The Neuro‐m Method for Fitting Neural Network Parametric Pedotransfer Functions

Abstract

be described adequately by a soil hydraulic model that is a closed-form equation with a certain number of param-Parametric pedotransfer functions (PTFs), which predict parameeters, e.g., Brooks and Corey or van Genuchten equation. ters of a model from basic soil properties are useful in deriving continuous functions of soil properties, such as water retention curves. The A parametric approach is usually preferred to singlecommon method for deriving parametric water retention PTFs in-point regression (predicting water retention at a specific volves estimating the parameters of a soil hydraulic model by fitting potential), as it yields a continuous function of the (h) the model to the data, and then forming empirical relationships berelationship. Water retention at any potential can be estitween basic soil properties and parameters. The latter step usually mated. Many soil-water transport models only require utilizes multiple linear regression or artificial neural networks. Neural the parameters of the soil hydraulic models as inputs, network analysis is a powerful tool and has been shown to perform thus the predicted parameters can be used directly to better than multiple linear regression. However neural-network PTFs run them. are usually trained with an objective function that fits the estimated The usual steps in deriving parametric PTFs are fitting parameters of a soil hydraulic model. We called this the neuro-p method. a soil hydraulic model to individual water-retention The estimated parameters may carry errors and since the aim is to be able to estimate water retention, it is sensible to train the network data, estimating the parameters of the model, and formto fit the measured water content. We propose a new objective func-ing empirical relationships between basic soil properties tion for neural network training, which predicts the parameters of and parameters. The latter step can be achieved by varithe soil hydraulic model and optimizes the PTF to match the measured ous mathematical methods, e.g., multiple linear regresand observed water content, we called this neuro-m method. This sion (Wö sten et al., 1995), or artificial neural networks method was used to predict the parameters of the van Genuchten (ANN) (Schaap et al., 1998). model. Using Australian soil hydraulic data as a training set, neuro-m The most widely used soil hydraulic model is the van predicted the water retention from bulk density and particle-size dis-Genuchten function (van Genuchten, 1980): tribution with a mean accuracy of 0.04 m 3 m Ϫ3. The relative improvement of neuro-m over neural networks that was optimized to fit the Abbreviations: AIC, Akaike's information criterion; ANN, artificial neural network; MD, mean deviation; MR, mean residuals; neuro-m, neural network PTF with objective function that matches the mea-B. Minasny, Australian Cotton Cooperative Research Centre, Departsured values; neuro-p, neural network PTF with objective function

Analysis of Soil Water Retention Data Using Artificial Neural Networks

“…Artificial neural networks have also recently found widespread application to predictions of the water retention curve from soil texture and related data using pedotransfer functions ͑PTFs͒ ͑e.g., Pachepsky et al 1996;Schaap et al 1998;Koekkoek and Booltink 1999;Minasny and McBratney 2002͒. The basic premise of these approaches is to assume the applicability of a certain retention model ͓e.g., Eqs.…”

Determining Soil – Water Content by Data Driven Modeling When Relatively Small Data Sets Are Available

“…This approach has been described e.g. in [4] or [7]. Briefly summarized, a neural network consists of input, hidden and output layers, which contains processing elements.…”

“…A relatively large number of works have appeared which were devoted to determining the water retention curve which is needed for this purpose from more easily available soil properties such as particle size distribution, dry bulk density, organic C content, etc., e.g. [1], [2], [4], etc. Pedotransfer functions (PTF) have become the term for such relationships between soil hydraulic parameters and the more easily measurable properties usually available from a soil survey [1].…”

Hydraulic characterization from porous aquifers of the Brazilian Federal District

“…Cresswell et al (1999) reviewed the application of PTFs to predict hydraulic properties of soils from Australia. Also in Australia, Minasny and McBratney (2002) applied the neural network method to predict the parameters of water retention of the van Genuchten (1980) equation. McKenzie and Jacquier (1997) presented a regression tree that predicts saturated hydraulic conductivity from soil morphology classes, including texture, structure and porosity.…”