A PARADIGM FOR SPATIAL MAPPING A PARADIGM FOR SPATIAL MAPPING OF GROUNDWATER CONTAMINATION OF GROUNDWATER CONTAMINATION IN RURAL SETTINGS: LESSONS FROM IN RURAL SETTINGS: LESSONS FROM

ARSENIC CONTAMINATION IN ARSENIC CONTAMINATION IN BANGLADESHBANGLADESH

Faisal HossainFaisal Hossain

Department of Civil and Environmental Department of Civil and Environmental EngineeringEngineering

Tennessee Technological UniversityTennessee Technological University

Collaborating Institutions Tennessee Technological University

Tri-State University – Jason Hill

University of Connecticut – Dr. A.C. Bagtzoglou

Griffith University, Australia – Dr. B. Sivakumar

University of Texas, Austin – Dr. Sanjay Srinivasan (and Louis Forster)

Supporting Organizations in Bangladesh – Institute of Water Modeling, Rajshahi University, Bangladesh Council for Scientific and Industrial Research (BCSIR), Ministry of Environment

Others – Nurun Nahar, Md. Delawer Hossain, Sayma Rahman, Shamshuddin Shahid, Abu Saleh Khan, Mafizur Rahman

Spatial Mapping 101Spatial Mapping 101

Groundwater Contamination and Groundwater Contamination and BangladeshBangladesh

From – British Geological Survey

HIGH

LOW HIGH

HIGH

LOW

WHAT MAKES SPATIAL MAPPING OF WHAT MAKES SPATIAL MAPPING OF ARSENIC CHALLENGING?ARSENIC CHALLENGING?

Question?

How can we spatially map aquifer contamination for rural Bangladesh with limited in-situ sampling data?

1. More than 50% of Bangladesh population at risk due to Arsenic contamination in shallow aquifers (< 150m).

2. Total number of shallow operational drinking wells UNKNOWN (10-18 million).

4. UNICEF/Government has ‘tested’ about 4-5 million wells using semi-quantitative field kits.

3. Most shallow wells privately-owned, sunk randomly at short notice, difficult to be updated through inventory control.

5. Field kits have large false positives and negatives.

6. Accurate and time-varying sampling of groundwater quality EXPENSIVE.

7. Spatial mapping accuracy depends of accurate sampling at adequate resolution

The near impossibility of testing every single shallow well in Bangladesh requires a simulation methodology that can accurately characterize a well as being safe/unsafe without the need for extensive and expensive in-situ sampling tests.

Such a method can then act as a fast-running and inexpensive proxy to the time-consuming lab-based field campaigns and save considerable testing resources by judiciously directing them to those wells pre-determined by the simulation method to have a high likelihood of being unsafe.

Furthermore, by flagging a safer cluster of wells functional (and an unsafe cluster of wells as non-operational), villagers are expected to find this approach socially more convenient than the more expensive house-hold treatment options currently available in Bangladesh.

Justification for a New Spatial Justification for a New Spatial Mapping Scheme for Developing Mapping Scheme for Developing

NationsNations

Outline of SeminarOutline of Seminar

Overview of Groundwater Arsenic Contamination in Bangladesh:

Spatial extent and results from a recent social survey.

Development of Paradigm on Spatial Mapping:

Marriage of Non-Linear Chaos Theory with Linear Stochastic Dynamics. Assessment of conventional geostatistical methods Chaos-based analysis of spatial pattern of arsenic Merit of a chaos-based approach

Vision for the Future: A Cost-effective Mapping Scheme that integrates the

‘physics’ of contamination

2nd Part

1st Part

3rd Part

A DISCLAIMERA DISCLAIMER

Work presented from a data-based Work presented from a data-based perspective of spatial mapping.perspective of spatial mapping.

PART ONEPART ONE

OVERVIEWOVERVIEW

Overview of Arsenic Contamination Overview of Arsenic Contamination in Bangladeshin Bangladesh

First case of Arsenic in 1993 Nationwide (BGS-DPHE) survey

indicated widespread arsenic - shallow ground water (<150 m)

80% of population (> 100 million) depend on shallow ground water.

Arsenic is geologic in origin: Pleistocene-Holocene

Million health cases per year projected.

A major Health Disaster in the making for the rural poor

Large-Scale Remedial EffortsLarge-Scale Remedial Efforts(For Rural Bangladesh)(For Rural Bangladesh)

1. Exploration of the potential of deep aquifers – High $$$ and Long Waiting Time

2. Understanding the mechanism of Arsenic contamination for long-term structural solution– High $$$ and Waiting Time

3. Closing cluster of unsafe shallow wells. Replacement with treatment options or drill safe shallow wells. Low-Medium $$$ and Waiting Time

Limitations of Ongoing Efforts Limitations of Ongoing Efforts (Option 3-Closing Wells)(Option 3-Closing Wells)

1. Safe/Unsafe Well detection is by UNRELIABLE FIELD KITS (but very inexpensive).

2. Total Number of Shallow wells UNKNOWN (10-18 million). Lack of accurate census.

3. Testing every well and flagging it manually requires LONG WAITING TIME (only 4-5 million wells ‘tested’ so far)+ Inventory is ‘dynamic’ (difficult to monitor).

4. Not all treatment options (e.g., Filter) appeal to the rural public. – Social compatibility issues.

Villagers would rather travel faraway once a day to collect their drinking water (after Haque et al., 2004, Public Health) – Our recent surveys confirm this

Why are Field Kits Unreliable?Why are Field Kits Unreliable?

A. Semi-quantitative – based on subjective interpretation.

B. Detection is ‘probabilistic’: (4 possible outcomes)1. Successful Safe Well Detection2. Unsuccessful Safe Well

Detection (False Alarm)3. Successful Unsafe Well

Detection4. Unsuccessful Unsafe Well

Detection (False Hope)[Safe/Unsafe according to 50 or 10

ppb limit]

Major Field Kit Brands in use in Bangladesh

False Hopes – Silent Poisoning

False Alarms – Unnecessary $$$ and Time wastage

Reliability Analysis of Field KitsReliability Analysis of Field Kits

WHO limit(10ppb)

BD Limit (50ppb)

POD safe 12.5% 80.3%

PODunsafe 96.9% 95.2%

P-false alarm

3.1% 4.8%

P-false hope

87.5% 19.7%

Asia Arsenic Network (AAN) kit- After Hossain et al. (2006) – Hydrological Processes

After Rahman et al. (2002)- Env. Sci. Technol.

Dep

th (

m)

Exceedance Probability (>10 ppb)

Exceedance Probability (>50 ppb)

Cost-effectiveness of Field Kits: Should Cost-effectiveness of Field Kits: Should we discard them altogether? we discard them altogether?

Field Kit

Capital Cost

Testing Time

Merck $50 30 min

GPL $43 20 min

NIPSOM $18 10 min

Field Kit test requires minimal training for staff (unlike AAS)

Field Kit tests are ‘quick and dirty’, no complicated protocols to follow

Field Kits are highly portable and commercially available in bulk qty

Field Kits can be ‘soft data’Source: NAISU – NGO Arsenic Information Support Unit www.naisu.org

What type of Spatial Mapping Scheme What type of Spatial Mapping Scheme do We Need for Rural Settings?do We Need for Rural Settings?

A rapid and low-cost methodology to identify cluster of unsafe shallow wells for immediate closure.

Justifications:

1. Rapid? – Too many wells- status unknown (10-18 million). Reduce exposure (Time is of the essence)

2. Low-cost? – Rural setting (Money is of the essence)

3. Closure of Unsafe well cluster? – The major difficulty/unknown of remediation effort is accurate identification-

Implications for Cambodia, Vietnam, Mexico, West Bengal (India)

Attitude of Rural PublicAttitude of Rural PublicAfter a Decade: Results from a Recent After a Decade: Results from a Recent

SurveySurvey1. Current awareness among

villagers is GOOD.

2. Haque et al. (2004) survey indicates that not all treatment options are socially compatible.

3. Villagers seem to prefer minimum maintenance, high flow rates, central distribution system.

4. Traditional water collection by females is still widespread.

5. Our Survey (conducted by Nurun Nahar of Japan Advanced Institute of Sci and Tech – JAIST and Ministry of Environment, Bangladesh)

Attitude of Rural PublicAttitude of Rural PublicAfter a Decade: Results from Our After a Decade: Results from Our

SurveySurvey

5675757512416128565Total

152016164.135316616Mianpur

91214144.025315614Rajarampur

324335354.7649916335Ranihati

FMFMTotal

No of Patients

Number of Contamina-ted TW

No of TW

Average number of person per HH

PopulationNumber of Affected HHs

Name of Village

Table 1:Population Statistics of the household samples from questionnaire survey

Legend: HH- Household; TW-Tubewell; M-Male; F-female

Contamination is based on arsenic test exceeding 50 ppb

Table 2: Households willingness to pay monthly for getting safe water (in taka)

00.00%00.00%3.57%59.31%Mianpur

00.00%3.48%43.32%22.74%30.46%Rajarampur

00.00%1.85%1.75%61.21%35.19%Ranihati

>200 Taka100-200 Taka50-100 Taka00-50 Taka00 TakaAffected Village

3.7400.00%14.60%76.7%8.7%Mianpur

4.6000.00%3.77%96.23%00.00%Rajarampur

3.882.56%3.31 %66.72%27.41%Ranihati

Average Minutes

10-15 minutes

5-10 minutes

0-5 minutes

00 minutesAffected Village

Table 3: Female Heads of households’ willingness to walk (in minutes)

Attitude of Rural PublicAttitude of Rural PublicAfter a Decade: Results from Our After a Decade: Results from Our

SurveySurvey1. Income plays a role lower income lower nutrition

higher susceptibility to arsenic problems?

2. Men are more exposed to arsenicosis then women (Reason? outfield work more water intake?)

3. Marked absence of discrimination – NGO campaigns seem to be effective

4. 60% willing to pay extra for safe water (up to a dollar)

5. 70% of womenfolk willing to walk for at least 5 minutes to collect safe drinking water

Part TwoPart Two

DEVELOPING THE PARADIGM FOR

SPATIAL MAPPING

Conventional Spatial Mapping Scheme Conventional Spatial Mapping Scheme (Estimating at Unsampled Locations)(Estimating at Unsampled Locations)

1. Conventional approach is Geostatistical; E.g. Kriging (and many others…)

2. Based on linear stochastic dynamics.

3. Estimate at unsampled location is a weighted linear combination

Assessment of Ordinary Kriging Assessment of Ordinary Kriging for Arsenic Contaminationfor Arsenic Contamination

Assessment of Kriging

Generate gridded fields of arsenic in log 10 (ppb)

Kriging

i) Compute Empirical Variogram

ii) Model Exponential Variogram

Random Selection of Zones for an exploratory network

(or field campaign)

i=i+1Step 1

Step 2

Step 3

Step 4

Step 5

Assessment of Ordinary KrigingAssessment of Ordinary Kriging

1. General trends are picked up satisfactorily at scales of > 50 km with large underestimation.

2. Kriging misses the local hot spots due to its smoothing function (Conditional Indicator simulation may be needed)

ND NCUnsafe

NB NASafeKri

gg

ing

Pre

dic

tion Unsafe Safe

Truth

Pre

dict

ion

Kri

gin

g

Pre

dic

tion

Confusion Matrix numbers (1000 MC realization)

Probability of False Hope(%)

Probability of Successful safe well Detection(%)

Probability of False Alarms (%)

Probability of Successful unsafe well Detection(%)

Mean Error (ppb)

Safety Limit NA NB NC ND

10 ppb

MeanMinMax

13422

4018

12325

126115138

23.2064.3

76.810035.7

8.717.22.3

91.382.897.7

-52.6

50 ppb

MeanMinMax

352347

14128

14425

9474108

27.82.639.8

72.297.460.2

12.718.13.9

87.377.996.10

-52.6

Indicator Kriging/SimulationIndicator Kriging/Simulation

Does not require assumption of normality.

Good for threshold-based estimation. Handles skewness well (zeros,

detection limit issues etc.). Handles scarce data well. 3-D Indicator kriging.

Sanjay Srinivasan and Louis Forster – ongoing work

Indicator kriging represents the spatial continuity of higher arsenic concentrations more accurately than ordinary kriging.

Why Search for Alternative Why Search for Alternative Approaches for Mapping?Approaches for Mapping?

Why?:

1. Conventional Geostatistical methods are two-point schemes – linear correlation between two points separated by a lag ‘h’ – pattern filling approach

2. Linear Stochastic in nature – makes no recognition of deterministic nature of data (the physics) (treats uncertainty as irreducible)

3. Simplifies spatial pattern manifested by complex interactions between geology and time-sensitive fluid flow dynamics.

Arsenic in groundwater is not a purely random occurrence and that there exist distinct geological and geochemical factors controlling its variability.

It is no longer defensible to continue to use pure geo-statistical approaches of pattern filling as stand-alone techniques for its spatial interpolation in resource poor settings that are typical of developing nations.

Chaos Theory as an Alternative Chaos Theory as an Alternative ApproachApproach

Why Chaos Theory?:

1. Evidence for a number of ‘hypotheses’ on arsenic contamination have been observed in Bangladesh.

2. Opinion Poll by Akmam (2002) revealed lack of a unifying theory:

58% support for Oxy-Hydroxide Reduction hypothesis;

33% support for Pyrite Oxidation hypothesis;

75% support groundwater extraction causes arsenic release;

3. Each hypothesis can be represented as a sum of at least 3 partial differential equations – necessary condition for phenomenon to exhibit ‘Chaos’

4. Chaos theory is based on non-linear deterministic theory and can potentially bridge the gap between mechanistic understanding (physics) and pure stochastic modeling (data-based).

5. Correlation Dimension (CD) is one measure of chaos – Grassberger-Procaccia Algorithm.

Evidence of Chaos in Arsenic data in Evidence of Chaos in Arsenic data in Bangladesh: Correlation Dimension Bangladesh: Correlation Dimension

AnalysisAnalysis Hossain and Sivakumar

(2006), Stochastic Env. Res. and Risk Analysis – demonstrated Chaos in Arsenic spatial variability using BGS data.

Correlation Dimension of 8-10 observed. Embedding Dimension of 10-12.

Arsenic contamination in space, from the chaotic point of view, is a medium- to high-dimensional problem.

Hypothesis - At least 8 variables/dimensions needed to optimally model spatial variability ‘deterministically’

Deterministic Randomness

The Hénon map is given by: x(t) = a + b * y(t-1) – x(t-1)^2 y(t) = x(t) ; a=1.4, b=0.3.

Assessment of Correlation Assessment of Correlation DimensionDimension

Is Correlation Dimension a Reliable Proxy for the Number of Dominant Influencing Variables for Modeling Risk of Arsenic

Contamination in Groundwater?

1. Using Ordinary Logistic Regression Models, the value of CD as a proxy was assessed:

ln[p/(1-p)] =logit (p) = α + βx

Where, p = probability of a well exceeding a concentration limit; x=vector of influencing variables; α is a constant, β is a vector of slope coefficients

2. INFLUENCING VARIABLES? – CD does not inform on the choice but only the ‘optimal’ number of variables in a deterministic model

Assessment of Correlation Assessment of Correlation DimensionDimension

All possible combinations of LR models considered – 2048 combinations

Uncertainty associated with prediction of wells as safe and unsafe by LR model declines systematically as the total number of influencing variables increases from 8 to 11.

Sensitivity of the mean predictive performance also increases noticeably for this range.

The Selected Influencing Variables for Logistic Regression Modeling

Variable Mean Minimum Maximum

Well depth (m) 60.55 00.60 362.00

Ba(ppb) 87.34 2.00 1360.00

Ca (mg/L) 51.59 00.10 366.00

Fe (mg/L) 3.353 00.005 61.00

Mg (mg/L) 20.75 00.04 305.00

Mn (mg/L) 0.555 0.001 9.98

Na (mg/L) 88.936 0.700 2700.00

P (mg/L) 0.765 0.100 18.90

Si (mg/L) 20.519 0.030 45.20

SO4 (mg/L) 5.917 00.20 753.00

Precip (cm) 86.001 25.35 596.14

As (ppb) 55.205 00.50 1660.00

Part ThreePart Three

VISION FOR THE FUTURE

The Future of GW Contamination The Future of GW Contamination Mapping in Rural SettingsMapping in Rural Settings

Where are we right now?

Linear Geostatistical techniques – two-point only correlation, smoothing filter, misses local hot spots, treats contaminant as a pure random variable with no regard for the physics behind the spatial variability

Chaos-based non-linear models –does not treat contaminant as a pure random variable; deterministic randomness can be quantified; Correlation Dimension appears to have merit as a proxy in deterministic models; but does not prioritize influencing variables

Can we use current arsenic geochemistry knowledge to prioritize influencing variables in chaos-based non-linear models?

Can chaos-theory be a bridge between linear stochastic techniques and contamination physics?

Can we use multiple point techniques?

Combines two paradigms: Geostatistical Paradigm and Chaotic Paradigm

Geostatistical Paradigm – Pattern Filling (Kriging – and/or conditional simulation)

Chaos Paradigm – Pattern Recognition (number of variables defining spatial variability) – Physics-based

Combining both may increase success rate of identifying unsafe wells (reducing false hopes).

Success Ratio (Geostatistics.AND.Chaos Theory) IS GREATER THAN Success Ratio (Geostatistics.OR. Chaos Theory) ?

New Paradigm for Spatial MappingNew Paradigm for Spatial Mapping

Implications for *any* contaminant variable and other rural regions – Southeast Asia, Mexico, South America – probably the US

General Formulation of Our General Formulation of Our Mapping SchemeMapping Scheme

1. Theoretical formulation recognizes explicitly the complex fluid flow patterns through multiple connection statistics

2. Mapping scheme explicitly integrates the dominant physical knowledge in the parameterization of the chaos-based models

1.Arsenic Geochemistry & Transport Mechanism

2. Non linear Deterministic Dynamics CD analysis of Arsenic spatial variability

3. Multiple point Correlation Functions

In-situ Sampling

Advanced Mapping Scheme

Indicator Kriging /Simulation method

Calibration data requirement should stay invariant

Integration of techniques is Bayesian and treated as a priori for indicator simulation

The Future of Mapping in Rural The Future of Mapping in Rural SettingsSettings

Agenda – what is needed to move forward?

1. Greater Collaboration with community engaged in mechanistic understanding of arsenic contamination (geologists, soil geochemist, groundwater hydrologists etc) to identify ‘influencing variables’ and integrate them physically in chaos-based mapping schemes.

2. Assess enhanced geostatistical methods – Conditional Indicator Simulation

3. Address the transient nature of the problem – leverage realtime environmental monitoring network

4. Implement the proposed scheme (and paradigm) in real-world using limited sampling data.

5. Search for ways to generalize the approach for any contaminant variable under a resource-poor setting for a developing country.

SALIENT POINTS (Current Progress SALIENT POINTS (Current Progress Report)Report)

1. Typical Field Kits used in Bangladesh have large false positives and negatives (25%-80%). Social survey indicates villagers willingness to ‘walk/pay’.

2. Mainstream linear geostatistical methods for spatial mapping are inadequate for locating local scale hot spots/variability at scales < 50 km.

3. Mainstream geostatistical methods smoothen the complexities of contamination and should be augmented with enhanced methods. Examples are: non-linear chaos, multi-point and indicator kriging.

4. Arsenic contamination exhibits clear deterministic dynamics in spatial pattern – sensitive to geology.

5. Correlation Dimension analysis indicates 8 or higher influencing variables needed to spatial model variability optimally.

6. Correlation Dimension has information value as a rapid proxy (at least for Logistic regression).

7. As a path forward, greater collaboration is now needed with community on mechanistic understanding of contamination to bridge the gaps between mapping scheme and integration of physics in the interpolation.

Relevant Publications Relevant Publications (available at (available at

iweb.tntech.edu/fhossain/publications.html)iweb.tntech.edu/fhossain/publications.html)

7. Rahman, S., and F. Hossain . (2007). A Forensic Look at Groundwater Arsenic Contamination in Bangladesh, Environmental Forensics. 8(4), December (In press)

6. Nahar, N., F. Hossain, and M.D. Hossain (2007). Health and Socio-economic Effects of Groundwater Arsenic Contamination in Rural Bangladesh: Evidence from Field Surveys, International Perspectives Journal of Environmental Health. (Provisionally accepted)

5. Hill, A.J., F. Hossain and B. Sivakumar. (2006). Is Correlation Dimension a Reliable Proxy for the Number of Influencing Variables required to Model Risk of Arsenic Contamination in Groundwater? Stochastic Environmental Research and Risk Assessment, (In press; doi: 10.1007/s00477-006-0098-6).

4. Hossain, F., A.J. Hill, and A.C. Bagtzoglou (2006). Geostatistically-based management of Arsenic Contaminated Ground water in Shallow wells of Bangladesh. Water Resources Management. (In press, doi: 10.1007/s11269-006-9079-2)

2. Hossain, F. and B. Sivakumar. (2006). Spatial Pattern of Arsenic Contamination in Shallow Tubewells of Bangladesh: Regional Geology and Non-linear Dynamics Stochastic Environmental Research and Risk Assessment , vol 20(1-2), pp. 66-763. Hossain, F. and B. Sivakumar (2007). Spatial Interpolation of Contaminantion based on Linear and Non-linear Paradigms for Developing Countries, Stochastic Environmental Research and Risk Assessment (Revised and in review).

1. Hossain, F., A.C. Bagtzoglou, N. Nahar* and M.D. Hossain. (2006). Statistical Characterization of Arsenic Contamination in Shallow Tube wells of Western Bangladesh. Hydrological Processes. vol. 20(7), pp. 1497-1510 (doi:10.1002/hyp.5946).

AcknowledgementsAcknowledgements

1. Center for Management, Protection, Utilization of Water Resources, Tennessee Technological University (TTU)

2. Department of Civil and Environmental Engineering, TTU

3. Office of Sponsored Research, TTU

4. Ministry of Environment, Bangladesh

5. Institute of Water Modeling, Bangladesh (5-year MOU with TTU)

6. Bangladesh Council for Scientific and Industrial Research (BCSIR)

7. British Geological Survey and Department of Public Health, Bangladesh

8. Asia Arsenic Network (Japan)

9. Rajshahi University, Bangladesh

10.And many other friends and colleagues

Thank You!Thank You!

Questions?

“When a large portion of the rural population continues to suffer from the arsenic calamity, we, the more fortunate ones with time to brainstorm, have the responsibility to critically assess any novel idea until a long-term structural solution is in the horizon. “