Transforming subsidence vulnerability indexing based on ALPRIFT into risk indexing using a new fuzzy-catastrophe scheme

Environmental Impact Assessment Review 82 (2020) 106352

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Transforming subsidence vulnerability indexing based on ALPRIFT into risk indexing using a new fuzzy-catastrophe scheme

T

Sina Sadeghfama, , Rahman Khatibib, Sorayya Dadashia, Ata Allah Nadiric,d ⁎

a

Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh, East Azerbaijan, Iran GTEV-ReX Limited, Swindon, UK c Department of Earth Sciences, Faculty of Natural Sciences, University of Tabriz, 29 Bahman Boulevard, Tabriz, East Azerbaijan, Iran d Institute of Environment, University of Tabriz, East Azerbaijan, Iran b

ARTICLE INFO

ABSTRACT

Keywords: Decision theory (FL and CT) Groundwater decline Risk indexing/mapping Data fusion

Poor anthropogenic activities give rise to declining water table in aquifers, which in turn induces land subsidence, an issue of concern to planning systems. Modelling subsidence depends on data and this paper considers impacts over plains with sparse data by building on the ALPRIFT framework, the acronym of 7 data layers, similar to DRASTIC. It uses a scoring system of prescribed rates in terms of physical variations and prescribed weights in terms relative importance of each data layer. The conceptual innovation on ALPRIFT by the paper includes its transformation from Vulnerability Indexing (VI) into Risk Indexing (RI) by discerning the data layers into 5 ALRIF and two PT data layers. These cater for Passive Vulnerability Indices (PVI) and Active Vulnerability Indices (AVI) respectively. Their additions are equivalent to ALPRIFT VI but their products lead to innovative RI capabilities. The paper presents the proof-of-concept for RI and learning its inherent weight values by using an innovative hybrid scheme of fuzzy logic and catastrophe theory. The case study of Marand plain provides a challenging case, where the data are sparse but the analysis of the results provides an insight into the study areas. Subsidence RI is readily applicable to any similar problems.

1. Introduction Subsidence vulnerability indexing of plains over aquifers is investigated in this paper for aquifers exposed to the decline of water table, where subsidence refers to normally downward settlement of land including sudden sinking or gradual vertical downward movements with little horizontal movements. Subsidence problems vary from one location to another and depend on a host of factors. Their impacts are wide and include impacting on the environment, health and safety, and interruption (e.g. transportation) and incurring damage. Subsidence stems from a loss of hydrostatic pressure on soil particles and is catered for by theoretical and/or empirical techniques, see Van Hardeveld et al. (2017). Bouwer (1977) uses simplified cases with sample calculations and shows that as much as 5–50 cm subsidence can occur per 10 m decline of water table. Arguably, this indicative amount may serve as a rule-of-thumb without considering more involved processes, such as soil depth. The focus of the paper is on vulnerability and risk mapping/indexing for expressing risk as relative and not absolute values. Research on land subsidence is topical and the ongoing activities,

⁎

summarised in Table 1, are categorised as follows: (i) mathematical models using groundwater flow models and subsidence models to investigate impacts of decline in water table giving rise to subsidence (e.g., Sundell et al., 2019); (ii) remote sensing techniques to monitor land subsidence with capabilities to investigate possible relationships with hydrogeological settings (e.g., Zhou et al., 2019); and (iii) using GIS techniques for mapping areas vulnerable to subsidence. The latter group is suitable for cases with sparse data but without much published works. Published literature shown in Table 1 includes: Nadiri et al. (2018a) who introducing ALPRIFT as a new technique; and Huang et al. (2012) who presented a simple hazard risk assessment index technique. The scope of each group depends on their capabilities but the techniques in the first and second categories are precluded in the paper owing to the constraint of data requirement. The focus is on ALPRIFT by innovating it to a risk mapping capability, as detailed below. The paper builds on the ALPRIFT framework for Subsidence Vulnerability Indexing (SVI), introduced by Nadiri et al. (2018a). Its rationale is inspired by the DRASTIC framework by Aller et al. (1987), where a framework refers to the use of heuristic methodologies, without having a theoretical or empirical basis. Whilst DRASTIC is a

Corresponding author. E-mail addresses: [email protected] (S. Sadeghfam), [email protected] (A.A. Nadiri).

https://doi.org/10.1016/j.eiar.2019.106352 Received 28 June 2019; Received in revised form 25 August 2019; Accepted 22 November 2019 0195-9255/ © 2019 Elsevier Inc. All rights reserved.

GIS based

InSAR processingb

Modoni et al. (2013)

Empirical equation and mathematical models

2

Huang et al. (2012)

Hu et al. (2009)

Zhou et al. (2019)

Hu et al. (2009)

Chen et al. (2016)

Gao et al. (2016)

Sundell et al. (2019)

Shrestha et al. (2017)

Faunt et al. (2016)

Reference

Group

Table 1 Summary of studies related to land subsidence.

1. 2. 3. 1. 2. 3.

Urbanisation level Volume of reducing groundwater exploitation Length of level survey per km2 Annual recovery rate of GWL Thickness of the confined aquifer Thickness of the soft clay

1. Construction land proportion 2. Population density 3. Gross Domestic Product per km2 Disaster reducing data layers:

1. Groundwater exploitation intensity 2. Cumulative subsidence volume 3. Land subsidence velocity Vulnerability data layers:

Hazard data layers:

ASAR images • Envisat • TerraSAR-X stripmap data • GPS • Sentinel-1 ASAR • ENVISAT • RADARSAT-2

• Envisat ASAR images

inflows • Surface-water maps • Land-use data • Climate characteristics • Physical • Hydro-meteorology abstraction • GW raster • Compressibility thickness raster • Soil fluctuation • GWL data • Borehole data • Hydrogeological • Damage data

deformation • Ground characterisation • Subsoil • Groundwater regime

Models or data

Hazard risk assessment of land subsidence

Overlay analysis

GAMMA software

GAMMA software

DORIS

c

soil-stratification • Geostatistical model calibrated groundwater • Inverse model model of subsidence • Elasto-plastic A model to estimate damages • DORIS

fluctuation rasters

for GWL predictions • SHETRAN processing for overlaying • GIS compressibility, Soil thickness, GWL

CVHMa

Classical principle of Terzaghi (1943)

Model or software

Wuxi city (China)

Tianjin (China)

Beijing (China)

Beijing (China)

Beijing (China)

Beijing (China)

A railway shaft and tunnel in Varberg (Sweden)

Kathmandu Valley (Nepal)

California (USA)

Bologna (Italy)

Location

(continued on next page)

hazard risk of land subsidence over the • Delineated study area. • Used AHP to assign weight for data layers.

• •

•

GWL changes, dynamic and static loads and compressible deposit thickness. Identified greater role of groundwater exploitation in confined aquifers having larger impacts on land subsidence over the plain under study. Determined weights of land subsidence velocity of each group using AHPd technique. Prepared land subsidence risk maps for land subsidence prevention and reduction by combing hazard and vulnerability.

causes of land subsidence in Beijing • Investigated stemming from over-extraction of groundwater. “gradient lifting decision tree model” to • Selected quantitatively analyse land subsidence in response to

types.

them.

subsidence in terms of, GWL, accumulated • Investigated soft soil thickness, active faults and different aquifer

behaviours of groundwater and • Investigated subsidence and identified some relationship between

subsidence probabilities and damage costs • Integrated by GIS processing to estimate economic risks.

management.

subsidence hazard with respect to the • Highlights location and potential levels for hazard prevention

subsoil was modified in terms of effective stress.

management strategies to mitigate adverse • Evaluated impacts of subsidence.

correlation among land subsidence, • Identified groundwater withdrawal and subsoil composition. measurements were interpreted using • Subsidence Terzaghi (1943), in which cumulated deformation in

Key findings

S. Sadeghfam, et al.

Environmental Impact Assessment Review 82 (2020) 106352

3

i

h

g

f

e

d

c

b

a

Models or data

1. Altitude, 2. Slope, 3. Aspect, 4. Lithology, 5. Distance from fault, 6. Distance from river, 7. NDVIe, 8. Soil, 9. Stream power index, 10. Topographic wetness index 1. Land use, 2. GWL, 3. Aspect, 4. DEM, 5. Distance to streams, 6. Rainfall, 7. Density of wells, 8. Slope, 9. Lithology

1. Aquifer media, 2. Land use, 3. Pumping, 4. Recharge, 5. Aquifer thickness impact, 6. Fault distance, 7. Decline of water table

1. Elevation, 2. Slope, 3. Distance from stream, 4. Drainage density, 5. Groundwater drawdown, 6. Lithology

1. Distance from Qanat systems, 2. Land use, 3. Distance from forested land, 4. Lithology, 5. Distance from faults, 6. Drawdown of the GWL

1. Aquifer media, 2. Land use, 3. Pumping, 4. Recharge, 5. Aquifer thickness impact, 6. Fault distance, 7. Decline of water table

Reference

Pradhan et al. (2014)

Ghorbanzadeh et al. (2018)

Nadiri et al. (2018a)

Rahmati et al. (2019a)

Rahmati et al. (2019b)

Present study

CVHM: Central Valley Hydrologic Model. InSAR: Interferometric Synthetic-Aperture Radar. DORIS: Delft Object oriented Radar Interferometric Software. Analytic Hierarchy Process. Normalized Difference Vegetation Index. Evidential Belief Function. Frequency Ratio. Adaptive Neuro Fuzzy Inference System. Sugeno Fuzzy Logic.

Group

Table 1 (continued)

f

h

• Fuzzy Catastrophe Scheme (FCS)

• • Maximum entropy Genetic algorithm

machine learning • Tree-based models

i

• ALPRIFT, • SFL

g

• EBF • FR • ANFIS

Model or software

Marand (Iran)

Kashmar (Iran)

Hamadan (Iran)

Shabestar (Iran)

Amol (Iran)

Kinta Valley (Malaysian)

Location

the land subsidence hazard maps. • Delineated relationships between geo-environmental • Investigated factors and land subsidence. performances of two machine learning • Compared techniques. ALPRIFT to risk indexing. • Transforming subjectivity associated with weights and rates • Decreasing of ALPRIFT data layers by FCS. total vulnerability to passive and active • Breaking vulnerability. passive/active/total vulnerability and risk • Delineating index maps.

streams and lithology.

images) as target for ANFIS.

6 membership functions and selected Gaussian • Evaluated membership as the best. ALPRIFT as a framework to map • Introduced subsidence. ALPRIFT to assess subsidence potential and • Applied learned inherent weights from data. • Processed SAR data and used them as target data. the land subsidence susceptibility. • Delineated a set of data layers as input data and measured • Used subsidence as target data. drawdown was seen as a key factor to • Groundwater induce land subsidence, followed by distance from

land subsidence by groundwater over• Compared exploitation with that by other geologic hazards. EBF and FR for mapping subsidence-prone areas. • Used that FR model is less accurate in prediction • Observed than the evidential belief function model. nine data layers as input data and • Considered subsidence layer by InSAR processing (Sentinel-1

Key findings

S. Sadeghfam, et al.

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mature technique for mapping intrinsic vulnerability against anthropogenic contamination, the proof-of-concept on ALPRIFT for subsidence studies has to be tested extensively. The methodology is as follows: (i) use 7 general-purpose data layers pooled together consensually; (ii) develop a scoring system of prescribed rates and weights, in which prescribed rates consider physical variations and prescribed weights consider relative importance of each data layer. Prescribed values make ALPRIFT frameworks susceptible to subjectivity but this is not a problem as the authors program of research in using DRASTIC consistently shows that these values can be learned from site-specific data by data-driven models, see Nadiri et al. (2018b), which may be referred to as local models. The 7 ALPRIFT data layers are largely general-purpose data, not collected for such studies in the first place and the data are detailed later. The data nominally comprise: Aquifer media (A), Land use (L), Pumping of groundwater, Recharge (R), aquifer thickness Impact (I), Fault distance (F) and decline of water Table (T). A focus on these data layers indicates that three data layers are related to the presence of water and these are RPT, where R accounts for natural processes (but it is not anthropogenic), P is solely related to anthropogenic activities, and T accounts for its impacts. Thus, the 7 data layers are broken down into two groups: (i) passive vulnerability comprising five data layers of ALRIF, including the R data layer; and (ii) the PT data layers accounting for active withdrawal of hydrostatic pressure due to human activities. The processing of the 7 ALPRIFT data layers are through dividing a study area into grid squares (pixels). In general, the following observations are made: (i) the higher ALRIF and/or PT values, the higher the capacity for subsidence; (ii) the ALRIF data layers are largely geogenic properties at individual pixels, which are expected to be locally correlated but with numerous discontinuity; (iii) the PT data layers are largely anthropogenic properties and are expected to prevail systemwide but with local variations. Notably, an additive model of ALRIF and PT is equivalent to the basic ALPRIFT framework. As a benchmark, the paper uses basic ALPRIFT but with the following innovations: (i) the weight values are estimated by a new scheme based on using a FuzzyCatastrophe Scheme (FCS), which is a hybrid of fuzzy logic and catastrophe theory; and (ii) a multiplicative model as the products of ALRIF and PT data layers. These are detailed in due course. The product of ALRIF and PT data layers renders a new quantity equivalent to risk mapping as a measure of relative risk and this is the key innovation in the paper. In general, risk quantification problems use the definition of mathematical products of the consequence of a hazard (or losses or an adverse effect/incident) and its likelihood, see Khatibi (2011) for a review of the emergence of the concept of risk, where the definition sets the basis for absolute values of quantified risks. Likewise, Sadeghfam et al. (2018) and Nadiri et al. (2018c) outline particular applications of the definition for risk mapping or risk indexing, where mapping or indexing refers to relative values. In spite of the classic definition, the concept of risk has diversified to cope with a wide range of applications and is the subject of many reviews, e.g. Ganoulis (2009). Arguably, the building blocks in the classic definition consider operational systems as intertwined with adverse effects. The concept of risk stipulates two dimension, in which hazards cover intrinsic potentials of the system for adverse effects of inflicting harm (passive processes); whereas likelihood considers mechanisms capable of creating system-wide impacts (as active processes). The data layers of ALRIF represent passive processes and PT those of active processes, as discussed later. The transformation of ALRIFT into a risk mapping technique in the paper is a heuristic representation and as such, the paper treats the hazard dimension as Passive Vulnerability Index (PVI) for subsidence and the likelihood dimension as Active Vulnerability Index (AVI), which expresses the impact of withdrawal of hydrostatic pressures providing the right conditions for activating gravity and thereby initiating subsidence. Besides the novelty of exploring ALPRIFT towards the vulnerability

and risk mapping problem, the paper also investigates a new scheme for learning the weight values for the ALPRIFT data layers through using a hybrid of Fuzzy Logic (FL) with catastrophe theory, as in the decision theory presented by Zhang et al. (2009), where the paper refers to it as FCS (Fuzzy-Catastrophe Scheme). Successful performances of diverse FCS applications include vulnerability of aquifer pollution (Sadeghfam et al., 2016a; Sadeghfam et al., 2018) and groundwater potential mapping (Sadeghfam et al., 2016b). These studies learn weights from catastrophe functions towards the objective of reducing subjectivity but without testing many different techniques to manage the scope of the paper. The paper introduces a new scheme by using an implicit overlay procedure to learn from catastrophe functions, as to be presented in due course. 2. Methodology The methodology presents a vulnerability indexing scheme based on FCS with the goal of transforming the ALPRIFT framework into a risk mapping problem. The paper is primarily concerned with the proof-ofconcept for using FCS for both vulnerability and risk mapping through the following procedure: Pre-processing: identifies data availability and the basic heuristic rules for processing the data; Modelling: presents the ALPRIFT Framework (AF) and breaks it into ALRIF and PT data layers and implements them as: (i) an additive model of ALRIF and PT data layers to produce a new scheme for vulnerability mapping; and (ii) a multiplicative model to transform ALPRIFT into a risk indexing technique. 2.1. Pre-processing: basic algorithms, concepts and data 2.1.1. Basic ALPRIFT The ALPRIFT framework (Nadiri et al., 2018a) is a capability to map Subsidence Vulnerability Indices (SVI) over aquifer areas by incorporating 7 data layers of: Aquifer media (A), Land use (L), Pumping of groundwater, Recharge (R), aquifer thickness Impact (I), Fault distance (F) and decline of water Table (T). Notably, any variation to the number of ALPRIFT data layers or to any framework would be tantamount to a different framework. The basic definition and their processing are explained later in Section 4. Inspired by the DRASTIC framework introduced by Aller et al. (1987), ALPRIFT uses a scoring system, which accounts for local physical variations by using prescribed rating values and relative importance of the data layer are accounted for by prescribed weighting values. Rates are worked out by dividing the study area into square grids (pixel) and the GIS model of each pixel is associated with 7 data layers, as follows:

SVI = Aw Ar + L w Lr + Pw Pr + Rw Rr + Iw Ir + Fw Fr + Tw Tr

(1a)

where the subscripts r denote rates and w denotes weights. As reproduced in Appendix I, the data layers are divided into appropriate numbers of classes to capture most generic variabilities in the data layer with prescribed rates (ranged from 1 to 10). Prescribed weights by Nadiri et al. (2018a) range from 1 to 5 and do not vary from one pixel to another, as described by Eq. (1b):

SVI = 5Ar + 4Lr + 4Pr + 3Rr + 2Ir + 1Fr + 5Tr

(1b)

The ALPRIFT framework is applied through dividing a study area to pixels, where the 7 data layers are processed by collating the appropriate data, information and maps at the initial stage to form datasets, as illustrated in Fig. 1. Higher calculated SVI values indicate that their region is vulnerable to subsidence. It is noted that the minimum and maximum possible values of SVI are 23 and 230, respectively. 2.1.2. Reappraising internal structure of ALPRIFT data layers The above equation for the ALPRIFT framework is broken down into the following two passive and active components, in which Passive Vulnerability Index (PVI) accounts for local variations and Active 4

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Fig. 1. Data layer preparation and InSAR possessing.

Vulnerability Index (AVI) accounts for the withdrawal of hydrostatic pressures from a control volume. These are expressed as follows:

PVI = Aw Ar + L w Lr + Rw Rr + Iw Ir + Fw Fr

(2a)

AVI = Pw Pr + Tw Tr

(2b)

This equation is used for risk indexing of the cases with insufficient data, where data are not available for estimating likelihood through frequency analysis. It is therefore a matter of attributing PVI to vulnerability and AVI to hazard but this crosses semantics, which makes it rather hard to reconcile Eqs. (4b) with (4c) in semantic terms. Notably, in the Venn diagram, Eq. (3) is equivalent to the union of PVI and AVI but Eq. (4b) to their intersection operations, which respectively express vulnerability indexing and risk indexing.

If the domain of AVI of is local, it is reasonable to assume that both AVI and PVI are additive at each pixel of a study area and they will together account for the Total Vulnerability Index (TVI) for subsidence and is expressed as:

2.1.3. Interferometric synthetic-aperture radar (InSAR) processing Information on Earth surface is derived from Sentinel-1 satellite and processed using phase difference between two SAR observations, where phase refers to the fraction of one complete sine wave cycle. Notably, the phase is often highly correlated with terrain topography and SAR images together with the phase information contain amplitude information related to the strength of radar responses. The Interferometric Wide (IW) swath products in this study comprise a 250 km swath (spatial resolution: 5 m × 20 m), which include three sub-swaths captured by Terrain Observation with Progressive Scans SAR (TOPSAR). It provides homogeneous image quality throughout the swath with uniform Signal-to-Noise Ratio (SNR) and Distributed Target Ambiguity Ratio (DTAR). Some more information is provided in Fig. 1 but reference may be made to Hanssen (2001) for further details.

TVI = PVI + AVI = (Aw Ar + L w Lr + Rw Rr + Iw Ir + Fw Fr ) + (Pw Pr + Tw Tr )

(3)

Eq. (3) expressing vulnerability to subsidence is likely to prevail under annual fluctuation of water table regimes, subject to a balanced regime of recharge and depletion. However, under persistently declining water tables, the AVI component is likely to be system-wide but with local variations. Under these conditions, as a proposition, one can think that the role of AVI is equivalent to the likelihood dimension in the classical definition of risk. Generally, risk quantification refers to the scope of tools capable of estimating absolute values of risk defined in terms of mathematical products of consequences of hazards and their likelihoods, expressed as follows (Khatibi, 2011; Spickett et al., 2012):

Quanitified Risk = Consequences of Hazards × Likelihood

(4a)

From the above arguments, consequences of hazards would be equivalent to PVI and likelihood to AVI, which concerns with the loss of hydrostatic pressure and thereby amplifying the potential for compaction and consolidation towards subsidence accounted for by the PT data layers. These effects induce spontaneously subsidence, in which Risk Index (RI) at a pixel may be defined as:

2.2. Modelling: fuzzy-catastrophe scheme to map passive/active vulnerability The paper builds on the Fuzzy-Catastrophe technique, outlined by Sadeghfam et al. (2016a, 2016b) and Nadiri et al. (2018b). This adapts the multicriteria decision-making theory given by Cheng et al. (1996). The learning of the weight values is through combining the FL Membership Function with catastrophe theory. Fuzzy logic by Zadeh (1965) uses: fuzzy sets, membership functions and fuzzy inference engines. In this way, fuzzy logic extended mathematical capabilities towards accounting for ambiguous quantities. Catastrophe theory by Thom (1987) uses a function of dependent variables (known as state variables) and a set of independent parameters (known as control parameters). The outcome of catastrophe theory is a capability to cope with an

RI = PVI × AVI = (Aw Ar + L w Lr + Rw Rr + Iw Ir + Fw Fr ) × (Pw Pr + Tw Tr ) (4b) The key to (4a) is that both hazard and likelihood are open-ended and they have to be defined to each problem area through risk analysis. Another approach is to express risk as a product of vulnerability and hazard, often expressed as (e.g. see LwR, 2004):

Relative Risk = Vulnerability × Hazards

(4c) 5

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Table 2 Catastrophe fuzzy membership functions (Cheng et al. 1996) – note control parameters correspond with ALPRIFT rates. Name

State variable

Control parameter

Catastrophe fuzzy membership functions

Rate

Data layers

Col:1 Fold Cusp

Col:2 1 1

Col:3 1 2

Col:4 xa = 2 a

Col:5 1 2

Col:6 – PT for AVI; PVI & AVI for TVI

4

–

Swallowtail

1

Butterfly

3

1

Wigwam

4

1

5

xa =

2

a , xb =

3

b

xa =

2

a , xb =

3

b , xc =

4

c

xa =

2

a , xb =

3

b , xc =

4

c , xd =

xa =

2

a , xb =

3

b , xc =

4

c , xd =

3

5

d

5

d , xe =

6

e

5

–

ALRIF for PVI

Note: a, b, c, d, e are control parameters. xa, xb, xc, xd, xe are state variables.

instantaneous loss of functional dependence between dependent parameters and state variables. Both are well-developed and serve sophisticated models. The decision theory uses catastrophe theory through the priority of the data layers, for more details, see Nadiri et al. (2018b), as in Table 2, which presents the types of functions available for catastrophe theory. They comprise fold, cusp, swallowtail, butterfly and wigwam and are defined by state variables (each with 1 state variable) and control parameters from 1 to 5. The paper present a scheme, which determine the type of catastrophe function and the estimation of their inherent parameters, as described in due course. The scheme presented by the paper comprises 5 data layers and therefore uses wigwam to represent PVI and AVI by two parameters and therefore uses cusp to represent AVI. Consider AVI for simplicity, which has two parameters of a and b. Therefore, it is a reasonable scheme to associate the third power, b-parameter, with the T-data layer, as it has ALPRIFT weight of 5 and the P-data layer with the second power, aparameter, as it has ALPRIFT weight of 4. The scheme uses the rate value of the data layer at each grid, which transforms the scheme to a variable value changing from one pixel to another. Thus, the paper defines the following implicit function for both PVI and AVI:

PVI =

AVI =

2

F(w = 1) +

3

I(w = 2) +

4

R(w = 3) + 5

2

P(w = 4) + 2

3

T(w = 5)

.

5

L(w = 4) +

6

A(w = 5)

fuzzy membership function; and (iii) calculate PVI and AVI as per Eqs. (5a) and (5b). Notably in Eq. (5a,b), the mean operator refers to the calculation of the state of the system, which is known as the complementary principle, the other approach is minimum operator which does not arise in the subsidence problem (Wang et al., 2011). 2.2.1. Assigning rates The rates of the 7 data layers at each pixel are assigned as per Nadiri et al. (2018a) but are normalised to produce fuzzy membership function (ranging from 0 to 1), and hence assigned rate values are normalised involving two cases: (i) Values are directly proportional to those of data layers for 5 data layers (A, L, P, I, T), hence the normalisation uses:

Xin =

Xi Xmin Xmax Xmin

(6a)

(ii) The two R and F data layers are inversely proportional and hence the normalisation uses:

Xin =

Xmax Xi Xmax Xmin

(6b)

where, i counts pixels; Xmax and Xmin are maximum and minimum values, respectively; and xin normalises particular values at the ith pixels. Each data layer is treated as a fuzzy variable (in contrast to random variables or crisp variables), which is known as vague quantity. Fuzzy variables account for inherent uncertainties by expressing them as a matter of degree; represents them using fuzzy sets with partial membership functions (ranging from 0 to – 1), for more details, see Grande et al. (2011). Weights: The basis for learning the weight values is transformed from an explicit scoring system in the ALPRIFT framework into an implicit functional expression by FCS where the index of the radical (nth root) plays the role of the implicit and nonlinear weights. The procedure is displayed in Fig. 2. The TVI and RI values are calculated by FCS through the additive and multiplicative operators respectively as follows,

(5a) (5b)

where Eq. (5a) consists of 5 sub-terms and Eq. (5b) of 2 sub-terms with each sub-term formulated using the following rationale: (i) identify the prescribed ALPRIFT weight for the data layers; (ii) use the actual rate value under the radical for each data layer; and (iii) reorder the ALRIF data later as FIRLA following the prescribed ALPRIFT weights and insert them in a wigwam catastrophe type; whereas use the cusp catastrophe type for PT, which are in the order of their prescribed ALPRIFT weights. The procedure for calculating the rate values is as follows: (i) assign rates to each data layer; (ii) normalise data layer values by using

Fig. 2. Forming implicit catastrophe functions by FCS.

6

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Fig. 3. Study area: (a) Location map, river and observation wells; (b) groundwater flow direction and abstraction wells; (c) lithological map.

7

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TVI =

2

PVI + 2

3

AVI

RI = PVI × AVI

(7a) (7b)

2.3. Performance metrics The performance of ALPRIFT and risk mapping for land subsidence is evaluated by the Receiver Operating Characteristic (ROC) curve and the Area Under Curve (AUC). Swets (1988) developed this metric to measure the accuracy of a diagnostic system. It divides a particular outcome of the events into 4 possible groups: True Positive (TP), True Negative (TN), False-Positive (FP), False Negative (FN). In subsidence problems, an event refers to vulnerability or risk indices, while outcome refers to subsidence. ROC curve plots FP proportions versus TP proportions at various threshold setting. A preferable ROC curve bulges heavily towards the upper left corner. AUC quantifies the accuracy of ROC curves and defines as the proportion of the area beneath the ROC curve to the total area. Thus, AUC varies between 0.5 and 1. At AUC = 0.5, FP is equal to the TP proportion with no indication of their

Fig. 4. Average GWL for all observation wells and the trend of water table decline.

Table 3 Definition, required raw data and process for 7 data layers (abridged from Nadiri et al., 2018a). Passive Vulnerability

Aquifer media

Definition Raw data Process

Land use

Definition Raw data Process

Recharge

Definition Raw data Process

Impact of aquifer thickness

Definition Raw data

Fault distancea,b

Definition

Process

Raw data Process Active Vulnerability

Pumpage of groundwater

Water Table decline

a

Definition Raw data Process

Definition Raw data Process

Soil texture (mixture of clay, silt, sand and gravel) at the saturated zone has direct proportionality with vulnerability of land subsidence. 49 geological logs at the location of observation wells Assigning rate based on recommendation by Nadiri et al. (2018a) If storitivity or porosity are available, they can also be used to assign rates Interpolate by IDW techniques

• • • •

Human activities can affect directly vulnerability. Nadiri et al. (2018a) categorised land uses to different groups as, mining/resources extraction, irrigated farming, dam construction, built-up, dry farming/grassland, barren land. Sentinel-2 image satellite on 1 July 2017 with 20 m resolution Image processing by ENVI software High recharge can mitigates the effect of water decline and has indirect proportionality with vulnerability of land subsidence. Slope: obtained by Landsat satellite image Soil permeability: obtained by geological logs Precipitation: obtained by Marand meteorological station Assign rates based on Piscopo (2001) Overlay

• • • • • Higher thickness of aquifer at the saturated and unsaturated zones, the greater potential to subsidence logs • Geological profiles • Geo-electrical • Interpolate by IDW techniques

Faults and related tectonic movement can amplify the subsidence of granular material. Therefore, distance from fault has indirect proportionality with subsidence vulnerability. Location of faults regarding geological map Calculate Euclidian distance by GIS software

• • pumpage to meet the demand is an external factor that can induces land subsidence. Therefore, • Groundwater it has direct proportionality with subsidence. volume of groundwater discharge at abstraction wells • Annual Voronoi polygon for observation wells • Draw the equivalent height of groundwater pumpage for each polygon and assign the obtained values for the • Calculate corresponding observation well • Interpolate by Inverse Distance Weighted (IDW) technique table decline increases effective stress and induces subsidence. • Water level time series at 49 observation wells • Groundwater the trend (slope) of water table decline/increase for each observation well • Calculate • Interpolate the obtained trend by IDW techniques

Subsidence induced by earthquakes include (Konagai et al., 2013; Bobrowsky and Bobrowsky, 2013):

subsidence in unconsolidated sediments, especially in layers with declining water table, which increases the subsidence vulnerability of • Compaction-induced plains against water table decline. shallow subsoil subsidence. • Liquefaction-induced Vertical subsidence due to tectonic movement. •Different studies refer to the 10 to 20 km interval as the closest to the fault in which aquifers show response to earthquakes (e.g., Lai et al. (2004)).

b

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Table 4 Details of SAR images. Acquisition date

Acquisition time

Orbit number

Orbital heading

2017.04.22

03:00:50

16,251

Descending

2017.06.21

07:24:45

17,126

Descending

2017.09.01

06:17:39

18,176

Descending

2017.11.12

06:22:22

19,226

Descending

2018.01.23

07:17:00

20,276

Descending

2018.04.05

03:00:55

21,326

Descending

Temporal base line (days)

Master image

Slave image

60

2017.04.22

2017.06.21

71

2017.06.21

2017.09.01

83

2017.09.01

2017.11.23

61

2017.11.23

2018.01.23

71

2018.01.23

2018.04.05

aquifer with their thickness increasing from the margin at the mountains towards the centre of the plain; (ii) sediment deposits are finer in the centre of the plain than the margins; and (iii) the aquifer is unconfined throughout the plain and confined at the central part, but the performance of the confined aquifer failed owing to over-abstraction and water table declines. There are 515 deep tubewells, which discharge an estimated 115 million m3 per annum; and 41 semi-deep wells, which discharge an estimated 1.2 m3 per annum. Also, as per East Azerbaijan Water Authority, there are 135 qanats and 71 springs abstracting 25 × 106 m3 and 4 × 106 m3 respectively per annum (EAWA 2013). Due to the failure of management policies and unauthorised abstraction, the Marand basin is faced with serious problems due to a decline in water table. Fig. 4 depicts the averaged Groundwater Level (GWL) for all observation wells and the trend of water decline that equals to 18.9 cm per month (approx. 2.25 m per annum).

discrimination and its ROC curve lies along the major diagonal line; whereas, a perfect discrimination is indicated by AUC approaching 1 and its ROC curve follows upper and left axes. 2.4. Jenks optimization method The calculated PVI, AVI, TVI and Ri values are variables but an understanding of their inherent variabilities is challenging. However, the results can be communicated better by classifying them into bands and for this, the paper uses Jenks' optimisation method. It is a data clustering method to identify the optimum arrangement of different classes through finding the minimum average deviation from the class mean by maximising the deviation of each class from the means of other classes. The variance is reduced within the classes and is maximised between classes and this is the key feature of the Jenks optimization method (Jenks 1967). The paper uses 5 bands as follows, Band 1 (low), Band 2 (relatively low), Band 3 (moderate), Band 4 (relatively high), Band 5 (high). Using this technique reduces the subjectivity associated with indices classification by expert judgment.

3.2. Data perepation 3.2.1. ALPRIFT data layers The definition of the 7 ALPRIFT data layers with appropriate details are given in Table 3, which is an adoption from that of Nadiri et al. (2018a). It gives definitions and sources for raw data. Of these, the processing for data layers L and T (Land cover and water Table decline) differ from those of Nadiri et al. (2018a) as follows: (i) prepare L by image processing using Envi software in three steps: pre-processing, processing and post-processing, as detailed below; and (ii) the yearly decline in water table considered by Nadiri et al. (2018a) is replaced with the trend of water table decline, which is arguably more representative on impacting the risk of land subsidence. The data layer L is processed as follows: Step 1 (pre-processing): apply atmospheric and geometric corrections; Step 2 (processing): identify different land uses by Normalised Difference Vegetation Index (NDVI) as a representative land use based on local knowledge and image interpretations. This is further aided by a supervised classification approach by using the maximum likelihood method; Step 3 (postprocessing): evaluate the results using local knowledge and expert judgment; modify further, if required; and apply to the processing step.

3. Study area 3.1. System description Marand plain is located in the Marand basin, north-west of East Azerbaijan province, north-west Iran (see Fig. 3a). The plain is within the the Araz basin flowing to the Caspian Sea but some 300 km west of the sea and is bordered by the Julfa region at its north and by the Urmia basin at its south. Mountains in the region are Mishovdagh and Pirdagh mountains located at the south of the plain and Budagh and Qaladagh mountains located north of the plain, which sandwich the plain in between the area rising towards the eastern moutntains of Qaradagh ranges and sloping gentely to the west, see Fig. 3b. Watercourses on alluvial formations are Zilberchay and Zunuzchay and flow into Qoturchay flowing northerly into the River Araz, a major river flowing into the Caspian Sea. Marand is a historic city located within the basin, where agriculture driven by groundwater is a main sector of activities. The hydrometeorlogical characterisation of the study includes: (i) as per Emberger (1930), the study area is arid and in the cold climate; and (ii) as per meteorological data of Marand station, the average annual precipitation is 242 mm and average annual temperature is 11.4 °C for a 10-year period 2008–2018 (provided by Meteorological Organisation of Iran). Lithology of the study area is shown in Fig. 3c. It depicts the following: (i) alluvial deposits form the main part of the undelaying

3.2.2. SAR images Table 4 represents 6 SAR Single Look Complex (SLC) images from Sentinel-1A satellite acquired during April 2017 to April 2018. These images processed 5 times as illustrated in the last two columns. The final result of InSAR processing is cumulative displacement for 5 interferometry analysis as discussed in Section 2.1.3.

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Fig. 5. Processed data layers passive vulnerability indexing: (a) Aquifer media; (b) Land use; (c) Recharge; (d) Impact of aquifer thickness; (e) Fault distance; active vulnerability indexing: (f) Pumpage of groundwater; (g) water decline trend.

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Fig. 6. Result: (a) InSAR subsidence map; (b) vulnerability by ALPRIFT; (c) PVI; (d) AVI; (e) TVI; (f) RI.

4. Results

weight values of the data layers are implicit functions and therefore their outputs gives variable weight values of the data layers at each pixel. The data layers are processed as per flowchart in Fig. 2 for mapping PVI, AVI, TVI and RI values.

4.1. Pre-processing The ALPRIFT rate values are assigned for each data layer as per Nadiri et al. (2018a) and the results are given in Fig. 5. The data layers, R and F are normalised by Eq. (6a) but the remaining data layers by Eq. (6b). The ALPRIFT procedure may be contrasted with those for processing the FCS data layers in flowchart in Fig. 1, as a result of which

4.2. Passive and active vulnerability indices Three set of results presented in Fig. 6 comprise: (i) InSAR results serving as observed data; (ii) SVI values mapping based on ALPRIFT,

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which involves no direct learning from the site-specific data; and (iii) PVI, AVI, TVI and RI mappings, which involve some learning from the site-specific data based on FCS. Both InSAR results and PVI, AVI, TVI and RI values are classifed into 5 bands based on Jenks' optimisation method (Jenks 1967). The processed InSAR results produce vertical land displacements in a specific period. A visual comparison between InSAR values in Fig. 6a and SVI values by ALPRIFT in Fig. 6b displays convergences and divergences. However, performance metrics presented in Fig. 7 for ALPRIFT using ROC/ AUC shows that the curve is suggestive of significant TP (True Postive) values and a concaved curvature with AUC value of 0.61. These are sufficient to conclude that the signals inherent in SVI values by ALPRIFT are not random but significant. As such, the results would be in developed countries as fit-for-purpose for planning activities but not defensible for specific activities, such as planning for the construction of building works. A further visual comparison between InSAR values in Fig. 6a and PVI, AVI, TVI and RI values in Fig. 6c, d, e and f by FCS also display convergences and divergences but strong similaries between PVI and TVI mappings are striking; as well as that between AVI and RI mappings. Their performance metrics displayed in Fig. 7 for PVI, AVI, TVI and RI using ROC/AUC show further concaved curvatures in TP (True Postive) values with AUC value 0.59, 0.67, 0.66 and 0.68, respective. These are sufficient to conclude that the signals inherent in SVI values by PVI, AVI, TVI and RI are not random but fit for broad planning activities, although for specific activities such as construction works, decisions would not be defensible if they are solely based on these values. Notably, RI values have the highest AUC and this confirms that the products of PVI and AVI is a feasible proposition and their underpinning concepts have significant correspondence with inherent information base in the site-specific data. These results discussed so far confirms a proof-of-concept for: (i) FCS is capable of learning from site specific data; (ii) breaking up ALPRIFT data layers into passive and active components is likely to have a real basis; and (iii) the results may serve as a proof-of-concept for PVI, AVI, TVI and above all for RI.

Fig. 7. Performance Metrics by ROC/AUC.

Table 5 Learning from variability of the results using PVI and AVI. Cases

Attributes of convergences and divergences

High PVI and high AVI

Occurrence: the central part of plain, Impacts: At these locations TVI and RI are high. Groundtruthing: Evident based on InSAR results Learning: Identify bands at an urgent need of attension Occurrence: the west part of the plain – PVI: high; AVI: lower Impacts: TVI and RI are low to moderate Groundtruthing: Evident based on InSAR results Learning: lower anthropogenic pressures at western parts Occurrence: central up to southeast parts of the plain – PVI: lower; AVI: high Impacts: TVI and RI are low to moderate Groundtruthing: Evident based on InSAR results Learning: anthropogenic pressures are predominant as per RI Occurrence: easternmost parts of the plain – PVI: low; AVI: high Impacts: TVI and RI are low to moderate Groundtruthing: Evident based on InSAR results Learning: inherently less vulnerable and low anthropogenic pressures

High PVI Lower AVI

Low PVI higher AVI

Low PVI Lower AVI

4.3. Inter-comparison of the results Further information contained in Figs. 5, 6 and 7 is extracted through their inter-comparisons as follows. The InSAR results in Fig. 6a is directly compared with the land use map (Fig. 5b). These maps provides a glimpse of the poor planning practices within the study area, as irrigation areas are located in recharge areas often using fertilisers.

Table 6 Areas of PVI, AVI, TVI and RI swept by each band.

Band 1 Band 2 Band 3 Band 4 Band 5

ALPRIFT 22% 49% 14% 13% 2%

PVI 21% 23% 32% 11% 13%

AVI 11% 27% 32% 23% 7%

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TVI 10% 24% 27% 20% 19 %

RI 15% 26% 31% 17% 11%

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Fig. 8. Field evidence for land subsidence in Marand plain, as documented in 13 October 2018.

Of course, during the times for traditional irrigation practices this was not a problem because there was no pumping, as the practices were sustainable but recent uses of fertilisers and pumping at high risk areas create serious risk exposures to health and subsidence. Whilst the convergences and divergences between SVI using ALPRIFT and InSAR results are not clear-cut, it is noted that the correspondence between PVI and TVI is obvious, as well as that between AVI and RI. These are captured in Table 5 using PVI and AVI, for which four cases are identified. Notably, the terms higher or lower signify their relative values (higher would mean from the base level of low, and lower would mean from the base level of high). The defferences between ALPRIFT and PVI/AVI/TVI may be attributed to the following possible factors: (i) unlike basic ALPRIFT, the T data layer is calucated by trend of water table decline instead of water table differences in a spesific year; (ii) FCS involves a learning process from the site-specific data, which is absent in ALPRIFT; (iii) weights through FCS are variable and use implicit (nonlinear) weights by FCS, as opposed to those by ALPRIFT.

Consider the difference between PVI (Fig. 6c) as a represention of geogenic vulnerability and AVI (Fig. 6d) as that of anthropogenic impacts. Their broad comparisons are indicative of passive processes being dominat at middle to lower parts of the basin but active processes at upper to middle parts of the basin. Likewise, high TVI and RI values display distinct behaviours tending towards the overlapped area of both high passive and/or active processes. The proportions of the study area swept by each band is investigated by taking off their results and displaying in Table 6. The bands may be characterised as: Band 1 - low; Band 2 - relatively low; Band 3 - moderate; Band 4 - relatively high; Band 5 - high. According to the table, ALPRIFT is seemingly biased to lower indices and its Band 5 is as little as 2.2% of the study area. The remaining indices by PVI, AVI, TVI and RI are indicative of less than half of the study to be in Bands 1 and 2 and some 30% of the area is swept by Band 3 and the remaining areas by Bands 4 and 5. These should be significant findings for the future practices on water utilisation of aquifer of the study area. The authors have not yet correlated the bands with the onset of any physical

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impacts, such as the emergence of cracks in the building, failure of road, ancillary works or building, as these studies are at their infancy and there is hardly any data to find, unless ALPRIFT is applied in situations that prevail in developed countries normally rich in data. This is why numerical banding (e.g. Band 1 or 5) is preferred to natural language descriptions to dispel possible misunderstandings. Nonetheless, Band 3 should be taken as the onset of warning, Band 4 as onset of demonstrable problems and Band 5 would signify emergency situations. Fig. 8 illustrates the field evidences for land subsidence. The reported subsidence values from field observations do not provide sufficiently reliable data to test the developed methodology, since observation wells in the vicinity of subsidence are often filled by granular material, there are also other uncertainties associated with the material of the piezometers.

RI for a further learning. One possible approach is to use multiple model through two levels of modelling, similar to Nadiri et al. (2018b), in which AI can be used for estimating PVI, AVI, TVI and RI. Whilst the authors use consistently the term framework to emphasise that there is no theory or empirical knowledge to justify the selected 7 data layers of ALPRIFT, the justification comes from the success of a framework to act as a decision tool. Also, the paper uses the term scheme in the sense of referring to a plan or arrangement for a particular procedure through a particular process, e.g. finite difference scheme. Since the emergence of computer sciences, there is a raft of techniques without any rational justification normally judged by the efficacy of the results, which enable modellers to discover or learn about data for gaining a new insight. On this basis, the totality of the techniques presented in the paper for both vulnerability and risk mapping may be regarded as heuristics.

5. Discussion

6. Conclusion

The paper presents a set of investigations, which is a link in the author's program of research towards developing a GIS-based ‘working tool’ for mapping SVI values for aquifers. The results presented in the paper are sufficient to serve as a proof-of-concept (TRL4 or higher) evidence for the concepts underlying PVI, RVI, TVI and RI, similar to the classification by the NASA, see: https://www.nasa.gov/sites/ default/files/trl.png. As such, RI can be used to identify hotspots of a study area. The aim is to raise these technique to Technical Readiness Level 9 (TRL9). To this end, various investigations are already under way, in which the authors are exploring different ways of dividing ALPRIFT data layers into PVI and AVI. ALPRIFT data layers are assumed to be independent of one another and the results in Fig. 5 provide a visual evidence for their independence. However, a fully independent data layer is unlikely, as natural conditions would shape each data layer in similar ways. Thus, normally some correlation is expected but its amount would be unknown in advance of modelling. Local models are data-driven and any finding from these models are bottom-up and as such they thrive on exploring correlation. Arguably, fully independent data layers are unlikely to be highly-correlated. PVI and AVI extract information on geogenic and anthropogenic vulnerability, respectively with PVI in terms of ALRIF and AVI in terms of PT. Although ROC/AUC indicates that their inherent signals are significant, different combinations of data layers are possible. For example, data layers can be divide to ALIF and RPT with respect to the role of water creating a system-wide impact. Furthermore, different modelling strategies may identify better correlation values. For a direct comparison of the results reported by the paper by published results, there is not much published works yet by ALPRIFT other than the one by Nadiri et al. (2018a). Even, then, a direct comparison is not quite possible, as the techniques are widely different. However, both papers show that the results of ALPRIFT are fit-forpurpose and a higher level of learning the values of weights from the site-specific data improves the performances. FCS implements a novel method for mapping PVI/AVI/TVI and reduces the subjectivity associated with assigning weight values and implicitly deriving from rate values to collectively reduce inherent subjectivity through FCS. Future plans are under way to investigate ways of extracting more improved information from PVI/AVI/TVI and

The ALPRIFT framework, introduced recently by the authors, is the basis of this paper for further innovations by testing the performances of ALPRIFT for subsidence Vulnerability Indexing (VI) and developing it further for Risk Indexing (RI). Indexing or mapping techniques are particularly suitable for cases, where the data availability is sparse and this is the case for the study area under investigation at Marand plain. The water table of the aquifer in Marand plain is subjected to unplanned pumpage and therefore it is declining at an approximate rate of 0.2 m/month. The loss of water from the saturation zone causes a loss of hydrostatic forces and subsequent subsidence, which is observed both on site and through InSAR processing. This paper breaks the 7 ALPRIFT data layers into two groups of ALRIF data layers, characterised as Passive Vulnerability Index (PVI); as well as of PT data layers, characterised as Active Vulnerability Index (AVI). Their additive model leads to the Total Vulnerability Indexing (TVI) problem and their multiplicative model to that of the Risk Indexing (RI) problem. The methodology for PVI, AVI, TVI and RI were tested at Marand plain, where there are poor planning practices and the water levels within the aquifer are declining. The study shows areas, where fair planning practices need to be developed. The performance of PVI, AVI, TVI and RI results are investigated by using ROC/AUC metrics and they show that the basic ALPRIFT is fit-forpurpose but its inherent noise due to prescribed values can be treated by FCS with significant improvement for the performances of PVI, AVI, TVI and RI. A further analysis shows that ALPRIFT is biased towards lower risk of subsidence, as it sweeps 71% of the study area under Bands 1 and 2; whereas the results by FCS reveal a significant proportion of the study area is exposed to subsidence, as per InSAR results. These results serve as a proof-of-concept for ALRIFT, PVI, AVI, TVI and RI and as such they can be used for identifying hotspots of over plains at risk of subsidence. Acknowledgement The authors express their thanks to East Azerbaijan Regional Water Authority, who cooperated by proving and preparing the data. The project was supported financially by Iran National Science Foundation (97009383).

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Range

Rate

8–10 8–9 6–8 3–5 2–3 1–3 8–10

Range

Clay Silt Karstic Sediments Sand Gravel Rock types e.g. (Sedimentary, etc.) Oxidised Organic soil

Mining/resources extraction Irrigated farming Dam construction Built-up (residential etc.) Transportation Dry farming/grassland Barren land

Land use (L)

Aquifer media (A)

9–10 7–9 6–9 4–8 3–4 1–2 1

Rate < 0.0001 0.0001 ≤ r < 0.005 0.005 ≤ r < 0.01 0.01 ≤ r < 0.5 0.5 ≤ r < 1 1≤r < 5 5 ≤ r < 20 20 ≤ r < 40 40 ≤ r < 65 > 65

Range 1 2 3 4 5 6 7 8 9 10

Rate

Pumping of groundwater (P)

Appendix I. The prescribed rates for ALPRIFT framework by Nadiri et al. (2018a)

0≤r < 4 4≤r < 9 9 ≤ r < 14 14 ≤ r < 19 19 ≤ r < 24 > 24

Range

Recharge (R)

10 9 7 5 3 1

Rate

0 ≤ r < 25 25 ≤ r < 55 55 ≤ r < 90 90 ≤ r < 130 130 ≤ r < 175 175 ≤ r < 225 225 ≤ r < 280 280 ≤ r < 340 340 ≤ r < 405 > 405

Range

1 2 3 4 5 6 7 8 9 10

Rate

Impacts of aquifer thickness (I)

0≤r 1≤r 2≤r 3≤r 4≤r >5

Range < < < < <

1 2 3 4 5

10 8 6 4 2 1

Rate

Fault distance (F)

0 ≤ r < 0.2 0.2 ≤ r < 0.5 0.5 ≤ r < 0.9 0.9 ≤ r < 1.4 1.4 ≤ r < 2 2 ≤ r < 2.7 2.7 ≤ r < 3.5 3.5 ≤ r < 4.4 4.4 ≤ r < 5.4 > 5.4

Range

1 2 3 4 5 6 7 8 9 10

Rate

Decline of water table (T)

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