1 Introduction

Deforestation is a quasi-natural processes occurring presently over the earth’s surface. Some of the major problems associated with deforestation are climate change, disruption in atmospheric carbon balance and loss of biodiversity. Deforestation and forest degradation is the second largest source of carbon emission [1]. Today most of the county’s population are continuing expectations of improvement their standard of living which leads the pressure on natural resources [2]. So, as a result, increasing pressure of human development is reflected on forest degradation [3], fragmentation of ecological niche [4], loss of wildlife corridors [5], enhanced rate of soil erosion [6] and finally it initiates the human animal conflict [7]. About 9 million sq. km of tropical humid forest area are lost in less than 50 years but surpassingly the present rate of deforestation is not only high but its increasing continuously. Today a number of methods are used for assessing the rate of deforestation at different scale (i.e., local, regional and global). The models proposed in the literature are commonly subdivided into two main categories; such as quantitative and qualitative [8]. The qualitative models are used for risk assessments and quantitative models are helpful for estimation of deforestation rate, based on measured data or modelling. Various models based on various methods (i.e., empirical and physical based models) are used to quantify deforestations. Today a large number of studies are completed based on remote sensing and geographical information system (GIS) for effective forest cover management [5, 9]. Recent advancement in technologies, such as remote sensing and GIS, and numerical modelling techniques are not only developed as powerful tools for ecological and environmental assessment but also predict land use/land cover assessment more efficiently than ever-before [10]. Numbers of approaches are developed to model and predict the dynamics of land use/land cover [11,12,13,14,15]. Forest cover analysis based on temporal basis correlated with geospatial modelling is no doubt helpful in forecasting the future forest cover scenarios, but spatial modelling can be an immensely useful activity to understand the future of the forests. As various factors like Deforestation, logging, diversion of forests for non-forestry purposes etc. will be operative in future too, which cause continuous changes in forest cover [16].

The present study aims to analysis of deforestation probability at Pathro river basin based on logistic regression model (LRM). Preparation of deforestation probability map is useful to decision makers for identifying deforestation prone areas and existing forest management. In this context, the objective of this study is to identify the probable deforested areas applying logistic regression model which will give us a comprehensive idea about the deforestation rate.

2 Study area

Pathro river basin is a 6th order tributary of Ajay River of Jharkhand (Fig. 1). From the ultimate point of view, the study area is located between 24°9′58″N–24°29′50″N latitudes and 86°15′34″E–86°48′18″E longitudes, covering an area of 709 sq. km. Elevation of this basin ranges from 168 to 461 m. Maximum area of this basin fall under moderate to moderately steep slopes with ranges from 50 to 530. Average annual rainfall receives of this basin is 1247 mm mainly intermediate July and October. This area are facing drought like situation from December to June due to high surface runoff potential, and poor infiltration. Due to continuous changes in climatic conditions as well as land use pattern, this region is now facing deforestation problems through environmental degradation.

Fig. 1
figure 1

Location of the study area a The Ajay river basin in south-western part of West Bengal, b Pathro river basin with altitude and drainage network

Full size image

Local people of this study area use wood immensely for repairing and construction of houses, manufacturing equipment and as a source of fuel. People of surrounding villages cut down lots of valuable wood producing trees illegally from the adjoining forest. The major threat of this area is illegal grazing in the forest which leads to the disruption of forest regeneration.

3 Methodology

3.1 Database and methods

Deforestation is influenced by complex factors, such as, surface cover and environmental factors. Therefore, to assess the deforestation hazard of the area a range of evaluation criteria, objectives and attributes should be identified with respect to the problem situation. For deforestation probability analysis, seven deforestation conditioning factors are used based on field survey and expert knowledge such as, distance from settlement, distance from forest edge, distance from road, distance from river, slope in degree, slope aspect and altitude. In this study, first the forest cover areas are extracted from both 1991 and 2016 digital maps and finally obtained deforestation map and then the values of 0 and 1 are labelled to non-forested and forested areas, respectively (Fig. 2). With the help of Logistic Regression Model using said deforestation conditioning factors, the deforestation probability map of the Pathro river basin has been prepared.

Fig. 2
figure 2

Location of remained forest area and deforestation area of Pathro river basin

Full size image

Finally, the receiver operating characteristic (ROC) curves of the deforestation probability model has been constructed and the area under the curve (AUC) has commuted for verification and accuracy purposes (Fig. 3).

Fig. 3
figure 3

Validation of LRM prediction (AUC/ROC)

Full size image

3.2 Preparation a data base of effective factors

3.2.1 The dependent variable: forest cover change

Regards this model, the forest cover changed (Since 1991–2016) is considered as dependent variable (Fig. 4). First, with the help of GIS software normalized difference vegetation index (NDVI) has been calculated, and the NDVI value greater than .3 is consider as forest in both cases [17]. Hence, a Boolean image with the categories ‘forest change’ (forest to no forest) and ‘no change’ (forest remained unchanged) were generated for the period 1991–2016 by subtracting the forest cover of 1991 from 2016 (Fig. 5).

Fig. 4
figure 4

Forest cover change, during 1991–2016 (Dependent variable), used for calibration and prediction of LRM

Full size image
Fig. 5
figure 5

Forest covers during a 1991 and b 2016

Full size image

3.2.2 The independent variables of forest cover change

Distance from settlement, forest edge, roads, river, slope, slope aspect and altitude are considered as potential independent variables for forest cover change (Fig. 2). Distance form forest edges are considered as one of the important explanatory variable because deforestation tends to start from the edge of existing forest [18] so, forest edge considered as of high probability of deforestation [19]. Deforestation is also highly correlated with roads and settlements [19] and hence these are considered as independent variables. Due to Construction of roads, railways and bridges open up the land for further developmental projects and that ultimately attract large number of population to the forest frontiers [20, 21]. These population are usually colonized the forest by using logging trails or construct the new roads to access the forest for subsistence land [20]. Topographical factors such as altitude, slope and slope aspect are strongly correlated with forest cover change [16]. Altitude considered as independent variable due to its significant direct relationship with total vegetation cover and a significant inverse relationship with annual grass cover [22]. Slope steepness was also showed an inverse relationship with vegetation cover [22] but in respect to slope aspect it’s found that north-facing forests had more tree species and higher tree density than the south-facing forests [23]. Beside this expansion of agricultural land is one of the main leading causes of deforestation [24]. Usually the agricultural land is mostly growing near the river side. Therefore distance from river is considered as an important factor for deforestation analysis (Fig. 6c).

Fig. 6
figure 6

Explanatory variables used for calibration of LRM a distance from settlements, b distance from forest edge, c distance from rivers, d slope in degree, e slope aspect and f altitude, g distance from road

Full size image

3.3 Statistical test for association between dependent and independent variables: Cramer’s V test

χ 2 (for a contingency table larger than two rows by two columns) test is transformed by Cramer’s V statistic to a range of 0–1, where unit value represents complete equality between the two nominal variables [25]. In this research work Cramer’s V has used to represent the intensity of association between dependent and independent variables. For the Cramer’s V test the deforestation conditioning factors have been considered as independent variables and forest change between 1991 and 2016 is considered as dependent variable. The result of the explanatory test procedure for each variable is Cramer’s V values and associated p values. The p values signify the probability that the Cramer’s V is not significantly different from 0 [18]. Cramer’s V represents the relationship between an individual independent variable and forest cover change. Logistic regression model (LRM) is used to provide a perfect sagacity into this (Table 1).

Table 1 Association between dependent variable (forest cover change) and explanatory variable using Cramer’s V
Full size table

3.4 Logistic regression model (LRM)

Logistic regression model has been used for the analysis of deforestation probability of Pathro river basin. This LRM is developed based on the binary response variables i.e. 1 for ‘forest change’ and 0 for ‘no change’ (Fig. 2) [26] and the explanatory variables (elevation, slope, slope aspect, distance from river, settlements, roads and forest edges). The natural log transformation was done for the continuous variables (distances). The natural log transformation was applied for the continuous variables such as, elevation, slope, distance from river, forest edge, roads and settlements. For the categorical explanatory variable (slope aspect class), the evidence of likelihood transformation was applied. The logistic regression model was calibrated before prediction by including the explanatory variables for 2016 in the Logistic Regression Module as independent variables and the forest change during 1991–2016 as dependent variable.

The logistic regression provides the probability of forest loss a function of the explanatory variables. The logistic function (Eq. 1) based on Pontius and Schneider [14] results bounded between 0 and 1 as follows:

$$P = E\left( Y \right) = \frac{{\exp \left( {\beta_{0} + \beta_{1} x_{1} + \beta_{2} x_{2} \cdots + \beta_{i} x_{i} } \right)}}{{1 + \exp \left( {\beta_{0} + \beta_{1} x_{1} + \beta_{2} x_{2} \cdots + \beta_{i} x_{i} } \right)}}$$
(1)

where P is the probability of forest change, E(Y) is the expected value of the dependent variable Y, β0 is a constant to be estimated, βi is the coefficient to be estimated for each explanatory variable \(x_{i}\). This logistic function (Eq. 1) is transformed (Eq. 2) into a linier function (Eq. 3) which is calculated logistic transformation:

$$Logit\left( p \right) = \log e\left( {\frac{p}{1 - p}} \right)$$
(2)
$$Logit\left( p \right) = \beta_{0} + \beta_{1} x_{1} + \beta_{2} x_{2} \cdots + \beta_{i} x_{i}$$
(3)

The final result is a probability score (p) for each cell [14].

Here it represents that the logit conversion of dichotomous data confirm that the dependent variable of the regression is continuous, and the new dependent variable (logit transformation of the probability) is infinite. Finally, it confirms that the predicted probability will be continuous within range from 0 to 1 (Fig. 7). The regression equation of the best-fitted predictor set and the probability of forest change were generated. For evaluate the significance of Logistic regression model, the goodness of fit is an alternative to model χ 2. It is calculated based on the differences between the predicted and the observed values of the dependent variable.

Fig. 7
figure 7

Deforestation Probability map prepared based on logistic regression (LRM)

Full size image

3.5 Validation of prediction

Regard quantitative validation, Receiver Operating Characteristics (ROC) curve has been used by comparing the existing deforestation location in the validation datasets with the deforestation probability map obtained by LRM model. The accuracy of model was evaluated based on Google earth, satellite image and field verification. The ROC curve has been constructed based on true positive rate (sensitivity) corresponding false positive rate (1-specificity) with the various cut-off thresholds. Area under the curve (AUC) has used for qualitative analysis of LR model. An AUC value of 1 indicates a perfect model and when AUC equals 0 is indicates a non-informative model. However, the success rate method is useful to define how well the resulting deforestation probability maps are classified the areas of the existing deforestation [27]. Finally, it is stated that GIS-based logistic regression model as an expert knowledge-based approach is very useful for solving complex problems.

Figure 3 show the ROC curve of the deforestation map obtained using LRM models. These curves indicate that the AUC is 76.6% which corresponds overall accuracy of 78% (Table 2), therefore, it can be said that the model applied in this study is showing reasonably good accuracy in spatial prediction of deforestation.

4 Result and discussion

Logistic regression model is used to determine the magnitude of correlation between deforestation locations and effective factors. The LRM value was range from 0 to 1 where, value 1 represents highly probability of deforestation. The forest maps of Pathro river basin for 1991 and 2016 are depicted in Fig. 4. Approximately 13.674% (96.948 sq km) of the total area was forest in 1991 but in the year 2016 the forest area is reduced to 8.022% (56.875 sq km). So, within 25 years 40.073 sq km area became deforested.

Based on this analysis it is revealed that the spatial pattern of deforestation is depended on a number of physiographic and anthropogenic factors and the logistic regression model (LRM) is successful to accurately predict future deforestation trend. Among these factors, slope is an important one, as the areas which have steeper slope represent more rugged terrain and less adequate for human activities. It is partly explaining that low slope forests are the most threatened forest type [28]. Finally, its represent that lower slope is more suitable for agricultural practice, another factor that leads deforestation. Roads and built-up areas are also important in determining deforestation patterns [29].

According to the logistic regression result at the selected time period the rate of deforestation is noticeably and negatively determined by slope (Wald = 6.908, Exp(B) = 1.863, df = 1), distance from roads (Wald = 5.491, Exp(B) = 1.401 df = 1), and distance from residential areas (Wald = 7.863, Exp(B) = 1.997 df = 1) and Distance from forest edge (Wald = 6.004, Exp(B) = 3.290 df = 1). So, the deforestation is not the result of single factor but it is result of a group of factors like slope, altitude, distance from the roads and distance from the settlement areas (Table 2).

Table 2 Error matrix derived for deforestation probability in Pathro river basin
Full size table

Though all the factors like distance from roads, distance from the forest edge, altitude and distance from the river have control on the deforestation rate but the determining power of slope and settlements are more than these factors. Odd ratio is greater in case of slope and distance from the settlements than of other factors (Table 3).

Table 3 Logistic Regression result
Full size table

The area under the ROC curve of the model is .766. The logistic regression model has considerable amount of accuracy and that can be used for further work [28]. Honesty of the logistic regression is always measured by the Nagelkerke R 2 statistic and χ 2 value. The probability of χ 2 value = 378.293; Nagelkerke R2 = .959; ROC = .766, SE = .016, Sig = .000; Hosmer and Lemeshow test χ 2 = 7.023, Sig = .219 which are designating the good worthiness of the model in amplification the relationship between independent and dependent variables. This perfectly fit model of deforestation has used to explore the future prosperity of deforestation of the remaining areas of this watershed.

The driving factors of forest cover change may vary from one place to another. In the present study, the selected illustrative variables enclose a substantial share of the factors driving forest cover changes. Especially, the accessibility variables such as distance from settlement seem to be more important than the topographical variables. The present study reveals that the distance from settlement, distance from road, slope aspect and elevation were to be the main drivers of forest cover change in Pathro river basin.

5 Conclusion

Present day deforestation is burning issue not only in India but also in the rest of the world. In the present paper using some suitable parameters that are strongly related with the deforestation, probability map has been prepared with the help of logistic regression model of Pathro river basin in GIS environment. Deforestation data has been collected through analysis of two NDVI maps of 1991 and 2016 respectively. De-forestation is in fact as interplay between several factors. Accessibility has been found to be an important variable for explaining the patterns of deforestation observed in the study area. The results indicated that distance from forest edge, settlement and slope areas have a strongly significant correlation with deforestation. This deforestation probability map is showing satisfied accuracy that has been proved by the ROC. It is the government responsibility to take care of forested areas and keeps these forested areas unaffected from the greedy economic people. This deforestation potentiality map can be used by environmental planners and managers to build up policies intended at controlling the adverse ecological and social effects of deforestation.