1 Introduction

Forest and landscape managers are planning the utilization of the non-wood values in the landscape to maximize the efficiency of forest ecosystems (Franco et al. 2003). Tourists are typically getting interested in forested landscapes due to visual aesthetic quality and natural phenomena (Scarfo et al. 2013). Forest visitors consider the forest landscapes as a natural environment with natural visual features and less human intervention. Therefore forest managers must rely on the protection of public visual quality preferences to produce and maintain users desired conditions. In the temperate forests area, the most critical issue in managing the landscape visual quality focuses mainly on different forests natural phenomena. Temperate Hyrcanian forests, administered by the Forests and Rangelands Organization of Iran (FROI), provide visual aesthetic features with natural elements such as trees, shrubs, streams, rivers, rocky hills and so on. Therefore, forest managers and stakeholders consider visual quality evaluation and prediction as a high priority aim. Forest managers, therefore, request decision support system tools that can help to solve stochastic problems such as the visual quality of forest sites with diversity in natural or man-made physical features, particularly in the development of non-wood management plans (Jahani 2019b). In this matter, Ebenberger and Arnberger (2019) explored visitors’ visual preferences for forest structures in temperate Central European mixed forests where the varying degrees of naturalness are obvious.

The visual quality of landscapes is based on the psychological perception of the observant about the visible landscape characteristics (Daniel 2001). The visual quality of a landscape results from the experiences of the visitors; hence it is very complicated to measure them with stochastic objective parameters (Chen et al. 2009; Sahraoui et al. 2016). Indeed, visual landscape quality evaluation needs the inventory and evaluation of the visible landscape characteristics for stochastic and probabilistic modeling, management, and planning (Palmer and Hoffman 2001). Literature review reveals four main criteria in the determination of the visual quality of landscape which are naturalness (Polat 2012), diversity (de la Fuente et al. 2006), vividness, maintenance (Sevenant and Antrop 2009), and safety (Özguner and Kendle 2006).

Three universally well-known approaches have been suggested to evaluate the landscape visual quality: perception-based approach, expert/design approach, and expert/perception-based approach (Howley 2011; Daniel 2001). The perception-based approach measures the human preference (subjective) of the landscape (Howley 2011; Omidi et al. 2017). On the other hand, the expert/design approach relies on the physical and biological values of the landscape to assess landscape visual quality (Franco et al. 2003). Indeed highly skilled people evaluate landscape visual quality by physical attributes of the landscape such as vegetation, water, or man-made structures. This approach is commonly applied to environmental practices such as forest management (Arriaza et al. 2004). However, using just experts for landscape evaluation might cause bias between public and expert preferences. The expert/human-perception-based approach develops stochastic modeling techniques to detect the relationship between landscape characteristics and the visual preference of the people in a mathematical manner (Dwyer et al. 2006).

Visual quality evaluation needs costly and time-consuming ecological inventories, and forest incomes may not justify these costs. To reduce the value of these inventories, Eyvindson et al. (2019) proposed the stochastic approaches for multiple criteria methods to improve ecological data. Recently, artificial intelligence techniques such as multi-layer regression (MLR), multi-layer perceptron (MLP) neural network, and radial basis function (RBF) neural network as nonlinear and dynamic modeling techniques have been employed for the development of accurate models in environmental sciences (Aghajani et al. 2014; Wang et al. 2018; Aziz et al. 2014; Azimi et al. 2019) and landscape assessment (Jahani 2019b; Jahani and Mohammadi Fazel 2017). The new quantitative modeling methods and data mining approaches are essential to deal with complicated and subjective assessments. In recent researches, ANN has been used for stochastic phenomena prediction in natural ecosystems. Aziz et al. (2014) applied artificial neural networks in regional flood frequency analysis in Australia. They found that ANNs are able to predict floods in catchments with higher accuracy compared with traditional methods. Aghelpour and Varshavian (2020) assessed stochastic and artificial intelligence models in predicting of river daily flow. Two stochastic and three artificial intelligence models were compared, and MLP showed the best validation performance. The MLR and MLP have been used in aesthetic quality prediction in the natural environment in Jahani (2019b) and Jahani and Mohammadi Fazel (2017) researches. On the other hands, in environmental modeling researches we found other data mining techniques such as RBF neural network in comparison with MLP (refer to Jahani et al. 2016; Wang et al. 2018; Jahani 2019a). These modeling techniques have been developed based on the structure of the human brain in data processing. A variety of mathematical functions have been applied in artificial intelligence modeling techniques to increase the ability of the model in output prediction. For example, Jahani (2019b) proved that artificial neural network with multi-layer perceptron predicts the aesthetic quality of forest landscapes, based on tourists’ preferences, with higher accuracy in comparison with multi-layer regression models. The forest natural and man-made attributes were assigned to the model for prediction of landscape aesthetic quality. ANN methods have been resulted in a significant increase in prediction accuracy (approximately up to 80% of water discharge studies) in comparison with multiple regressions (Shams et al. 2020). ANN modeling has been applied by Jahani et al. (2020) in tourism impact assessment of natural protected areas in recent years. They compared multi-layer perceptron (MLP), radial basis function neural network (RBFNN) and support vector machine (SVM) models to predict tourism impact on land vegetation density changes in three national parks of Iran. Jahani et al. (2020) proved that MLP model create the most accurate predictions with 97% and 80% accuracy in training and test phases respectively. However, they only focused on tourism activities and vegetation density without developing any decision support tool for inexperienced users to execute model for prediction. In the other research Mosaffaei et al. (2020) developed ANN model to predict Soil texture and plant degradation in Sorkheh Hesar National Park. They used Margalef biodiversity index as model output, but the accuracy of model was not so reliable (R = 0.54). Mosaffaei et al. (2020) proposed the investigation on other biodiversity indexes and developing decision support tool for execution of accurate model.

This study discovers the most accurate artificial intelligence model for stochastic problems solving with spatiotemporal analysis and mapping of forest ecosystems. This model will be introduced as the most successful stochastic model in visual quality prediction and the reliability analysis in decision making. Also Renshaw et al. (2009) declared that forest modeling is a key tool for optimal management strategies formulation and development. However, we aimed to landscape visual quality evaluation by expert/human-perception-based approach and application of artificial intelligence modeling techniques with stochastic nature such as MLR, MLP, and RBF for the visual quality prediction of forest landscapes. The sensitivity of the most accurate model will prioritize forest landscape attributes in visual quality. Finally, the Graphical User Interface (GUI) tool as an environmental decision support system will be provided for forest managers to evaluate the forest sites visual quality.

2 Materials and methods

2.1 Study area

The studied forest area is located in the Alborz Mountains, within the Mazandaran province of Iran (36° 30′ 30″ to 36° 32′30″ N latitude and 51° 40′ 00″ to 51° 41′ 30″ E longitude). This forest is covered by 3000 ha of the broadleaf tree and shrub species. Hyrcanian forests of Iran are adjacent to the Caspian Sea and are considered as temperate forests (Fig. 1). The forest landscape is diverse, consisting of dense trees, shrubs, river and streams, rocky hills, and roads as the main visual elements.

Fig. 1
figure 1

The geographic location of the studied forest area

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3 Methods

In temperate forests, landscapes are structurally diverse consisting of trees and shrubs, roads, rivers, and groundwater streams, and rocky hills. However, there is not defined any standard or knowledge about the composition of these structures which increase the visual quality of forest landscapes. Therefore, we investigated a forest area in the north of Iran, where the diversity in natural and man-made landscapes consisting of trees and shrubs, roads, rivers, and groundwater streams, and rocky hills.

In this study, we applied the expert/human-perception-based approach in five phases of (1) taking photographs from the forest landscapes; (2) designing photo-questionnaire; (3) taking interviews of experts and stakeholders (4) conducting the mathematical analysis and developing models and (5) designing GUI tool as decision support system in landscape visual quality evaluation. Figure 2 illustrates flow diagram for the mechanism of study problem and the methodology steps for decision making.

Fig. 2
figure 2

The flow diagram for the mechanism of study problem

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The methods generally applied to assess aesthetics quality are questionnaire surveys, cartographic representations, and simulated assessments. Landscape researchers believe that, in natural or near natural landscapes, aesthetics quality assessments based on color-photographic representations have closely matched assessments regarding direct landscape experience and perception (Daniel 2001). A questionnaire-based one-time survey was carried out in the context of several workshops. We provided 100 landscape color photographs containing five features such as trees, shrubs, water (rivers and streams), rocks, and roads. To allow an unbiased comparison among photographs, a strict routine was followed in taking photographs. First, all photographs were taken with a resolution of 4608 × 3456 pixels and the same camera. Second, the focal length of the objective was kept constant at 50 mm and was obtained equal visual angles. Third, a constant shot height of 1.70 m was assured using a tripod. Fourth, a constant proportion of sky and land (2/3 of land, 1/3 of the sky) was assured in all photographs based on a constant horizon position. Fifth, all photographs were taken in similar lighting and atmospheric conditions, and none of them contained people. Finally, to assure consistency about the status of the foliage (Dupont et al. 2016; Jahani 2019b), all the photographs were taken in the summer season.

3.1 Expert/human-perception-based evaluation

The natural resources and fine arts students and faculty members of Tehran University were used as the experts to perform the expert/human-perception-based photo-questionnaire. Also, the stockholders of forest area were used as the human perception base evaluation group. In total, 500 individuals participated (250 regional experts and 250 stakeholders) in expert/human-perception-based photo-questionnaire. The group of experts was composed of 47 faculty member and 203 students. The group of stakeholders was composed of forestry project employees (48), wood products contractor (15), local farmers (22), and tourists (165). Male and female individual proportions are 60% and 40%, respectively, which were in a broad range in the age (18–70 years).

Photo-questionnaire was distributed to 500 participants were divided into groups with at least 10 participants in each group. Before filling the photo-questionnaire, the participants were trained about the landscape quality criteria such as diversity, naturalness, vividness, safety, and maintenance (refer to Polat 2012; de la Fuente et al. 2006; Sevenant and Antrop 2009; Özguner and Kendle 2006). The participants were asked to assess each landscape photograph in terms of the five landscape criteria in Likert scale (5 scales). The sum of five scores was recorded as landscape score for each photograph. Indeed the landscape scores could be 0–25 from the lowest to the best visual quality (five criteria scores in five scales).

3.2 Forest landscape visual quality evaluation modeling

The landscape attribute were extracted from recent researches on visual quality assessment of natural ecosystems (Wang et al. 2017, 2019; Hoyle et al. 2017; White et al. 2010; Jahani 2019b; Jahani et al. 2011; Saffariha et al. 2014a, b, 2019) which are: (1) Trees in landscape: all trees species and physical dimension, (2) shrubs in landscape: all species, (3) water in landscape: rivers and groundwater streams, (4) Rocky hills: Great cliffs and rocks, and (5) Roads in landscape: roads and trails. These features maybe affect the quality of landscape positively or negatively (Jahani 2019b; Jahani and Mohammadi Fazel 2017). Using 1 mm × 1 mm network, the percentage coverage of each variable (landscape features) in the photographs was calculated to model the landscape score. Five influential variables on the photographs were chosen as the model inputs, and landscape scores were tagged as model outputs.

3.2.1 Multi-layer regression (MLR) analysis

The 100 forest landscapes as modeling samples were divided into two data sets randomly, which include training data set with 80% of all samples, and test data set with 20% of all samples. Random selection of training and test data was conducted to avoid any possible bias in the selection of test set individuals. The test samples were separated from training data to test the generalization potential of the MLR model.

The MLR was used to design the structure of the MLP model.

3.2.2 Multi-layer perceptron (MLP) neural network

Artificial neural network (ANN) model such as MLP is a multi-layer network that uses self-learning mechanism by samples for prediction of phenomena. Generally, in MLP, the samples are usually acquired from real samples of the particular process. Therefore, ANN models are suitable where the modeling focuses on complex phenomena with subjective data (Wang et al. 2017; Jahani 2016) such as visual quality of landscape prediction. In this research, three activation functions consisting of a hyperbolic tangent, logarithmic sigmoid, and linear transfer functions were tested to optimize the performance of the model. To optimize the model accuracy, the number of hidden layers, the number of neurons and activation functions were defined by trial and error and recursive testing and comparison. Trial and error is the most common method for detecting the most accurate structure of MLP (Pourmohammad et al. 2020; Shams et al. 2020; Tajmiri et al. 2020). Back Propagation (BP) method propagates the error of outputs (different from the target) to the input layer where the first random weights have been defined. The weights change until the best performance is achieved, and the learning process will be ended (Jahani 2019a, b; Azimi 2019).

BP reduces errors between Ynet (MLP output) and Y (real landscape score) where the weight of PEs (w) and input variables (x) are adjusting, and the output of jth PE on the kth layer (PEkj) is calculated by Eq. 1 (Mosaffaei et al. 2020):

$${{\rm net}}_{{\rm j}}^{{\rm k}} = \sum\limits_{{{{\rm i}} = 0}}^{{\rm n}} {{{\rm w}}_{{\rm ji}} {{\rm x}}_{{\rm ji}} }$$
(1)

The transfer functions are introduced to the network, and the output value of neurons is calculated by Eq. 2 (Mosaffaei et al. 2020).

$${{\rm Y}}_{{\rm net}} = \int {{{\rm net}}_{{\rm j}} }$$
(2)

In the next step, the weights of t samples will be changed by delta rule in Eq. 3 (Mosaffaei et al. 2020).

$${{\rm w}}_{{\rm ji}}^{{\rm t}} = {{\rm w}}_{{\rm ji}}^{{{{\rm t}} - 1}} + \Delta {{\rm w}}_{{\rm ji}}^{{\rm t}}$$
(3)

The 100 forest landscapes as modeling samples were divided into three data sets randomly which include training data set with 60% of all samples, validation data set with 20% of all samples and test data set with 20% of all samples. The ANN function in MATLAB 2018, was used to design the structure of the MLP model.

3.2.3 Radial basis function neural network

The RBFNNs, like MLPs, have been structured with input, hidden, and output layer but they are different in the type of activation function in the hidden layer. The samples, in RBFNN, are divided into two types of data sets which are training and test. The different of RBFNNs is in the application of the radial function in neurons of the hidden layer. This function creates the circular classifiers and spheres of answers in the multidimensional decision space where the number of neurons is determined based on input variables. Considering function approximation in forest landscape score prediction in this research, we have an output layer in the structure of RBFNN. Gaussian function (Eq. 4) is the most popular function applied in RBFNN structure (Kalantary et al. 2019, 2020; Jafari et al. 2014). The primary role of the Gaussian function is to calculate the center of circular classifiers with Eq. 4 (Jahani et al. 2020).

$${{\rm R}}_{{\rm j}} ({{\rm x}}) = \exp \left( {\frac{{\left\| {{{\rm x}} - {{\rm a}}_{{\rm j}} } \right\|^{2} }}{{2\upsigma^{2} }}} \right)$$
(4)

In Eq. 4, Rj(x) = the radial basis function, ||x − aj|| = the determined Euclidean distance between the total of aj (RBF function center), x = (input vector or variables), and σ = a positive real number. Finally, the network outputs should be calculated with Eq. 5 (Jahani et al. 2020):

$${{\rm y}}_{{\rm k}} = \sum\limits_{{{{\rm j}} = 1}}^{{\rm m}} {{{\rm w}}_{{\rm jk}} {{\rm R}}_{{\rm j}} ({{\rm x}}) + {{\rm b}}_{{\rm j}} }$$
(5)

In Eq. 5, wik = the weights of neurons, j = the number of each node in the hidden layer, m = the number of neurons, and bj = bias.

The weights of neurons (wjk) will be adjusted to reduce the error of the outputs when the training of network ends. After the end of the training, the number of neurons and the weights is fixed, and the performance of the network will be defined (Jahani et al. 2020).

3.3 Model selection

The model’s performance is evaluated by simulation of the test data set, which is not applied in the training process. There are several statistical indicators which have been used in performance assessment of MLP, RBFNN, and SVM such as Mean Squared Error (MSE, Eq. 6), Root Mean Squared Error (RMSE, Eq. 7), Mean Absolute Error (MAE, Eq. 8) and coefficient of determination (R2, Eq. 9) (Jahani 2019a, b).

$${{\rm MSE}} = \frac{{\sum\nolimits_{{{{\rm i}} = 1}}^{{\rm n}} {\left( {{{\rm y}}_{{\rm i}} - {\hat{{\rm y}}}_{{\rm i}} } \right)^{2} } }}{{\rm n}}$$
(6)
$${{\rm RMSE}} = \frac{{\sum\nolimits_{{{{\rm i}} = {{\rm n}}}}^{{\rm n}} {\left( {{{\rm y}}_{{\rm i}} - {\hat{{\rm y}}}_{{\rm i}} } \right)^{2} } }}{{\rm n}}$$
(7)
$${{\rm MAE}} = \frac{{\sum\nolimits_{{{{\rm i}} = {{\rm n}}}}^{{\rm n}} {\left| {{{\rm y}}_{{\rm i}} - {\hat{{\rm y}}}_{{\rm i}} } \right|} }}{{\rm n}}$$
(8)
$${{\rm R}}^{2} = \frac{{\sum\nolimits_{{{{\rm i}} = 1}}^{{\rm n}} {\left( {{\hat{{\rm y}}}_{{\rm i}} - {\bar{{\rm y}}}_{{\rm i}} } \right)^{2} } }}{{\sum\nolimits_{{{{\rm i}} = {{\rm n}}}}^{{\rm n}} {\left( {{{\rm y}}_{{\rm i}} - {\bar{{\rm y}}}_{{\rm i}} } \right)^{2} } }}$$
(9)

yi and \({\hat{{\rm y}}}\) = the target and predicted classes of tree hazard, \({\bar{{\rm y}}}\) = the mean of target values, N = the number of samples.

In designed models, each variable has a specific role in the outputs of the model. If we know the value of variables in model outputs, it is possible in practice to modify the variables in the landscape for required changes in forest landscape score. A sensitivity analysis for the most accurate model was designed to prioritize the variables concerning their significance in model output. In the sensitivity analysis, we changed each variable in the range of standard deviation with 50 steps while the other variables were fixed at the value of average. Then, the standard deviation of outputs for each variable changes was measured as optimized model sensitivity for that variable. Finally GUI tool was designed as an environmental decision support system for forest landscape visual quality evaluation by forest managers who are looking for high visual quality landscapes to plan for human activities.

4 Results

4.1 Demographics

The demographic characteristics of participants involved in expert/human-perception-based were summarized in Table 1. Considering the results, the rate of males in landscape evaluation was more than females. The rate of expert participants was more than non-expert. The rate of middle age (41–50) and the young age (18–30) participants was more than other age groups. Also, most of the participants had a high level of education.

Table 1 The demographic characteristics of participants
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For visual quality prediction in forest landscapes, five recorded variables of forest landscape attributes and landscape score, which have been used as model input and output variables are illustrated in Table 2. Indeed, the minimum, mean, and maximum of model variables define the limits of model validity in practice.

Table 2 Statistical data of forest landscapes
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4.1.1 Prediction performance of MLR

MLR analysis with 95.0% confidence interval performed with 80% of total samples (100 landscapes) to calculated constant coefficients of regression equation while the summation of square errors was minimized. The Eq. 10 was introduced as the predictive model with MLR technique in the prediction of forest landscape visual quality. The variable tree did not meet 95.0% confidence interval, so it is not used in achieved MLR model.

$${{\rm VQM}} = 16.507 - (0.028 * {{\rm Sh}}) + (0.035 * {{\rm W}}) - (0.042 * {{\rm Rd}}) + (0.008 * {{\rm Rk}})$$
(10)

In Eq. 10, VQM is Visual Quality Model, and independent variables are Sh (shrubs), W (water), Rd (roads), and Rk (rocky hills) in the forest landscapes.

The accuracy of the MLR model in training and test data sets are presented in Table 3. The scatter plots of training and test samples illustrate the relationship between the target and predict the visual quality of the landscape by the MLR model In Fig. 3.

Table 3 Statistical indices of the MLR model in training and test sets
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Fig. 3
figure 3

The scatter plot of target and VQM output using MLR analysis

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4.1.2 Prediction performance of MLP

The number of neurons and hidden layers, and the activation function were optimized to achieve the most accurate predictive model with the MLP technique (Table 4).

Table 4 The results of parameters tuning in MLP structure
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Based on the values of R2 (Table 4), MLP model optimization detected the structure of ‘5–19–1’ as the most successful topology of the model in the visual quality of forest landscape prediction. The determined topology contains five variables as inputs, 19 neurons in the hidden layers, and one neuron (landscape score) in the output layer. The sigmoid tangent and linear transfer function detected as the most accurate estimation functions in the hidden layer and output layer, respectively.

The scatter plot illustrates the correlation between variables which is applied in accuracy definition of ANNs (Jahani 2019a, b). Figure 4 presents the scatter plot of MLP outputs versus targets values for training, and test data. The determination of coefficient (R2), prove the strong correlation between the MLP outputs and target values.

Fig. 4
figure 4

Scatter plots of MLP outputs versus target values

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Figure 5 compares the target and simulated (output) values of MLP in the training and test data sets. A significant and distinctive agreement between values has been illustrated in Fig. 5.

Fig. 5
figure 5

Targets and outputs of the MLP model

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4.1.3 Prediction performance of RBF

RBF, as a type of ANNs, uses a Gaussian transfer function in a hidden layer, which is the main difference with MLP. It has an input layer and an output layer to receive samples for the training process. There are two main parameters to be optimized along the training process. These parameters are the number of neurons and the spreads of radial basis functions. In the best RBF model performance, the number of neurons was 23, and the spread of radial basis functions was 10. The best results of RBF in training and test data sets have been represented in Table 5.

Table 5 The results of parameters (spread and neurons) tuning in RBF structure
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The values of R2 determine the best structure in training and test data sets (Table 5). The optimized RBF structure is 5–23–1 with five variables as inputs, 23 neurons in the hidden layer with Gaussian transfer function, and one neuron (landscape score) in the output layer.

Figure 6 presents the scatter plot of RBF outputs versus targets values of the landscape score for training, and test data sets. The determination of coefficient (R2), prove the notable correlation between the RBF neural network outputs and targets values.

Fig. 6
figure 6

Scatter plots of RBF outputs versus targets values

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Figure 7 compares the target and output values of RBF in the data sets. A significant and distinctive agreement between values has been illustrated in Fig. 7.

Fig. 7
figure 7

Targets and RBF outputs values

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When we comprise the results of NLR, MLP, and RBFNN models, in Fig. 8, we arrive at this result that the RBF model is the most accurate model in visual quality prediction in forests landscapes. The results of RBF, especially its high accuracy (R2 = 0.887) in comparison with MLR (R2 = 0.588), and MLP (R2 = 0.847) test results introduced RBF as a comparative visual quality of landscape evaluation model in forests. Indeed the RBF predictive model was the most successful model when the new data was used to test the accuracy of model predictions in practice.

Fig. 8
figure 8

The performance measures of the designed models

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4.1.4 Sensitivity analysis of the SVM model

We conducted a sensitivity analysis of the predicted outputs of the optimal RBF model. In Fig. 9, RBF model sensitivities for input variables have been detected by sensitivity analysis. According to the results of sensitivity analysis, the values of the water, shrubs, roads, rocky hills, and trees are prioritized respectively as the most significant inputs which influence RBF model (Fig. 9).

Fig. 9
figure 9

Sensitivity analysis of the RBF model

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Considering trends in Fig. 10a, d, water bodies and rocky hills, are positively correlated to landscape score, so forest landscapes with the higher water and rocky hills cover, represent a higher potential in visual quality. Considering trends in Fig. 10b, e, the shrubs and trees in the forest landscapes, is negatively correlated to landscape score, so forest landscapes where the trees and shrubs are dense, the potential of visual quality reduces. On the other hand, trends in Fig. 10c illustrates that the roads in the forest landscapes, increase the visual quality, but this trend is reversed where the density of roads is more than a threshold.

Fig. 10
figure 10

The trend of RBF model output changes with varying the variables

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RBF model provides a new tool as an EDSS in the forests to find the landscapes which are more attractive for visitors. The results of sensitivities analysis could be used in forest landscape management with respect to the trends.

Finally, a graphical user interface (GUI) was designed to run the RBF model on new data where the forest landscape managers need to evaluate forest landscapes. Indeed, new forest landscapes have new composition of attributes (RBF model inputs). The forest manager can easily evaluate the visual quality of landscape. The GUI as an EDSS tool will be run on new data just by pushing the visual quality evaluation button in Fig. 11.

Fig. 11
figure 11

The results of visual quality evaluation of forest landscape landscapes

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5 Discussion

The visual quality of the natural regions is so effective on people’s psychology. They also play a significant role in meeting the social expectations of having rest, stress restoration, and recreation (Güngör and Polat 2018). In this matter, the expert/human-perception-based approach that we developed to evaluate the visual quality of landscape meets the benefits of two approaches of expert assessment and human perceptions simultaneously. Carvalho-Ribeiro et al. (2013) declared that physical landscape attributes (such as trees, water, shrubs, etc.) completely influence subjective landscape dimensions. As Dwyer et al. (2006) declared the statistical techniques make a tool to detect the relationship between landscape attributes and the visual preference in a mathematical method. Accordingly, our modeling approach combined a quantitative evaluation of the visual quality of forest landscapes with an expert/human-perception-based method to investigate experts and human perceptions of visual beauty. RBF model provides a framework for clearly analyzing how objective attributes of forest landscapes will result in human preferences subjectively. However, Simensen et al. (2018) in review research on landscape assessment suggest that more emphasis is on testing the relation of the landscape characterization about the purpose of the study, as well as methods’ accuracy and reliability. The data set presented in this research is reliable for the visual quality modeling because both landscape features and subjective assessment of landscape scores are available with 100 forest landscapes which support model development, testing the prediction ability of different data mining techniques, and evaluating the visual quality potential. The results of RBF modeling, especially its high accuracy (R2 = 0.887) in comparison with MLR (R2 = 0.588), and MLP (R2 = 0.847), introduced RBF visual quality model as a comparative model of forest landscape visual quality evaluation. Mathematical models such as regression and artificial neural network were recently developed to model the aesthetic quality of the landscape (Jahani 2019b). The MLP was successful and more accurate than multi-layer regression in aesthetic quality prediction in forest landscapes in Jahani (2019b), but he did not test the other popular data mining techniques such as RBF neural network. Kao et al. (2016) divided the landscape images into three categories of “scene,” “object” and “texture” to develop a convolutional neural network (CNN) for learning the aesthetic which is obtained by 200 voters. It means that the characteristics of the landscape could be categorized in visual or land ecological features. Anyway, the artificial techniques resulted in the accurate models for visual and aesthetic evaluation even if researches are based on remote sensing images such as Saeidi et al. (2017) researches. Also in our method, RBF visual quality model indicates the significant relationship between objective attributes of the forest landscape and human preferences which can be applied to compare the visual quality of forest landscapes and development plans in future. RBF visual quality model was designed for forest decision makers to evaluate the visual quality of forest landscapes based on landscape attributes. However, Kasiviswanathan and Sudheer (2017) believe that the prediction uncertainty reduces the reliability and the ANN prediction does not explain any information about uncertainties. Thus, scientists are trying for developing stochastic methods to quantify the uncertainties of neural network models. Therefore, evaluation of uncertainty methods for ANN models is a future way for further researches.

The results of sensitivity analysis demonstrate that landscape attributes play the primary role in the RBF model outputs so that water bodies, and rocky hills positively and shrubs, roads, and trees negatively are correlated with the landscape scores in forests. Kerebel et al. (2019) prioritized the landscape characteristics in aesthetic quality in the eyes of the beholders. They developed a Bayesian network (the same algorithm in RBF) for ecosystem services where the sensitivity analysis resulted that landscape aesthetic predictions were most sensitive to waterfall presence indicator. Natural phenomena are more effective than man-made variables, such as roads, on the aesthetic quality of the landscape in many types of research (Güngör and Polat 2018; Jahani 2019b). Roads in the forest create safety feeling for visitors, but when the density of roads increases, visual quality of landscape decrease due to the naturalness of the environment. It is apparent in the trend results of RBF Output changes with varying the roads in the landscape. The safety feelings decrease in dense forests with a large number of trees and shrubs either. As Misgav (2000), Shelby et al. (2003) and Bjerke et al. (2006), we believe that this result is related to limited visual penetrability which causes the reduction in people’s safety feelings.

The last aim of this research was achieved by designing an applicable graphical user interface tool. Such a graphical user interface tool is a shortcoming in most of recent neural network and stochastic modeling (e.g. Jahani et al. 2020; Mosaffaei et al. 2020). We should remember that ANN models have very complicated structure with a huge matrix of variabls’ weights in neurons and hidden layers; hence these models are not applicable without such a tool.

The strength of this research is in ANN model development with artificial (roads) and natural (vegetation, land and water) elements in forest ecosystems simultaneously; and designing environmental decision support tool in MATLAB software. The accuracy of RBF in visual quality prediction was proved, but there is still shortcoming in influential variable identification and quantification. However, we do not deny that a variety of ecological attributes influence aesthetic quality. In future research attention should be paid to ecological variable determination; and the quantification of artificial structures. For instance forest succession variables have not been considered in our study that is probably the cause of errors in output predictions. Also, other variables such as climate, tree canopy coverage, and seasonality (Shirani Sarmazeh et al. 2018a, b) may increase the accuracy of the model.

6 Conclusions

A sustainable forest management plan aims at the utilization of non-wood potential of forest ecosystems such as scenic landscapes with higher visual and aesthetic quality. RBF model with the designed graphical user interface, as an environmental decision support system, evaluate landscape visual quality of temperate broadleaf forests based on the forest components, and it helps to find the most scenic landscapes for forest planning. Such a tool is the main advantage of this research in comparison with other landscape visual quality assessment where the output is only a method or procedure without any mathematical tool or software preparation. The designed tool can support any forest stakeholder who committed to implementing sustainable forest management based on optimal use of scenic landscapes.