Comparison of different approaches to the ...

Geoderma 93 Ž1999. 225–253

Comparison of different approaches to the development of pedotransfer functions for water-retention curves Budiman Minasny a

a,)

, Alex B. McBratney

a,b

, Keith L. Bristow

c

Department of Agricultural Chemistry and Soil Science, Ross St. Building A03, The UniÕersity of Sydney, Sydney, NSW 2006, Australia b CRC for Australian Cotton, Ross St. Building A03, The UniÕersity of Sydney, Sydney, NSW 2006, Australia c CSIRO Land and Waterr CRC for Sustainable Sugar Production, PMB AitkenÕale, TownsÕille, QLD 4814, Australia Received 28 January 1999; accepted 9 June 1999

Abstract Pedotransfer functions ŽPTFs. for estimating water-retention from particle-size and bulk density are presented for Australian soil. The water-retention data sets contain 733 samples for prediction and 109 samples for validation. We present both parametric and point estimation PTFs using different approaches: multiple linear regression ŽMLR., extended nonlinear regression ŽENR. and artificial neural network ŽANN.. ENR was found to be the most adequate for parametric PTFs. Multiple linear regression cannot be used to predict van Genuchten parameters as no linear relationship was found between soil properties and the curve shape parameters. Using

AbbreÕiations: AIC s Aikake information criterion; ANNsartificial neural network; ANNP s parametric PTF using ANN; AWC savailable water content; CAMsCampbell Ž1985. PTF to estimate Campbell parameters; dagrkg sdecagramrkilograms% by mass; ENR sextended nonlinear regression; HALL s Hall et al. Ž1977. PTF to estimate PWP; MLPs multilayer perceptron; MLR s point estimation with multiple linear regression; MRPs parametric PTF with multiple linear regression; P-2 s mass of articles - 2 mm Ždagrkg.; P2 – 20 s mass of particles 2–20 mm Ždagrkg.; P20 – 2000 s mass of particles 20–2000 mm Ždagrkg.; PTF s pedotransfer function; PWPs permanent wilting point; QCVs cross validation prediction error; RMSR s root mean squared of residuals; RNBsRawls and Brakensiek Ž1985. PTF to estimate Brooks Corey parameters; SSR ssum of squared residuals ) Corresponding author. Tel.: q61-2-9351 5813; Fax: q61-2-9351 3706. E-mail address: [email protected] ŽB. Minasny. 0016-7061r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 6 - 7 0 6 1 Ž 9 9 . 0 0 0 6 1 - 0

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B. Minasny et al.r Geoderma 93 (1999) 225–253

the prediction set, ANN performance was similar to the ENR performance for the prediction dataset, but ENR performed better on the validation set. Since ANN is still considered as a black-box approach, the ENR approach which has a more physical basis is preferred. Point estimation PTFs were estimated for water contents at y10, y33 and y1500 kPa. Multiple linear regression performed better for point estimation. An exponential increase trend was found between particles - 2 mm and water contents held at y10, y33 and y1500 kPa. The point estimation ANN did not improve prediction compared to MLR. Increasing the number of functions and parameters in developing PTFs does not necessary improve the prediction. The effect of parameter uncertainty, differences in texture determination and spatial variability on the error in prediction is also discussed. q 1999 Elsevier Science B.V. All rights reserved. Keywords: hydraulic properties; field capacity; unsaturated zone; artificial neural network; uncertainty; Monte Carlo analysis

1. Introduction The water-retention curve, which defines the relationship between soil water content Ž u . and hydraulic potential Ž h. is an important physical property of soil material. Determining this property directly can be expensive and time consuming. Since water retention by soil is affected by other physical properties, such as texture and structure, it is possible to develop empirical relationships to predict soil water retention. Many attempts have been made to determine the water retention curve indirectly from easily measured properties or properties available from routine soil survey data. Bouma Ž 1989. introduced the term pedotransfer function Ž PTF., which he described as translating data we haÕe into what we need, i.e., predictive functions of certain soil properties from other easily, routinely, or cheaply measured properties. In the past, attempts were made to correlate basic soil properties, such as percentage of sand, silt, clay and organic carbon, with the water content held at certain hydraulic potentials Žusually at y33 kPa and y1500 kPa.. This was made in order to estimate water content at field capacity, permanent wilting point and the availability of soil water to plants Ž Briggs and Shantz, 1912; Salter et al., 1966.. Developments in computer modelling of water and solute transport in soil is advancing rapidly, as speed of computation increases and complexity of models expand. The models are used to solve both production and environmental problems. With this advance, the need for appropriate u Ž h. data as an input to the models is becoming more and more critical. Many hydraulic properties pedotransfer functions have been developed in an attempt to accommodate this need ŽGupta and Larson, 1979; Rawls et al., 1982. . Pedotransfer functions for predicting the water-retention curve can be divided into 3 types. Ž1. Point estimation: This PTF is an empirical function that predicts the water content at a pre-defined potential. The most frequently estimated u are at y10,


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y33 kPa Žcorresponding to field capacity. and at y1500 kPa Žcorresponding to permanent wilting point., which are needed to determine plant available water content. Ž2. Parametric estimation: Parametric PTFs are based on the assumption that the u Ž h. relationship can be described adequately by a hydraulic model that is a closed-form equation with a certain number of parameters, for example Brooks and Corey Ž1964. , Campbell Ž 1974. and van Genuchten Ž 1980. . The parametric approach is preferred in soil–water transport modelling as it yields a continuous function of the u Ž h. relationship. Empirical functions are developed to estimate parameters of the hydraulic model from easily measured properties. Ž3. Physico-empirical model: In this approach, the water-retention curve is derived from physical attributes. Arya and Paris Ž 1981. translated the particle-size distribution into a water-retention curve by converting solid mass fractions to water content, and pore-size distribution into hydraulic potential by means of a capillary equation. The problem with this method is the need for information about the packing of soil particles. Comprehensive soil hydraulic properties databases have been developed in the USA ŽUNSODA, Leij et al. 1996. and Europe ŽHYPRES, Wosten et al., ¨ . 1999 while in Australia there is still little published data available and collation of a national database has just begun ŽCresswell et al., 1997. . Because of the supposed distinctive properties of Australian soil, PTFs developed elsewhere might not be directly applicable. As noted by Bastet et al. Ž1997. , the performance of published PTFs varied according to the pedological origin of the soil on which they were developed. Consequently PTFs should not be extrapolated beyond their geographical training area without first assessing their general validity. Previous attempts at developing PTFs for predicting soil water-retention for Australian soils from physical and morphological data have been described by Williams et al. Ž1992., Cresswell and Paydar Ž 1996. , Smettem and Gregory Ž1996. and Bristow et al. Ž1997. . In this paper we compare different approaches for deriving point estimation and parametric PTFs from particle-size and bulk density data. The performances of developed PTFs for estimating water retention for Australian soil is compared, and the effect of parameter uncertainty and alternate textural determinations evaluated. 2. Methods to fit water-retention PTFs 2.1. Multiple linear regression The most common method used in point estimation PTF is to employ multiple linear regression. For example: up s a sand q b silt q c clay q d organic matterq e bulk density

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where up is the water content Ž m3 my3 . at potential p and a, b, c, d, e are regression coefficients Ž Gupta and Larson, 1979. . Multiple linear regression is also used in parametric PTFs. Parameters of the hydraulic models are estimated by fitting the model to water-retention data with nonlinear regression and empirical relationships between basic soil properties and model parameters are then formed. 2.2. Extended nonlinear regression Scheinost et al. Ž1997. found difficulty in estimating the scaling and shape parameter a and n of the van Genuchten equation using the regression approach. Realizing the over-parametization Ž too many adjustable parameters relative to number of data points. of the van Genuchten equation, they proposed the following approach: 1. set-up the expected relationship between the parameters of the hydraulic model and soil properties, 2. insert the relationship into the model and estimate the parameters of the relationship simultaneously by fitting the extended model using nonlinear regression to all data.

2.3. Artificial neural network A recent approach for fitting PTFs is to use artificial neural networks Ž ANN. ŽPachepsky et al., 1996; Schaap and Bouten, 1996; Schaap et al., 1998; Tamari et al., 1996. . The ANN is a network of many simple processors Ž ‘‘units’’ or ‘‘neurons’’. each possibly having a small amount of local memory. The units are connected by communication channels Ž ‘‘connections’’. which usually carry numeric data, encoded by any of various means, and often organized into subgroups or layers. The mathematical model of an ANN comprises of a set of simple functions linked together by weights. The network consist of a set of input units, a set of output units and a set of hidden units, which link the inputs to outputs. The hidden units extract useful information from input units and use them to predict the output units. The type of ANN model considered here is called the multilayer perceptron Ž MLP. . A review on the use of ANN in predicting soil Ž 1997. . hydraulic properties can be found in Tamari and Wosten ¨ Pachepsky et al. Ž1996. used ANNs to estimate water content at eight hydraulic potentials as well as van Genuchten parameters from particle-size and bulk density data for 230 soil samples. They found that for point estimation PTFs, the ANN performed better than the regression method, but for parametric PTFs the performance of both approaches were comparable. Schaap et al. Ž 1998.


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estimated van Genuchten parameters for 1209 soil samples from the USA using ANNs. They found that ANN performed better than four published PTFs, and that the accuracy of prediction generally increased if more input data were used, but there was always a considerable difference between predicted and measured values.

3. Materials and methods 3.1. Data set Six previously published water-retention datasets from across Australia are used in this paper Ž Table 1. . The particle-size data are given in Fig. 1. As can be seen from Fig. 1b the texture range for the Australian data is largely similar to that for European data contained in HYPRES Ž Nemes et al., 1999., except that there are more points in the clay–clay loam range in the Australian data. This suggests that different PTFs might be required. A subset of data from Prebble, Forrest, Geeves, Smettem and Bristow were randomly selected and used with all the data from SydU as a validation set Žsee Table 2.. 3.2. Data analysis The soil physical properties common to all data sets were used as the predictive variables to estimate the water-retention curve. The properties used were the following. Ž1. bulk density Ž r b . in Mg my3. Ž2. porosity Ž f . in m3 my3 calculated as f s 1 y r brrs , where rs is the soil particle density; if no measurement was available we used 2.65 Mg my3. Ž4. saturated water content Ž us .. With the exception of the Forrest, Smettem and Bristow data sets, which contain measured values of us , the empirical relationship of Williams et al. Ž1992. was used:

us s 0.93 f Ž5. The mass of particles - 2 mm Ž P- 2 ., 2–20 mm Ž P2 – 20 . and 20–2000 mm Ž P20 – 2000 ., which were normalized to sum to 100 dagrkg. Ž6. Geometric mean particle-size diameter Ž d g in mm. and geometric standard deviation Ž sg in mm.. These were calculated according to Shirazi and Boersma Ž 1984. as d g sexp a

sg sexp b

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Table 1 Description of data sets used in this paper Location

Samples

Particle size ranges Žmm.

Water potential ŽkPa.

Prebble Ž1970.

Queensland

- 2, 2–20, 20–2000 Ždata from Stace et al., 1968.

0, y4, y10, y33, y68, y200, y700, y1500

Forrest et al. Ž1985.

wheatlands of eastern Australia ŽSouthern Queensland to South Australia. wheat-belt, southern New South Wales and northern Victoria

undisturbed cores Ž0.06 m diameter, 0.034 m deep. from various depths undisturbed cores Ž0.076 m diameter, 0.050 m deep. from top- and subsoil undisturbed cores Ž0.098 m diameter, 0.075m deep. from top- and subsoil undisturbed cores Ž0.047 m diameter, 0.03 m deep. from various depths undisturbed cores Ž0.075 m diameter, 0.050 m deep. from various depths disturbed samples from various depths

- 2, 2–20, 20–200, 200–2000

0, y5, y10, y100, y1500

- 2, 2–20, 20–63, 63–212, 212–425, 425–1000, 1000–2000, ) 2000

y1, y3, y5, y10, y33.3, y66.6, y100, y300, y500, y1500

- 2, 2–20, 20–53, 53–125, 125–180, 180–250, 250–355, 355–500, 500–1000, 1000–1400, 1400–2000 - 2, 2–20, 20–200, 200–2000, ) 2000

0, y1.5, y4.0, y9.0, y30, y100, y300, y1500

- 2, 2–20, 20–200, 200–2000

0, y10, y33, y100, y320, y1000, y1500, y10,000

Geeves et al. Ž1995.

Smettem and Gregory Ž1996.

northern and central wheat-belt, Western Australia

Bristow et al. Ž1997.

tropical north Queensland

SydU ŽDept. Agricultural Chemistry and Soil Science, The University of Sydney.

various locations in New South Wales

0, y1, y3, y5, y10, y30, y100, y300, y1500


Data set


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Fig. 1. Particle size distribution of soil database in this paper Ža. FAO system, shaded area represents texture range from European database Ž HYPRES . Žb. Australian system.


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Table 2 Summary of the data sets used in this study Dataset

All data

Prebble Forrest Geeves Smettem Bristow SydU Total

Sites

Samples

17 60 74 4 46 17 218

78 118 146 15 450 35 842

Prediction set

Validation set

Sites

Samples

Sites

Samples

15 54 60 3 42

71 106 132 10 414

174

733

2 6 14 1 4 17 42

7 12 14 5 36 35 109

with n

a s 0.01 Ý f i ln Mi is1

bs

(

n

0.01 Ý f i ln2 Mi y a 2 is1

where n is the number of particle fractions, and f i is the percent of total soil mass having a diameter equal to or less than Mi . The number of particle fractions used for calculation depends on the availability of particle-size distribution data. Scheinost et al. Ž1997. found that calculations made from 18 rather than 4 fractions did not improve PTF performance. Organic carbon was not included as a predictive variable for developing the PTFs because of the unavailability of this measurement in some data sets and the relatively small amount of organic matter content in some Australian soil materials Ž Bristow et al, 1997. . A summary of the soil properties is given on Table 3. The van Genuchten equation,

u Ž h . s ur q

us y ur

ž Ž1 q Ž a < h