^{1}

^{*}

^{1}

^{*}

^{2}

^{*}

^{3}

^{*}

In this research, a gamma ray sensor (The Mole) was used to get the natural radionuclides concentration in *situ* in the surface layer of cultivated soils. For sand, silt and clay predictions, an adaptive neuro fuzzy inference system (ANFIS) was performed to predict such fractions (Sugeno model). The inputs to the system were Potassium (^{40}K), Uranium (^{238}U), Thorium (^{232}Th) and Cesium (^{137}Cs) concentrations. It is concluded that ANFIS structure is acceptable in the prediction of sand, silt and clay considering the studied inputs. Test results and predicted outcomes were compared and acceptable correlations were obtained.

Soil texture refers to the percentage by weight of sand (particles between 0.05 to 2.0 mm), silt (0.002 to 0.05 mm), and clay (<0.002 mm) in a soil sample. It is based on that part of a field dried soil sample that passes through a 2-mm sieve. Soil texture is also classified by a soil’s particle size fractions (sand, silt and clay) [

The quantitative method for determining soil texture is by using special soil sieves with meshes of different grades. It is found that direct measurement of soil texture components is time consuming and relatively expensive. In the conventional procedure, a pre-weighed sample of dried soil is put on top of a column of the sieves and shaken for 30 minutes. The soil collected in each progressively smaller mesh sieve is carefully collected and weighed, and distributions of the various size soil particles can calculated as a percent of the total weight of the sample. Another quantitative method for determining soil texture uses special hydrometers that measure the density of a suspended soil solution over time as the soil particles settle. Indirect methods for determining soil texture are used as an alternative solution. They are based on developing predictive equations for the fraction of sand, silt, and/or clay at the soil surface. They can be achieved with varying levels of success reflectance measurements over tilled fields [

Soil texture influences the suitability of the soil as a medium for rooting [

The laboratory or field determination of sand, silt and clay is often very difficult, expensive and requires devices. Therefore mathematical modeling techniques must be suggested for determination of such fractions. In the research conducted by van Egmond et al. [^{232}Th. On the other hand, soft computing techniques are widely applied to soil science. One of them is fuzzy logic which is particularly attractive due to its ability to solve problems in the absence of accurate mathematical models [

The measurement of the natural radionuclides concentration in a soil can be influenced by the fractions of the grain size of the soil [

(ANFIS) in the prediction of sand, silt and clay values of soils. The data from field experiments conducted in this study were used for training and testing of the ANFIS. The inputs were natural radionuclides concentration in the surface layer of cultivated soils at different regions in Saudi Arabia. They were of ^{40}K, ^{238}U, ^{232}Th and ^{137}Cs.

Natural radionuclides concentrations using gamma-ray spectrometer (The Mole) in situ were investigated to correlate them with soil fractions. The measurements of natural radionuclides concentration, in the surface layer of seven regions, in Saudi Arabia were achieved. These regions include: Al-Kharj, Al-Qassim, Wadi Aldawaser, Hail, Aljouf, Tabuk and Riyadh. Different soil surfaces were scanned by the Mole in each region. The length of the scanned area was about 100 m and the width was about 1 m. The distance between the detector and the soil surface was about 1 m. Ten samples were taken for soil particles analysis form each region. Soil particles analysis determined in laboratory according to standard methods.

Studied region | Sample No. | Latitude | Longitude | Sand | Silt | Clay | ^{40}K | ^{238}U | ^{232}Th | ^{137}Cs |
---|---|---|---|---|---|---|---|---|---|---|

˚N | ˚E | % | % | % | Bq/kg | Bq/kg | Bq/kg | Bq/kg | ||

Al-Qassim | 1 | 26.21 | 43.89 | 72.8 | 15.2 | 12.0 | 283.11 | 23.61 | 27.96 | 4.62 |

2 | 26.41 | 43.82 | 88.8 | 7.2 | 4.0 | 163.16 | 27.45 | 20.19 | 4.09 | |

3 | 26.44 | 43.69 | 88.9 | 8.1 | 3.0 | 153.98 | 22.07 | 24.95 | 4.25 | |

4 | 26.43 | 43.71 | 84.8 | 10.2 | 5.0 | 241.53 | 28.04 | 33.65 | 4.88 | |

Tabuk | 1 | 28.40 | 36.87 | 80.6 | 9.4 | 10.0 | 313.39 | 45.67 | 45.28 | 16.51 |

2 | 28.40 | 36.87 | 75.7 | 12.3 | 12.0 | 310.45 | 48.06 | 60.55 | 16.09 | |

3 | 28.40 | 36.80 | 68.5 | 17.5 | 14.0 | 350.18 | 42.20 | 64.10 | 18.68 | |

4 | 28.40 | 36.78 | 63.6 | 16.4 | 20.0 | 311.20 | 77.84 | 113.15 | 19.91 | |

5 | 28.43 | 36.62 | 63.8 | 15.2 | 21.0 | 338.37 | 76.46 | 75.59 | 21.19 | |

Al-Kharj | 1 | 24.32 | 47.13 | 82.2 | 9.9 | 7.9 | 159.48 | 18.42 | 13.42 | 4.12 |

2 | 24.18 | 47.22 | 86.4 | 8.8 | 4.8 | 204.80 | 17.49 | 25.03 | 4.59 | |

3 | 24.26 | 47.26 | 75.3 | 16.7 | 8.0 | 141.11 | 16.88 | 12.45 | 3.55 | |

4 | 24.21 | 47.57 | 71.8 | 17.2 | 11.0 | 129.20 | 18.81 | 12.26 | 3.94 | |

5 | 24.20 | 47.56 | 85.7 | 7.3 | 7.0 | 103.24 | 19.38 | 15.00 | 3.03 | |

Wadi Aldawaser | 1 | 20.42 | 44.74 | 74.8 | 17.2 | 8.0 | 199.12 | 21.05 | 20.14 | 5.54 |

2 | 20.43 | 44.73 | 80.3 | 15.7 | 4.0 | 217.15 | 23.30 | 24.62 | 5.52 | |

3 | 20.42 | 44.71 | 79.7 | 16.3 | 4.0 | 195.98 | 23.75 | 24.81 | 5.17 | |

4 | 20.44 | 44.74 | 84.4 | 12.6 | 3.0 | 169.92 | 22.25 | 27.69 | 4.79 | |

Aljouf | 1 | 29.99 | 40.12 | 88.8 | 7.2 | 4.0 | 234.23 | 29.63 | 25.19 | 11.46 |

2 | 30.00 | 40.12 | 80.7 | 8.3 | 11.0 | 565.57 | 41.78 | 54.35 | 18.06 | |

Hail | 1 | 27.79 | 41.73 | 74.1 | 15.9 | 10.0 | 518.03 | 51.01 | 56.76 | 19.75 |

2 | 27.80 | 41.75 | 77.3 | 13.7 | 9.0 | 492.63 | 43.73 | 36.18 | 13.96 | |

3 | 27.80 | 41.75 | 71.7 | 15.3 | 13.0 | 477.64 | 71.95 | 55.78 | 23.63 | |

4 | 27.82 | 41.73 | 65.9 | 20.1 | 14.0 | 644.54 | 49.58 | 47.62 | 18.77 | |

Riyadh | 1 | 24.41 | 46.65 | 84.6 | 12.4 | 3.0 | 185.30 | 21.28 | 17.23 | 10.45 |

2 | 24.41 | 45.89 | 86.5 | 9.5 | 4.0 | 221.63 | 19.83 | 19.21 | 9.44 | |

3 | 24.23 | 47.65 | 75.6 | 12.4 | 12.0 | 162.10 | 20.19 | 17.88 | 9.58 | |

4 | 24.33 | 47.14 | 83.2 | 9.8 | 7 | 114.65 | 12.88 | 10.42 | 4.81 |

The Mole is consisted of a detector, GPS and laptop and calibrated based on measurements of natural gamma radiation in a field [^{40}K, ^{238}U, ^{232}Th and ^{137}Cs.

ANFIS is a fuzzy mapping algorithm that is based on Tagaki-Sugeno-Kang (TSK) fuzzy inference system [

A conceptual ANFIS consists of five components: inputs and output database, a Fuzzy system generator, a Fuzzy Inference System (FIS), and an Adaptive Neural Network. The Sugeno-type Fuzzy Inference System [

Rule 1: If x_{1} is A_{1} and x_{2} is B_{1}, then f_{1} = a_{1}x_{1} + b_{1}x_{2} + q_{1}

Rule 2: If x_{1} is A_{2} and x_{2} is B_{2}, then f_{2} = a_{2}x_{1} + b_{2}x_{2} + q_{2}

where, x_{1} and x_{2} are the crisp inputs to the node and A_{1}, B_{1}, A_{2}, B_{2} are fuzzy sets, a_{i}, b_{i} and q_{i}(i = 1, 2) are the coefficients of the first-order polynomial linear functions. Structure of a two-input first-order Sugeno fuzzy model with two rules is shown in

Layer1: (Input nodes): Each node output in this layer is fuzzified by membership grade of a fuzzy set corresponding to each input.

where, x_{1} and x_{2} are the inputs to node i (i = 1, 2 for x_{1} and j = 1, 2 for x_{2}) and x_{1} (or x_{2}) is the input to the i^{th} node and A_{i} (or B_{j}) is a fuzzy label.

Layer 2: (Rule nodes): Each node output in this layer represents the firing strength of a rule, which performs fuzzy, AND operation. Each node in this layer, labeled Π, is a stable node which multiplies incoming signals and sends the product out.

Layer 3: (Average nodes): In this layer, the nodes calculate the ratio of the i^{th} rules firing strength to the sum of all rules firing strengths

Layer 4: (Consequent nodes): In this layer, the contribution of i^{th} rules towards the total output or the model output and/or the function calculated as follows:

where _{i}, b_{i}, q_{i} are the coefficients of linear combination in Sugeno inference system. These parameters of this layer are referred to as consequent parameters.

Layer 5: (Output nodes): The node output in this layer is the overall output of the system, which is the summation of all coming signals

ANFIS requires a training data set of desired input/output pair (x_{1}, x_{2}···x_{m }, Y) depicting the target system to be modeled. ANFIS adaptively maps the inputs (x_{1}, x_{2}···x_{m}) to the outputs (Y) through Membership Functions (MFs), the rule base and the related parameters emulating the given training data set. It starts with initial MFs, in terms of type and number, and the rule base that can be designed intuitively. In this study, the training process continues till the desired number of training steps (epochs) is achieved. Detailed information of ANFIS can be found in Jang [

There are no fixed rules for developing an ANFIS model [^{40}K, ^{238}U, ^{232}Th and ^{137}Cs which were measured in-situ were used as inputs and sand, silt and clay contents were used as outputs. The data in ANFIS are usually divided into two sets: training set and testing set. The training data are used for the training of ANFIS, while the testing data are used to evaluate the model performance. In this study (total of 31 observations) were divided into two data sets. The first data set containing 25 patterns of the records was used as the training data; the second data set containing 6 patterns of the records was applied as the testing data.

ANFIS model developed in this study using MATLAB toolbox (MATLAB 7.11.0.584 (R2010b)) has four inputs (^{40}K, ^{238}U, ^{232}Th and ^{137}Cs) and three outputs. Different MFs available in MATLAB toolbox and numbers were tested (data not included) and 5 “trimf” (triangle) MFs were elected for each input due to their small training error compared with other MFs. The numerical range was used for ^{40}K (103.2 - 644.5 Bq/kg), for ^{238}U (12.88 - 77.84 Bq/kg), for ^{232}Th (10.42 - 113.2 Bq/kg) and for ^{137}Cs (3.03 - 23.63 Bq/kg). The numerical range was used for sand (63.6% - 88.9%), for silt (7.2% - 20.1%) and for clay (3.0% - 21.0%).

In the training of the model, a “hybrid learning algorithm” was used and the number of epochs was chosen as 3. The number of the MFs is 5 for each input with five linguistic terms {very low, low, medium, high, very high} and the total rules were 625 (5 × 5 × 5 × 5). The number of nodes was 1297, of linear parameters was 3125, and of nonlinear parameters were 60. The total number of parameters was 3185 in the model. The error of the model was 0.00057268 for clay and the type of the membership function was “trimf”, output membership function is linear. For sand ANFIS model, the error was 0.000207015 and for silt ANFIS model, the error was 0.000378577.

After building and training the ANFIS models, in order to evaluate the accuracy of them, the predicted results were compared with experimental data. In fact, the coefficient of determination (R^{2}) between the measured and predicted values is a good indicator to check the prediction performance of the model [

where, Y and

The estimation of sand, silt and clay contents in a soil is highly important for soil and agricultural engineering researches; in particular for the determination of draft requirements in specified soil. As a result of this study, the variation of concentration of soil natural radionuclides namely, Potassium (^{40}K), Uranium (^{238}U), Thorium (^{232}Th) and Cesium (^{137}Cs) with the quantity of sand, silt and clay in a soil were investigated through experimental work. Figures 4-6 illustrate the relationship among sand, silt and clay contents and ^{40}K, ^{238}U, ^{232}Th and ^{137}Cs concentrations, respectively. The obtained values of activity concentration are in good agreement with the recommended values for background gamma radiation reported for soils worldwide [^{238}U, 16 - 64 for ^{232}Th, and 140 - 850 for ^{40}K.

The levels of detected radionuclides in soil surface layer in this research indicated variations among regions and this may be attributed to the diversity of formations and textures of the soil in the studied regions as reported by Saleh [^{238}U, ^{232}Th, ^{40}K and ^{137}Cs to soil type.

It is clear that increasing concentration of ^{40}K, ^{238}U, ^{232}Th and ^{137}Cs in soil surface layer results to decrease sand content in the soil, as illustrated in

due to larger pores the vertical mobility of radionuclides in the soil as reported by Golmakani et al. [^{40}K. Also, the variability of ^{40}K among regions could be due to the differences in land management, for example, fertilization, plowing practices, geology and geography [

It is noted that increasing concentration of ^{40}K, ^{238}U, ^{232}Th and ^{137}Cs in soil surface layer results to increase silt and clay contents in the soil, as illustrated in

To estimate the quantity of sand, silt and clay in a soil, an ANFIS model was developed. It uses ^{40}K, ^{238}U, ^{232}Th and ^{137}Cs concentrations as inputs. The experimental results and the results of the ANFIS method were compared. It was seen that the sand, silt and clay contents in the soil have various values depending on the quantity of natural radionuclides concentration. The relationships between experimental results and ANFIS model exhibited a good correlation for test set. The coefficients of determination were found to be R^{2} = 0.852 for the testing

data set with ANFIS model of sand prediction, R^{2} = 0.7631 for the testing data set with ANFIS model of slit prediction and R^{2} = 0.7788 for the testing data set with ANFIS model of clay prediction. Based on the results of the study, it could be said that the ANFIS method can be used for modeling of the sand, silt and clay of the soil according to the ^{40}K, ^{238}U, ^{232}Th and ^{137}Cs concentrations in the soil. The experimental and ANFIS results and correlations of sand, silt and clay are given in ^{40}K, ^{238}U, ^{232}Th and ^{137}Cs concentrations inputs have a weight on prediction of sand, silt and clay percentage of a soil.

In this study Adaptive Neural-based Fuzzy Inference System (ANFIS) was used for prediction of sand, silt and clay content in a soil using natural radionuclides concentration in it namely, Potassium (^{40}K), Uranium (^{238}U), Thorium (^{232}Th) and Cesium (^{137}Cs). The results showed that constructed ANFIS was effectively able to predict sand, silt and clay contents. The prediction accuracy of the model was fairly good (predictive ability and for the coefficient of correlation) based on the results of the testing data performance, and the calculated coefficient of correlation of training and testing data.

RMSE (%) | RMSE (%) | RMSE (%) | MAD (%) | MAD (%) | MAD (%) |
---|---|---|---|---|---|

Sand | Silt | Clay | Sand | Silt | Clay |

14.047 | 3.727 | 3.266 | 4.483 | 1.550 | 1.050 |

Authors express their gratitude to the National Plan for Science, Technology and Innovation Program, King Saud University, Saudi Arabia for financially supporting this research effort as a part of the project entitled “Modeling of energy consumption during seed bed preparation operation based on soil mechanical properties”, No. 09-SPA876-02.