachaud and Dane 2002). Although still most reliable, these methods have proven to be expensive and laborious and also require the imposition of restrictive initial and boundary conditions for arriving at analytical or semi-analytical solutions. This has prompted attempts to find a more efficient way of determining these properties. An alternative approach is the application of what is known as the inverse procedure, whereby the hydraulic functions K([theta]) and/or [theta](h) are indirectly predicted from measurable easily determined properties such as water content or pressure heads by optimising and estimating the model parameters.
Kool and Parker (1988) in their analysis of inverse modelling, listed several advantages connected with this approach: (i) it allows for some flexibility in initial and boundary conditions, (ii) parameters determined in this way give the optimal reproduction of the transient flow event by a numerical model, and (iii) the availability and use of computers makes it even more convenient to apply. The inverse procedures are equally applicable to field experiments even under non-trivial boundary conditions (Kool and Parker 1988; Hopmans et al. 2002) and large-scale spatially distributed properties (Vrugt et al. 2004).
There has been an increasing interest in several models which describe the non-linear soil hydraulic functions K([partial derivative]) and/or [partial derivative](h) analytically and not all are generally applicable to all conditions, van Dam van Dam (Dutch for "of the dam") may refer to:
(2) [S.sub.e] = [theta] - [[theta].sub.r] / [[theta].sub.s] - [[theta].sub.r] = [[1 + [([alpha]|h|).sup.n]].sup.-m]
(3) [KAPPA] = [[KAPPA].sub.s][S.sup.[tau].sub.e][[1 - [(1 - [S.sup.1/m.sub.e]).sup.m]].sup.2]
(4) m = 1 - 1/n
where [S.sub.e] is the effective saturation (-); [[theta].sub.r] and [[theta].sub.s], are residual and saturated soil water content ([cm.sup.3]/[cm.sup.3]), respectively; [tau] is the tortuosity tortuosity
1. The quality or condition of being tortuous; twistedness or crookedness.
2. A bent or twisted part, passage, or thing. (-); [K.sub.s] is the saturated hydraulic conductivity (cm/h); K is the unsaturated hydraulic conductivity (cm/h); [alpha] is the inverse of the air entry value (1/cm); and n is a parameter which depends on the width of the pore size distribution (-). These empirical relations are used to predict soil hydraulic properties during a transient flow process. An improved prediction will be realised if the model parameters ([tau], [alpha], n, [[theta].sub.r], [[theta].sub.s], [[KAPPA].sub.s]) are well estimated using a nonlinear least square parametric estimation technique. Typically the number of parameters needed to describe the soil hydraulic functions varies between 4 and 7 (Durner et al. 1997) and may reach 8 for bimodal bi·mod·al
1. Having or exhibiting two contrasting modes or forms: "American supermarket shopping shows bimodal behavior hydraulic models (Zurmuhl and Durner 1998).
Dane and Hruska (1983) found that this model gave a good description of water retention and/or conductivity data for a large number of soils. While the water retention data showed good agreement between predicted and measured values, the comparison for the conductivity data was less satisfactory. It was argued that this was because of the overestimation of the saturated hydraulic conductivity attributed to soil structure or macropores because of their influence to water flow regimes near saturation (van Genuchten et al. 1999; Chaudhari and Batta 2003). It therefore becomes essential to comprehensively evaluate different approaches before they can be accepted as suitable for predicting soil hydraulic properties (Tseng and Jury 1993).
The objective of this study was to compare the instantaneous profile method and the inverse modelling in effectively predicting soil hydraulic properties during lysimeter Ly`sim´e`ter
n. 1. An instrument for measuring the water that percolates through a certain depth of soil. drainage experiments for sandy and loamy soils. The inverse modelling was also evaluated for its effectiveness following the optimisation of parameters in various datasets including water content, pressure head, and/or a combination of both.
Materials and methods
Materials and experimental set up
In this study, determinations of soil hydraulic properties were carried out using a lysimeter drainage experiment for 1-dimensional transient flow for 2 distinct soils with contrasting textural properties (Table 1). Collected samples of sand and loam soils were filled into 2 lysimeters, each with a cross-sectional area of 1 [m.sup.2] and depth of 1.20 m, and were set up for the drainage experiment. Both lysimeters had holes drilled in the sides, for positioning of tensiometer ten·si·om·e·ter
1. An instrument for measuring tensile strength.
2. An instrument used to measure the surface tension of a liquid.
[tensio(n) + -meter. cups attached to mercury manometers, and an outlet or holes at the bottom through which water could drain.
Soil water content and pressure heads were measured during gravity drainage at selected depths following flooding of the lysimeters with tap water. Soil water contents were measured using time domain reflectrometry (TDR TDR - time domain reflectometer ), while soil water potentials were measured using the tensiometers. Prior to the taking of measurements, the lysimeters were flooded until water ran out through the outlet to ensure uniform distribution of water. Before flooding, measurements of [theta] and h were made in order to estimate residual water content Or from measured low water content under dry conditions for the soil, which is also one of the model parameters. The experiment took place in a period (i.e. winter time) when there was small amount of evaporation. The lysimeters were also shielded against wind in order to prevent evaporation, while the soil surface was covered by plastic sheets to maintain a zero flux as top boundary condition boundary condition
The set of conditions specified for behavior of the solution to a set of differential equations at the boundary of its domain. and maintain a constant temperature during the experiment. The bottom boundary condition was achieved with a lysimeter with free drainage. Lysimeters had holes or outlets at the bottom to allow water to drain freely under gravity. Measurements and monitoring of soil water content and pressure heads continued over a period of approximately 2 weeks, from which reliable data with higher resolution were obtained in the first 10 days.
The unknown parameters are estimated by minimising the difference between observed and fitted values as illustrated below:
(5) [Min.sub.b]O(b) = [k summation over [i = 1] [[w.sub.i]([Q.sub.1]-[Q.sub.2]*).sup.2]
where, [Min.sub.b]O(b) is the objective function; [Q.sub.i] is observed attribute like soil water content, pressure heads or cumulative infiltration; [Q.sub.i]* is the model predicted values of attributes corresponding to observed values and for a particular set of estimated parameters; k is the number of observed values; and [w.sub.i] is the weighting factor for ith observation. The weighting factor weighs the observed values depending on their accuracy and correlation with other values. Additional weighting can be assigned to individual data (Hollenbeck and Jensen 1998a). The best optimised parameter set could be judged by the lowest sum of squares SSQ SSQ Society for Software Quality
SSQ La Sarre, Quebec, Canada (Airport Code)
SSQ Sun Red Capital Corporation (stock symbol)
SSQ Space Station Quality
SSQ Standardized Safety Questionnaire
SSQ Single Server Queue such that the difference between the measured and the predicted data is minimal, when there is no longer a change in the sum of squares.
Tensiometry or water potential measurements
Tensiometer ceramic cups with mercury manometers were installed horizontally and sealed into the holes drilled in the sides at the depths 0.15, 0.25, 0.35, 0.45, 0.55, and 0.75m. These were tilted slightly upwards to enable air to escape from the system. The cups were connected to a mercury reservoir and the system was flushed with deaerated water to avoid air entrapment entrapment, in law, the instigation of a crime in the attempt to obtain cause for a criminal prosecution. Situations in which a government operative merely provides the occasion for the commission of a criminal act (e.g. . In all cases, holes of comparable sizes to the tensiometers were made to ensure good contact between tensiometer cups and soil to provide rapid adjustment to changes in soil water status. The first reading was taken as soon as water disappeared from the surface of the soil. Initial observations were made at small time intervals, since the changes in drainage were relatively faster at initially high water contents. Subsequently the time intervals were increased to about 3 days. The water potential or pressure heads at selected depths were computed according to according to
1. As stated or indicated by; on the authority of: according to historians.
2. In keeping with: according to instructions.
3. h = -12.61 + [z.sub.1] + [z.sub.2], H = h + z, where h is pressure head in the ceramic cup (cm), l is mercury column length (cm), [z.sub.1] is the depth of tensiometer cup below soil surface (cm), [z.sub.2] is the height of mercury level above soil surface (cm), and H is the hydraulic head Hydraulic head is a specific measurement of water pressure or total energy per unit weight above a datum. It is usually measured as a water surface elevation, expressed in units of length, but represents the energy at the entrance (or bottom) of a piezometer. (cm).
Water content measurements
The TDR method was used to determine water contents simultaneously with water potential at selected depths. The Tektronix TDR cable tester A cable tester is an electronic device used to verify the electrical connections in a cable or other wired assembly. Generally a cable tester consists of:
An electronic circuit capable of producing a waveform that rises abruptly, maintains a relatively flat top for an extremely short interval, and then rapidly falls to zero. , voltmeter, 4-5-m-long coaxial cable feeder, TDR probes, and personal computer for data logging (data) data logging - (data acquisition) Storing a series of measurements over time, usually from a sensor that converts a physical quantity such as temperature, pressure, relative humidity, light, resistance, current, power, speed, vibration into a voltage that is then converted . TDR indirectly measures soil water content over a quasi-elliptical area of approximately 10[cm.sup.2], and is therefore suitable for high resolution soil water regime measurements. The determination of water content by this method follows from the notion that there exists a unique relationship between volumetric water content [theta] ([cm.sup.3]/[cm.sup.3]) and soil permittivity Permittivity
A property of a dielectric medium that determines the forces that electric charges placed in the medium exert on each other. If two charges of q1 and q2 coulombs in free space are separated by a distance r or water dielectric constant dielectric constant
See permittivity. [epsilon](-). Several studies have indicated the value of TDR as a non-destructive method of soil water measurements (Topp et al. 1980, 1994) and do not require frequent calibrations in most field measurements (Lane and Mckenzie 2001).
The following empirical relationship In science, an empirical relationship is one based solely on observation rather than theory. An empirical relationship requires only confirmatory data irrespective of theoretical basis. for most mineral soils was used to estimate water content (Topp et al. 1980): [theta] = -0.053 + 0.029[epsilon] -5.5 * [l0.sup.-4][[epsilon].sup.2] + 4.3 * [10.sup.- 6][[epsilon].sup.3]. The field exercise revealed the Topp equation to be superior to the laboratory derived equations and other published empirical equations (Lane and Mckenzie 2001). The TDR probes were installed horizontally at 0.10-m increments for the following selected locations or depths: 0.15, 0.25, 0.35, 0.45, 0.55, and 0.75 m. A good contact was ensured between cable probes and soil by pushing the probes until the base touched the soil.
Instantaneous profile method
The more commonly used field method to measure K([theta]) and [theta](h) is the IPM (Rose et al. 1965; Van Bavel et al. 1968) and has undergone several modifications (Libardi et al. 1980). The IPM, although laborious, has proven to be reliable and is still considered a standard method in terms of precision of estimation when applied correctly (Vachaud and Dane 2002). The technique has been applied by Normand et al. (1997) in the leaching of nitrate below the root-zone and by Hutchinson and Bond (2001) in routine measurement of soil water potential gradient A potential gradient is the local space rate of change of the potential.
In electrostatics then, it is the local space rate of change of the electric potential:
(6) [partial derivative][theta]/[partial derivative]t = [partial derivative]q/[partial derivative]z
(7) q(z,t) = -[SIGMA] [[partial derivative][theta]/[partial derivative]t] [partial derivative]z and L([theta]) = q(z,t)/ [partial derivative]H/[partial derivative]z
Soil water flux and hydraulic conductivity were calculated for the layers of soil water contents, and pressure heads were measured. Soil water contents for each layer were plotted against time. Soil water gradients ([partial derivative]q/[partial derivative]z) were determined for selected depths by interpolation interpolation
In mathematics, estimation of a value between two known data points. A simple example is calculating the mean (see mean, median, and mode) of two population counts made 10 years apart to estimate the population in the fifth year. from graphs of [theta] v. time t. Particular attention was paid to the first few days of the experiment when measurements were quite sensitive to water changes. Hydraulic heads H were also plotted against time t, and hydraulic gradients ([partial derivative]H/[partial derivative]z) were determined at the same selected times for soil water gradient. Finally, hydraulic conductivity K([theta]) was calculated for each depth and together with water retention [theta](h) presented graphically.
The second part of the data analysis involved optimisation of the soil hydraulic functions and was carried out by applying van Genuchten's (1980) parametric model In statistics, a parametric model is a parametrized family of probability distributions, one of which is presumed to describe the way a population is distributed. Examples
Results and discussion
Instantaneous profile method
In all cases, both water content and tensiometry data showed good responses indicating that the methods were valid for the lysimeter drainage experimental set up. Volumetric water content as a function of time and depth [theta](z,t) was collected from the water content measurements, while hydraulic head as a function of time and depth H(z,t) was obtained from the tensiometry measurements at different times and depths in a draining profile. The H(z) profile, especially for the wetter part and initial times, showed some similarity with those generated in other studies (deBoer and Rice 1968; Ahuja et al. 1980), which reported a cubic spline In computer graphics, a smooth curve that runs through a series of given points. The term is often used to refer to any curve, because long before computers, a spline was a flat, pliable strip of wood or metal that was bent into a desired shape for drawing curves on paper. See Bezier and B-spline. curve flexible fitting for the H v. z curve. For computational analysis, [theta](z,t) and H(z,t) curves were plotted as shown in Figs 1 and 2, respectively, for sandy and loamy soils. Figure 1 shows a monotonic monotonic - In domain theory, a function f : D -> C is monotonic (or monotone) if
for all x,y in D, x <= y => f(x) <= f(y).
("<=" is written in LaTeX as \sqsubseteq). decrease of water content with time reflecting a draining profile, while Fig. 2 shows a more or less linear (though with cubic spline-like shape) relationship between hydraulic head and depth. The faster drainage in the sandy soil is reflected by the sharp drop in water content with time, while in the slower draining loamy soil there was a slower response in the changes. Vachaud and Dane (2002) commented that that the IPM is not applicable to heavy (or non-drainable) soils.
[FIGURES 1-2 OMITTED]
Flux (q) was calculated by applying the continuity principle, Eqns 6 and 7. Hydraulic conductivity (K) was computed from ([partial derivative]H/[partial derivative]z) at selected times and by application of Darcy's equation: q = K[partial derivative]H/[partial derivative]z. The conductivity data together with water retention were computed to describe the hydraulic functions K([theta]) and [theta](h) for both soils and are shown in Figs 3 and 4. respectively. The data processing data processing or information processing, operations (e.g., handling, merging, sorting, and computing) performed upon data in accordance with strictly defined procedures, such as recording and summarizing the financial transactions of a was quite sensitive, more especially for estimating slopes [partial derivative][theta]/[partial derivative]t for the driest part of the profile (where slopes were almost flat for a loam soil), and this might account for the more variable hydraulic conductivity data in a loam soil. The IPM data also showed highly scattered K([theta]) data (Fig. 4) for both soils with regression coefficient Regression coefficient
Term yielded by regression analysis that indicates the sensitivity of the dependent variable to a particular independent variable. See: Parameter.
regression coefficient ([R.sup.2]) of 0.57 and 0.29, respectively, for sandy and loamy soils for a semi-logarithm plot of K([theta]) data. High scatter data accounted for errors associated with qualitative estimations of [partial derivative][theta]/[partial derivative]t and [partial derivative]H/[partial derivative]z in predicting hydraulic properties, while the relatively higher scatter data in loamy soil is attributed to its poor drainage (Vachaud and Dane 2002). Yseng and Jury (1993) also reported that accuracy of K([theta]) data may be affected by errors such as measurement of [theta] and h values at various locations and also due to limited number of observations in space and time, producing poor estimates of hydraulic gradients and time derivatives of integrated water content at specified times and positions.
[FIGURES 3 & 4 OMITTED]
In arriving at theoretical predictions of soil properties, 3 datasets, water content (WC) only, pressure heads (P-h) only, and a combination of water content and pressure heads (WC & P-h), were used. The objective was to see which of the data [theta](z,t) or H(z,t) and/or a combination resulted in the most accurate estimates of the soil hydraulic functions when inverse modelling was applied. The optimised parameters as verified for their statistical accuracy for each dataset are tabulated in Table 2 for the sandy and loamy soils for [r.sup.2], the correlation coefficient Correlation Coefficient
A measure that determines the degree to which two variable's movements are associated.
The correlation coefficient is calculated as: , and SSQ, the lowest sum of squares for optimised parameters in the various datasets for measured attributes including water content and pressure heads.
Comparative analysis: IPM and inverse modelling
The results generally showed a better curve fitting for a sandy soil than for the loamy soil for both water retention and hydraulic conductivity functions. It also showed better agreement of experimental data with data from parameters estimated using both soil water data and pressure head data. The fast soil water drainage in the sandy soil seems to provide better data resolution compared with the slow-draining loamy soil. Similar results were obtained by Knopman and Voss (1987) when they concluded that more accurate model parameters are obtained from data with rapid change in soil water contents.
The experimental (IPM) water retention curve (Fig. 3) fitted well with predicted (inverse modelling) data from optimisation of both water content and pressure heads. The optimisation of pressure heads did not produce much difference, while the water content showed a large difference (more significantly for the wetter profile) between predicted and experimental data. Comparison of predicted and measured data was possible in the common wetness range only (Chaudhari and Batta 2003). Similarly Vachaud and Dane (2002) commented that the IPM yields a direct field estimation of K([theta]) data in wet range. This suggests that though optimisation of water content was well accomplished, it does not necessarily mean that the predicted soil hydraulic functions will fit well with the functions obtained from the IPM method. The hydraulic conductivity function was treated in the same way as water retention. As presented in Fig. 4, predictions from all treatments fitted well with experimental data, except for the difference from exclusive optimisation of pressure heads.
[FIGURE 3 OMITTED]
Figures 3 and 4 indicate that predicted and experimental hydraulic properties agree better when both pressure heads and soil water contents are used to estimate the hydraulic parameters, especially at near saturation. There was some deviation after the soil water content drained to 24% by volume. The predicted curves from either soil water contents or pressure heads data do not agree. Curves from pressure heads show some similarity with the curve from the measured data during the initial stages but later diverge as the soil dries. The predicted curve using soil water content data does not show any agreement with experimental data. Using data from a tension infiltration experiment, Simunek and van Genuchten (1997) found that optimisation with water content was the best practical set up for predicting soil hydraulic parameters.
The hydraulic conductivity curve (Fig. 4) calculated from the instantaneous profile method does not agree well with other curves. It only shows some similarities with the curve predicted using soil water content and pressure head data during the initial stages of drainage. The hydraulic conductivities calculated using IPM were always higher than the 3 sets of predicted hydraulic conductivities. Dane and Hruska (1983) showed the same trend in their drainage experiment, that is, less comparable results for the hydraulic conductivity curve than for the water retention curve. This difference could be explained by the relative insensitivity of unsaturated flow to saturated hydraulic conductivity [K.sub.s], especially near saturation (Kool and Parker 1987; Durner 1994). Furthermore, Kool and Parker (1988) indicated less sensitivity of hydraulic conductivity (K) and parameter n to both drainage and infiltration processes.
[FIGURE 4 OMITTED]
Summary and conclusions
The study has demonstrated that the IPM method, though laborious and time-consuming, is still applicable as there was a good fit for the hydraulic conductivity and water retention data with inverse modelling. The results have also indicated that good parameter estimation can be obtained from the combination of soil water content and pressure head data. Soils with relatively high hydraulic conductivity influence the data resolution positively, because of the rapid change in soil water content. Predicted hydraulic conductivity and measured hydraulic conductivity in most cases do not show good comparison because of the low sensitivity of the unsaturated transient flow to the saturated hydraulic conductivity. Parameter estimation of sandy soil with relatively high hydraulic conductivity shows rather good results; hence, the inverse modelling looks quite attractive compared with traditional methods (IPM). From this investigation it was shown that the predicted and experimental data fitted well for both the hydraulic conductivity and water retention data. Though there was a discrepancy in water retention curve for exclusive optimisation of water content, some theoretical considerations were still held. The results showed that the sandy soil gave a much better resolution and close agreement for fitted and measured properties than the loamy soil, and hence the applicability of the inverse modelling approach for the sandy soil is appropriate.
This work was carried out during my MSc studies at the University of Wageningen, The Netherlands. I would like to thank my MSc project supervisors; Drs C. Dirksen and J. C. van Dam for their guidance and supervision, l am also thankful to the anonymous reviewers for their constructive comments on the manuscript.
Arya LM (2002) Plane of zero flux. In 'Methods of soil analysis: Part 4, Physical methods'. SSSA Book Series, Vol. 5. (Eds JH Dane, GC Topp) pp. 937-962. (Soil Science Society of America The Soil Science Society of America (SSSA), is a scientific and professional society of soil scientists, principally in the U.S. but with a large number of non-U.S. members as well. : Madison, WI)
Arya LM, Leij FJ, Shouse PJ, van Genuchten MTH mth abbr (= month) → m
mth abbr (= month) → m
mth abbr (= month) → m (1999b) Relationship between the hydraulic conductivity function and the particle size distribution The particle size distribution ("PSD") of a powder, or granular material, or particles dispersed in fluid, is a list of values or a mathematical function that defines the relative amounts of particles present, sorted according to size. . Soil Science Society of America Journal 63, 1063 1070.
Ahuja LR, Green RE, Chong SK, Nielsen DR (1980) A simplified functions approach for determining soil hydraulic conductivities and water characteristics in situ In place. When something is "in situ," it is in its original location. . Water Resources Research 16, 947-953.
deBoer C, Rice RJ (1968) 'Least square cubic spline approximation. I. Fixed knots.' CSD CSD Commission on Sustainable Development
CSD Serbian Dinar (ISO currency code)
CSD Christopher Street Day
CSD Circuit Switched Data (Sprint)
CSD Computer Science Department
CSD Community School District TR 20, pp. 1-30. (Purdue University: Lafayette, IN)
Chaudhari SK, Batta RK (2003) Predicting unsaturated hydraulic conductivity functions of three Indian soils from particle size distribution data. Australian Journal of Soil Research 41, 1457-1466. doi: 10.1071/SR03040
Chen J, Hopmans JW, Grismer ME (1999) Parameter estimation of two-fluid capillary pressure-saturation and permeability functions. Advances in Water Resources 22, 479-493. doi: 10.1016/S03091708(98)00025-6
van Dam JC, Stricker JNM JNM Journal of Nuclear Medicine
JNM Job Network Member
JNM Japan Nagoya Mission
JNM Joint Network Management , Droogers P (1994) Inverse method to determine soil hydraulic functions from multi-step outflow experiments. Soil Science Society of America Journal 58, 647-652.
Dane JH, Hruska S (1983) In situ determination of soil hydraulic properties during drainage. Soil Science Society of America Journal 47, 61%624.
Dirksen C (1991) Unsaturated hydraulic conductivity, in 'Soil analysis: Physical methods'. (Eds K Smith, C Mullins) (Marcel Dekker: New York New York, state, United States
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of )
Durner W (1994) Hydraulic conductivity estimation for soils with heterogeneous pore structure. Water Resources Research 30, 211-233. doi: 10.1029/93WR02676
Durner W, Schultze EB, Zurmuhl T (1997) State of-the-art in inverse modelling of inflow/outflow experiments. In 'Characterization and measurement of the hydraulic properties of unsaturated porous media. Proceedings of International Workshop'. Riverside, CA. (Eds MTh van Genuchten, FJ Leij, L Wu) pp. 661-681. (University of California The University of California has a combined student body of more than 191,000 students, over 1,340,000 living alumni, and a combined systemwide and campus endowment of just over $7.3 billion (8th largest in the United States). : Riverside, CA)
van Genuchten MTh (1980) A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journa 44, 892-898.
van Genuchten MTh, Leij FJ, Wu L (1999) 'Characterisation and Measurement of Hydraulic Properties of Unsaturated Porous media.' (Eds MTh van Genuchten, FJ Leij, L Wu) (University of California: Riverside, CA)
Hopmans ,lW, Simunek J, Romano N, Durner W (2002) Simultaneous determination of water transmission and retention properties inverse methods. In 'Methods of soil analysis: Part 4, Physical methods'. SSSA Book Series, Vol. 5. (Eds JH Dane, GC Topp, L Wu) pp. 963-1008. (Soil Science Society of America: Madison, WI)
Hollenbeck KJ, Jensen KH (1998a) Maximum-likelihood estimation of unsaturated hydraulic conductivity parameters. Journal of Hydrology hydrology, study of water and its properties, including its distribution and movement in and through the land areas of the earth. The hydrologic cycle consists of the passage of water from the oceans into the atmosphere by evaporation and transpiration (or 210, 319-327.
Hutchinson PA, Bond WJ (2001) Routine measurement of soil water potential gradient near saturation using a pair of tube tensiometers. Australian Journal of Soil Research 39, 1147-1156. doi: 10.1071/SR00079
Klute A (1973) Soil water flow theory and its application in field situations. In 'Field soil water regime'. Special Publication No. 5. (Ed. RR Bruce) (Soil Science Society of America: Madison, WI)
Klute A, Dirksen C (1986) Hydraulic conductivity and diffusivity Dif`fu`siv´i`ty
n. 1. Tendency to become diffused; tendency, as of heat, to become equalized by spreading through a conducting medium. . In 'Methods of soil analysis. Part 1'. Agronomy agronomy (əgrŏn`əmē), branch of agriculture dealing with various physical and biological factors—including soil management, tillage, crop rotation, breeding, weed control, and climate—related to crop production. Monograph No. 9. (Ed. A Klute) pp. 687-734. (ASA Asa (ā`sə), in the Bible, king of Judah, son and successor of Abijah. He was a good king, zealous in his extirpation of idols. When Baasha of Israel took Ramah (a few miles N of Jerusalem), Asa bought the help of Benhadad of Damascus and and SSSA: Madison, WI)
Knopman DS, Voss CI (1987) Behaviour of sensitivities in the one-dimensional advection-dispersion equations: Implications for parameter estimation and sampling design. Water Resources Research 23, 253-272.
Kool JB, Parker JC (1987) Estimating soil hydraulic properties from transient flow experiments: SFIT SFIT Swiss Federal Institute of Technology (Lausanne, Switzerland) users's guide. Soil and Environmental Sciences, Virginia Polytechnic Institute and State University Virginia Polytechnic Institute and State University, at Blacksburg; land-grant and state supported; coeducational; chartered and opened 1872 as an agricultural and mechanical college. , VA.
Kool JB, Parker JC (1988) Analysis of the inverse problem for transient unsaturated flow. Water Resources Research 24, 817-830.
Lane NJ, Mckenzie DH (2001) Field and laboratory calibration and test of TDR and capacitance techniques for indirect measurement of soil water content. Australian Journal of Soil Research 39, 1371-1386. doi: 10.1071/SR00095
Libardi PL, Reichardt K, Nielsen DR, Biggar JW (1980) Simple field methods for estimating soil hydraulic conductivity. Soil Science Society of America Journal 44, 3-7.
Millington RJ, Quirk JP (1961) Permeability of porous solids. Transactions of the Faraday Society 57, 1200-1206. doi: 10.1039/tf9615701200
Mualem Y (1976) A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research 12, 513-522.
Mualem Y (1992) Modelling the hydraulic conductivity of unsaturated porous media. In ' Proceedings of International Workshop on Indirect Methods of Estimating the Hydraulic Properties of Unsaturated Soils'. 11-13 October 1989. (Eds FJ Leij, LJ Lund, L Wu) pp. 15-36. (US Salinity Laboratory and Department of Soil and Environmental Science, University of California: Riverside, CA)
Normand B, Recous S, Vachaud L, Kenngni, Garino B (1997) Nitrogen-15 tracers combined with tension-neutronic method to estimate the nitrogen balance nitrogen balance
The difference between the amount of nitrogen taken into the body and the amount excreted or lost.
n of irrigated maize. Soil Science Society of America Journal 61, 1508-1518.
Parkin GW, Elrick DE, Kachanoski RG, Gibson RG (1995) Unsaturated hydraulic conductivity measured by TDR under a rainfall simulator. Water Resources Research 31, 447-154. doi: 10.1029/94WR02535
Rose CW, Stern WR, Drummond JE (1965) Determination of hydraulic conductivity as a function of depth and water content for soil in situ. Australian Journal of Soil Research 3, 1-9. doi: 10.1071/S R965000 I
Simunek J, van Genuchten MTh (1997) Estimating unsaturated soil hydraulic properties from multiple tension disc infiltrometer data. Soil Science Society of America Journal 162, 383-398.
Topp GC, Davids JL, Annan AP (1980) Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resources Research 16, 574-582.
Topp GC, Zegelin SJ, White I (1994) Monitoring soil water content using TDR: an overview of progress. In 'Proceedings of the Symposium on TDR in Environmental, Infrastructure and Mining applications'. US Department of the Interior Special Publication No. 19-94. (Eds KM O'Connor, CH Dowding, CC Jones) pp. 67-80. (University of Evanston: Evanston, IL)
Tseng P-H, Jury WA (1993) Simulation of field measurement of hydraulic conductivity in unsaturated heterogeneous soil. Water Resources Research 29, 2087-2099. doi: 10.1029/ 93WR00578
Van Bavel CHM chm - Compiled HTML , Stirk stirk
a heifer or bullock 6 to 12 months of age. GB, Brust KJ (1968) Hydraulic properties of clay loamy soil and the field measurement of water uptake by roots. I. Interpretation of water content and pressure profiles. Soil Science Society of America Proceedings. 32, 310-317.
Vachaud G, Dane JH (2002) Instantaneous Profile. In 'Methods of soil analysis: Part 4, Physical methods'. SSSA Book Series, Vol. 5. (Eds JH Dane, GC Topp, CC Jones) pp. 937-962. (Soil Science Society of America: Madison, WI)
Vrugt JA, Schoups G, Hopmans JW, Young C, Wallender WW, Bouten W (2004) Inverse modelling of large scale spatially distributed vadose zone properties using global optimization. Water Resources Research 40, W06503. doi: 10.1029/ 2003WR002706
Zurmuhl T, Durner W (1998) Determination of parameters for bimodal hydraulic functions by inverse modelling. Soil Science Society of America Journal 62, 874-880.
Oagile Dikinya Department of Environmental Science, The University of Botswana The University of Botswana, or UB was established in 1982 as the first institution of Higher Education in Botswana. The university has a total of four campuses: two in the capital city Gaborone, one in Francistown, and another in Maun. , Private Bag 0022, Gaborone, Botswana. Current address: School of Earth and Geographical Sciences, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia. Email: firstname.lastname@example.org
Table 1. Particle size distribution (by mass) for sandy and loamy soils Soil % Sand % Silt % Clay Sandy soil 86 6 8 Loamy soil 42 37 21 Table 2. Optimised parameters with statistical indicators for sandy soil and loamy soil Soil data Model parameters [alpha] n [tau] [[theta] [[theta] [[KAPPA] (1/cm) (-) (-) .sub.s] .sub.r] .sub.s] ([cm.sup.3]/ (cm/h) [cm.sup.3]) Sandy soil WC only 0.2500 2.9552 0.0001 0.346 0.035 1.453 WC & P-h 0.0429 3.0525 0.0001 0.346 0.035 1.653 P-h only 0.0287 2.7052 0.0040 0.346 0.035 0.500 Loamy soil WC only 0.0080 2.394 0.5000 0.375 0.050 0.050 WC & P-h 0.2397 2.1089 0.2463 0.375 0.050 0.311 P-h only 0.0171 2.2228 0.0001 0.375 0.050 0.348 Soil data Statistical criterion [r.sup.2] SSQ Sandy soil WC only 0.9340 0.013 WC & P-h 0.9853 0.025 P-h only 0.9305 303.5 Loamy soil WC only 0.821 0.012 WC & P-h 0.979 0.015 P-h only 0.850 1475