Abstract

Various factors affect the development of social, cultural, and economic aspects of societies. One of these factors is the state of water resources. In this study, countries of the world with decreasing renewable water per capita were examined during the period 2005–2017. Specifically, 35, 5, 20, 48, 43, and 151 countries were selected from the American, Oceania, European, African, Asian continents, and the world respectively. Further, three hydro-socio-technology-knowledge indicators associated with demographic, technology, and knowledge dimensions were estimated with soft-computing methods (i.e. Group Method of Data Handling (GMDH), Radial Basis Function (RBF), and Regression Trees (R Trees)) for the world's continents). The GMDH model's performance was the best among the other soft-computing methods in estimating the hydro-socio-technology-knowledge indicators for all the world's continents based on statistical criteria (coefficient of determination (R2), root mean square error (RMSE) and mean absolute error (MAE)). The values of RMSE for GMDH models for the ratio of rural to urban population (PRUP), population density (PD), number of internet users (IU) and education index (EI) indicators equaled (0.291, 0.046, 0.127, 0.199), (0.094, 0.023, 0.174, 0.137), (0.237, 0.044, 0.166, 0.225), (0.173, 0.031, 0.126, 0.163), (0.218, 0.058, 0.142, 0.196) and (0.231, 0.049, 0.167, 0.195) for America, Oceania, Europe, Africa, Asia and the world, respectively. The results indicate that there is an interaction between socio-technology-knowledge indicators. Thus, for water resources in all continents and the world, the hydro-socio-technology-knowledge indicators can be used for proper planning and management of water resources.

HIGHLIGHTS

  • Investigated the relationship between hydro-socio-technology-knowledge sciences using soft-computing techniques.

  • Indicators of demographic, technology and knowledge dimensions are estimated according to the water resources for each continent and the world.

  • The interaction of socio-technology-knowledge indicators with renewable water per capita in each continent and the world.

INTRODUCTION

Water is an essential resource for human societies to survive, which is unequally accessible in the world (Fang et al. 2007; Vittala et al. 2008). Increasing population and technological-economic advances have led to excessive use of water and the destruction of related ecosystems. Therefore, sustainable management of water resources in the world is essential (Ortega-Reig et al. 2014; El Khanji 2017; Lazaridou et al. 2019; Rebai & Mastere 2020). There are various definitions of water scarcity, and water shortages due to natural or human causes are a broad topic (Pereira et al. 2002; Rijsberman 2006). Thus, the term ‘water scarcity’ does not cover all factors and dimensions related to the true meaning of these phenomena, namely social, infrastructural, and economic dimensions. Therefore, ‘water poverty’ is a new term and concept to cover various dimensions very important for humans (Sullivan et al. 2003).

In recent years, soft computing techniques such as an Artificial Neural Network (ANN), Adaptive Neural-Fuzzy Inference System (ANFIS), Group Method of Data Handling (GMDH), M5 tree model, Support Vector Machine (SVM), Regression Trees (RT), and Radial Base Performance (RBF) have been used in research related to water resources (Najafzadeh 2015; Sanikhani et al. 2015; Ivani et al. 2016; Montaseri et al. 2018; Zamanzad-Ghavidel et al. 2020).

Park et al. (2015) evaluated the efficiency of RT in the development of a stressor–response model for chlorophyll-a (Chl-a) concentrations, using the results from site-specific mechanistic water quality modeling. Finally, regression tree models yielded acceptable results from the stressor-response relationship for chlorine and its sensitivity. Ghorbani et al. (2016) examined the application of multilayer perceptron (MLP), RBF, and SVM for river flow prediction in time series. The results of time series prediction of river flow using the MLP and RBF models showed better performance than the SVM model. On the other hand, the SVM model showed less uncertainty in prediction than the RBF and MLP models. Tornabene et al. (2016) used differential squares of moving minimum squares (MLSDQ) method based on RBF to solve two-way curved shells made of composite materials and provided excellent results. Likewise, Talebi et al. (2017) investigated the load of suspended sediment in the watershed of Hyderabad, which is located in western Iran, using RT and model (MT) trees. Results of the comparison showed that RT and MT performed better in the study area than ANN and Sediment Ranking Curve methods. Kutyłowska (2017) used the RT method to predict the rate of failure of water distribution pipes and home connections and obtained a high correlation between predicted and observed failure rates of water ducts. The results of a data-driven approach for modeling and predicting wastewater flow showed that RT provides enhanced skillful predictions compared to an existing numerical model (Hu et al. 2018). To predict the groundwater level, Barzegar et al. (2017) evaluated the performance of different hybrid wavelet-group methods of data handling (WA-GMDH) and wavelet-extreme learning machine (WA-ELM) and showed that the ELM model performed better than the GMDH. They also showed that the use of wave-based models improved the performance of GMDH and ELM models for groundwater level prediction. Ebtehaj et al. (2018) used a Genetic Algorithm (GA) to identify the best choice of membership functions in an adaptive neural and fuzzy inference system (ANFIS), and evolutionary design is a general group method of data manipulation structure (GMDH) to predict a coefficient. They used lateral overflow drainage, and the results showed that ANFIS-GA/SVD performance is better than ANFIS-GA, GMDH-GA/SVD, GMDH-GA, and regression-based and regression-based learning equations. Mehri et al. (2019) used GMDH and DGMDH methods to predict the Cd discharge coefficient (lateral overflow of the piano key) and compared it with experimental data. The results showed that the DGMDH algorithm performs better than the other technique (GMDH). Moosavi (2019) used the Data Processing Group (GMDH) method in addition to signal processing approaches to predict rainfall in monthly time stages. For this purpose, three different signal processing approaches were used, namely the experimental state analysis group (EEMD), wavelet conversion (WT), and wavelet packet conversion (WPT) along with the GMDH model. The results of this study showed that all three of the above approaches to signal to the process could enhance the ability of the GMDH model. Zhang et al. (2019) presented a combined model based on VMD-WT and PCA-BP-RBF neural networks to increase the accuracy of short-term wind speed forecasting. Using the PCA-BP method to filter model input data, waste, and irrelevant information is lost, model complexity is reduced, and RBF predictive performance is improved. Compared to other traditional models, the combined model presented in this paper has dramatically improved accuracy in predicting short-term wind speeds. Saberi-Movahed et al. (2020) modified the overall structure of the data mining group method (GMDH) using Limit Learning Machines (ELM) to obtain accurate LDC predictions. Inspired by ELM, they introduced a new GMDH method called GMDH-based GMDH-ELM. Finally, the results showed that GMDH-ELM was far superior to other soft software tools and conventional predictive models. Li et al. (2020) proposed a hybrid model based on the Singular Spectrum Analysis (SSA) method, Group Method of Data Handling (GMDH) neural network, Weighted Integration based on Accuracy and Diversity (WIAD) and Kernel Extreme Learning Machine (KELM) algorithm, namely the SSA-WIAD GMDH-KELM model, to achieve the predicting of river water level. The results showed that the performance of the SSA-WIAD-GMDH-KELM model is satisfactory for predicting river water levels, the GMDH model has excellent predictive performance, and both WIAD and KELM methods can effectively improve the forecast precision of the model. Other researchers who investigated the Hydro-socio-technology-knowledge dimensions integrated with water resources management could be mentioned Fang et al. (2007), Vittala et al. (2008), Bouleau & Pont (2015), Jordanova et al. (2015), Reidsma et al. (2015), Pires et al. (2017), El Khanji (2017), Honti et al. (2017), O'Connell (2017), Odhiambo (2017), Baki et al. (2018), Lazaridou et al. (2019) and Rebai & Mastere (2020).

Hydro-socio-technology-knowledge science examines the relationship between water science and the social sciences. The innovations of this research are: (1) application of three soft-computing techniques (Group Method of Data Handling (GMDH), Radial Basis Function (RBF), and Regression Trees (R Trees)) to investigate the relationship between hydro-socio-technology-knowledge sciences; (2) formulation of four indicators of three demographic, technology and knowledge dimensions (The ratio of rural to urban population (PRUP), population density (PD), the number of internet users (IU) and education index (EI)) are estimated according to the water resources of each continent and the world; and (3) interaction of socio-technology-knowledge indicators with renewable water per capita in each continent, and the world.

METHODOLOGY

Selected indicators and case studies

The renewable water per capita (RWPC) is herein chosen as the overall indicator of water resources status. The indicators corresponding to demographic, technology and knowledge dimensions are the ratio of rural to urban population (PRUP) and population density (PD), the number of internet users (IU), and education index (EI) indicators, respectively. The selected socio-technology-knowledge indicators (Zamanzad-Ghavidel 2020; Zamanzad-Ghavidel et al. 2020) have a significant Pearson correlation (sig = 0.000) with RWPC. In the current research, countries of the world with decreasing renewable water per capita are selected as case studies. The statistical period of study is 13 years (2005–2017). The names of the study countries on each continent, America, Oceania, Europe, Africa, Asia, and the world are listed in Table 1, which includes 35, 5, 20, 48, 43, and 151 countries across multiple weather conditions, respectively. Here, 70% of the countries of each continent and the world are used for model training and 30% for model testing, randomly. The data information used in this research is extracted from the database (https://knoema.com). Table 2 shows the statistical characteristics of the hydro-socio-technology-knowledge indicators such as average (Mean), standard deviation (S), and coefficient of variation (CV). The standard deviation of renewable water per capita was equal (0.317, 0.315, 0.329, 0.314, and 0.324) for America, Oceania, Europe, Africa, and Asia, respectively. Europe has the minimum amount of CV for PRUP, PD, IU, and EI indicators among other continents.

Table 1

Countries included in this study in the training and testing periods

No.ContinentsCountries
America Train United States of America, Mexico, Canada, Cuba, Guatemala, Haiti, Honduras, Dominican Republic, El Salvador, Costa Rica, Nicaragua, Panama, Jamaica, Trinidad and Tobago, Bahamas, Belize, Barbados, Saint Lucia, Saint Vincent and the Grenadines, Grenada, Antigua and Barbuda, Dominica, Argentina, Bolivia, Brazil 
Test Chile, Colombia, Ecuador, Guyana, Paraguay, Peru, Saint Kitts and Nevis, Suriname, Uruguay, Venezuela 
Oceania Train Australia, Fiji, New Zealand 
Test Solomon Islands, Vanuatu 
Europe Train Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands, Norway 
Test Slovakia, Slovenia, Spain, Sweden, Switzerland, United Kingdom 
Africa Train  Algeria, Angola, Benin, Botswana, Burkina Faso, Burundi, Cabo Verde, Cameroon, Central African Republic, Chad, Comoros, Congo, Côte d'Ivoire, Djibouti, Equatorial Guinea, Eswatini, Ethiopia, Gabon, Gambia, Ghana, Guinea, Guinea Bissau, Kenya, Lesotho, Liberia, Libya, Madagascar, Malawi, Mali, Mauritania, Mauritius, Mozambique, Namibia, Niger 
Test Nigeria, Rwanda, Sao Tome and Principe, Senegal, Sierra Leone, South Africa, Sudan, Togo, Tunisia, Uganda, United Republic of Tanzania, Zambia, Zimbabwe, Morocco 
Asia Train Afghanistan, Azerbaijan, Bahrain, Bangladesh, Brunei Darussalam, Cambodia, China, Cyprus, Egypt, India, Indonesia, Iran, Iraq, Israel, Jordan, Kazakhstan, Kyrgyzstan, Lao People's Democratic Republic, Lebanon, Malaysia, Maldives, Mongolia, Myanmar, Nepal, Oman, Pakistan, Papua New Guinea, Philippines, Qatar, Russian Federation 
Test Saudi Arabia, Singapore, Sri Lanka, Tajikistan, Thailand, Timor-Leste, Turkey, Turkmenistan, United Arab Emirates, Uzbekistan, Viet Nam, Yemen, Palestine 
No.ContinentsCountries
America Train United States of America, Mexico, Canada, Cuba, Guatemala, Haiti, Honduras, Dominican Republic, El Salvador, Costa Rica, Nicaragua, Panama, Jamaica, Trinidad and Tobago, Bahamas, Belize, Barbados, Saint Lucia, Saint Vincent and the Grenadines, Grenada, Antigua and Barbuda, Dominica, Argentina, Bolivia, Brazil 
Test Chile, Colombia, Ecuador, Guyana, Paraguay, Peru, Saint Kitts and Nevis, Suriname, Uruguay, Venezuela 
Oceania Train Australia, Fiji, New Zealand 
Test Solomon Islands, Vanuatu 
Europe Train Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands, Norway 
Test Slovakia, Slovenia, Spain, Sweden, Switzerland, United Kingdom 
Africa Train  Algeria, Angola, Benin, Botswana, Burkina Faso, Burundi, Cabo Verde, Cameroon, Central African Republic, Chad, Comoros, Congo, Côte d'Ivoire, Djibouti, Equatorial Guinea, Eswatini, Ethiopia, Gabon, Gambia, Ghana, Guinea, Guinea Bissau, Kenya, Lesotho, Liberia, Libya, Madagascar, Malawi, Mali, Mauritania, Mauritius, Mozambique, Namibia, Niger 
Test Nigeria, Rwanda, Sao Tome and Principe, Senegal, Sierra Leone, South Africa, Sudan, Togo, Tunisia, Uganda, United Republic of Tanzania, Zambia, Zimbabwe, Morocco 
Asia Train Afghanistan, Azerbaijan, Bahrain, Bangladesh, Brunei Darussalam, Cambodia, China, Cyprus, Egypt, India, Indonesia, Iran, Iraq, Israel, Jordan, Kazakhstan, Kyrgyzstan, Lao People's Democratic Republic, Lebanon, Malaysia, Maldives, Mongolia, Myanmar, Nepal, Oman, Pakistan, Papua New Guinea, Philippines, Qatar, Russian Federation 
Test Saudi Arabia, Singapore, Sri Lanka, Tajikistan, Thailand, Timor-Leste, Turkey, Turkmenistan, United Arab Emirates, Uzbekistan, Viet Nam, Yemen, Palestine 
Table 2

The statistical characteristics of hydro-socio-technology-knowledge indicators used in the current study

ContinentsCharacteristicsDimensions
Indicators
Demographic
TechnologyKnowledgeHydro
PRUP (I1)PD (I2)IU (I3)EI (I4)RWPC
America Mean 0.525 0.498 0.499 0.550 0.484 
0.335 0.318 0.335 0.342 0.317 
CV 0.638 0.638 0.671 0.621 0.654 
Oceania Mean 0.467 0.472 0.482 0.579 0.492 
0.312 0.323 0.337 0.337 0.315 
CV 0.668 0.684 0.700 0.582 0.640 
Europe Mean 0.496 0.525 0.621 0.564 0.475 
0.329 0.330 0.310 0.345 0.329 
CV 0.329 0.330 0.310 0.345 0.329 
Africa Mean 0.512 0.478 0.393 0.582 0.473 
0.328 0.317 0.351 0.343 0.314 
CV 0.640 0.663 0.894 0.589 0.663 
Asia Mean 0.504 0.486 0.462 0.559 0.474 
0.338 0.328 0.352 0.351 0.324 
CV 0.670 0.675 0.762 0.628 0.683 
ContinentsCharacteristicsDimensions
Indicators
Demographic
TechnologyKnowledgeHydro
PRUP (I1)PD (I2)IU (I3)EI (I4)RWPC
America Mean 0.525 0.498 0.499 0.550 0.484 
0.335 0.318 0.335 0.342 0.317 
CV 0.638 0.638 0.671 0.621 0.654 
Oceania Mean 0.467 0.472 0.482 0.579 0.492 
0.312 0.323 0.337 0.337 0.315 
CV 0.668 0.684 0.700 0.582 0.640 
Europe Mean 0.496 0.525 0.621 0.564 0.475 
0.329 0.330 0.310 0.345 0.329 
CV 0.329 0.330 0.310 0.345 0.329 
Africa Mean 0.512 0.478 0.393 0.582 0.473 
0.328 0.317 0.351 0.343 0.314 
CV 0.640 0.663 0.894 0.589 0.663 
Asia Mean 0.504 0.486 0.462 0.559 0.474 
0.338 0.328 0.352 0.351 0.324 
CV 0.670 0.675 0.762 0.628 0.683 

Soft-computing techniques

Group method of data handling approaches (GMDH)

The GMDH model is one of the machine learning techniques that can be used in predicting environmental problems with water resources engineering. The operation of this model is self-organized in such a way that using the combination of all input variables, the best model is selected and the amount of error is calculated according to the previous layer. This algorithm is self-organizing (Onwubolu 2008; Rayegani & Onwubolu 2014).
formula
(1)
where ai is the coefficient and s is the vector number, in a way and so that p is the maximum power of a few sentences and k is the number of inputs.

This model can be introduced as a set of neurons in which different pairs in each layer are connected through several second- and third-order sentences, thus layer-by-layer neurons. Then the minimum accuracy is required by determining the appropriate number of neurons along with the appropriate existing layers. In fact, in the GMDH algorithm, a number of self-organized networks are created with multiple layers and each layer has several neurons (Onwubolu 2008; Rayegani & Onwubolu 2014; Garg 2015). This model offers the best solution through partial derivatives. The least-squares are used to determine the coefficients. In this algorithm, the partial models are increased during a complex process, and from among them a selected model with the appropriate complexity is presented.

Radial basis function approaches (RBF)

Another machine learning method is the RBF method, which is mostly used in computer engineering to process images. This model consists of two layers, in the hidden layer of which a linear mapping is performed, and in the output layer, the spectrum and the input data of the spectrum are segmented (Schwenker et al. 2001; Er et al. 2002). The RBF transfer function can be seen in Equation (2):
formula
(2)
where M represents the number of base functions and the vector X of the input data and the weighted relationship between the base function and the output. The noted the nonlinear function in unit and is an arc shape shown in relation (3) where x and are input and is the center of the Gaussian function (Er et al. 2002; Sarra 2005).
formula
(3)

Regression trees approaches (R tree)

The tree regression model is a binary decision tree that has linear regression relations at each end node (leaf) that can predict numerical values. The production of a tree model takes place in two stages: the first stage involves determining the most appropriate entry parameter for the branch and the need for a division (criterion) for the production of a decision tree. In this method, the data is divided into different parts by predictive variables so that the predicted variables (answers) are constant in almost every region. The regression tree contains questions with the answer yes or no. This method can also be assumed to be a simple form of a set of if-then questions to estimate the values of the answers for a given set of prediction values. Each question asks whether a predictor satisfies certain conditions. Depending on the type of answer to a question, it is either transferred to another question or a certain amount of appropriate answer is obtained (Breiman et al. 1984). The mathematical foundations of this method are explained in Breiman et al. (1984).

In the current study, socio-technology-knowledge indicators such as PRUP, PD, IU, and EI are estimated with RWPC; also, to achieve the interaction of hydro-socio-technology-knowledge indicators, the RWPC is estimated with PRUP, PD, IU, and EI indicators using soft-computing methods of GMDH, RBF, and R Tree in America, Oceania, Europe, Africa, Asia, and the world, respectively. The components of this research methodology are shown in Figure 1.

Figure 1

The methodology components of the current study.

Figure 1

The methodology components of the current study.

To improve the performance of model training, the data used in the current study included hydro-socio-technology-knowledge indicators, for each continent and the world, normalized in the range of 0–1 by Equation (4) (Ghavidel & Montaseri 2014):
formula
(4)

Here, XN, Xi, Xmin, and Xmax define the normalized value, the real value, minimal value, and the maximal value, respectively. Figure 2 shows the stages of the current study.

Evaluating models' performance

Three evaluation criteria, coefficient of determination (R2) (Akoglu 2018), root mean squared error (RMSE) (Kvalheim et al. 2018), and mean absolute error (MAE) (Willmott & Matsuura 2005), were applied in the current study to evaluate the models' performance. The R2, RMSE, and MAE are defined as:
formula
(5)
formula
(6)
formula
(7)
where and denote respectively the average of observed and estimated hydro-socio-technology-knowledge indicators' values, and denote respectively the observed and estimated hydro-socio-technology-knowledge indicators' values and N denotes the total number of data sets. The coefficient of determination (R2) shows the degree of adaptation of the data generated by the model and the actual data (Montaseri et al. 2018). In general, the models’ performances are optimum if R2 and RMSE are closer to 1 and 0, respectively (Chai & Draxler 2014; Zamanzad-Ghavidel et al. 2020). In this study, various graphical methods were used to evaluate and determine the optimal models.

RESULTS AND DISCUSSION

Evaluating indicators

By evaluating the hydro-socio-technology-knowledge indicators, it was determined that the rate of rural to urban population ratio is directly related to renewable water per capita, while population density, internet users, and education index are inversely related to renewable water per capita around the world. Therefore, with increasing rural to urban population ratio and decreasing population density, internet users, and education index, renewable water per capita indicator will increase. Conversely, with increasing population density, the per capita renewable water is decreased.

Evaluating and developing hydro-socio-technology-knowledge models

In order to estimate hydro-socio-technology-knowledge indicators around the world, three approaches have been used, namely GMDH, RBF, and R trees. Table 3 indicates the results of optimal model performance for estimating hydro-socio-technology-knowledge indicators such as proportion of rural to urban population (PRUP), population density (PD), internet users (IU), and education index (EI) that are denoted by I1 through I4, respectively, during the test period in the world's continents and in the whole of the world. Table 4 indicates the characteristics of the GMDH, RBF, and R trees optimal models. In GMDH models, the amount of maximum number of neurons in a layer, maximum number of layers and selection pressure for I1 through I4 indicators were equal to [(44, 15, 0.85), (47, 15, 0.88), (40, 14, 0.63), (47, 13, 0.86)], [(12, 6, 0.88), (11, 4, 0.95), (12, 5, 0.89), (10, 4, 0.91)], [(25, 14, 0.90), (32, 12, 0.87), (32, 11, 0.86), (28, 10, 0.81)], [(52, 21, 0.85), (51, 23, 0.85), (60, 20, 0.88), (65, 21, 0.87)], [(50, 39, 0.88), (43, 40, 0.89), (47, 44, 0.85), (47, 46, 0.90)], [(73, 38, 0.86), (78, 33, 0.85), (75, 34, 0.89), (76, 35, 0.85)], for America, Oceania, Europe, Africa, Asia and the world, respectively. The amount of spread and max neuron of RBF models for I1 through I4 indicators equaled [(0.49, 30), (0.44, 36), (0.48, 37), (0.44, 35)], [(0.49, 11), (0.50, 10), (0.48, 11), (0.45, 9)], [(0.51, 29), (0.54, 28), (0.60, 25), (0.48,24)], [(0.49, 54), (0.49, 56), (0.43, 57), (0.41, 51)], [(0.48, 30), (0.48, 31), (0.52, 37), (0.51, 33)], [(0.44, 63), (0.39, 63), (0.45, 61), (0.45, 64)], for America, Oceania, Europe, Africa, Asia, and the world, respectively. The number of leaf and branches of R Trees models for I1 through I4 indicators equaled [(7, 12), (8, 14), (8, 14), (8, 14)], [(5, 13), (4, 10), (7, 11), (7, 11)], [(4, 6), (5, 8), (4, 6), (5, 8)], [(11, 22), (13, 24), (12, 22), (12, 22)], [(10, 18), (9, 16), (11, 20), (11, 20)], [(33, 64), (31, 60), (32, 62), (32, 62)], for America, Oceania, Europe, Africa, Asia, and the world, respectively.

Table 3

The results of optimal models performance for estimating hydro-socio-technology-knowledge indicators

DimensionsEstimated indicators (Ii)ModelAmerica
Oceania
R2RMSEMAER2RMSEMAE
Demographic PRUP (I1GMDH1 0.248 0.291 0.218 0.951
 
0.094 0.083 
RBF1 0.237 0.292 0.227 0.789
 
0.170 0.145 
R Tree1 0.223 0.297 0.220 0.665
 
0.218 0.192 
PD (I2GMDH2 0.978 0.046 0.026 0.995
 
0.023 0.019 
RBF2 0.975 0.050 0.030 0.934
 
0.085 0.067 
R Tree2 0.961 0.062 0.047 0.864
 
0.115 0.090 
Technology IU (I3GMDH3 0.857 0.127 0.083 0.757
 
0.174 0.131 
RBF3 0.847 0.131 0.086 0.692
 
0.194 0.148 
R Tree3 0.828 0.139 0.099 0.501
 
0.249 0.204 
Knowledge EI (I4GMDH4 0.662 0.199 0.149 0.841
 
0.137 0.102 
RBF4 0.655 0.200 0.151 0.786
 
0.163 0.122 
R Tree4 0.657 0.200 0.150 0.652
 
0.201 0.151 
DimensionsEstimated indicators (Ii)ModelEurope
Africa
R2RMSEMAER2RMSEMAE
Demographic PRUP (I1GMDH1 0.479 0.237 0.192 0.717 0.173 0.097 
RBF1 0.418 0.249 0.203 0.713 0.174 0.098 
R Tree1 0.393 0.255 0.206 0.709 0.176 0.099 
PD (I2GMDH2 0.981 0.044 0.029 0.990 0.031 0.021 
RBF2 0.970 0.057 0.043 0.990 0.031 0.021 
R Tree2 0.944 0.078 0.062 0.989 0.032 0.022 
Technology IU (I3GMDH3 0.707 0.166 0.120 0.869 0.126 0.087 
RBF3 0.642 0.183 0.143 0.868 0.126 0.087 
R Tree3 0.636 0.185 0.144 0.872 0.124 0.084 
Knowledge EI (I4GMDH4 0.562 0.225 0.178 0.777 0.163 0.102 
RBF4 0.560 0.226 0.179 0.703 0.188 0.144 
R Tree4 0.544 0.230 0.181 0.764 0.168 0.105 
DimensionsEstimated indicators (Ii)ModelAsia
World
R2RMSEMAER2RMSEMAE
Demographic PRUP (I1GMDH1 0.589 0.218 0.142 0.519 0.231 0.155 
RBF1 0.567 0.224 0.147 0.509 0.233 0.158 
R Tree1 0.554 0.227 0.151 0.501 0.235 0.158 
PD (I2GMDH2 0.968 0.058 0.032 0.976 0.049 0.030 
RBF2 0.966 0.060 0.037 0.974 0.051 0.032 
R Tree2 0.954 0.069 0.044 0.974 0.051 0.031 
Technology IU (I3GMDH3 0.830 0.142 0.103 0.767 0.167 0.122 
RBF3 0.818 0.147 0.111 0.764 0.168 0.122 
R Tree3 0.819 0.147 0.106 0.768 0.167 0.120 
Knowledge EI (I4GMDH4 0.688 0.196 0.145 0.678 0.195 0.136 
RBF4 0.688 0.196 0.146 0.673 0.196 0.137 
R Tree4 0.666 0.203 0.150 0.666 0.200 0.139 
DimensionsEstimated indicators (Ii)ModelAmerica
Oceania
R2RMSEMAER2RMSEMAE
Demographic PRUP (I1GMDH1 0.248 0.291 0.218 0.951
 
0.094 0.083 
RBF1 0.237 0.292 0.227 0.789
 
0.170 0.145 
R Tree1 0.223 0.297 0.220 0.665
 
0.218 0.192 
PD (I2GMDH2 0.978 0.046 0.026 0.995
 
0.023 0.019 
RBF2 0.975 0.050 0.030 0.934
 
0.085 0.067 
R Tree2 0.961 0.062 0.047 0.864
 
0.115 0.090 
Technology IU (I3GMDH3 0.857 0.127 0.083 0.757
 
0.174 0.131 
RBF3 0.847 0.131 0.086 0.692
 
0.194 0.148 
R Tree3 0.828 0.139 0.099 0.501
 
0.249 0.204 
Knowledge EI (I4GMDH4 0.662 0.199 0.149 0.841
 
0.137 0.102 
RBF4 0.655 0.200 0.151 0.786
 
0.163 0.122 
R Tree4 0.657 0.200 0.150 0.652
 
0.201 0.151 
DimensionsEstimated indicators (Ii)ModelEurope
Africa
R2RMSEMAER2RMSEMAE
Demographic PRUP (I1GMDH1 0.479 0.237 0.192 0.717 0.173 0.097 
RBF1 0.418 0.249 0.203 0.713 0.174 0.098 
R Tree1 0.393 0.255 0.206 0.709 0.176 0.099 
PD (I2GMDH2 0.981 0.044 0.029 0.990 0.031 0.021 
RBF2 0.970 0.057 0.043 0.990 0.031 0.021 
R Tree2 0.944 0.078 0.062 0.989 0.032 0.022 
Technology IU (I3GMDH3 0.707 0.166 0.120 0.869 0.126 0.087 
RBF3 0.642 0.183 0.143 0.868 0.126 0.087 
R Tree3 0.636 0.185 0.144 0.872 0.124 0.084 
Knowledge EI (I4GMDH4 0.562 0.225 0.178 0.777 0.163 0.102 
RBF4 0.560 0.226 0.179 0.703 0.188 0.144 
R Tree4 0.544 0.230 0.181 0.764 0.168 0.105 
DimensionsEstimated indicators (Ii)ModelAsia
World
R2RMSEMAER2RMSEMAE
Demographic PRUP (I1GMDH1 0.589 0.218 0.142 0.519 0.231 0.155 
RBF1 0.567 0.224 0.147 0.509 0.233 0.158 
R Tree1 0.554 0.227 0.151 0.501 0.235 0.158 
PD (I2GMDH2 0.968 0.058 0.032 0.976 0.049 0.030 
RBF2 0.966 0.060 0.037 0.974 0.051 0.032 
R Tree2 0.954 0.069 0.044 0.974 0.051 0.031 
Technology IU (I3GMDH3 0.830 0.142 0.103 0.767 0.167 0.122 
RBF3 0.818 0.147 0.111 0.764 0.168 0.122 
R Tree3 0.819 0.147 0.106 0.768 0.167 0.120 
Knowledge EI (I4GMDH4 0.688 0.196 0.145 0.678 0.195 0.136 
RBF4 0.688 0.196 0.146 0.673 0.196 0.137 
R Tree4 0.666 0.203 0.150 0.666 0.200 0.139 
Table 4

Specifications of used models for estimating hydro-socio-technology-knowledge indicators

ContinentsDimensionDemographic
TechnologyKnowledge
Estimated Indicator (Ii)PRUP (I1)PD (I2)IU (I3)EI (I4)
CharacteristicsGMDH model
America MNNL, MNL, SPa 44, 15, 0.85 47, 15, 0.88
 
40, 14, 0.63 47, 13, 0.86 
Oceania 12, 6, 0.88 11, 4, 0.95
 
12, 5, 0.89 10, 4, 0.91 
Europe 25, 14, 0.9 32, 12, 0.87
 
32, 11, 0.86 28, 10, 0.81 
Africa 52, 21, 0.85 51, 23, 0.85
 
60, 20, 0.88 65, 21, 0.87 
Asia 50, 39, 0.88 43, 40, 0.89
 
47, 44, 0.85 47, 46, 0.90 
World 73, 38, 0.86 78, 33, 0.85
 
75, 34, 0.89 76, 35, 0.85 
Continents Characteristics RBF model 
America S, MNb 0.49, 30 0.44, 36 0.48, 37 0.44, 35 
Oceania 0.49, 11 0.50, 10 0.48, 11 0.45, 9 
Europe 0.51, 29 0.54, 28 0.60, 25 0.48, 24 
Africa 0.49, 54 0.49, 56 0.43, 57 0.41, 51 
Asia 0.48, 30 0.48, 31 0.52, 37 0.51, 33 
World 0.44, 63 0.39, 63 0.45, 61 0.45, 64 
Continents Characteristics R tree model 
America L, Bc 7, 12 8, 14 8, 14 8, 14 
Oceania 5, 13 4, 10 7, 11 7, 11 
Europe 4, 6 5, 8 4, 6 5, 8 
Africa 11, 22 13, 24 12, 22 12, 22 
Asia 10, 18 9, 16 11, 20 11, 20 
World 33, 64 31, 60 32, 62 32, 62 
ContinentsDimensionDemographic
TechnologyKnowledge
Estimated Indicator (Ii)PRUP (I1)PD (I2)IU (I3)EI (I4)
CharacteristicsGMDH model
America MNNL, MNL, SPa 44, 15, 0.85 47, 15, 0.88
 
40, 14, 0.63 47, 13, 0.86 
Oceania 12, 6, 0.88 11, 4, 0.95
 
12, 5, 0.89 10, 4, 0.91 
Europe 25, 14, 0.9 32, 12, 0.87
 
32, 11, 0.86 28, 10, 0.81 
Africa 52, 21, 0.85 51, 23, 0.85
 
60, 20, 0.88 65, 21, 0.87 
Asia 50, 39, 0.88 43, 40, 0.89
 
47, 44, 0.85 47, 46, 0.90 
World 73, 38, 0.86 78, 33, 0.85
 
75, 34, 0.89 76, 35, 0.85 
Continents Characteristics RBF model 
America S, MNb 0.49, 30 0.44, 36 0.48, 37 0.44, 35 
Oceania 0.49, 11 0.50, 10 0.48, 11 0.45, 9 
Europe 0.51, 29 0.54, 28 0.60, 25 0.48, 24 
Africa 0.49, 54 0.49, 56 0.43, 57 0.41, 51 
Asia 0.48, 30 0.48, 31 0.52, 37 0.51, 33 
World 0.44, 63 0.39, 63 0.45, 61 0.45, 64 
Continents Characteristics R tree model 
America L, Bc 7, 12 8, 14 8, 14 8, 14 
Oceania 5, 13 4, 10 7, 11 7, 11 
Europe 4, 6 5, 8 4, 6 5, 8 
Africa 11, 22 13, 24 12, 22 12, 22 
Asia 10, 18 9, 16 11, 20 11, 20 
World 33, 64 31, 60 32, 62 32, 62 

aMaximum number of neurons in a layer, maximum number of layers, selection pressure.

bSpread, MaxNeuron.

cLeaf, branches.

In each continent of the world, for all indicators, the performance of the GMDH model is better than both RBF and R Trees models for estimating hydro-socio-technology-knowledge indicators. For estimating the PRUP indicator by GMDH model, the values of RMSE in Oceania, Africa and Asia were less than the value of RMSE found for the world. Also, the RMSE values obtained for the American and European continents were more than the values obtained for the world. The PD indicator is estimated with close equal amounts of R2 and RMSE in the world and in each continent. For estimating the IU indicator, the values of RMSE in the American, African, European and Asian continents were found to be less than the value of RMSE values obtained for the world. Similarly, the Oceania RMSE values were greater than the world's RMSE value. Further, for estimating the EI indicator using the GMDH model, the values of RMSE in the Oceania and African continents were less than the values of the world. Conversely, the RMSE values obtained for the Asian, American and European continents were more than the world RMSE values. The optimality of the model compared to the global model shows the higher ability of modeling and the relationship between these indicators in the mentioned cases.

Figure 3, 4, 5, 6, 7 and 8 illustrate the observed and estimated socio-technology-knowledge indicators obtained with the soft-computing models during the test period in America, Oceania, Europe, Africa, Asia, and the world respectively. Figure 9 shows a comparison of model results for estimating hydro-socio-technology-knowledge indicators and compares the R2, RMSE, and MAE values with the soft-computing models. The R2 values for soft-computing models are close to 1, with the quality relations being: R2GMDH>R2RBF>R2RTrees for all socio-technology-knowledge indicators. The RMSE and MAE values for soft-computing models are close to 0, with the quality relations being: RMSEGMDH < RMSERBF < RMSER Trees and MAEGMDH < MAERBF < MAER Trees for all socio-technology-knowledge indicators. Figure 9 shows the GMDH models to have better performance than the RBF and R Trees for estimating the proportion of rural to urban population (PRUP), population density (PD), internet users (IU), and education index (EI) parameters in America, Oceania, Europe, Africa, Asia, and the world.

Figure 2

The stages of the current study.

Figure 2

The stages of the current study.

Figure 3

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in America.

Figure 3

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in America.

Figure 4

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in Oceania.

Figure 4

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in Oceania.

Figure 5

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in Europe.

Figure 5

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in Europe.

Figure 6

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in Africa.

Figure 6

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in Africa.

Figure 7

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in Asia.

Figure 7

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in Asia.

Figure 8

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in the World.

Figure 8

Observed and estimated hydro-socio-technology-knowledge indicators during the testing period in the World.

Figure 9

Comparison of model results for estimating hydro-socio-technology-knowledge indicator.

Figure 9

Comparison of model results for estimating hydro-socio-technology-knowledge indicator.

By examining and comparing the RMSE values obtained for three models, GMDH, RBF, and R Tree, it was determined that for the Oceania continent, the GMDH estimation performance model of the ratio of urban to rural population indicator (PRUP) improved from 45% to 57% compared to RBF and R Tree models, respectively. Additionally, for estimates of the population density indicator (PD), the GMDH model improved from 73% to 80% compared to the RBF model and the GMDH and R Tree models, respectively. For estimates of the internet user indicator (IU), the GMDH model improved from 10% to 30% compared to the RBF model and the GMDH and R Tree models, respectively. Finally, for the education index (EI) estimates, the GMDH model improved from 16% to 32% compared to the RBF and R Tree models, respectively.

The relationship between hydro-socio-technology-knowledge indicators is crossed and they have interaction with each other. The set of socio-technology-knowledge indicators can indicate the status of water resources. For this purpose, renewable water per capita was estimated using a set of socio-technology-knowledge indicators including PRUP, PD, IU, and EI based on the GMDH method. The results of GMDH models to estimate RWPC corresponding to the testing period in the world's continents are listed in Tables 5 and 6. Table 5 illustrates the specifications of used models for estimating the interaction of hydro-socio-technology-knowledge indicators. In GMDH models, the maximum amount of neurons in a layer, and selection pressure for renewable water per capita (RWPC) were equal to (45, 15, 0.85), (9, 5, 0.90), (30, 12, 0.88), (54, 23, 0.85), (48, 45, 0.89), and (78, 33, 0.87) for America, Oceania, Europe, Africa, Asia, and the world, respectively. The amount of spread and maximum neurons of RBF models for estimating renewable water per capita (RWPC) equaled (0.44, 38), (0.48, 10), (0.48, 12), (0.45, 56), (0.49, 30), and (0.47, 15) for America, Oceania, Europe, Africa, Asia and the world, respectively. The number of leafs and branches of R Trees models for estimating renewable water per capita (RWPC) equaled (8, 14), (5, 13), (4, 6), (12, 22), (10, 18), and (32, 62) for America, Oceania, Europe, Africa, Asia and the world, respectively.

Table 5

Specifications of used models for estimating interaction of hydro-socio-technology-knowledge indicator

ContinentsEstimated indicator (I5)RWPC
characteristicsGMDH model
America MNNL, MNL, SP 45, 15, 0.85 
Oceania 9, 5, 0.90 
Europe 30, 12, 0.88 
Africa 54, 23, 0.85 
Asia 48, 45, 0.89 
World 78, 33, 0.87 
ContinentsCharacteristicsRBF model
America S, MN 0.44, 38 
Oceania 0.48, 10 
Europe 0.48, 12 
Africa 0.45, 56 
Asia 0.49, 30 
World 0.47, 15 
ContinentsCharacteristicsR tree model
America L, B 8, 14 
Oceania 5, 13 
Europe 4, 6 
Africa 12, 22 
Asia 10, 18 
World 32, 62 
ContinentsEstimated indicator (I5)RWPC
characteristicsGMDH model
America MNNL, MNL, SP 45, 15, 0.85 
Oceania 9, 5, 0.90 
Europe 30, 12, 0.88 
Africa 54, 23, 0.85 
Asia 48, 45, 0.89 
World 78, 33, 0.87 
ContinentsCharacteristicsRBF model
America S, MN 0.44, 38 
Oceania 0.48, 10 
Europe 0.48, 12 
Africa 0.45, 56 
Asia 0.49, 30 
World 0.47, 15 
ContinentsCharacteristicsR tree model
America L, B 8, 14 
Oceania 5, 13 
Europe 4, 6 
Africa 12, 22 
Asia 10, 18 
World 32, 62 
Table 6

The results of optimal model performance for estimating interaction of hydro-socio-technology-knowledge indicator

Estimated Indicator (I5)ContinentsModelR2RMSEMAE
RWPC America GMDH5 0.977 0.047 0.029 
RBF5 0.974 0.050 0.031 
R Tree5 0.968 0.056 0.044 
Oceania GMDH5 0.993 0.024 0.016 
RBF5 0.987 0.039 0.031 
R Tree5 0.965 0.059 0.045 
Europe GMDH5 0.982 0.043 0.030 
RBF5 0.965 0.061 0.047 
R Tree5 0.931 0.086 0.075 
Africa GMDH5 0.990 0.031 0.022 
RBF5 0.988 0.033 0.020 
R Tree5 0.987 0.035 0.023 
Asia GMDH5 0.970 0.055 0.031 
RBF5 0.966 0.058 0.033 
R Tree5 0.948 0.073 0.048 
World GMDH5 0.975 0.050 0.030 
RBF5 0.974 0.050 0.030 
R Tree5 0.974 0.050 0.031 
Estimated Indicator (I5)ContinentsModelR2RMSEMAE
RWPC America GMDH5 0.977 0.047 0.029 
RBF5 0.974 0.050 0.031 
R Tree5 0.968 0.056 0.044 
Oceania GMDH5 0.993 0.024 0.016 
RBF5 0.987 0.039 0.031 
R Tree5 0.965 0.059 0.045 
Europe GMDH5 0.982 0.043 0.030 
RBF5 0.965 0.061 0.047 
R Tree5 0.931 0.086 0.075 
Africa GMDH5 0.990 0.031 0.022 
RBF5 0.988 0.033 0.020 
R Tree5 0.987 0.035 0.023 
Asia GMDH5 0.970 0.055 0.031 
RBF5 0.966 0.058 0.033 
R Tree5 0.948 0.073 0.048 
World GMDH5 0.975 0.050 0.030 
RBF5 0.974 0.050 0.030 
R Tree5 0.974 0.050 0.031 

Table 6 shows the results of optimal model performance for estimating the interaction of hydro-socio-technology-knowledge indicators. According to this table, for each continent, the performance of the GMDH model is better than the two RBF and R Trees models. In the case of the world, the performances of the three models for estimating interaction of hydro-socio-technology-knowledge were almost equal. By comparing the values of R2, RMSE, and MAE in Table 6, the optimal model performance of indicators in the American, Oceanian, European, and African continents are better than the world, and in the Asian continent is weaker than the world.

Figure 10 illustrates the observed and estimated interaction of hydro-socio-technology-knowledge indicators using GMDH, RBF, and R Tree methods during the testing period in America, Oceania, Europe, Africa, Asia, and the world, respectively. Figure 11 shows a comparison of model results for estimating the interaction of hydro-socio-technology-knowledge indicators and compares the R2, RMSE, and MAE values from the soft-computing models. The R2 values resulting from soft-computing models are close to 1, with the quality relations being: R2GMDH> R2RBF> R2R Trees for indicators. The RMSE and MAE values from soft-computing models are close to 0, with the quality relations being: RMSEGMDH< RMSERBF< RMSER Trees and MAEGMDH< MAERBF< MAER Trees for indicators. Figure 11 establishes the GMDH models had better performance than the RBF and R Trees for estimating the renewable water per capita (RWPC) indicator in America, Oceania, Europe, Africa, Asia, and the world.

Figure 10

Observed and estimated interaction of hydro-socio-technology-knowledge indicators using (a) GMDH, (b) RBF and (c) R Tree methods during the testing period in the case studied.

Figure 10

Observed and estimated interaction of hydro-socio-technology-knowledge indicators using (a) GMDH, (b) RBF and (c) R Tree methods during the testing period in the case studied.

Figure 11

Comparison of model results for estimating interaction of hydro-socio-technology-knowledge indicator.

Figure 11

Comparison of model results for estimating interaction of hydro-socio-technology-knowledge indicator.

The performance of GMDH models for estimating interaction of hydro-socio-technology-knowledge indicators with various ranges of values; namely, 30% of maximum estimated values (30%max), 40% of middle estimated values (40%mid or 30%min to 30%max) and 30% of minimum estimated values (30%min), during the test period for the renewable water per capita (RWPC) parameter of America, Oceania, Europe, Africa, Asia and the world are listed in Table 7. The results show that the correlation of the estimated results in Europe in 30% minimum is less than both 30% maximum and 40% middle estimated values. In other continents and the world, the values of R2, RMSE, and MAE, in three ranges 30%max, 40%mid, and 30%min are almost identical and close together.

Table 7

The performance of GMDH models for estimating interaction of hydro-socio-technology-knowledge indicator with various ranges

ContinentRangeR2RMSEMAE
America 30%min 0.830 0.045 0.02 
40%mean 0.880 0.049 0.03 
30%max 0.770 0.047 0.033 
Oceania 30%min 1.000 0.004 0.003 
40%mean 0.980 0.027 0.023 
30%max 0.940 0.03 0.017 
Europe 30%min 0.910 0.021 0.015 
40%mean 0.900 0.047 0.037 
30%max 0.750 0.055 0.037 
Africa 30%min 0.940 0.022 0.008 
40%mean 0.910 0.038 0.018 
30%max 0.920 0.03 0.024 
Asia 30%min 0.860 0.032 0.02 
40%mean 0.790 0.074 0.031 
30%max 0.830 0.043 0.029 
World 30%min 0.840 0.035 0.002 
40%mean 0.820 0.06 0.006 
30%max 0.800 0.049 0.011 
ContinentRangeR2RMSEMAE
America 30%min 0.830 0.045 0.02 
40%mean 0.880 0.049 0.03 
30%max 0.770 0.047 0.033 
Oceania 30%min 1.000 0.004 0.003 
40%mean 0.980 0.027 0.023 
30%max 0.940 0.03 0.017 
Europe 30%min 0.910 0.021 0.015 
40%mean 0.900 0.047 0.037 
30%max 0.750 0.055 0.037 
Africa 30%min 0.940 0.022 0.008 
40%mean 0.910 0.038 0.018 
30%max 0.920 0.03 0.024 
Asia 30%min 0.860 0.032 0.02 
40%mean 0.790 0.074 0.031 
30%max 0.830 0.043 0.029 
World 30%min 0.840 0.035 0.002 
40%mean 0.820 0.06 0.006 
30%max 0.800 0.049 0.011 
Table 8

The results ranking of the hydro-socio-technology-knowledge indicators with GMDH method

IndicatorsRankingAmericaOceaniaEuropeAfricaAsiaWorld
Hydro-socio- technology-knowledge indicators PD PD PD PD PD PD 
IU PRUP IU IU IU IU 
EI EI EI EI EI EI 
PRUP IU PRUP PRUP PRUP PRUP 
IndicatorsRankingAmericaOceaniaEuropeAfricaAsiaWorld
Hydro-socio- technology-knowledge indicators PD PD PD PD PD PD 
IU PRUP IU IU IU IU 
EI EI EI EI EI EI 
PRUP IU PRUP PRUP PRUP PRUP 

In the GMDH neural network, the structure of the model chooses the most appropriate indicators; it automatically organizes the removal of additional indicators and does not interfere with modeling. The combination of Columbrog Gabor function and neural network data t are well related to each other. It increases the accuracy of the model. In this model, due to its mathematical basis, the amount of data and clutter does not significantly affect its performance. However, this is not the case with the RBF neural network. One of the weaknesses of the RBF neural network, in addition to being dependent on the amount of data, is the complexity of the transfer function. This item can also be seen in the R Tree model. One of the disadvantages of this model is its instability, which acts as a predictor of instability with little confusion in the training data. The structure of this model may change completely with a slight change in the data set.

Figure 12 illustrates the distribution of estimated hydro-socio-technology-knowledge indicator data with the GMDH method. The box plots are a graphic display integrating multiple numerical relations. One approach to understanding the distribution or dispersion of data is through the box diagram, which is based on the ‘minimum’, ‘first quartile-Q1 (0.25%)’, ‘median (0.50%)’, ‘third quartile-Q3 (0.75%)’ and ‘maximum’ statistical indicators. Estimated values of the PRUP indicator in all continents and the world have the lowest scattering among other indicators. Also, the minimum median value was obtained for the IU, PRUP, IU, IU, and IU indicators in America, Oceania, Europe, Africa, Asia, and the world, respectively.

Figure 12

The distribution of estimated hydro-socio-technology-knowledge indicator data with GMDH method.

Figure 12

The distribution of estimated hydro-socio-technology-knowledge indicator data with GMDH method.

The summary of results ranking of the hydro-socio-technology-knowledge indicators with the GMDH method are listed in Table 7, where it is seen the best models’ performances are such that PD>IU>EI>PRUP, PD>PRUP>IU>EI, PD>IU>EI>PRUP> , PD>IU>EI>PRUP, and PD>IU>EI>PRUP for America, Oceania, Europe, Africa, and Asia, respectively.

The results of this paper illustrate the importance of examining the interaction between water resources status and socio-technology-knowledge indicators. Therefore, this study has shown that sustainable and successful management of water resources in a country needs to be examined from a socio-technology-knowledge context, analyzing issues and how they relate to and affect water resources. The results of the current study concerning hydro-socio-technology-knowledge indicators (Table 8) are consistent with the results mentioned by Fang et al. (2007), Vittala et al. (2008), Bouleau & Pont (2015), Jordanova et al. (2015), Reidsma et al. (2015), Pires et al. (2017), El Khanji (2017), Honti et al. (2017), O'Connell (2017), Odhiambo (2017), Baki et al. (2018), Lazaridou et al. (2019), and Rebai & Mastere (2020) about the interrelationship of different fields of integrated water resources systems management such as demand management, catchment management, ecological management, and so on, with various dimensions of the social system of the study area. For example, Odhiambo (2017) attributes water scarcity to rapidly growing demand due to rapid population growth, unsustainable consumption, climate change, and the weakness of management institutions and regulations. The researcher introduces water scarcity as the cause of destroying the socio-economic sustainability of communities. Also, El Khanji (2017) explored the interaction between socio-economic productivity and water withdrawal for agriculture and non-agriculture sectors, which shows that increasing demand for water uses of non-agricultural purposes is increasing pressure on the agricultural sector and may eventually lead to higher food prices. On the other hand, based on the results of Lazaridou et al. (2019), socio-economic indicators that affect stakeholders’ environmental decisions can be an important and useful tool in extending public participation and integrating water resources management. Therefore, there is a strong relationship between water resources management and social systems of societies with various dimensions. Current research is consistent with these results in international scales for the world.

CONCLUDING REMARKS

Examining social issues and how they interact with water consumption per capita makes it possible to properly manage water resources in order to achieve the desired goals and improve water resources systems. This study assesses several social indicators; that is, the ratio of rural to urban population (PRUP), population density (PD), internet users (IU), and education index (EI) worldwide and concludes these indicators have a high correlation with the per capita renewable water. In this research, it was shown that using soft-computing techniques, the interaction between hydro-socio-technology-knowledge indicators and renewable water per capita can be modeled. The performance criteria of the GMDH models performed better than those of the RBF and R Trees models for the continents and the world. According to the findings of this article, if there is a lack of information for the management and planning of water resources in a society, it is possible to use social parameters and their interaction with renewable water per capita and, when there is a lack of information to assess the social status of a community, it is possible to use per capita information on renewable water per capita and its interaction with the desired parameters for correct management. It is also suggested that other soft-computing models should be applied to determine the relationship of various dimensions and indicators of socio-economic science with the water and environmental resources parameters at different spatial and temporal scales.

ACKNOWLEDGMENTS

The authors thank Iran's National Science Foundation (INSF) for its financial support of Dr Sarvin Zamanzad-Ghavidel for her post-doctoral position.

CONFLICT OF INTERESTS

None.

DATA AVAILABILITY STATEMENT

All relevant data are available from an online repository or repositories at https://knoema.com.

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