Fitting particle size distribution models to data from Burundian soils for the BEST procedure and other purposes

doi:10.1016/j.biosystemseng.2009.07.008

Biosystems Engineering

Volume 104, Issue 3, November 2009, Pages 435-441

https://doi.org/10.1016/j.biosystemseng.2009.07.008 Get rights and content

Testing the Beerkan Estimation of Soil Transfer (BEST) soil particle size distribution (PSD) model is necessary to evaluate the applicability of the BEST procedure for characterising soil hydraulics. In this investigation, the fitting performance of the BEST PSD model was tested using a database of 114 Burundian soils with 14 measured particle size fractions for each soil sample, and also by considering a reduced number of measured particle size fractions for a sample. The fitting performance of the model developed by Fredlund et al. (2000) (FR model) was also considered for comparative purposes. On average, the BEST model yielded satisfactory results (i.e., mean relative error, $\bar{E_{r}} = 3.9 %$ ). However, low values of E_r (<5%) were always obtained in soils with relatively high clay content (≥48%) and E_r increased up to 14.3% with the sand content of the soil. In fine textured soils, using 11–12 measured particle size fractions, or 1–3 h of suspension density measurement, did not affect substantially the ability of the BEST model to reproduce the complete PSD. An $\bar{E_{r}} = 2.4 %$ was obtained with the FR model. It was concluded that, on average, the BEST PSD model is expected to give a reliable description of PSD of Burundian soils. In fine textured soils, reduced experimental information is enough to reproduce the complete PSD. If the objective of fitting a PSD to measured data is theoretical, and not the application of the BEST procedure, then the FR model is preferred.

Introduction

Studying soil hydrological processes requires the determination of soil hydraulic properties. Several methods have been developed to determine the hydraulic characteristics curves of the soil, i.e., the relationships between soil water content, θ, soil water pressure head, h, and soil hydraulic conductivity, K, both in the laboratory and the field. However, determining these properties using traditional methods is both expensive and time consuming. Haverkamp et al. (1996) pioneered a specific method for soil hydraulic characterisation known as the “Beerkan method”. An improved version of this methodology, called the Beerkan Estimation of Soil Transfer (BEST) parameters, was developed by Lassabatère et al. (2006). BEST considers certain analytic formulae for hydraulic characteristics curves (Burdine, 1953, Brooks and Corey, 1964, van Genuchten, 1980) and estimates their shape parameters, which are texture dependent, from simple particle size analysis by classical pedotransfer functions. Particle size analysis is carried out on a soil sample that is also used to determine its initial gravimetric water content. Another sample of known volume is extracted to determine soil bulk density and volumetric soil water content. Structure dependent scale parameters are estimated from a three-dimensional field infiltration experiment at zero pressure head, using the two-term infiltration equation developed by Haverkamp et al. (1994). The saturated water content is measured directly in situ at the end of the infiltration experiment. BEST is very attractive for practical use since substantially it facilitates the hydraulic characterisation of unsaturated soils, and it is becoming an applied method in soil science (Mubarak et al., 2009). However, the factors affecting the BEST performances are still largely unknown.

With BEST, the measured particle size distribution (PSD) has to be fitted on a modified version of the original PSD model by Haverkamp and Parlange (1986). Lassabatère et al. (2006) showed that the measured PSDs for three different soils fitted well using this theoretical PSD model. However, PSD models are known to differ in their fitting ability (Hwang et al., 2002), and the performances of a particular model may vary with the soil textural characteristics (Hwang, 2004). Therefore, the selected model may have a significant impact on both the estimated soil particle percentage at a given particle size limit (Nemes et al., 1999) and the predicted soil hydraulic properties (Hwang and Powers, 2003). The number of measured particle size fractions is also expected to affect the fitting. In particular, Arya et al., 1999a, Arya et al., 1999b suggested that PSDs comprised of at least twenty fractions are necessary to reasonably calculate their own models (Hwang and Powers, 2003), whereas Minasny and McBratney (2007) suggested that at least five particle size fractions are needed to characterise PSD properly. The geometric mean particle diameter and its standard deviation varied with the number of measured fractions in the investigation by Scheinost et al. (1997), but the predictability of the water retention curve was not improved by using more information about the PSD. Moreover, the accuracy of several procedures for estimating cumulative fraction of a particular particle size limit was found to depend on particle size limits for which fractions were measured (Nemes et al., 1999). Therefore, testing the performances of the BEST PSD model for different soils and different scenarios in terms of measured particle size fractions is clearly necessary to establish the real potential of the BEST procedure of soil hydraulic characterisation.

Burundi is a central African country having a great agricultural potential since adequate surface water is available and the climate is favourable. According to Eswaran et al. (1997) and Bationo et al. (2006), the Oxisol order (USDA classification) is the most frequently represented soil order used in Burundi. The hydraulic properties of Burundian soils are largely unknown and the direct measurement of these properties does not commonly occur (Bagarello et al., 2007).

Testing the applicability of the BEST PSD model for Burundian soils has both a local and a general interest since Burundi is rarely considered in soil investigations and Burundian soils are not widely represented in international soil databases.

In this investigation, a database of 114 experimental PSDs with 14 measured particle size fractions was developed by sampling Burundian soils with different textures. This database was used to (i) determine the fitting ability of the BEST PSD model and an alternative model, and (ii) establish if reduced experimental information is feasible to mathematically describe the complete PSD.

Section snippets

Materials and methods

The Burundian database considered in this investigation includes 114 soil samples, mainly collected in the Ruyigi area. According to Tessens et al. (1992), the investigated area is largely characterised by Hygroxeroferralsols typique, Hygroxeroferrisol limoneux, and Hygroxeroferralsols humique sous-groupes (Tessens et al., 1991, Institut des Sciences Agronomiques du Burundi, 1992).

For each sampling point, the PSD was measured using conventional methods following H₂O₂ pre-treatment to eliminate

Results and discussion

The cl, si and sa percentages are summarised in Table 1 and the textural composition of the sampled Burundian soils was reported in Fig. 1. Most of the USDA textural classes were included in the database.

The E_r values calculated with the BEST PSD model varied between 0.3% and 14.3% (Table 2). The mean value of E_r, $\bar{E_{r}}$ , was 3.9% and E_r < 5% was obtained for 76% of the considered soil samples. Therefore, according to the criterion suggested by Lassabatère et al. (2006), the BEST model yielded, on

Conclusions

The applicability of the BEST procedure for soil hydraulic characterisation depends on several factors, including the ability of the BEST PSD model to fit the experimentally determined PSD curve.

Using a database of 114 Burundian soils with 14 measured particle size fractions for each soil sample, a mean fitting error, $\bar{E_{r}}$ , equal to 3.9% (<5%) was obtained for the BEST PSD model, suggesting that the expected mean performance of this model for Burundian soils is satisfactory. In particular, a

Acknowledgements

This study was supported by a grant of the Università degli Studi di Palermo, Italy. All authors contributed to setting up the research, analysing the results and writing the paper. Simone Di Prima collected some of the soil samples used in this investigation. The authors wish to thank the anonymous reviewer for the clear and constructive comments and for the time he/she was willing to expend in the revision of the manuscript. We wish to dedicate this paper to our friend Marguerite (Maggy)

References (27)

H. Eswaran et al.
An assessment of the soil resources of Africa in relation to productivity
Geoderma
(1997)
S.I. Hwang
Effect of texture on the performance of soil particle-size distribution models
Geoderma
(2004)
I. Mubarak et al.
Temporal variability in soil hydraulic properties under drip irrigation
Geoderma
(2009)
A. Nemes et al.
Evaluation of different procedures to interpolate particle-size distributions to achieve compatibility within soil databases
Geoderma
(1999)
A.C. Scheinost et al.
Regionalization of soil water retention curves in a highly variable soilscape, I. Developing a new pedotransfer function
Geoderma
(1997)
O. Tietje et al.
Accuracy of the saturated hydraulic conductivity prediction by pedo-transfer functions compared to the variability within FAO textural classes
Geoderma
(1996)
L.M. Arya et al.
Scaling parameters to predict the soil water characteristic from particle-size distribution data
Soil Science Society of America Journal
(1999)
L.M. Arya et al.
Relationship between the hydraulic conductivity function and the particle-size distribution
Soil Science Society of America Journal
(1999)
V. Bagarello et al.
Agro-meteorological characteristics and soil properties in the Ruyigi area, Burundi
(2007)
Bationo A; Hartemink A; Lungu O; Naimi M; Okoth P; Smaling E; Thiombiano L (2006). Africans soils: their productivity...

R.H. Brooks et al.

Hydraulic Properties of Porous Media

(1964)

N.T. Burdine

Relative permeability calculation from pore size distribution data

Transactions of the American Institute of Mining, Metallurgical, and Petroleum Engineers

(1953)

M.D. Fredlund et al.

An equation to represent grain-size distribution

Canadian Geotechnical Journal

(2000)

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Such equations have performed well for fitting cumulative PSD for some specific soil textures. For instance S-shape (Esmaeelnejad et al., 2016), Anderson model (Botula et al., 2013), Gray and Skaggs models (Meskini-Vishkaee and Davatgar, 2018) and Weibull model (Bayat et al., 2017) have shown better fittings for coarse-texture soils, whereas Fredlund model (Meskini-Vishkaee and Davatgar, 2018; Bagarello et al., 2009; Hwang, 2004), Beerkan Estimation of Soil Transfer-BEST model (Bayat et al., 2017), hyperbolic (Bayat et al., 2015) and others have been better suited to fine-textured soils. However, no general model has shown to fit efficiently PSD data of all soil classes, different origins and regions (temperate and tropical areas).
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Downscaling of American National Aeronautics and Space Administration (NASA) daily air temperature in Sicily, Italy, and effects on crop reference evapotranspiration
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Air temperature (T_a) is one of the key factors in agro-hydrological studies including estimation of crop reference evapotranspiration (ET₀), which is crucial for irrigation water management and sustainability of agro-ecosystem productivity. Because direct measurements of ET₀ are difficult, expensive and time consuming, the use of physically based or empirical approaches linked to meteorological information is often preferred. The Prediction of Worldwide Energy Resource project developed by the American National Aeronautics and Space Administration (POWER-NASA) provides daily meteorological information on a 1° latitude by 1° longitude grid. Despite the poor spatial resolution characterizing this archive, the data is global and continuous in time, so that it can be used in particular regions of the globe where weather measurements are not well spatially distributed and/or there are some missing weather data to fill.
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SW—Soil and WaterFitting particle size distribution models to data from Burundian soils for the BEST procedure and other purposes

Introduction

Section snippets

Materials and methods

Results and discussion

Conclusions

Acknowledgements

Geoderma

Geoderma

Geoderma

Geoderma

Geoderma

Geoderma

Scaling parameters to predict the soil water characteristic from particle-size distribution data

Soil Science Society of America Journal

Relationship between the hydraulic conductivity function and the particle-size distribution

Soil Science Society of America Journal

Agro-meteorological characteristics and soil properties in the Ruyigi area, Burundi

Hydraulic Properties of Porous Media

Relative permeability calculation from pore size distribution data

Transactions of the American Institute of Mining, Metallurgical, and Petroleum Engineers

An equation to represent grain-size distribution

Canadian Geotechnical Journal

SW—Soil and Water
Fitting particle size distribution models to data from Burundian soils for the BEST procedure and other purposes