Assessment of a data-driven evidential belief function model and GIS for groundwater potential...

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Assessment of a data-driven evidential belief functionmodel and GIS for groundwater potential mapping inthe Koohrang Watershed, IranHamid Reza Pourghasemia & Masood Beheshtiradb

a Department of Watershed Management Engineering, College of Natural Resources andMarine Sciences, Tarbiat Modares University (TMU), Noor, Mazandaran, Iran,b Department of natural resources, Sirjan Branch, Islamic Azad University, Sirjan, IranAccepted author version posted online: 17 Sep 2014.

To cite this article: Hamid Reza Pourghasemi & Masood Beheshtirad (2014): Assessment of a data-driven evidential belieffunction model and GIS for groundwater potential mapping in the Koohrang Watershed, Iran, Geocarto International, DOI:10.1080/10106049.2014.966161

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DOI: http://dx.doi.org/10.1080/10106049.2014.966161

Assessment of a data-driven evidential belief function model and GIS for groundwater potential mapping in the Koohrang Watershed, Iran

Hamid Reza Pourghasemi1, Masood Beheshtirad2

1Department of Watershed Management Engineering, College of Natural Resources and Marine

Sciences, Tarbiat Modares University (TMU), Noor, Mazandaran, Iran,

2Department of natural resources, Sirjan Branch, Islamic Azad University, Sirjan, Iran

Email: hamidreza.pourghasemi@yahoo.com (Corresponding author)

Abstract:

The objective of this study is to produce groundwater potential map (GPM) and its performance

assessment using a data-driven evidential belief function (EBF) model. This study was carried

out in the Koohrang Watershed, Chaharmahal-e-Bakhtiari Province, Iran. It’s conducted in three

main stages such as data preparation, groundwater potential mapping using EBF, and validation

of constructed model using receiver operating characteristic (ROC) curve. At first, 864

groundwater data was collected from spring locations; out of that, 605 (70 %) locations were

selected for training/model building and the remaining 259 (30 %) cases were used for the model

validation. In the next step, twelve effective factors such as altitude, slope aspect, slope degree,

slope-length (LS), topographic wetness index (TWI), plan curvature, landuse, lithology, distance

from rivers, drainage density, distance from faults, and fault density were extracted from the

spatial database. Subsequently, groundwater potential map was prepared using EBF model in

ArcGIS environment. Finally, the receiver operating characteristic (ROC) curve and area under

the curves (AUC) were drawn for verification purposes. The validation of results showed that the

area under the curve for evidential belief function model is 81.72%. In general, this result can be

helpful for planners and engineers in water resource management and landuse planning.

Keywords: Groundwater potential mapping, Evidential belief function, GIS, Iran

1. Introduction

Groundwater is known as one of the most important natural resources in the worldwide, and is

major source in industries and agricultural purposes (Pradhan, 2009; Ayazi et al., 2010, Manap et

al., 2012, 2013, Neshat et al., 2013; Nampak et al. 2014). Groundwater is the water occurring

beneath the earth’s surface that completely fills (saturates) the void space of rocks or sediment

(Heath 1983). BGR (2011) reported that the yearly, consumption of groundwater worldwide is

calculated to 1000 cubic kilometers, and the global groundwater recharge at 12,700 cubic

kilometers per year.

In general, Iran is a very dry country, and only 10 percent of the country receives enough rainfall

to meet its needs. Thus it’s heavily reliant on groundwater, because of almost 50% of Iran's

water being supplied by aquifers (Ravilious 2008). By the way, rapid population growth,

urbanization, drought, and low irrigation efficiency in agricultural sector have increased the

demand for groundwater resources. Basically, the most important groundwater resource types are

spring, qanat, and wells in Iran. According to Assadollahi (2009) number of these structures

(spring (N=124,443), qanat (N=37,197), and well (N=624,838)) were 786,478 by a discharge of

79, 196 million cubic meters in a water year 2006-2007. So, groundwater potential mapping can

be helpful for planners and engineers in water resource management and landuse planning in this

country. Over the years, many studies have been carried out groundwater potential mapping

using GIS and different models such as frequency ratio (Oh et al. 2011; Ozdemir 2011a; Manap

et al. 2012; Davoodi Moghaddam et al. 2013), weights-of-evidence (Corsini et al. 2009; Lee et

al. 2012b; Pourtaghi and Pourghasemi 2014), logistic regression (Ozdemir 2011b), artificial

neural network (Corsini et al. 2009; Lee et al. 2012a), Analytical hierarchy process (Kaliraj et al.

2013; Awawdeh et al. 2013), and evidential belief function (Nampak et al. 2014).

The aim of current research is to assess groundwater spring potential map using evidential belief

function model and evaluation of its performance in the Koohrang Watershed, Chaharmahal-e-

Bakhtiari Province, Iran. The main difference between this research and the approaches

described in the aforementioned publications is that a GIS-based data-driven EBF model is

applied and the result is validated for groundwater spring potential mapping in the study area.

The application of GIS-based EBF in groundwater spring potential mapping provides originality

to this study, because of in above several literature review were used of groundwater well

locations.

2. Study area

The study area is located in the western part of Chaharmahal-e-Bakhtiari Province, Iran, between

latitudes 32° 00′ to 32° 36′ N, and longitudes 49° 54′ to 50° 38′ E (Fig. 1). It covers an area about

1,239 km2. Elevation in the study area ranges from 1,660 to 4,200 meters above sea level, with

an average of 2,658m. According to Mojiri and Zarei (2006), the mean annual precipitation is

almost 1,425mm in the area (Mojiri and Zarei, 2006). The study area consisted of four landuse

types namely agriculture, forest, orchard, and rangeland areas that the main landuse is rangeland

types and covers almost 60% of Koohrang Watershed. According to geological survey of Iran

(GSI 1997), 44% of the lithology covering the study area falls within the units represented as C

class, which includes the Undivided Bangestan Group, composed of mainly limestone and shale,

which serves as suitable lithology for groundwater abundance (Table 1). Additionally, this study

area is endowed with favorable topological, geological, hydrogeological, geomorphologic and

environmental characteristics that lead to the abundance of springs. Exploitation of groundwater

resources in the study area includes use of qanats, springs, and deep and semi-deep wells. The

most important springs in the study area are Rostam-Abad, Cheshmeh-Mola, Morvarid, Mar-

Boran, Sardab-Marboran, Kooghrang, Kochak-Koohrang, Cal-Gachi, Chel-Cheshmeh, and

Khak-Dalon. The average spring discharge is approximately 4 gallons per second. The study area

also consists of 27 wells where water is withdrawn from the alluvial fan and the well depths

range between 7 and 20m. The general trend of groundwater flow is from the north of the basin

toward the south of the plain, and the general topographic gradient of the plain is north to east.

The relatively uneven topography of the study area leads to a range of water-table depths, from 2

to 230m in different regions.

3. Methodology

Figure 2 is an overview of the approach that was applied for the groundwater potential mapping

in the study area. The flowchart consists of three phases: 1) thematic data preparation, 2)

groundwater potential mapping using evidential belief function (EBF) algorithm, and 3)

validation of the constructed model using receiver operating characteristic (ROC) curve.

3.1 Thematic data preparation

3.1.1 Spring characteristics

The spring inventory mapping is essential for studying the relationship between the spring

distribution and the effective factors. In the Koohrang Watershed, a total of 864 springs were

mapped at 1:50,000-scale using topographic maps and extensive field survey. A randomly

partition algorithm was used to separate training springs from the validation springs (Lee et al.

2012; Oh et al., 2011). Of the 864 spring locations, 605 springs (70%) were selected for the

training dataset and the remaining 259 springs (30 %) were used for the validation dataset (Fig.

3.1.2 Groundwater effective factors

The basic database that has been used to produce thematic maps is the topographic maps

at1:50,000-scale, geological maps at 1:100,000-scale, and the Landsat 7/ETM+ (Enhanced

Thematic Mapper) satellite imagery by 30*30m spatial resolution. All the data layers were

constructed on a 20*20-m grid cell, with area of 3,437 columns and 3,383 rows, respectively. In

total, twelve groundwater factors were taken into computations, which are altitude, slope aspect,

slope degree, slope-length, topographic wetness index, plan curvature, landuse, lithology,

distance from rivers, drainage density, distance from faults, and fault density. At first, a digital

elevation model (DEM) was created of contour lines and points with 20-m resolution. Using this

DEM, the primary (altitude, slope aspect, and slope degree) and secondary (slope-length, TWI,

and plan curvature) topographical attributes maps were produced.

3.1.2.1 Primary topographical attributes maps

Altitude is one of the parameters influencing on groundwater potential map (Manap et al. 2012;

Pourtaghi and Pourghasemi 2014). Altitude was created directly from the 20-m digital elevation

model (DEM) based on the topographic maps and classified into five categories (<2,200,

2,200−2,700, 2,700−3,200, 3,200- 3,700 and >3,700m) according to an equal-interval

classification scheme (Fig. 3a). Slope aspect is another effective factor that was produced using

the mentioned DEM and grouped into nine classes such as: flat (-1°), north (337.5°-360°, 0°-

22.5°), north-east (22.5°-67.5°), east (67.5°-112.5°), south-east (112.5°-157.5°), south (157.5°-

202.5°), south-west (202.5°-247.5°), west (247.5°-292.5°), and north-west (292.5°-337.5°) (Fig.

3b). The third primary topographical attribute map is slope degree. The slope degree map was

prepared of DEM and classified into four classes as: (1) 0°-5°, (2) 5°-15°, (3) 15°-30°, and (4) >30°

(Fig. 3c).

3.1.2.2 Secondary topographical attributes maps

The slope-length (LS) is a secondary topographical attribute map. The LS factor in the Universal

Soil Loss Equation (USLE) is defined as following (Moore and Burch 1986):

LS = (��

��.��)�.�(

�.�� )�.� (1)

where, B�is the specific catchment area (m2) and α is the cumulative upslope area draining

through a point.

The LS map was created in a System for Automated Geoscientific Analyses (SAGA-GIS) and

classified into four classes in the study area (Fig. 3d).

Another secondary topographic factor within the runoff model is the topographic wetness index

(Fig. 3e). A topographic wetness index measures the degree of accumulation of water at a

specific site (Fig. 3e). It is defined as (Beven and Kirkby 1979; Moore et al. 1991):

TWI = ln(α/ tan β) (2)

where, tan ß is the slope angle at the point.

Plan curvature is described as the curvature of a contour line formed by intersecting a horizontal

plane with the surface Moore and Burch (1986). The plan curvature map was produced using a

SAGA-GIS and classified as concave, flat, and convex (Fig. 3f).

3.1.3 Landuse

Landsat 7/ETM+ images for 2010 were used to derive the landuse map for the study area based

on the supervised classification method with maximum likelihood algorithm. According to Fig.

3g these landuse types are agriculture, forest, orchard, and rangeland types. Most part of the

study area (59.21%) is covered by rangeland type. subsequently; agriculture, forest, and orchard

types are covered by 24.96%, 11.94%, and 3.90% of the study area, respectively.

3.1.4 Lithology

The lithology map was digitized using a 1:100,000-scale geological map in the ArcGIS

environment. The study area is covered by various types of lithological formations and was

classified into ten groups such as: A (Surmeh, Hith Anhydrite, Fahlian, Gadvan, and Darian), B

(Khaneshkat and Neyriz), C (Kazhdumi, Sarvak, Surgah, and Ilam), D (Ilam), E (Dalan), G

(Mila), H (Mishan) and K (Asmari). Lithological units of F and I consisted of undivided Eocene

rock and low level piedmont fan and valley terraces deposits, respectively. The undivided

Bangestan group, mainly limestone and shale (C) cover about 44.32% of the study area. The general

geological setting of the area is shown in Fig. (3h) and the lithological properties are summarized

in Table 1.

3.1.5 Distance from rivers

The distance from rivers is calculated at 100-m intervals using the topographic map (Fig. 3k).

Euclidean distance method was applied in ArcGIS, and a visual inspection was done to see the

correlation between the rivers and springs.

3.1.6 Drainage density

The drainage density depends on the slope, nature, and attitude of bedrocks and the existing

regional and local fracture patterns. They reflect the lithology and structure of a given area and

can be of great value for groundwater resources evaluation (Godebo 2005). The drainage density

map was prepared using river lines and classified based on natural break classification scheme

(Fig. 3m)

3.1.7 Distance from faults

Lineaments are linearly fractured zones on geological structure of an area such as faults and

dykes and they can control the movement of water between surface and subsurface (Davoodi

Moghaddam et al. 2013). The distance from faults is calculated at 250-m intervals using the

geological map (Fig. 3n).

3.1.8 Fault density

The fault density map was determined as the ratio of sum of the fault lengths in the cell and the

area of the corresponding cell. The mentioned map was prepared in ArcGIS by Spatial Analyst

Tools (Line Density) and classified into four classes (<(8.52), (8.52)–(25.57), (25.57)–(42.39),

(42.39)–(58.97)) according to on natural break classification scheme (Fig. 3p).

3.2 Evidential belief function

The evidential belief function (EBF) theory is according to Dempster rule in generalization of

Bayesian lower and upper probabilities (Dempster 1967, 1968). The lower and upper

probabilities are belief (Bel) and plausibility (Pls) degrees, respectively. By the way, the EBF is

consisted of other functions namely degree of uncertainty (Unc) and degree of disbelief (Dis), as

well as (Carranza and Hale, 2002; Althuwaynee et al., 2014). In general, the Pls is greater than or

equal to degree of belief (Bel). Whereas, degree of uncertainty is difference between Pls and Bel,

and is ignorance or doubt of an evidence for supporting of a proposition. In the contrast, degree

of disbelief (Dis) is equal to the belief of false proposition according to given evidential data or

mathematically is 1- Pls. Thus, the sum of Bel, Dis, and Unc is 1 (Carranza and Hale 2002;

Carranza et al. 2005; Lee et al. 2012). Meanwhile, the details of the algorithm can be found in

Carranza et al. (2005, 2008), but in groundwater potential mapping based on evidential belief

function, a frame of discernment can be defined by following equation (Dempster, 1967; Shafer,

1976):

{ }Θ=Θ ,,,2: PP TTm φ With { }PP TT ,=Θ (3)

where PT : Class pixels affected by spring

�� : Class pixels not influenced by spring,

φ : Empty set.

Based on the above equation (Eq. 3), the belief function can be calculated as following (Park 2011):

�� = ��∩�� − �� ∩ �� −�� (4)

�� = � � ��∑� ��

� (5)

where ( )ijASN ∩ : The density of spring pixels that occurred in ijA ,

( )SN : The total density of whole spring that have occurred in the study area,

( )ijAN : The density of pixels in ijA , and

( )PN : The density of pixels in the whole study area P .

On the contrary, the disbelief function can be expressed according to Equations 6 and 7:

�� = ��∩��

��− ��− �� +�� ∩ �� − ��⁄ �!" (6)

�#�$%�� = �� ∑ �� (7)

Finally, equations 8 and 9 were used to calculate uncertainty and plausibility functions.

�'()�*+,�(+-� = �1 − ��− (#�$%��)� (8)

��,.$�%��+-� = �1 − �#�$%�� (9)

4. Results and discussion

4.1 Groundwater potential mapping using evidential belief function algorithm

After definition the effective factors, one of the important keys in any research is consideration

of multi-collinearity problem among independent variables. Tolerance and the variance inflation

factor (VIF) are two important indices for multi-collinearity diagnosis (O'Brien 2007). A

tolerance of less than 0.20 or 0.10 and/or a VIF of 5 or 10 and above indicates a multi-

collinearity problem (O'Brien 2007). According to Table 3, the smallest tolerance and highest

variance inflation factor were 0.351 and 2.849, respectively. So, there isn’t any multi-collinearity

between independent factors in current research. By the way, results of spatial relationship

between spring and conditioning factors using evidential belief function (belief, disbelief,

uncertainty, and plausibility) model are shown in Table 4. According to Park (2011) and Nampak

et al. (2014), an important constraint about EBF is that if there is no value for belief in a certain

class, then it indicates that there is no spring occurrence in the same class.

The relationship between spring occurrence and altitude reflects that the elevations <2200 m and

2200-2700m have the highest Bel values (0.555 and 0.397) respectively, indicating that the

probability of spring occurrence in these altitudes is high. In contrast, elevations > 3200m have

the lowest belief values. In the case of slope aspect, the highest Bel values were related to south-

west, south, and south-east (0.175, 0.175, and 0.158, respectively) and it show that these

categories has positive spatial association with spring occurrence. On the other hand, the degree

of belief was lowest for north, north-east, and north-west by values of 0.055, 0.057, and 0.064,

respectively. Based on Table 4, for the slope degree of 5°- 15°, the belief and disbelief values

were 0.414 and 0.175, which indicates a very high probability of spring occurrence. In contrast, a

slope >30° has the lowest belief value (0.044). In general, the results showed that there is an

inverse relationship between slope degree and belief values. The higher (Belief degree) and

lower (Disbelief degree) probability of spring occurrence is obtained in the areas having a slope-

length >60 meter by values of 0.396 and 0.166, respectively. In the case of topographic wetness

index, there was a direct relationship between spring occurrence and belief degree. Basically, the

belief values show that when TWI increases, the probability of spring occurrence increases. For

plan curvature, there is a high belief and low disbelief value for flat (0.471, 0.269) and convex

(0.312, 0.351) curvatures, respectively.

In the case of land use, the degree of belief was higher for orchard (0.527) and agriculture

(0.362) landuse types; as well in these classes Dis values were lower by value of 0.215 and

0.148, respectively. On the other hand, the results showed that 52% of springs fall in agriculture

landuse type. In the case of lithology, there are ten classes. The degree of belief, with respect to

spring occurrence, was higher for I (in generally, consisted of Low level piedmont fan and valley

terraces deposits) and f (including Undivided Eocene rock) classes (0.297 and 0.188), but lower

or zero for B, D, E, and H classes (Table 1). In the case of distance from rivers, there is highest

belief and lowest disbelief values at distance <100m. It is indicate that spring occurrence

decrease by the increase in distance of rivers. The highest belief and lowest disbelief values in

case of drainage density were related to the class of >7.32. The results revealed that this class

had the highest probability in spring occurrence. By the way, the results stated that when

drainage density is increasing, then spring occurrence is increasing, so there is a direct

relationship between drainage density and groundwater spring potential mapping. In the case of

distance from faults, <500m classes had the highest and lowest belief and disbelief values,

respectively. The Bel and Dis values between spring occurrence and fault density show that

higher Bel (0.433) and lower Dis (0.93) values are related to the class of 42.39 – 58.97km/km2.

The integrated results of evidential belief function model are shown in Fig. 4. The belief map

(Fig. 4a) was compared to the disbelief map (Fig. 4b) which showed that belief values were high

for areas where disbelief values are low and vice versa. It indicated that high groundwater

potential was for the areas where there were high degrees of belief and low degree of disbelief

for the occurrence. The uncertainty map (Fig. 4c) showed lack of information to provide a real

prove for spring occurrences. The high uncertainty values were in the areas where belief values

were low. The plausibility map (Fig. 4d) shows high values for areas where both belief and

uncertainty values are high. Our results are in agreement with those of Carranza and Hale (2002);

Carranza et al. (2008); Tien Bui et al. (2012); Lee et al. (2012); Althuwaynee et al. (2014);

Nampak et al. (2014); Pradhan et al. (2014). Nampak et al. (2014) stated that the main advantage

of Dempster-Shafer theory is that, the application of the EBF allows not only the predictive

mapping of favourable zones, but also allows modeling of the degrees of uncertainty in the

prediction. Furthermore, according to results reported by Park (2011) and Lee et al. (2012),

evidential belief function model supports a series of mass functions including belief, disbelief,

uncertainty and plausibility. Thus, the results of this model present quantitative relationships

between spring occurrence and effective factors by modeling the degree of uncertainty. Finally,

the groundwater spring potential map (GSPM) using EBF model was constructed using the

following equation (Fig. 5):

GSPMEBF= ([AltitudeBel]) + ([Slope AspectBel]) + ([Slope DegreeBel]) + ([slope-lengthBel]) + ([TWIBel]) + ([LanduseBel]) + ([LithologyBel]) + ([Distance from RiversBel]) + ([Drainage DensityBel]) + ([Distance from FaultsBel]) + ([Fault DensityBel]) (10)

4.2 Validation of groundwater potential map

Validation is considered to be the most important process of modeling and it’s without; the

models will have no scientific significance (Chung and Fabbri, 2003; Nampak et al. 2014). To

determine the accuracy of the groundwater spring potential map created in the current research

using evidential belief function, the receiver operating characteristics (ROC) curve was used

(Ozdemir and Altural, 2013; Akgun et al., 2012; Mohammady et al., 2012; Pourghasemi et al.,

2013). ROC curve analysis is a common method used to assess the accuracy of a diagnostic test

(Egan, 1975). The ROC curve plots the false positive rate on the X-axis and the true positive rate

on the Y-axis. It represents the trade-off between the two rates (Negnevitsky, 2002). In this

study, the spring locations which were not used during the model building process (30% or 259

cases) were used to verify the groundwater spring potential map. The AUC value of the ROC

curve for EBF model was 0.8172 and the prediction accuracy was 81.72% (Fig. 6). Hence, it is

concluded that the map produced by evidential belief function exhibited satisfactory result in the

Koohrang Watershed, Iran.

5. Conclusions

Iran is one of the arid and semi-arid countries of the world with average precipitation of 251

mm/year. Of total 130 Billion m3 renewable water resources of Iran, 92% is used for agriculture,

6% for domestic use and services and 2% for industrial activities. Groundwater plays a dominant

role in sustainable development of human society. In Iran, rapid population growth and low

irrigation efficiency in agricultural sector have increased the demand for groundwater resources.

Therefore, regional management for water supply and optimum use of the existing water

resources is necessary. In resulting, groundwater spring potential mapping is one of the most

important activities in this context.

The main objective of this study was to produce groundwater spring potential map in the

Koohrang Watershed, Chaharmahal-e-Bakhtiari Province, Iran, using a data-driven evidential

belief function model. At first, a spring locations map was prepared for the study area based on

topographical map and extensive field surveys. Of total 864 spring locations identified in the

study area, 605 cases were used for model building (training) and the remaining 259 were used

for validation purposes. In order to groundwater spring potential zonation, twelve effective

factors such as altitude, slope aspect, slope degree, slope-length, topographic wetness index, plan

curvature, landuse, lithology, distance from rivers, drainage density, distance from faults, and

fault density were considered. For validation of created groundwater spring map in ArcGIS, the

area under the curve (AUC) was used. The validation results indicated that the prediction rate for

the evidential belief function model was 81.72%. In summary, according to achieved results and

reported by different researchers, evidential belief function model supports a series of mass

functions including belief, disbelief, uncertainty and plausibility. Thus, the results of the

mentioned model present quantitative relationships between springs occurrence and effective

factors by modeling the degree of uncertainty. As a final conclusion, the model results can be

useful for planners and engineers in water-resource management and land-use planning in the

study area and we believe that the results obtained from our study provide a considerable

contribution to the groundwater literature.

Acknowledgement

The authors would like to thank the anonymous reviewers and editor for their helpful comments

on the previous version of the manuscript.

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List of Figures

Fig. 1 Location of the study area with spring location map Fig. 2 The flowchart of used methodology in the Koohrang Watershed, Iran Fig. 3 Groundwater effective factors maps in the Koohrang Watershed, Iran; (a) Altitude, (b) Slope aspect, (c) Slope degree, (d) Slope-Length, (e) Topographic wetness index, (f) Plan curvature, (g) Landuse, (h) Lithology, (k) Distance from rivers, (m) Drainage density, (n) Distance from faults, (p) Fault density

Fig. 4 Integrated results of evidential belief function model in the Koohrang Watershed, Iran; (a) belief, (b) disbelief, (c) uncertainty, (d) plausibility Fig. 5 Groundwater spring potential map (GSPM) produced by evidential belief function model in the Koohrang Watershed, Iran Fig. 6 Prediction rate curve for the groundwater spring potential map by EBF model in the Koohrang Watershed, Iran

List of Tables Table 1 Lithology of Koohrang Watershed, Iran (GSI 1997) Table 2 Groundwater database of Koohrang Watershed, Iran

Table 3 The multi-collinearity diagnosis indexes for variables Table 4 Spatial relationship between effective factor and springs using evidential belief function

Fig. 1 Location of the study area with spring location map

Fig. 2 The flowchart of used methodology in the Koohrang Watershed, Iran

- Altitude - Slope Aspect - Slope Degree - Slope-Length - TWI - Plan curvature - Landuse - Lithology - Distance from Rivers - Drainage Density - Distance from Faults - Fault Density

Data (864 Groundwater data set)

Random Partition

Validation Groundwater Potential Mapping

Validation Springs (259 locations) Training Springs (605 locations)

Area Under the Curve (AUC)

- Prediction rate for validation data set

Evidential Belief Function (EBF)

Belief Value Map

Uncertainty

Value Map

Plausibility

Value M

Disbelief Value Map

Fig. 3 Groundwater effective factors maps in the Koohrang Watershed, Iran; (a) Altitude, (b) Slope aspect, (c) Slope degree, (d) Slope-Length, (e) Topographic wetness index, (f) Plan curvature, (g) Landuse, (h) Lithology, (k) Distance from rivers, (m) Drainage density, (n) Distance from faults, (p) Fault density

Fig. 4 Integrated results of evidential belief function model in the Koohrang Watershed, Iran; (a) belief, (b) disbelief, (c) uncertainty, (d) plausibility

Fig. 5 Groundwater spring potential map (GSPM) produced by evidential belief function model in the Koohrang Watershed, Iran

Fig. 6 Prediction rate curve for the groundwater spring potential map by EBF model in the Koohrang Watershed, Iran

Table 1 Lithology of Koohrang Watershed, Iran (GSI 1997)

Table 2 Groundwater database of Koohrang Watershed, Iran

Source of data Data layers Data format Scale Topographic maps, and field

surveys Spring Locations Map Point 1:50,000

National Cartographic Center (NCC)

Topographic Map Line and Point 1:50,000

Geology Survey of Iran (GSI) Geological Map Polygon and line 1:100,000 National Geographic Organization (NGO)

Landuse Map Polygon Landsat 7/ETM+

(30*30m)

Name Lithology Formation

A Undivided Khami Group, consist of massive thin-bedded limestone Surmeh, Hith Anhydrite,

Fahlian, Gadvan, and Darian

B Thin to medium-bedded, dark grey dolomite ; thin-bedded dolomite, greenish shale

and thin-bedded argillaceous limestone Khaneshkat and Neyriz

C Undivided Bangestan Group, mainly limestone and shale Kazhdumi, Sarvak, Surgah,

and Ilam D Dark red, medium-grained arkosic to sub-arkosic sandstone and micaceous siltstone Lalun

E Limestone, dolomite, dolomitic limestone and thick layers of anhydrite in

alternation with dolomite in middle part Dalan

F Undivided Eocene rock - G Dolomite platy, and flaggy limestone containing trilobite; sandstone and shale Mila

H Low weathering grey marls alternating with bands of more resistant shelly

limestone Mishan

I Low level piedmont fan and valley terraces deposits -

K Cream to brown-weathering, feature-forming, well-jointed limestone with

intercalations of shale Asmari

Table 3 The multi-collinearity diagnosis indexes for variables

Factors

Unstandardized

Coefficients

Standardized

Coefficients t Sig. Collinearity Statistics

B Std. Error Beta Tolerance VIF

Altitude .000 .000 -.142 -6.060 .000 .596 1.678

Slope Aspect -.009 .004 -.046 -2.344 .019 .842 1.188

Slope Degree .000 .002 -.003 -.104 .917 .351 2.849

Slope-Length .000 .000 .078 3.531 .000 .669 1.494

TWI .017 .004 .127 4.639 .000 .435 2.299

Plan Curvature -6.530 1.764 -.071 -3.703 .000 .893 1.119

Lithology .010 .002 .086 4.279 .000 .806 1.241

Landuse -.007 .006 -.025 -1.295 .195 .876 1.142

Distance from Rivers -2.031E-5 .000 -.059 -2.448 .014 .562 1.780

Drainage Density -.019 .004 -.116 -4.544 .000 .499 2.005

Distance from Faults -1.113E-5 .000 -.200 -9.307 .000 .702 1.425

Fault Density .022 .002 .289 12.979 .000 .658 1.520

Table 4 Spatial relationship between effective factor and springs using evidential belief function

Factor Class No. of pixels

% pixels No. of

Springs % Springs FR Bel Dis Unc Pls

Altitude (m)

< 2200 535538 17.29 221 36.53 2.11 0.555 0.155 0.289 0.845 2200 - 2700 1241920 40.09 366 60.50 1.51 0.397 0.134 0.470 0.867 2700 - 3200 852342 27.52 15 2.48 0.09 0.024 0.273 0.704 0.728 3200 - 3700 390325 12.60 2 0.33 0.03 0.007 0.231 0.762 0.769

> 3700 77488 2.50 1 0.17 0.07 0.017 0.207 0.775 0.793

Slope Aspect

Flat 136358 4.40 32 5.29 1.20 0.135 0.99 0.110 0.755 North 372273 12.02 36 5.95 0.50 0.055 1.07 0.119 0.826

North East 533569 17.23 53 8.76 0.51 0.057 1.10 0.122 0.821 East 340851 11.00 42 6.94 0.63 0.071 1.05 0.116 0.813

South East 287468 9.28 79 13.06 1.41 0.158 0.96 0.107 0.736 South 422726 13.65 129 21.32 1.56 0.175 0.91 0.101 0.724

South West 514347 16.60 157 25.95 1.56 0.175 0.89 0.099 0.726 West 273554 8.83 53 8.76 0.99 0.111 1.00 0.111 0.778

North West 216467 6.99 24 3.97 0.57 0.064 1.03 0.115 0.822

Slope Degree

<5 326502 10.54 121 20 1.90 0.399 0.219 0.383 0.781 5-15 699442 22.58 269 44 1.97 0.414 0.175 0.411 0.825 15-30 1411851 45.58 188 31 0.68 0.143 0.310 0.547 0.690 >30 659818 21.30 27 4 0.21 0.044 0.297 0.659 0.703

Slope-Length (m)

0 - 20 479434 15.48 57 9 0.61 0.190 0.281 0.529 0.734 20 - 40 387596 12.51 67 11 0.89 0.276 0.266 0.457 0.714 40 - 60 440034 14.21 38 6 0.44 0.138 0.286 0.576 0.835

> 60 1790549 57.80 443 73 1.27 0.396 0.166 0.438 0.719

TWI < 8 446025 14.40 27 4 0.31 0.098 0.358 0.544 0.642

8 - 12 2137181 68.99 382 63 0.92 0.288 0.382 0.330 0.618 > 12 514407 16.61 196 32 1.95 0.614 0.260 0.126 0.740

Plan Curvature (100/m)

Concave 1060404 34.23 200 33 0.97 0.312 0.337 0.351 0.663 Flat 900986 29.09 256 42 1.45 0.471 0.269 0.260 0.731

Convex 1136223 36.68 149 25 0.67 0.217 0.394 0.389 0.606

Landuse

Agriculture 773211 24.96 317 52 2.10 0.362 0.148 0.490 0.852 Forest 369709 11.94 4 1 0.06 0.010 0.264 0.726 0.736

Orchard 120697 3.90 72 12 3.05 0.527 0.215 0.259 0.785 Rangeland 1833996 59.21 212 35 0.59 0.102 0.373 0.525 0.627

Lithology

A 389429 12.57 64 10.58 0.84 0.158 0.102 0.740 0.898 B 32756 1.06 0 0.00 0.00 0.000 0.101 0.899 0.899 C 1372975 44.32 235 38.84 0.88 0.165 0.110 0.725 0.890 D 47128 1.52 0 0.00 0.00 0.000 0.101 0.899 0.899 E 26731 0.86 0 0.00 0.00 0.000 0.101 0.899 0.899 F 461550 14.90 90 14.88 1.00 0.188 0.100 0.712 0.900 G 40466 1.31 1 0.17 0.13 0.024 0.101 0.875 0.899 H 5188 0.17 0 0.00 0.00 0.000 0.100 0.900 0.900 I 663928 21.43 205 33.88 1.58 0.297 0.084 0.618 0.916 K 57462 1.86 10 1.65 0.89 0.168 0.100 0.732 0.900

Distance from Rivers

0 - 100 298688 9.64 122 20.17 2.09 0.290 0.163 0.547 0.837 100 - 200 254374 8.21 76 12.56 1.53 0.212 0.175 0.613 0.825 200 - 300 236824 7.65 72 11.90 1.56 0.216 0.176 0.609 0.824 300 - 400 214785 6.93 57 9.42 1.36 0.188 0.179 0.632 0.821

> 400 2092942 67.57 278 45.95 0.68 0.094 0.307 0.599 0.693

Drainage Density

(km/km2)

< (1.23) 858045 27.70 52 9 0.31 0.065 0.311 0.624 0.689 (1.23) – (1.98) 976015 31.51 52 9 0.27 0.057 0.328 0.615 0.672 (1.98) – (7.32) 823773 26.59 301 50 1.87 0.391 0.168 0.440 0.832

(7.32) – (14.99) 439780 14.20 200 33 2.33 0.487 0.192 0.321 0.808

Distance from Faults

< 250 284042 9.17 60 9.92 1.08 0.230 0.200 0.570 0.800 250 - 500 265860 8.58 57 9.42 1.10 0.233 0.200 0.567 0.800 500 - 750 228608 7.38 35 5.79 0.78 0.166 0.205 0.629 0.795 750 - 1000 206299 6.66 29 4.79 0.72 0.153 0.206 0.642 0.794

> 1000 2112804 68.21 424 70.08 1.03 0.218 0.190 0.592 0.810

Fault Density (km/km2)

< (8.52) 2096826 67.69 382 63 0.93 0.259 0.279 0.462 0.721 (8.52) – (25.57) 607940 19.63 111 18 0.93 0.259 0.248 0.492 0.752 (25.57) – (42.39) 363765 11.74 111 18 1.56 0.433 0.226 0.340 0.774 (42.39) – (58.97) 29082 0.94 1 0 0.18 0.049 0.246 0.705 0.754

FR=Frequency Ratio; Bel= Belief; Dis=Disbelief; Unc=Uncertainty; Pls=Plausibility; Total Pixels=3,097,613; Total Training Springs=605

Assessment of a data-driven evidential belief function model and GIS for groundwater potential...

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