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COMMENTS & LETTERS TO THE EDITOR

Letter to the Editor on Soil Particle-Size Analysis by Hydraulic Pedotransfer Functions

Programa de Pós-Graduação em Fisica do Ambiente Agricola Departamento de Ciências Exatas ESALQ, USP Caixa Postal 9, 13418-900 Piracicaba, SP Brazil

eaelias{at}esalq.usp.br

Abbreviations: GP, granulometric permeameter • HPTF, hydraulic pedotransfer function • PSD, particle-size distribution • PTF, pedotransfer function

According to Schaap et al. (2001), soil hydraulic properties are necessary for many studies of water and solute transport but often cannot be measured directly because of practical and/or financial constraints. Hydraulic pedotransfer functions (PTFs) are useful in such situations, because they translate existing surrogate data, for example, particle-size distribution (PSD), bulk density, and organic matter content, into soil hydraulic data. According to McBratney et al. (2002), if one or more of these properties are not available, they can be estimated from available information using another PTF. For example, bulk density can be estimated from PSD. Conversely, a hydraulic PTF (HPTF) could conceivably be applied to measure PSD from soil hydraulic data, although this has, as yet, not been explored in the above articles or others, because there are no apparent advantages in doing so. The latter application may seem altogether pointless, since the input (hydraulic) data would be more difficult to obtain than the output (PSD) data.

In this letter to the Editor, of the subset Research Topic Ideas, I will suggest a reverse application for HPTFs. I will suggest the construction of an instrument, which I will call granulometric permeameter (GP), to measure PSD through HPTFs. In this case, the HPTF reverse application could be useful, because we would not be using field hydraulic data to determine PSD, but laboratory permeameter data, which could be easily obtainable. I will also present questions concerning implementation of this instrument.

As a first and preliminary approach, the GP would consist of a metallic cylinder holding an undisturbed soil core, submitted to a hydrostatic pressure difference, P (Pa). I will assume it possible to find a HPTF of the type:

[1]

where S is the silt content, C is the clay content, and f (m³ s^-1) is the volume of water flowing per unit time. The permeameter geometry would also influence the water flow, but it will not occur here as an independent variable, because the geometry would remain constant for all measurements with a particular permeameter. Now, our objective is to use this function f reversely, obtaining S and C from experimental flux data, instead of determining f from experimental values of S and C. To achieve this purpose, we need just two measurements of f, each at a different value of P:

The only unknowns of this system of equations are S and C; therefore, the system could be solved explicitly or numerically for them. Once S and C are determined, sand content can be readily obtained. Alternatively, we could write Eq. [1] as

to determine several particle-size limits, X₁, X₂,... X_n, rather than only three. This would demand n measurements of f at n different values of P, instead of just at two.

The following objection can be raised against the GP method. The water movement through a soil sample is affected by factors other than PSD, such as soil bulk density, D_b (Mg m^-3). Although D_b can be estimated from PSD in the absence of any other information, such estimation would make the GP very unreliable. We can imagine an example: two undisturbed soil cores, a and b, are exactly the same in terms of PSD, and have totally different values for D_b, because of compaction, so that D_ba >> D_bb. For such samples, measurements of f would certainly be different: f_a < f_b, implying that the method would return different PSDs when they actually are the same. To solve this problem, we could account for D_b by replacing f with another HPTF, F, so that F = F(S, C, P, D_b). This solution increases the model complexity, which is a disadvantage.

Another way to solve this problem, which demands a second approach for the GP, is provided by the following. Instead of using a rigid soil sample (soil core), the permeameter would hold a soil suspension of water and dispersant. Soil would be submitted to pretreatment; suspension would be the same used in sedimentation-based methods for PSD, like the pipette and the hydrometer methods, described by Gee and Bauder (1986), but it could possibly be more concentrated. The metallic cylinder would then need circular membranes or screens on its extremities, so that only water could flow through, not the clay. Thus the variable D_b would be removed from the model. We would need to replace functions like f or F by another HPTF, g = g (S, C, P), applicable to this second type of GP; g is, again, the water flow per unit time. The function g would be much more reliable than f, as the interference of soil compaction, structure, and possibly other variables, would be eliminated by the pretreatment. Our problem would mainly rely on finding the function g that correlates water flow to PSD. The correlation is very likely to exist, because the water movement through the permeameter would be dictated by forces between particles and water, and such forces are the same dictating the movement of particles down the water column, in the case of sedimentation. It is well known that such forces are not related to particle diameter only, and that the concept of diameter does not perfectly apply to irregularly shaped particles. So we cannot expect the GP method to return the true distribution of particle diameters, insofar as the pipette method does not. What is measured in the pipette method is the equivalent diameter (Gee and Bauder, 1986), and this is also what we can expect to measure in the GP method. So we expect the GP and the pipette methods to be in good agreement. I suppose it should not be difficult for specialists in the area to find this function g, considering the advanced stage that soil physics has now achieved in dealing with similar problems.

Another problem of this method would be precision. Solving a system of equations involves error propagation and may entirely invalidate this proposed method of soil particle-size analysis.

What would be the expected advantages of the GP over other methods to determine PSD, such as the pipette or the hydrometer? The GP would possibly be faster, as it does not demand waiting several hours for the silt to settle below a certain depth. It would also allow determination of several particle-size limits rather than only three. In addition, it could be interesting from an educational point of view and also in terms of basic soil physics knowledge, because of the modeling necessary to implement this instrument.

REFERENCES

• Gee, G.W., and J.W. Bauder. 1986. Particle-size analysis. p. 383–411. In A. Klute (ed.) Methods of soil analysis. Part 1. 2nd ed. Agron. Monogr. 9. ASA and SSSA, Madison, WI.
• McBratney, A.B., B. Minasny, S.R. Cattle, and R.W. Vervoort. 2002. From pedotransfer functions to soil inference systems. Geoderma 109:41–73.
• Schaap, M.G., F.J. Leij, and M.T. van Genuchten. 2001. ROSETTA: A computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions. J. Hydrol. (Amsterdam) 251:163–176.

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