# Experimental and Modeling Evaluation of Impacts of Different Tillage Practices on Fitting Parameters of Kostiakov’s Cumulative Infiltration Empirical Equation

^{1}

^{2}

^{*}

## Abstract

**:**

^{b}) for cumulative infiltration to acquire the fitting parameters of “q” and “b”, and in the last stage, we predicted the fitting parameters of “q” and “b” based on soil mean weight diameter, tillage depth, and four soil compaction levels by applying regression data mining approaches in Weka 3.8 software. The results show that the effects of relevant factors on the cumulative water infiltration depth of the soil could be statistically significant (p < 0.05). The Kostiakov model, with an average coefficient of determination of 0.939, had a good fitting effect on the cumulative water infiltration depth process of the investigated soil. The average, lowest, and maximum values of the “q” parameter were 2.7073, 2.2724, and 3.1277 mm/min

^{b}, respectively, while for the “b” parameter, they were 0.5523, 0.5424, and 0.5647, respectively. Furthermore, the evaluation of several regression data mining approaches determined that the KStar (K*) data mining approach, with a root mean square error of 0.0228 mm/min

^{b}, a mean absolute error of 0.0179 mm/min

^{b}, and a correlation coefficient of 0.997, was the most accurate method for fitting parameter “q” using the testing dataset. The most accurate method for fitting the parameter “b” estimation was determined to be the Multilayer Perceptron method, with a root mean square error of 0.0026, a mean absolute error of 0.0013, and a correlation coefficient of 0.962, using the testing dataset. Therefore, this research, which consisted of in situ field observation experiments and infiltration modeling of the infiltration process in a clay soil, provides an essential theoretical basis for improving models of the rate of cumulative infiltration. Moreover, the proposed methodology could be employed for simulation of the fitting parameters “q” and “b” for soil water cumulative infiltration processes, not only for irrigation management purposes under regular crop production conditions, but also for the selection of the most suitable tillage practices to modify the soil during the agriculture season to conserve water and prevent yield declines. The results support the understanding of the infiltration processes in a clay soil and demonstrate that tillage practices could reduce the water infiltration rate into the soil.

## 1. Introduction

^{2}values of 0.902 and 0.765 to obtain the “k” and “u” parameters, respectively, of the Kostiakov equation $(\mathrm{I}=\mathrm{k}\times {\mathrm{t}}^{\mathrm{u}}$) for infiltration rate (I) in units of mm/h, employing the multiple linear regression (MLR) method. In their model, the soil mean weight diameter, the number of tractor wheel passes on the surface of the plowed soil, and the tillage depth were used as inputs. Hossne García et al. [22] conducted field experiments to study the effects of wetness, soil depth, and compaction on infiltration rate (mm/h) and employed the Kostiakov equation $(\mathrm{I}=\mathrm{k}\times {\mathrm{t}}^{\mathrm{u}}$) for infiltration rate (I) in units of mm/h to acquire the Kostiakov fitting parameters “k” and “u”. They then employed the MLR method to model these two fitting parameters. Al-Sulaiman et al. [23] employed MLR to formulate the Kostiakov parameters “q” and “b” for water cumulative infiltration of the Kostiakov model. In their MLR model, the water electric conductivity, soil texture index, initial soil bulk density, soil sodium adsorption ratio, initial soil moisture content, soil electric conductivity, water sodium adsorption ratio, and organic matter percentage in the soil were used as inputs.

## 2. Materials and Methods

#### 2.1. Procedures of the First Stage of the Research (the Experimental Work)

^{3}, respectively. The experiments were conducted on an area of 0.405 ha. Water was applied to the test area, and it was then permitted to dry out until the soil moisture content was between 15% and 19% db.

_{i}is the average diameter of the aggregate class (mm), n is number of sieves, and W

_{i}is the proportion of each aggregate class in relation to the total aggregate weight.

#### 2.2. Double-Ring Infiltration Experiments

#### 2.3. Determination of Kostiakov Equation Fitting Parameters for Cumulative Infiltration (the Second Stage of the Research)

^{b}), and “b” is the experimental fitting constant called the infiltration index constant (dimensionless). However, “q” and “b” are fitting parameters that are site-specific and depend on soil conditions such as soil bulk density, soil texture, soil moisture content, and other soil properties [39]. As the Kostiakov infiltration equation is empirical, no physical implications are involved in its related fitting parameters [40].

^{2}was greater than 0.938). Figure 2 shows the steps in the research methodology for obtaining the fitting parameters “q” and “b”.

#### 2.4. Statistical Analysis

#### 2.5. Procedures of the Third Stage of the Research (Data Mining Algorithms)

_{j}) of the unit as follows:

_{ij}is the weight of the link from unit i to j, y

_{i}is the input value at the input layer, and Z

_{j}is the output obtained by the transfer function to yield an output for unit j. Haykin [54] has provided a detailed discussion about ANN. In the current research, a three-layer feed-forward ANN based on the back propagation algorithm was employed, which is the default in Weka 3.8 software.

#### 2.6. Statistical Criteria for Evaluation of Regression Data Mining Algorithms

^{2}) is also used to compare the predictions with the real values in the testing dataset. In addition, R

^{2}is a statistical procedure that identifies the proportion of a component’s variability that can be caused or explained by its relationship to another factor. The chosen metrics are the most well-known and widely applied success metrics [55]. The statistical criteria are computed as follows:

_{i}and O

_{i}are the predicted and calculated “q” or “b” values, respectively, and N is the total number of readings.

## 3. Results and Discussion

#### 3.1. Data Analysis of the First Stage of the Research (the Experimental Work) for Soil Mean Weight Diameter

#### 3.2. Data Analysis of the Second Stage of the Research (Water Cumulative Infiltration Depths)

#### 3.3. Kostiakov Fitting Parameters

^{b}, respectively for a clay soil, and these values were 0.5523, 0.5647, and 0.5424 (dimensionless), respectively, for the “b” parameter for the same clay soil. In another study in a plowed clay, soil “q” was 3.38 mm/min

^{b}and “b” was 0.53 (dimensionless) [26]. The infiltration parameters “q” and “b” varied strongly with respect to soil texture [76]. Thus, the Kostiakov model for predicting the water cumulative infiltration (Z, mm) for a clay soil for the present research was as follows:

^{2}value of 0.939, only slight variations were reported between the measured and predicted Z. The test results indicate that the cumulative infiltration predicted using Equation (8) is reasonably accurate and can be used to estimate cumulative infiltration over a reasonable time for irrigation in a clay soil. There is a good agreement between the measured and estimated cumulative infiltration under all treatments. In previous research [11], the Kostiakov, Philips, and Horton infiltration models were evaluated and the Kostiakov model was identified as the better alternative for evaluating the infiltration rate. Additionally, the Kostiakov model was considered the most appropriate for the prediction of water infiltration rate into the soil compared with the Horton and Philip models [77]. Fok [78] derived the Kostiakov equation parameters and fitting them to a physically based infiltration equation, derived five different sets of values for “q” and “b”, depending on initial moisture content, time, and hydraulic conductivity. The power constant “b” has more physical sense than the other Kostiakov equation fitting parameters, as its scale depends on the relationships and interactions of several infiltration reduction or increasing factors [78]. According to Dixon [79], large “q” values are related to micro-rough and macro-porous soil surfaces, or to situations with a moderately large gravitational impact on infiltration. On the other hand, small “q” values are linked to smooth, micro-porous surfaces where capillarity is the major force driving infiltration. The constant “b” is just an infiltration curve fitting coefficient. For the empirical infiltration models, it is commonly implicit that, while infiltration is defined as a function of time, the residual parameters are calibration constants signifying the situations under which the test was directed, including the initial soil moisture content and any other factors that may induce differences in infiltration [80].

#### 3.4. Data Analysis of the Third Stage of the Research (Data Mining Algorithms)

^{2}of 0.947, and for “b”, the Weka linear regression model result was calculated by Equation (9), with an R

^{2}of 0.786.

^{b}, “b” is dimensionless, MWD is in mm, NTT is soil compaction at 0, 1, 3 and 5 traffic levels, and TD is tillage depth in cm.

^{b}, and RMSE = 0.0228 mm/min

^{b}. For “b” estimation, the performance of the MLP was better than the other regression algorithms, with performance evaluation criteria as follows: correlation coefficient = 0.962, MAE = 0.0013 dimensionless, and RMSE = 0.0026 dimensionless.

^{b}in testing dataset (14 points), and the closed average for the K Star (K*) method was 2.8234 mm/min

^{b}.

## 4. Conclusions

^{2}value of 0.939, and found to be highly acceptable. Defining the precise infiltration features leads to correct management and design of an irrigation system, as governed by the accurate behavior of model parameters. Thus, in this research, regression algorithms in the Weka software, namely, M5Rules, Additive Regression, KStar (K*), SMOreg, Multilayer Perceptron (MLP), Linear Regression (LR), and Gaussian Processes, were used to predict the Kostiakov model parameters of “q” and “b” for the cumulative infiltration equation using field infiltration data. The inputs were as follows: mean weight diameter of the clay soil, which depending on different treatments, ranged from 9.2 to 80.2 mm; the level of tractor wheel traffic on the plowed soil surface (dimensionless) with 0, 1, 3, and 5 passes; and the tillage depth, ranging from 97 to 204 mm. The outputs were “q” and “b”. The obtained results indicated that the KStar (K*) model was the most effective regression algorithm for predicting “q” with a correlation coefficient of 0.997 for the given clay soil texture, while for parameter “b” for the same clay soil texture, the MLP regression algorithm with a correlation coefficient of 0.962 was the most effective method. Finally, we encourage repeating the same procedure in order to answer related problems. This research is not without limitations. Using only the data based on a clay soil is one limitation, although its reliability is high. The second limitation relates to the graphical method for determination of “q” and “b” fitting parameters, as many other methods could have been used, for example, the volume-balance method. The third limitation relates to the non-use of other relevant data mining algorithms that are not offered in Weka software, which should be addressed in coming research on this subject. This research contributes to research in the irrigation field on new computational methods applied to the soil infiltration process. It should encourage the irrigation and soil research community to share their datasets and improve the prediction models. The results also indicate that the regression algorithms can be suitable for the estimation of fitting parameters of cumulative infiltration depth from the accessible data. The fitting parameters generated by the investigated regression algorithms can be used to simulate the cumulative infiltration depth in the investigated soil texture. Moreover, the water infiltration rate into the soil can be used as a tool for the purposes of designing irrigation systems, the characterization of different tillage practices, and providing a localized management of this variable.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Average percentage of silt, clay, and sand content at the experimental location for two soil depths.

**Figure 2.**Steps of the research methodology used to obtain the parameters “q” and “b” (adopted from [42]).

**Figure 4.**Variation in average soil MWD under investigated tillage practices treatments for rotary, chisel, and moldboard plows (D1 represents a tillage depth of 100 mm and D2 represents a tillage depth of 200 mm).

**Figure 5.**Field measurements of cumulative infiltration depths for moldboard plow tillage with two tillage depths and under different soil compaction levels.

**Figure 6.**Field measurements of cumulative infiltration depths for chisel plow tillage with two tillage depths and under different soil compaction levels.

**Figure 7.**Field measurements of cumulative infiltration depths for rotary plow tillage with two tillage depths and under different soil compaction levels.

**Figure 8.**Impact of tillage depth on final water cumulative infiltration depth after 180 min at different levels of wheel traffic for moldboard plow. Data are shown as average values.

**Figure 9.**Impact of tillage depth on final water cumulative infiltration depth after 180 min at different levels of wheel traffic for chisel plow. Data are shown as average values.

**Figure 10.**Impact of tillage depth on final water cumulative infiltration depth after 180 min at different levels of wheel traffic for rotary plow. Data are shown as average values.

**Figure 11.**Bar graph for the average values of the parameter “q” using the investigated regression algorithms compared with actual values in testing dataset.

**Figure 12.**Bar graph for the average values of the parameter “b” using the investigated regression algorithms compared with observed values in testing dataset.

Class | Algorithms | Description |
---|---|---|

Rule | M5Rules | By using separate-and-conquer, this generates a decision list for regression issues. It employs M5 to construct a model tree in each cycle, turning the “best” leaf into a rule [47]. |

Meta | Additive Regression | A fitting model’s residuals are adjusted interactively for prediction while taking earlier iterations into account [47]. |

Lazy | KStar (K*) | An entropy-based distance function is used to calculate how similar the training examples are in order to make predictions [48]. |

Function | Gaussian Processes | Regression without hyper-parameter tweaking is performed. This measures the match between arguments to forecast the value using lazy learning [49]. |

SMOreg | The algorithm is dependent on the support vector machine method for regression predictions [50]. |

**Table 2.**Analysis of variance (ANOVA) table of the MWD (TI indicates tillage implement, NTT indicates the number of tractor wheel traffic passes on the plowed soil surface, and TD indicates the tillage depth).

Source of Variation | Degrees of Freedom | Anova SS | Mean Square | F-Value | p-Values |
---|---|---|---|---|---|

Replicates | 2 | 2.45 | 1.2 | 4.53 | 0.0160 |

TI | 2 | 21,752.6 | 10,876.3 | 40,159.1 | <0.0001 |

NTT | 3 | 6587.7 | 2195.9 | 8108.07 | <0.0001 |

TD | 1 | 168.2 | 168.2 | 621.01 | <0.0001 |

$\mathrm{T}\mathrm{I}\times \mathrm{N}\mathrm{T}\mathrm{T}$ | 6 | 1583.9 | 263.9 | 974.70 | <0.0001 |

$\mathrm{T}\mathrm{I}\times \mathrm{T}\mathrm{D}$ | 2 | 40.4 | 20.2 | 74.65 | <0.0001 |

$\mathrm{N}\mathrm{T}\mathrm{T}\times \mathrm{T}\mathrm{D}$ | 3 | 1.3 | 0.44 | 1.64 | 0.1942 |

$\mathrm{T}\mathrm{I}\times \mathrm{N}\mathrm{T}\mathrm{T}\times \mathrm{T}\mathrm{D}$ | 6 | 0.32 | 0.053 | 0.20 | 0.9762 |

**Table 3.**Mean values and least significance difference (LSD) for the MWD as impacted by tillage implement, soil compaction level, and tillage depth (Means significantly different if they are followed by a distinct letter).

Treatments | Mean MWD (mm) |
---|---|

Moldboard plow | 57.86 a |

Chisel plow | 32.98 b |

Rotary plow | 15.50 c |

LSD (5%) | 0.30 |

Soil compaction level-0 | 47.84 a |

Soil compaction level-1 | 40.67 b |

Soil compaction level-3 | 30.52 c |

Soil compaction level-5 | 22.76 d |

LSD (5%) | 0.35 |

Tillage depth (100 mm) | 33.92 b |

Tillage depth (200 mm) | 36.98 a |

LSD (5%) | 0.25 |

**Table 4.**Raw data of fitting parameters “q” and “b” in Equation (2) as affected by the number of tractor wheel passes on the plowed soil surface and the tillage depth for the moldboard plow.

Soil MWD (mm) | Number of Tractor Wheel Passes on the Plowed Soil Surface (-) | Tillage Depth (mm) | Replicates | “q” (mm/min^{b}) | “b” (Dimensionless) |
---|---|---|---|---|---|

75.5 | 0 | 104 | R1 | 2.979 | 0.5595 |

77.6 | 0 | 108 | R2 | 2.963 | 0.5637 |

74.8 | 0 | 103 | R3 | 2.962 | 0.5634 |

80.4 | 0 | 189 | R1 | 3.128 | 0.5595 |

79.7 | 0 | 201 | R2 | 3.124 | 0.5627 |

80.5 | 0 | 197 | R3 | 3.119 | 0.5627 |

63.4 | 1 | 105 | R1 | 2.889 | 0.5595 |

65.2 | 1 | 98 | R2 | 2.888 | 0.5627 |

62.8 | 1 | 106 | R3 | 2.879 | 0.5627 |

69.1 | 1 | 198 | R1 | 3.065 | 0.5595 |

68.5 | 1 | 204 | R2 | 3.051 | 0.5631 |

69.2 | 1 | 189 | R3 | 3.063 | 0.5624 |

46.9 | 3 | 102 | R1 | 2.745 | 0.5595 |

48.2 | 3 | 104 | R2 | 2.735 | 0.5627 |

46.5 | 3 | 105 | R3 | 2.738 | 0.5636 |

52.5 | 3 | 194 | R1 | 2.943 | 0.5595 |

52.1 | 3 | 198 | R2 | 2.926 | 0.5640 |

52.6 | 3 | 189 | R3 | 2.941 | 0.5621 |

34.3 | 5 | 98 | R1 | 2.663 | 0.5595 |

35.2 | 5 | 97 | R2 | 2.651 | 0.5632 |

33.9 | 5 | 108 | R3 | 2.642 | 0.5647 |

39.9 | 5 | 198 | R1 | 2.825 | 0.5595 |

39.6 | 5 | 194 | R2 | 2.801 | 0.5647 |

40.0 | 5 | 197 | R3 | 2.818 | 0.5625 |

**Table 5.**Raw data of fitting parameters “q” and “b” in Equation (2) as affected by the number of tractor wheel passes on the plowed soil surface and the tillage depth for the chisel plow.

Soil MWD (mm) | Number of Tractor Wheel Passes on the Plowed Soil Surface (-) | Tillage Depth (mm) | Replicates | “q” (mm/min^{b}) | “b” (Dimensionless) |
---|---|---|---|---|---|

43.0 | 0 | 104 | R1 | 2.918 | 0.546 |

44.2 | 0 | 107 | R2 | 2.900 | 0.551 |

42.6 | 0 | 106 | R3 | 2.900 | 0.551 |

45.8 | 0 | 195 | R1 | 2.976 | 0.546 |

45.4 | 0 | 203 | R2 | 2.971 | 0.550 |

45.9 | 0 | 198 | R3 | 2.966 | 0.550 |

36.1 | 1 | 107 | R1 | 2.626 | 0.546 |

37.2 | 1 | 102 | R2 | 2.623 | 0.550 |

35.8 | 1 | 114 | R3 | 2.615 | 0.550 |

39.4 | 1 | 207 | R1 | 2.827 | 0.546 |

39.1 | 1 | 197 | R2 | 2.812 | 0.551 |

39.5 | 1 | 207 | R3 | 2.824 | 0.550 |

26.8 | 3 | 104 | R1 | 2.469 | 0.546 |

27.5 | 3 | 103 | R2 | 2.457 | 0.550 |

26.5 | 3 | 98 | R3 | 2.460 | 0.551 |

30.0 | 3 | 187 | R1 | 2.658 | 0.546 |

29.7 | 3 | 197 | R2 | 2.639 | 0.552 |

30.0 | 3 | 198 | R3 | 2.655 | 0.550 |

19.5 | 5 | 102 | R1 | 2.345 | 0.546 |

20.1 | 5 | 99 | R2 | 2.332 | 0.551 |

19.3 | 5 | 108 | R3 | 2.322 | 0.553 |

22.8 | 5 | 201 | R1 | 2.551 | 0.546 |

22.6 | 5 | 194 | R2 | 2.526 | 0.553 |

22.8 | 5 | 198 | R3 | 2.543 | 0.550 |

**Table 6.**Raw data of fitting parameters “q” and “b” in Equation (2) as affected by the number of tractor wheel passes on the plowed soil surface and the tillage depth for the rotary plow.

Soil MWD (mm) | Number of Tractor Wheel Passes on the Plowed Soil Surface (-) | Tillage Depth (mm) | Replicates | “q” (mm/min^{b}) | “b” (Dimensionless) |
---|---|---|---|---|---|

20.2 | 0 | 98 | R1 | 2.679 | 0.5424 |

20.8 | 0 | 104 | R2 | 2.660 | 0.5475 |

20.0 | 0 | 103 | R3 | 2.660 | 0.5471 |

21.5 | 0 | 195 | R1 | 2.813 | 0.5424 |

21.4 | 0 | 198 | R2 | 2.808 | 0.5464 |

21.6 | 0 | 198 | R3 | 2.803 | 0.5463 |

17.0 | 1 | 104 | R1 | 2.599 | 0.5424 |

17.5 | 1 | 111 | R2 | 2.595 | 0.5464 |

16.8 | 1 | 109 | R3 | 2.587 | 0.5463 |

18.5 | 1 | 198 | R1 | 2.701 | 0.5424 |

18.4 | 1 | 196 | R2 | 2.684 | 0.5469 |

18.5 | 1 | 198 | R3 | 2.696 | 0.5461 |

12.6 | 3 | 97 | R1 | 2.469 | 0.5424 |

12.9 | 3 | 98 | R2 | 2.457 | 0.5463 |

12.5 | 3 | 97 | R3 | 2.460 | 0.5475 |

14.1 | 3 | 197 | R1 | 2.593 | 0.5424 |

14.0 | 3 | 195 | R2 | 2.574 | 0.5480 |

14.1 | 3 | 189 | R3 | 2.589 | 0.5457 |

9.2 | 5 | 104 | R1 | 2.296 | 0.5424 |

9.4 | 5 | 98 | R2 | 2.283 | 0.5471 |

9.1 | 5 | 108 | R3 | 2.272 | 0.5490 |

10.7 | 5 | 198 | R1 | 2.411 | 0.5424 |

10.6 | 5 | 187 | R2 | 2.385 | 0.5491 |

10.7 | 5 | 187 | R3 | 2.402 | 0.5463 |

**Table 7.**Source of variation, degrees of freedom (DF) and probability (p-values) from ANOVA table for e fitting parameters “q” and “b” in Equation (2).

Source of Variation | DF | p-Values | |
---|---|---|---|

“q” (mm/min^{b}) | “b” (Dimensionless) | ||

TI | 2 | <0.0001 | <0.0001 |

NTT | 3 | 0.0152 | 0.9868 |

TD | 1 | 0.0902 | 0.2770 |

$\mathrm{T}\mathrm{I}\times \mathrm{N}\mathrm{T}\mathrm{T}$ | 6 | 0.9950 | 1.000 |

$\mathrm{T}\mathrm{I}\times \mathrm{T}\mathrm{D}$ | 2 | 0.9714 | 0.9954 |

$\mathrm{N}\mathrm{T}\mathrm{T}\times \mathrm{T}\mathrm{D}$ | 3 | 0.9967 | 0.9355 |

$\mathrm{T}\mathrm{I}\times \mathrm{N}\mathrm{T}\mathrm{T}\times \mathrm{T}\mathrm{D}$ | 6 | 1.0000 | 1.000 |

**Table 8.**Mean fitting parameters (Equation (2)), as affected by tillage implements, number of wheel passes (soil compaction level) and tillage depths, and least significance difference (LSD) (Means are significantly different if they are followed by a distinct letter).

Treatments | Mean Fitting Parameters | |
---|---|---|

“q” (mm/min^{b}) | “b” (Dimensionless) | |

Moldboard plow | 2.89736 a | 0.5619581 a |

Chisel plow | 2.66316 b | 0.5493522 b |

Rotary plow | 2.56147 c | 0.5454777 c |

LSD (5%) | 0.0782 | 0.0015 |

Soil compaction level-0 | 2.78313 a | 0.5521947 a |

Soil compaction level-1 | 2.73002 ba | 0.5521412 a |

Soil compaction level-3 | 2.67475 b | 0.5522829 a |

Soil compaction level-5 | 2.64142 b | 0.5524318 a |

LSD (5%) | 0.0903 | 0.0017 |

Tillage depth (200 mm) | 2.73479 a | 0.5525892 a |

Tillage depth (100 mm) | 2.67987 a | 0.5519362 a |

LSD (5%) | 0.0639 | 0.0012 |

Regression Algorithm | WEKA Information |
---|---|

M5Rules | Scheme: weka.classifiers.rules.M5Rules -M 4.0 |

Additive Regression | Scheme: weka.classifiers.meta.AdditiveRegression -S 1.0 -I 10 -W weka.classifiers.trees.DecisionStump |

KStar (K*) | Scheme: weka.classifiers.lazy.KStar -B 20 -M a |

Gaussian Processes | Scheme: weka.classifiers.functions.GaussianProcesses -L 1.0 -N 0 -K “weka.classifiers.functions.supportVector.RBFKernel -C 250007 -G 1.0” |

SMOreg | Scheme: weka.classifiers.functions.SMOreg -C 1.0 -N 0 -I “weka.classifiers.functions.supportVector.RegSMOImproved -L 0.001 -W 1 -P 1.0E-12 -T 0.001 -V” -K “weka.classifiers.functions.supportVector.PolyKernel -C 250007 -E 1.0” |

LR | Scheme: weka.classifiers.functions.LinearRegression -S 0 -R 1.0E-8 |

MLP | Scheme: weka.classifiers.functions.MultilayerPerceptron -L 0.3 -M 0.2 -N 500 -V 0 -S 0 -E 20 -H a |

Regression Algorithm | “q” (mm/min^{b}) | “b” (Dimensionless) |
---|---|---|

Gaussian Processes | 1.60 | 1.62 |

Linear Regression | 0.01 | 0.01 |

Multilayer Perceptron | 0.15 | 0.17 |

SMOreg | 0.01 | 0.04 |

KStar (K*) | 0.00 | 0.00 |

Additive Regression | 0.03 | 0.02 |

M5Rules | 0.25 | 0.25 |

**Table 11.**The statistical data of evaluation criteria between actual and predicted values of the fitting parameters of “q” and “b” in Equation (2) using different regression algorithms using testing dataset.

Regression Algorithm | “q” (mm/min^{b}) | “b” (Dimensionless) | ||||
---|---|---|---|---|---|---|

MAE | RMSE | Correlation Coefficient | MAE | RMSE | Correlation Coefficient | |

M5Rules | 0.0575 | 0.0702 | 0.946 | 0.0021 | 0.0028 | 0.808 |

Additive Regression | 0.0459 | 0.0638 | 0.926 | 0.0026 | 0.0042 | 0.564 |

KStar (K*) | 0.0179 | 0.0228 | 0.997 | 0.0021 | 0.0027 | 0.805 |

SMOreg | 0.0373 | 0.0771 | 0.948 | 0.0019 | 0.0026 | 0.828 |

Multilayer Perceptron (MLP) | 0.0425 | 0.0910 | 0.951 | 0.0013 | 0.0026 | 0.962 |

Linear Regression (LR) | 0.0544 | 0.0667 | 0.947 | 0.0023 | 0.0029 | 0.786 |

Gaussian Processes | 0.0604 | 0.0817 | 0.959 | 0.0033 | 0.0042 | 0.711 |

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**MDPI and ACS Style**

Abdel-Sattar, M.; Al-Obeed, R.S.; Al-Hamed, S.A.; Aboukarima, A.M.
Experimental and Modeling Evaluation of Impacts of Different Tillage Practices on Fitting Parameters of Kostiakov’s Cumulative Infiltration Empirical Equation. *Water* **2023**, *15*, 2673.
https://doi.org/10.3390/w15142673

**AMA Style**

Abdel-Sattar M, Al-Obeed RS, Al-Hamed SA, Aboukarima AM.
Experimental and Modeling Evaluation of Impacts of Different Tillage Practices on Fitting Parameters of Kostiakov’s Cumulative Infiltration Empirical Equation. *Water*. 2023; 15(14):2673.
https://doi.org/10.3390/w15142673

**Chicago/Turabian Style**

Abdel-Sattar, Mahmoud, Rashid S. Al-Obeed, Saad A. Al-Hamed, and Abdulwahed M. Aboukarima.
2023. "Experimental and Modeling Evaluation of Impacts of Different Tillage Practices on Fitting Parameters of Kostiakov’s Cumulative Infiltration Empirical Equation" *Water* 15, no. 14: 2673.
https://doi.org/10.3390/w15142673