Modelling of soil permeability using different data driven algorithms based on physical properties of soil

Journal Pre-proofs Research papers Modelling of soil permeability using different data driven algorithms based on physical properties of soil Vijay Kumar Singh, Devendra Kumar, P.S. Kashyap, Pramod Kumar Singh, Akhilesh Kumar, Sudhir Kumar Singh PII: DOI: Reference:

S0022-1694(19)30958-8 https://doi.org/10.1016/j.jhydrol.2019.124223 HYDROL 124223

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Journal of Hydrology

Received Date: Revised Date: Accepted Date:

20 February 2019 5 October 2019 9 October 2019

Please cite this article as: Singh, V.K., Kumar, D., Kashyap, P.S., Singh, P.K., Kumar, A., Singh, S.K., Modelling of soil permeability using different data driven algorithms based on physical properties of soil, Journal of Hydrology (2019), doi: https://doi.org/10.1016/j.jhydrol.2019.124223

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Modelling of soil permeability using different data driven algorithms based on physical properties of soil Vijay Kumar Singh1, Devendra Kumar2, P.S. Kashyap3, Pramod Kumar Singh4, Akhilesh Kumar5, Sudhir Kumar Singh6 [email protected],

Research Scholar

[email protected], [email protected],

Professor

[email protected],

Professor

[email protected], [email protected], 1,2,3,5Department

Professor

Professor

Assistant Professor

of Soil and Water Conservation Engineering, Govind Ballabh Pant University

of Agriculture and Technology, Pantnagar, Uttarakhand, India – 263145 6K.

Banerjee Centre of Atmospheric and Ocean Studies, University of Allahabad, Prayagraj-211002, India

4Department

of Irrigation and Drainage Engineering, Govind Ballabh Pant University of

Agriculture and Technology, Pantnagar, Uttarakhand, India – 263145 Abstract: Soil permeability is an important parameter for assessment of infiltration, runoff, ground water, drainage and structures design. In the current research, five different data driven algorithms namely Multilayer Perceptron (MLP), Co-Active Neuro-Fuzzy Inference System (CANFIS), Support Vector Machine (SVM), Decision Tree (DT) and Random Forest (RF) algorithms and also, their wavelets (W-MLP, W-CANFIS, W-SVM, W-DT and W-RF algorithms) were used to predict soil permeability based on physical properties of soil. Also, 1

reliable information/input vectors were assessed based on Gamma Test (GT). Sand, silt, clay and organic content (OC) parameters were chosen as information vectors based on gamma test. The potential of data driven algorithms were evaluated based on different statistical indices during model development and validation phase. It was found that wavelet based algorithms viz. WMLP, W-CANFIS, W-SVM, W-DT and W-RF simulated better results of soil permeability compared to non-wavelet (MLP, CANFIS, SVM, DT and RF) algorithms. Among all wavelet and non-wavelet algorithms, W-RF algorithm had the highest accuracy and efficiency of model. The results of sensitivity analysis indicated that clay > silt > sand > OC > BD > PD was the order of sensitive parameters for soil permeability prediction based on data driven algorithms. Keyword: Soil permeability, Sensitivity, Wavelet, MLP, CANFIS, SVM, Decision Tree, Random Forest

1. Introduction Permeability is the most imperative building property of soils and it is used for understanding infiltration, runoff, drainage and settlement process (Mishra et al., 2010). Also, the management of water resources, drinking water supply, water detonations, ground water storage and surface water storage are highly affected with seepage properties of soil. Seepage is connected specifically to permeability of soil media (K) determined by Darcy's law (Darcy 1856). Permeability is a basic soil property depicting the hydraulic activities of unsaturated soils, and it is identified with the properties of water and soil (Dong et al., 2018). The permeability of various types of soils such as silty, clay, loamy, sandy varies wildly. It is demanding to decide the permeability for the reason that of the variation in mineral composition and the multifaceted texture of the soil (Dong et al., 2018). The permeability is likely the most vital hydrogeological

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parameter, alongside other parameters, as it affects the stream of flow and relocation of contaminants underneath the ground surface, particularly in aquifers system and soils (Li, 2014). The variability in permeability creates problem in construction of drainage structures, canals, check dams and other civil and soil water structures. The permeability of soil may be determined in the field or in the laboratory. However, field measurement of soil permeability is very complex, generally expensive, work concentrated and tedious (Vienken and Dietrich, 2011; Fereshte 2014). A number of methods have been developed to estimate the permeability of soil (McKinlay and Safiullah 1980; Lapierre et al. 1990; Vereecken et. al., 1990; Alyamani and Sen,1993; Fredlund et al., 1994; Pape et al., 1999; Nelson 2005; Shahnazari and Vahabikashi, 2011). But these methods require complex parameters and have limitations, assumption and low accuracy. Therefore, indirect techniques have been developed to simulate the permeability of soil, based on basic soil properties such as soil texture (sand, silt and clay), particle density, bulk density and total carbon content, using data driven algorithms (Akbulut, 2005; Donohue and Wensrich 2008; Ghanbarian-Alavijeh, 2010; Nosrati et al., 2012; Emami et al., 2012; Sihag et al., 2017; Sihag, 2018). The data driven algorithms have no limitations, assumptions and also have higher simulation accuracy as compared to other models (Chapuis, 2012). It is the motive behind that the authors decided to predict permeability of soil using data driven algorithms. In modern studies, some applications and recommendations of data driven algorithm namely Multilayer Perceptron (MLP), Co-Active Neuro-Fuzzy Inference System (CANFIS), Support Vector Machine (SVM), Decision Tree (DT), Self-organizing map (SOM) and Random Forest (RF) algorithms in different fields such as rainfall prediction (Singh et al., 2015; 2017a), runoff prediction (Noori et al., 2011; Rezaeianzadeh et al., 2013; Singh 2017; Singh et al., 2016b; 2017b; Kumar et al., 2019 ), evaporation estimation (Saran et al., 2017; Kisi and Alizamir, 2018;

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Rezaie-Balf et al., 2018; Shiri, 2018), sediment prediction (Mirbagheri et al., 2010; Kisi and Shiri, 2012; Singh et al, 2016c; 2018, Yaseen and Kisi, 2018; Kumar et al., 2019), soil temperature estimation ( Kisi et al., 2015; 2017; Singh et al., 2018) have been reported by the researchers. After review of potential of different algorithms, authors decided that MLP, SVM, CANFIS, Random Forest, Decision Tree algorithms and their wavelet transform may be applied to predict the permeability of soil. Some of basic questions rose related to pre-handling of vectors such as how many input vectors, what should be specific relation between input and output vectors for development of the best model? The gamma test (GT) is determination of the meaningful relation between input and output vector in non-linear modelling techniques during pre-development of vector. The input and output relation were chosen based on least value of gamma test and standard error (SE) value (Noori et al. 2012). The general details of gamma test may be obtained from given citation (Remesan et al., 2008; Lafdani et al., 2013). The gamma test (GT) is one of the most popular techniques to assess the most governing input and output relation (Singh et al. 2018a; b). The low correlation between input and output combination and large number of input vector have high complication and high chance of overfitting of developed model (Kumar et al., 2019). This was the reason for applying the gamma test for selection of governing input vectors to reduce complexity and chance of overfitting of models. The present study was undertaken with the objectives as: (a) to select specific input-output vector relation based on gamma test; (b) to concentrate on development of techniques for prediction of the soil permeability from soil texture (sand, silt and clay), particle density, bulk density and total carbon content by using different data driven algorithms; (c) to assess the rank of input vectors for prediction of soil permeability based on sensitivity analysis. 4

2. Material and methods 2.1 Field work and lab experiments A total of 180 soil samples were collected from a depth of 0-30 cm using auger from different locations in the study area. The physicochemical properties including grain size, density, permeability and total organic content (TOC) were determined in the Irrigation and Drainage Engineering and Soil and Water Conservation Engineering Laboratories, G. B. Pant University of Agriculture and Technology, Pantnagar, India. The particle size of soil was analyzed by hydrometer method (Bouyocos, 1962) in soil and water conservation engineering lab. Total organic content present in soil was evaluated using chemical titration (Walkley and Black, 1934) in water quality laboratory of Irrigation and Drainage Engineering. The particle density was determined by liquid pycnometer method and water was used as liquid material (Singh, 2001). The core or volumetric cylinder method was used to determine bulk density in soil and water conservation engineering lab. The particle and bulk density were determined by standard procedure of lab manual (Singh, 2001). The disturbed soil samples were used for determination of soil permeability. The details of experimental data such as texture, bulk density, particle density, organic carbon and permeability of soil are presented in Table 1. The permeability of soil (K) was determined by constant head permeability test. The constant head permeability test apparatus is shown in Fig. 1. The coefficient of permeability of soil was determined by the following equation. 𝐾=

𝑄×𝐿 𝐴𝐻𝑇

….

(1)

Where, K = soil permeability (cm/sec), Q = water discharge (cm3/sec), A = Cross sectional area of soil media (cm2), L = Soil media length (cm), T = Time (sec), H= Head difference (cm). 5

Fig: 1 Constant head permeability test diagram Table: 1 Statistical information of data set 2.2 Data driven algorithms 2.2.1 MLP algorithm MLP system is a supervised learning method and it is combination of different hyper-parameters that support in approximating complex connection between input and output (Ayyadevara, 2018). The hyper-parameters such as learning rate, momentum, hidden layers, iteration and number of neurons were used during the development of MLP system. The MLP networks were made up of three different layers viz. information (input), hidden and yield (output). The information level/layer is generally the independent factor and utilized to simulate the yield (output) level/layer (Kumar et al., 2019). The hidden level/layer is utilized to change the information factors into a simulated yield. The activation function is used to change the information signal into a yield signal in MLP system. In present scenario, tan hyperbolic transfer function was used because this function is marginally more rapid and better than logistic and sigmoid transfer functions (Maier and Dandy, 1998). The learning algorithm adjusts weights and biases for minimizing the overall inaccuracy in MLP (Kisi, 2007). The Levenberg–Marquardt algorithm is highly capable to minimize the overall error (Rezaeian et al., 2010). In this scenario, hyper-parameter namely learning rate (0.2), momentum (0.1), iteration (1000), hidden level (1) and neuron (2 to 40) were applied for development of efficient model (Table 2). The facts and fundamental literature of MLP was reported by these researchers (Kisi, 2007; Rezaeian et al., 2010; Singh et al., 2016a). The MLP and CANFIS models were developed using NeuroSolution 5.0.

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2.2.2 CANFIS algorithm The CANFIS algorithm is the combined form of fuzzy system and artificial neural system with quick and precise capacities (Zareabyaneh, et al., 2016). Generally, Tsukamoto and TSK fuzzy structures are used for CANFIS model development in NeuroSolution 5.0 software. Takagi-Sugeno and Kang (TSK) fuzzy structure (Takagi and Sugeno, 1985) with two participation capacities were favored in this investigation. The Gaussian membership function was utilized for each information neuron. These structures were selected on the basis of past investigations and the suggestions of scientists (Aytek, 2008; Wang et al., 2017, Pradhan et al., 2018). In current scenario, Gaussian membership functions (MFs) and Takagi-Sugeno-Kang fuzzy (TSK) fuzzy model were applied for development of CANFIS model. The value of MFs (2 to 6), threshold (0.001) and iteration (1000) were used to develop CANFIS model (Table 2). The information and elementary concept about CANFIS can be assessed from several literature (Tabari et al., 2012; Aziz et al., 2013; Pradhan et al., 2018; Singh et al., 2018b). 2.2.3 SVM algorithm SVM is a supervised learning technique which is applied to solve the prediction, pattern recognitions, regression and classification problem. SVM algorithm is frequently used more than other machine learning techniques. For example, neural systems are firmly identified with structural risk minimization hypotheses in statistics (Smola et al., 2007). The basic theory of SVM algorithm (Vapnik,1998) was developed for solving regression and classification problem. In this study, radial basis kernel function was used to develop SVM model and the hyper parameters of model were defined using a large number of trials in modeling approaches (Table 2). Details about technique are found in the literature (Kisi and Cimen, 2010; Chen et al. 2010;

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Kisi, 2015; Barzegar et al., 2017; Yu et al., 2017). R studio 3.5.1 was used for development of SVM, RF and DT models. 2.2.4 DT algorithm A decision tree is used for prediction of a target by learning decision methods. The decision tree is a supervised learning data driven technique and used for solving the regression, classification and prediction by learning decision techniques. It is constructing of groups as a tree structure and partitions a data set into smaller subsets. A decision tree is started from the root node (known as the first parent), each node can be split into left and right child nodes. These nodes can be further split and they themselves become parent nodes of their resulting children nodes. In the meantime, a related decision tree is gradually created. The last outcome is a tree with decision hubs (nods) and leaf hubs. A decision hub has at least two branches. Leaf hub is a representation to an arrangement. The highest decision hub in a tree, which relates to the finest forecaster is called root hub (Lee et al., 2013; Fakhari and Moghadam, 2013; Nasridinov et al., 2013). The details of parameters used in decision tree algorithm is presented in Table 2. Similar studies have been conducted by various researchers (Harb et al., 2009; Loh, 2014; Fakhari and Moghdam, 2013; Czajkowski and Kretowski, 2016; Nagalla et. al., 2017). 2.2.5 RF algorithm RF algorithm was first presented by Leo Breiman in 2001. RF algorithm is a flexible, simply hyper-parameter optimization and easily applicable machine learning algorithm. RF algorithm avoids avoiding overfitting problem during model development. RF algorithm can be applied to solve a classification, regression strategy and prediction problems. Additionally, excessive superiority of RF algorithm is that it is very simply to determine the virtual importance

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of respectively feature in the forecasting. In regression, tree indicator derives the numerical values instead of class labels utilized by the arbitrary tree classifier (Karimi et al., 2018). The RF model is built though fitting single trees in group (bagging system). The error of the bagged trees is equivalent that of the single tree, while the error of bagging is decreased by decrease in the relationship between trees (Hastie et al., 2009). The full-developed trees are not pruned back, and it is one of the real points of interest of random forest model over other tree strategies (Quinlan 1992). RF algorithm is developed based on the decision of the pruning techniques and not the variable choice measures, influence the execution of tree-based methods (Pal and Mather 2003). The ideal parameters were required for designing random forest model given in Table 2. The fundamental theory of random forest can acquire from (Chen et al., 2017; Singh et al. 2017c; Shiri, 2018). 2.2.6 Wavelet transform The wavelet transform algorithm is an efficient and powerful mathematical algorithm that gives an optimum time-frequency representation of an interpreted data in the time and frequency perspective. The modeling of permeability or hydraulic conductivity processes using the initial data that is without or with zero resolution makes the internal mechanism problematic to understand. Resolution of component is the separation of data into various frequency components. In present the study, Haar wavelet algorithm (Haar, 1910) was used to determine the wavelet transform. The literature of wavelet algorithm is well known and described by researcher (Si and Zeleke, 2005; Goyal, 2014; Hu and Si, 2016). The original discrete time series (C0(t)) can be resolved by Atrous decomposition algorithm as, +∞

𝐶𝑟(𝑡) = ∑𝓁 = ―∞h(𝓁)𝐶𝑟 ― 1(𝑡 + 2𝑟𝓁)(𝑟 = 1,2,.....)

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… (2)

𝑊𝑟(𝑡) = 𝐶𝑟 ― 1(𝑡) ― 𝐶𝑟(𝑡)(𝑟 = 1,2,.....)

… (3)

where, h(𝓁) is the discrete low-pass filter. Cr(t) and Wr(t) (r = 1, 2 ….) are respectively sub time series of scale coefficient and wavelet coefficient at rth resolution stage. In the current research, five data driven algorithms and wavelets models were applied to predict permeability of soil and also, performance of algorithms were assessed based on RMSE, WI, NSE, PI and CC values obtained from observed and simulated values of permeability of soil during training and testing periods. The qualitative results of different algorithms (MLP, CANFIS, SVM, DT and RF) and wavelets (W-MLP, W-CANFIS, W-DT, W-RF) models were analyzed in terms of scatter plot and time series plot between observed and predicted permeability of soil during testing period. Gamma test was applied to evaluate most dominant input vector for prediction of soil permeability. Sensitivity was analyzed with increasing and decreasing value of each input vector. The flow chart of model development is presented in Fig. 2. Table: 2 The hyper parameter of algorithms used for model development Fig: 2 Flow chart of model development 2.3 Model performance Evaluation The model performance was estimated by different statistical indicates namely Nash Sutcliffe Efficiency (NSE), Performance Index (PI), Root Mean Square Error (RMSE), Willmott’s Index of Agreement (WI) and Correlation Coefficient (CC). The details of statistical indicator can be assessed from given citations (Gandomi & Roke, 2015; Hyndman & Koehler, 2006; Nash & Sutcliffe, 1970; Singh, 2018a; Willmott et al, 2012)

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3

Results and Discussion

3.1 Gamma test The gamma test result is illustrated in Table 3. After masking the sand, silt and clay from inputs vector, values of gamma and SE had high deviation with respect to no masking (111111). Masking of PD, BD and OC also showed deviation with respect to no masking but it was less compared to masking sand, silt and clay. Therefore, sand, silt and clay input vectors affected the soil permeability output vector more compared to other input (PD, BD and OC) vectors. It was observed that clay particle of soil extremely affects the permeability of soil in non-linear relation. The particle density of soil had the least effect on soil permeability. After analyzing twenty-two models, based on minimum value of gamma and SE, Model-20 having governing inputs as sand, silt, clay and OC was selected as it had minimum values of gamma (0.05614) and SE (0.00424). The gamma and SE values of all models are presented by histogram plot in Fig.3. Fig: 3 Histogram plot between Models and values of gamma and SE Table: 3 Result of gamma test for input variable selection 3.2 Wavelet and non-wavelet data driven algorithms The results of MLP, CANFIS, SVM, DT and RF algorithms were analyzed into two phases (Table 4). First phase was training (model development) phase and another testing phase for validating developed model. The performance of models were assessed based on higher values of WI (close to 1 for good and close to 0 for poor), NSE (close to 1 for good and close to 0 for poor), CC (close to +1 for good and close to -1 for poor) and least values of RMSE (close to 0 for good and higher values (+ ∞) for poor), PI (close to 0 for good and higher values (+ ∞) for poor) during both phases. The RF model has value of NSE = 0.827, WI = 0.950, CC = 0.910, 11

RMSE = 2.789 cm/hr, PI = 0.212 in training phase and NSE = 0.849, WI = 0.956, CC = 0.922, RMSE = 2.304 cm/hr, PI = 0.165 in testing phase. After comparing the results of MLP, CANFIS, SVM, DT and RF models, models capability (RF > DT > SVM > CANFIS > MLP) was determined for soil permeability prediction. The performance of all models was found to be satisfactory. The RF and DT models had higher values of WI, NSE, CC and least values of RMSE, PI during training and testing phases as compared to MLP, CANFIS, SVM, models. It was finally observed that random forest and decision tree models outperformed other models for prediction of soil permeability. The WT was innovative algorithm coupled with data driven algorithms namely MLP, CANFIS, SVM, RF and DT models in the current study. The results of wavelet-based data driven algorithm viz. W-MLP, W-CANFIS, W-SVM, W-DT and W-RF models are presented in Table 4. The W-RF algorithm estimated the best values of NSE (0.880), WI (0.970), CC (0.942), RMSE (1.725 cm/hr) and PI (0.144) during model calibration and also, the best values of NSE (0.900), WI (0.972), CC (0.950), RMSE (1.530 cm/hr) and PI (0.108) during validation of model. Based on statistical indices of all developed models during training and testing phase, it was observed that all the models were capable to predict the permeability of soil. After comparing all developed models output, it was also observed that W-DT and W-RF algorithms outperformed W-MLP, W-CANFIS, and W-SVM models for prediction of soil permeability. It was observed that the results of data driven algorithms were mainly dependent on their hyper parameters. The defining of appropriate value of hyper parameters in data driven modelling is very complex. In the current study, this was solved by trial and error. So, this may be reason behind the lower performance of MLP, CANFIS and SVM algorithms as compared to RF and DT models. The performance of all developed models may be improved by optimizing the hyper 12

parameters of algorithm by different metaheuristic optimizing techniques. It was seen that all data driven algorithms results were improved by coupling wavelet algorithms in soil permeability prediction. It was also observed that wavelet-based data driven algorithms performance was better than only data driven algorithms. The qualitative analysis of developed data driven models were assessed through visual interpretation of time series, scatter plots and Taylor diagram. The time series and scatter diagram were plotted between observed soil permeability and predicted soil permeability during testing phase (Fig. 4 to 6). It may be inferred from time series and scatter plots that MLP and CANFIS models had high deviation from observed soil permeability compared to SVM, DT and RF models. Taylor diagram was plotted between standard deviation and correlation of observed and simulated by different models. It was observed from Taylor diagram that RF model has the better correlation as compared to other models. Fig: 4 Scatter and time series diagrams of non-wavelet based algorithms Fig: 5 Scatter and time series diagrams of wavelet-based algorithms Fig: 6 Taylor diagrams of non-wavelet and wavelet-based algorithms during testing period Table: 4 Results of different data driven algorithms 3.3 Sensitivity investigation of different variables The prospective of gamma test for input assortment and potential of independent vector in regression problem can be evaluated through sensitivity analysis. The best model, random forest, was used to measure sensitivity. The sensitivity analysis was achieved through 10 % increase and decrease of the parameter values. The sensitivity investigation (Singh et al., 2018a) was carried out in terms of relative sensitivity (RS). The sensitivity investigation results of 13

developed model are illustrated in Table 5. It was observed from results that bulk density and particle density have values of RS (1.481) and (-1.294) in training and (-0.487) and (-0.648) in testing of model. The RS values for soil texture parameters clay, sand and silt were estimated as 23.957, 17.894 and 18.177 respectively, during the development stage of model. Similarly, the RS values of clay, sand and silt were calculated as -18.487, 15.012 and 16.254 in validation stage of developed model. After comparing results of all variables, it was observed that soil texture (clay, sand, silt) was the most sensitive parameter for prediction of soil permeability by way of data driven algorithms. In the same way, it was also observed that clay soil particles has the highest influence on the soil permeability as compared to other parameters based on sensitivity analysis results. It can be stated that the rank of sensitive parameters was clay > silt > sand > OC > BD > PD for prediction of soil permeability by the data driven algorithms. The minimum and maximum permeability of soil values varied from 1.03 to 18.39 cm/hr. The permeability of soil was found to be depending on large numbers of parameters such as percentage of sand, silt, clay and organic carbon, soil salinity, compaction of soil, viscosity of water, pore size distribution etc. The bulk and particles density were dependent on soil texture. In the present study, most of the soil samples were sandy, sandy loam and loam. Therefore, the deviation in bulk and particles density of soil was found to be less. This may be the reason for less effect of bulk and particles density on permeability of soil. Table: 5 Sensitivity results of different parameters 4. Summary and Conclusions This research was conducted in three-parts; first part was collection of soil sample from different locations of field, second part was analysis of soil samples in laboratory, and third part was analysis and modelling of data. In third part, five different non wavelet data driven 14

algorithms (MLP, CANFIS, SVM, DT and RF) and wavelet data driven algorithms (W-MLP, WCANFIS, W-SVM, W-DT and W-RF) were applied for simulation of soil permeability based on various physical properties of soil. After analyzing the results of gamma test, it was concluded that soil particle viz. sand, silt, clay and OC parameters are appropriate input combination among sand, silt, clay, BD, PD and OC parameters for prediction of soil permeability. These selected parameters can be applied in future studies for prediction of soil permeability. Finally, it was concluded that RF algorithm was the best performing algorithm with high accuracy and efficiency for soil permeability prediction based on wavelet and non-wavelet algorithms. Sensitivity results indicated that soil texture (composition of sand, silt and clay particle) was the most sensitive vector as compared to OC, BD and PD parameters. It was recommended that RF model may be applied for soil permeability prediction in future works. Most of hydraulic structures are built on soil and if the soil under them is porous, it may be result in the seepage of the water, and may be also affect in piping action, this will decrease the strength of the soil to support structural load. Therefore, this research may be applied in design of canals, check dams, dam and drainage system. Similarly, it may be applied in assessment of surface and ground water for planning and management, ground water recharge from canals and monsoon rainfall. For future research point of view, authors suggest that the accuracy and efficiency of developed models may be increased by the hyper parameters optimization of algorithms. Acknowledgement: Author give special thanks to TEQIP-III for financial support. Conflict of Interest None. Reference

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List of Figure

Fig: 1

26

Output data (Permeability of soil) Input data (Sand, Silt, Clay, BD, PD, TOC)

Wavelet (Haar)

Gamma Test

C3, W1, W2, W3

Sand, Silt, Clay, TOC

MLP, CANFIS, SVM, RF, DT

WMLP, WCANFIS, WSVM, WRF, WDT Predicted Output (K) Compare with Statistical Indices

Model

Fig. 2

Fig: 3 27

28

Fig:4

29

Fig: 5

30

Fig.6 31

List of Table Table: 1 Statistics Mean Median Standard Deviation Kurtosis Skewness Minimum Maximum Number of Sample

Clay 17.01 16.59 7.29 7.37 1.74 1.96 57.24 172

Mean Median Standard Deviation Kurtosis Skewness Minimum Maximum Number of Sample

17.25 17.13 5.40 0.05 0.34 1.96 35.22 122

Mean Median Standard Deviation Kurtosis Skewness Minimum Maximum Number of Sample

16.42 12.94 10.64 5.47 2.03 6.68 57.24 50

All data Silt Sand 24.55 58.44 25.30 57.79 8.49 12.49 0.33 1.29 -0.03 0.00 0.00 14.20 48.01 97.66 172 172 Training data set 27.49 55.25 26.85 55.30 7.27 9.49 0.89 0.21 0.15 0.06 0.00 34.20 48.01 97.66 122 122 Testing data Set 17.36 66.22 15.75 67.30 6.82 15.33 0.12 3.22 -0.11 -1.13 2.65 14.20 29.18 91.66 50 50

OC 2.36 0.88 2.93 0.71 1.53 0.10 9.90 172

BD 1.35 1.36 0.07 2.05 -0.13 1.12 1.64 172

PD 2.52 2.54 0.12 0.17 -0.94 2.21 2.65 172

K 6.49 6.23 3.87 0.43 0.74 1.03 18.39 172

0.83 0.76 0.38 1.47 1.16 0.10 1.95 122

1.36 1.36 0.05 0.65 -0.42 1.21 1.65 122

2.49 2.53 0.10 0.36 -1.11 2.24 2.65 122

6.16 5.78 3.81 1.02 0.93 1.03 18.39 122

6.08 7.05 3.11 -1.00 -0.62 0.59 9.90 50

1.34 1.34 0.10 0.56 0.26 1.12 1.61 50

2.59 2.65 0.13 3.26 -2.12 2.21 2.65 50

7.28 7.17 3.95 -0.28 0.35 1.14 17.76 50

Table: 2 Model MLP CANFIS Random Forest Decision Tree SVM

Parameter of the algorithms Learning rate = 0.2, momentum = 0.1, number of neuron = 29, Iteration = 1000, Hidden layer = 1 Membership function (MFs) = Gaussian membership functions, MFs = 3, Fuzzy Model = TSK, threshold = 0.001, Iteration = 1000 Number of Tree = 300, mtry = 8 Size of tree = 6 SVM type = regression, Kernel function = Radial, Cast = 9, 32

Gamma = 0.25 Table: 3 Model M-1 M-2 M-3 M-4 M-5 M-6 M-7 M-8 M-9 M-10 M-11 M-12 M-13 M-14 M-15 M-16 M-17 M-18 M-19 M-20 M-21 M-22

Mask (Combination) 111111 011111 101111 110111 111011 111101 111110 001111 010111 011011 011101 011110 100111 110011 110101 110110 101011 101101 101110 111001 111010 111100

Input Vector Sand, Silt, Clay, PD, BD, OC Absent of Sand Absent of Silt Absent of Clay Absent of PD Absent of BD Absent of OC Absent of Sand and Silt Absent of Sand and clay Absent of Sand and PD Absent of Sand and BD Absent of Sand and OC Absent of Clay and Silt Absent of Clay and PD Absent of Clay and BD Absent of Clay and OC Absent of Silt and PD Absent of Silt and BD Absent of Silt and OC Absent of PD and BD Absent of PD and OC Absent of BD and OC

Gamma

SE

0.05818 0.06914 0.07245 0.09656 0.06014 0.06489 0.06748 0.14570 0.12489 0.09578 0.09145 0.08467 0.16481 0.08941 0.08815 0.09145 0.07515 0.07145 0.07234 0.05614 0.06440 0.06348

0.00459 0.00615 0.00684 0.01485 0.00478 0.00457 0.00601 0.17921 0.15421 0.01784 0.01472 0.01157 0.18759 0.01984 0.01847 0.02154 0.01255 0.01149 0.01189 0.00424 0.00548 0.05297

Table: 4

MLP CANFIS SVM DT RF W-MLP

NSE

WI

0.772 0.652 0.781 0.776 0.827 0.755

0.935 0.896 0.934 0.939 0.950 0.927

Training RMSE (cm/hr) 3.288 5.009 3.158 3.234 2.489 3.533

PI

CC

NSE

WI

0.284 0.448 0.272 0.278 0.212 0.307

0.879 0.813 0.884 0.885 0.910 0.869

0.724 0.739 0.803 0.847 0.849 0.781

0.914 0.926 0.945 0.959 0.956 0.936

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Testing RMSE (cm/hr) 4.208 3.974 3.006 2.338 2.304 3.334

PI

CC

0.312 0.293 0.218 0.167 0.165 0.243

0.851 0.870 0.896 0.922 0.922 0.885

WCANFIS W-SVM W-DT W-RF

0.846

0.958

2.215

0.187

0.920 0.792

0.938

3.174

0.231 0.891

0.806 0.841 0.880

0.945 0.956 0.970

2.789 2.295 1.725

0.238 0.194 0.144

0.898 0.824 0.917 0.889 0.942 0.900

0.952 0.969 0.972

2.679 1.699 1.530

0.193 0.909 0.120 0.943 0.108 0.950

Table: 5 Variable

Clay

Sand

Silt

BD

PD

OC

Variable values Clay (-10%) Clay Clay (+10%) Sand (-10%) Sand Sand (10%) Silt (-10%) Silt Silt (+10%) BD (-10%) BD BD (+10%) PB (-10%) PD PD (+10%) OC (-10%) OC OC (+10%)

Training NSE 0.684 0.880 0.672 0.784 0.880 0.779 0.769 0.880 0.768 0.861 0.880 0.859 0.872 0.880 0.875 0.815 0.880 0.834

WI 0.758 0.970 0.749 0.841 0.970 0.838 0.834 0.970 0.837 0.962 0.970 0.960 0.965 0.970 0.966 0.914 0.970 0.924

PI 0.491 0.144 0.517 0.394 0.144 0.401 0.415 0.144 0.428 0.198 0.144 0.208 0.197 0.144 0.194 0.345 0.144 0.319

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Testing RS -23.957

17.894

18.177

-1.294

1.481

11.648

NSE 0.771 0.900 0.789 0.829 0.900 0.831 0.786 0.900 0.798 0.873 0.900 0.864 0.891 0.900 0.895 0.834 0.900 0.851

WI 0.867 0.972 0.849 0.919 0.972 0.914 0.83 0.972 0.839 0.964 0.972 0.951 0.968 0.972 0.969 0.901 0.972 0.9174

PI 0.389 0.108 0.010 0.365 0.108 0.355 0.409 0.108 0.419 0.157 0.108 0.169 0.128 0.108 0.121 0.334 0.108 0.324

RS -18.487

15.012

16.254

-0.648

-0.487

5.089

Highlight 1. The W-RF algorithm have the highest accuracy and efficiency for soil permeability prediction based on physical properties. 2. The results of sensitivity analysis show that clay > sand > OC > BD > PD were the most sensitive parameters for soil permeability prediction. 3. The RF algorithm was the best performing algorithm with high accuracy and efficiency of model for permeability prediction based on wavelet and non-wavelet algorithms.

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