A new computational approach for estimation of wilting point for green infrastructure
Introduction
The wilting point (θpwp) is the soil moisture below which transpiration process tends to inhibit. It is usually estimated as the moisture content at a soil matric potential of −1500 kPa (Hillel, 1971). It is one of the important parameters for design and analysis of crop performance especially under drought conditions [1], [2], [3]. Understanding of θpwp is one of the essential input functions, which is often used in interpretation of behavior of crop water consumption [4], [5], [6]. Furthermore, the knowledge of θpwp is fundamental in analyzing the hydrological performance of green infrastructures for stormwater management (e.g. green roofs, biofiltration units) and ecological infrastructure (wetlands). The soil-water characteristics influence the evapotranspiration (ET) in green infrastructures which regulates their hydrological performance by regenerating the retention capacity of the system [7], [8]. Actual ET rates fall exponentially in proportion to the substrate’s plant accessible moisture content which is limited by θpwp [9]. θpwp not only depends on plant species but also on soil characteristics such as fractal dimension (Ds), the slope of soil water characteristic curve (SWCC) at inflection point (S index) (), clay content (C) and organic content (OM) [10], [11]. This is because any changes in these soil properties could alter the soil-water relations and hence behavior of plant at wilting point (soil moisture) [12], [13].
Several researchers have studied wilting point and its estimation from other soil parameters [14], [15] explored relationships of wilting point with the soil parameters. However, the approach used was traditional linear regression approach which relies on the statistical assumptions. This approach however, may not be able to take into account the interaction effects of parameters such as Ds, S index, C and OM on θpwp, in the model. Alternatively, the intelligent data-driven methods such as genetic programming (GP), artificial neural network, support vector regression have achieved tremendous popularity [16], [17], [18], [19] in developing the models in uncertain process behavior. These methods takes in the data of the input-output form and produces a model that predicts the output reasonably well.
Among these methods, the GP algorithm produces the explicit models that represents a function between the output and inputs of the process [20], [21]. Therefore, it would be interesting to explore the competency of the GP algorithm in modelling wilting point (θpwp) of the soil. In this study, the GP approach is proposed to formulate the relationship between θpwp, and Ds, S index, C and OM. The data for all the five parameters is obtained (with Ds estimated) from the experiments. This data is then input into the framework of GP to produce the wilting point model. The statistical metrics indicating the performance of the model is evaluated. The relationships between (θpwp) and each of the input is revealed by the sensitivity and parametric analysis on the best GP model. The complete statistical analysis is then used to check if the understanding obtained from the numerical analysis is in line with experimental study.
Section snippets
Soil properties and wilting point for various soils
In this study, θpwp, Ds, S index, clay content (C) and organic content (OM) were collected or estimated from several comprehensive databases [21], [22], [23], [24], [25]. This includes a total of 161 data sets to be analyzed. Ds was estimated from the fractal model proposed in [26] as shown in Eq. (1).where ϕ is the soil porosity, Ds is the fractal dimension, θi is the water content, ψaev is the air entry value (kPa), and ψi is the matric potential (kPa) at the ith time step of
Design of Genetic programming based wilting point model (GP_W)
This manuscript introduces evolutionary framework of Genetic programming (GP) (Fig. 3). The mechanism of GP is in very much line with GA except for the fact the solutions in GP are entire model structure whereas in GA the solutions are coefficients of the model. The following steps are listed for implementation of GP [28].
Steps:
- 1.
The parameters of GP are set before its implementation. Parameters such as functional set consisting of airthematic operations and non-linear functions, terminal set
Analysis of the GP based wilting point model
In this section, the performance analysis of the GP based wilting point model (Eq. (4)) is evaluated against the experimental data as discussed in Section 2. The four performance measures used to evaluate the performance of GP model is given by Eqs. (A1), (A2), (A3), (A4) in the appendix.
Table 1 clearly shows that the GP based wilting point model corresponding to data set 9 have very good training accuracy with coefficient of determination of 0.97 and lower values of MAPE of 3.79, RMSE of 0.007
2-D and 3-D plots for main and interaction effect from the wilting point model
This section discusses the parametric and sensitivity analysis procedure for evaluating the main and interaction effects of the four inputs (fractal dimension, S-index, clay content and organic content) on the GP based wilting point model. The detailed mathematical procedure for the parametric and sensitivity analysis is discussed in an empirical study conducted in [20].
For measuring the main effects, each of the four inputs is vary from its minimum to maximum value. During this procedure, on
Conclusions
The present paper laid significant emphasis on the need of formulation of a model for evaluating the wilting point based on soil parameters. In particular in this study the following parameters have been considered: fractal dimension, S-index, clay and organic content. While many studies in literature assumed wilting point as the moisture content at a soil matric potential of −1500 kPa, the current study aims at understanding the variations in wilting point with respect to soil parameters. This
Acknowledgement
The authors wish to acknowledge that this research has been supported by Shantou University Scientific Research Foundation (Grant No. NTF 16002, Grant No. NTF17007).
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