GEOSTATISTIC MAPPING OF ARSENIC, MANGANESE AND IRON CONTAMINATION RISK IN THE PORT OF SANTANA, AMAPA, BRAZIL

Joaquim Carlos Barbosa Queiroz, Universidade Estadual Paulista, Brazil, José Ricardo Sturaro, Universidade Estadual Paulista, Brazil,

and Paulina Setti Riedel, Universidade Estadual Paulista, Brazil ABSTRACT For over 4 decades intense industrial activity, brought on by manganese exploration and commercialization in Amapá, Brazil, produced profound changes in the region, both socially and environmentally. There are strong indications that a series of environmental problems caused by this activity, including surface and underground water contamination, mainly due to residue deposits produced at manganese pellet/sinter plant, in the industrial area of Santana, on the banks of the Amazon River, where the manganese is loaded on ships. From preliminary studies of surface and underground water samples, which showed concentrations of manganese, arsenic and iron above normal levels established for human health, an evaluation of the contamined water was done using geostatistic tools and stochastic simulation. Variografic models were used to describe the spatial continuity pattern for metal concentrations in the study. Conditional simulations, including annealing simulation, were done to evaluate the contamination level in unsampled areas, create risk maps showing contamination probabilities in the area and maps indicating established cut-off values. The results represented by pos-processed maps of simulated values and global uncertainties showed the areas of higher contamination and more need of recovery. Manganese and arsenic demonstrated significantly higher results. The areas with higher levels of arsenic contamination are located in and around the fine refuse basin while manganese occupied a much large section, covering almost the entire study area, including a small portion outside the industrial area. INTRODUCTION

There are many questions involving the problem of environmental contamination of surface and underground water. Generally, one seeks to find out when the concentration of a specific contaminant exceeds established standards, where the boundary lies between contaminated and uncontaminated areas, what the level of confidence is regarding those boundaries, how much contaminant (total mass) is present, and what needs to be removed. The main objective is to provide additional information beyond simple estimates of contamination in order to reduce the chances of any erroneous decisions.

Up until the end of the 1980's, a typical geostatistical study was carried out in three steps: exploratory analysis of the data, modelling of the spatial variability (semivariogram), and finally, prediction of the attributes of values in locations where no samples were taken. It is now known, however, that algorithms of interpolation by least square, such as kriging, tend to smooth out local details of spatial variation of the attribute, typically overestimating smaller values and underestimating larger values. The use of interpolated, smoothed-out maps is inappropriate for applications that are sensitive to the presence of extreme values and their patterns of continuity, such as the evaluation of sources of re-covering in mineral deposits (Journel & Alabert, 1990;

Nowak, Srivastava, & Sinclair, 1993), modelling of the flow of fluids in porous mediums (Schafmeister & De Marsily, 1993) or the delineation of contaminated areas (Desbarats, 1996; Goovaerts, 1997a). Stochastic simulation has increasingly become the method of choice for estimation due to the ease of generating maps realizations that reproduce the sample variability, as opposed to interpolation methods that produced maps estimated for one given criteria of optimization only. A set of realizations that adjust reasonably well to the same statistics (histograms and semivariograms) is particularly useful to evaluate uncertainty about the spatial distribution of attributes of values and to investigate the performance of various scenarios, such as mineral planning or remediation of pollution (Goovaerts, 1998). Although the principles of geostatistical simulation are known in the geostatistics literature, these techniques have not been widely applied to problems of contamination of underground water.

The realizations generated with conditional simulation techniques should honor

the data as closely as possible in order to be reliable numerical models for the attribute under study. The application of optimization methods, such as annealing simulation (AS), for stochastic simulation has the potential to honor the data more than the conventional geostatistical techniques of simulation. The essential characteristic of this approximation is the formulation of a stochastic image as a problem of optimization with some specific objective function. The data to be honored by the stochastic images are coded like components in an objective global function (Deustch, C. & Cockerham, P., 1994). There are various applications of annealing simulation in hydrogeology. The application of AS to model stochastic aquafiers involves a two-step procedure: first, the problem of interpolation is re-stated as a problem of optimization. Second, this optimization is solved using AS. Dougherty and Marryott (1991) were the first to apply this technique in the context of hydrogeology - the problem of optimization of management of underground water. In a later article, they deal with remediation of underground water in a contaminated area (Marryott, Dougherty, & Stollar, 1993). Deutsch and Journal (1991) applied AS in the stochastic modelling of reservoirs. Zeng and Wang (1996) used AS to identify parameters of structure in the modelling of underground water (Fang & Wang, 1997).

In this study, we present an approximation using simulations to evaluate the contamination of underground water with manganese, arsenic, and iron in the port city of Santana, located in the state of Amapá in northern Brazil. AS was utilized, which is a technique of flexible heuristic optimization commonly applied to obtain different realizations with specific spatial characteristics. The AS approximation requires no a priori considerations regarding the base structure of the model, is not limited to random Gaussian fields, and does not require any functional form of the variogram (Gupta, et al, 1995), making its use possible in situations where the variables have highly asymmetrical distributions, such as the present study. A visual and quantitative measure of the spatial uncertainty is provided by the generation of numerous realizations (simulations) that adjust reasonably well to the same statistical samples (histogram and variogram) and given conditions. Each realization is, therefore, consistent with the known concentrations of contaminants, the sample histogram, and spatial continuity models exhibited by the data. Thus, each realization is an equally valid description of contamination. Probability summaries are prepared, based on the set of realizations, to obtain maps of risk that show the probability of contamination in the area under study, to identify the location of boundaries between contaminated and uncontaminated zones, and to generate maps indicating the cut-off values established. Even if additional

significant information is obtained for decision-making regarding the evaluation of contaminated locations, this evaluation should always involve attention to the physical processes responsible for the placement and, potentially, redistribution of the contaminants. ANNEALING SIMULATION

Simulated annealing is a generic name for a family of optimization algorithms based on the principle of stochastic relaxation (Geman & Geman, 1984). References for the application of these techniques include Deutsch & Journel (1992), Deutsch & Cockerham (1994) and Goovaerts (1997). An initial image is gradually perturbed so as to match constraints such as the reproduction of target histogram and covariance while honoring data values at their locations. Unlike others simulation algorithms, the creation of a stochastic image is formulated as an optimization problem without reference to a random function model. Geostastitical simulated annealing requires an objective function that measures the deviation between the target and the current statistics of the realization at each ith perturbation. Once the objective function has been established, the simulation (actually an optimization) process amounts to systematically modifying an initial realization so as to decrease the value of that objective function, getting the realization acceptably close to the target statistics. There are many possible implementations of the general simulated annealing paradigm. Variants differ in the way the initial image is generated and then perturbed, in the components that enter the objective function, and the type of decision rule and convergence criteria that are adopted. In this study the initial image is generated honoring data values at their locations. The perturbation mechanism used is the swap the z-values at any two unsampled locations u and u chosen at random, so becomes and

vice-versa. After each swap the objective function value (1) is updated. Semivariografic models were used to describe the spatial continuity pattern for metal concentrations in the study. So the following objective function is used:

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where is the prespecified z-semivariogram model and is the

semivariogram value at lag h

)( sh� )(� )( si h�

s of the realization at the ith perturbation to a specified number S of lags. The decision rule used to accept unfavorable perturbations according to a negative exponential probability distribution is:

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The larger the parameter t(i) of the probability distribution, called temperature, the greater the probability that an unfavorable perturbation will be accepted at the ith

iteration. The temperature is lowered by multiplying the initial temperature t0 by a reduction factor � whenever enough perturbations have been accepted or too many have been tried. The maximum number of accepted (Kaccept) or attempted (Kmax) perturbations is chosen as a multiple of the number N of grid nodes. Deutsch & Journel (1992) suggest to use on the order of 100 and 10 times the number of nodes to Kmax and Kaccept, respectively. The convergence criteria for stopping the optimization process was defined when the objective function reaches a sufficiently small value (Omin) or the maximum number of perturbations attempted at the same temperature exceeded a certain number of times (S). LOCATION OF THE AREA AND CHARACTERIZATION OF THE PROBLEM

The area under study is located in the state of Amapá (Figure 01a), situated in the extreme north of Brazil, approximately between 50 and 55 W and 0 and 5 N, with an area of 143, 453.7 km2 and a population of 379,459 distributed among 16 municipalities. More than two-thirds of the population of the state is concentrated in the capital, Macapá, which has 282,745 inhabitants (IBGE, Census 2000). The majority of the state is covered with the Amazon forest, with some pasture lands and fields. The economy is based on agriculture (manioc, rice, corn, and beans); livestock (cattle, buffalo); natural resources (manganese, cassiterite, gold, cashew nuts, wood, rubber); and industry (lumber, foods, construction materials).

(a) (b) (c) Figure 01: (a) The state of Amapá in the extreme north of Brazil; (b) and (c) municipalities in the state of Amapá, with details of Serra do Navio, where the mining occurred, and Santana, where the [pellets/sinter] and embarkment of the manganese ore occurred.

In 1953, following the discovery of high quality manganese in Serra do Navio, about 200 km from Macapá, (Figure 01b and c), the Indústria de Comércio de Minérios S/A (ICOMI; in English, Ore Commerce Industry, Inc.) was established to carry out the mining and commercialization of the ore. A contract was signed between ICOMI and the Federal government conceding the authorization for the mines for a period of fifty years, with the contract ending in 2003 (CPI Informe. Legislative Assembly of Amapá, 1998).

In order to carry out the mining, ICOMI constructed, in addition to the industrial installation, a residential community near the manganese mines in Serra do Navio with complete infrastructure including sanitation, leisure, schools, a supermarket, hospital, and housing for the company�s employees and their families. A railroad was also built which linked the village of Serra do Navio to an industrial area on the banks of the north canal of the Amazon River, in the municipality of Santana (Figure 01b and c), about 30 km from Macapá, from where the sold manganese was shipped. This approximately 129 hectare area (Figure 02), characterized as being strictly for industrial use, was used basically to stock the ore (manganese and iron), products (pellets/sinter and alloys) and raw materials (fuel, coke, etc.) that arrived and departed via this ICOMI port and rail terminal (JAAKKO POYRY ENGENHARIA, 1998 report). The manganese and cromite ore were thus transported by railroad from the mines in Serra do Navio to the ICOMI industrial area in the Port of Santana, a distance of approximately 200 km.

Figure 03 presents a schematic geological section of the eastern sector of the ICOMI area where various units and stockpiles are concentrated. It was observed that the geological profile at the banks of the Amazon River present the following sequence from the top to the base: alluviums (silty organic clay) extending approximately 150m and measuring up to 40m in thickness; horizon of clay silts (superior/upper horizon) with a continuous thickness around 6 to 8m and a horizon of hard clays (inferior/lower horizon). The area of interest, which extrapolates the perimeter of ICOMI, sits atop sediments of the Barriers Formation, constituted of silty organic clays, clay silts, and hard clay with scarce intercalations of fine and coarse sand. The water level (WL) that separates the non-saturated horizon (above the WL) from the saturated (below the WL) varies in depth, ranging from a few centimeters near the riverbank up to a maximum value around 9.0m in the northern portion. These depths oscillate throughout the year due to the seasonal variations in the potenciometric surface of the underground water. The potenciometric surfaces, measured in the wells that were installed, condition the movement of the water underground (subterranean flow). Thus, for the information obtained in June and August, 1997, it was observed that the subterranean flow develops from the center of the area, the region between wells 16 and 21, flowing radially in direction of the Amazon River and other neighboring areas (JAAKKO POYRY ENGENHARIA, 1998 report).

After extracting 60 of the estimated 65 million tons of manganese ore reserve in Serra do Navio, ICOMI presented, in November of 1997, a report to demonstrate the exhaustion of the deposit. There are strong indications of a series of environmental problems caused by the mining of the manganese deposits in Amapá. A Parliamentary Commission of Inquiry established in April, 1999, to investigate the dismantling process of ICOMI presented documents (JAAKKO POYRY ENGENHARIA, 1998 report) about the environmental situation in the industrial area of Santana, denouncing that the quality of the surface and underground water had been affected, mainly due to the residue deposits generated in the manganese ore pellets/sinter plant in the area. Regarding the potential for contamination, Arsenic and Manganese were found to be present in levels exceeding standards established by the brazilian law in the surface and underground water linked to the fine residues stocked in the Refuse Basin and vicinity. The standards are established in accordance with the World Health Organization (WHO), which considers water containing more than 0.05 ppm of arsenic inappropriate for human consumption. However, the Environmental Protection Agency (EPA) is concluding regulations to reduce the risks to public health of arsenic in drinking water.

The EPA is establishing a new standard of 10 parts per billion (ppb) for arsenic in drinking water to protect consumers against long term effects of chronic exposure to arsenic in drinking water. Such effects include cancer and other health problems including cardiovascular disturbances, diabetes, as well as neurological effects (EPA, 2001).

To represent the area under study, fifty locations were selected corresponding to 37 monitoring wells and 13 samples of sub-surface/effluent water (Figure 02) where analysis of the contaminants (manganese, arsenic, and iron) was carried out. The physical-chemical analyses of soil and water samples and the characterization of residues were conducted by the S.G.S. laboratories of Brazil and CEIMIC Avaliação Ambientais S/C Ltda.(in English, Environmental Evaluation, Ltd.), selected based on their technical qualifications, equipment used, and recognition of their services (JAAKKO POYRY ENGENHARIA, 1998 report). RESULTS AND DISCUSSION Data and Statistical Description

Table 01 and Figure 04 (frequency distribution, right column), show that the arsenic, manganese and iron variables have highly asymmetric distributions, indicating the presence of a few large concentrations. The metal concentrations are expressed in parts per million (ppm). The manganese concentration showed the highest asymmetry (6,71), probably due to the occurrence of a single high value concentration (216 ppm). In Figure 04 (cumulative frequency distributions, right column), the vertical dashed lines indicate, for each metal, the tolerable maxima for water, as defined by the brazilian law; see Table 01 for exact values. The percentage of data exceeding these critical thresholds is given at the top of each graphic. These proportions are larger for manganese (58%) followed by iron (34%) and arsenic(22%). The gray scale maps in Fig. 04 (left column) provide a preliminary description of the extension of the contamination by the metals in study. The highest arsenic and manganese accumulations are located in the central and southern region. The highest iron accumulations are located in the southeast region of the study area. Contour maps would be prepared from these data to characterize the site . The boundaries between contaminated and uncontaminated zones would be identified by the location of these contours.

Table 02 gives the correlation coefficients among the variables. The correlation

coefficient of Pearson, �, provides a measure only of linear relation between two variables and is complemented by rank correlation coefficient, �rank, which considers the ranks of the data. Unlike the traditional correlation coefficient, the rank correlation coefficient is not strongly influenced by extreme pairs. Large differences between the two reflects either a nonlinear relation between the two variables or the presence of pairs of extreme values. The results show a significant relationship between arsenic and manganese concentrations. Larger manganese concentrations tend to be associated with larger concentrations of arsenic. Both measures, � and �rank, are similar, as arsenic vs. manganese as manganese vs. iron, which indicates that extreme values do not greatly affect the linear correlation coefficients. The sample does not show any sign of an association between arsenic and iron concentrations.

Table 01 � Descriptive Statistics of the variables (ppm) Statistics Arsenic Iron Manganese

Mean Median Standard Deviation Minimum Maximum Skewness Kurtosis Tolerable Max. Sample size

1.050.0453.160.01

17.803.85

18.550.05

50

4.020.309,810.02

56.003.62

17,620.30

50

5,760,15

30.550,02

216.006.71

46,650.10

50 Table 02. Correlation coefficient of Pearson (�) and Rank correlation coefficient (�rank) Variables � prob � t �rank prob � t

Arsenic vs Iron

Arsenic vs Manganese

Iron vs Manganese

0,028

0,434

0,274

0,847 ns

0,002 ***

0,054 ns

-0,104

0,455

0,235

0,4709 ns

0,0009 ***

0,1001 ns

ns : not significant *** 1% significant Sample semivariograms and spatial continuity model

Sample semivariograms were computed using the semivariogram estimator presented in Deustch & Journel, 1992. Because the sample size was small, it was not possible to calculate informative directional sample semivariograms. For this reason, the correlation structure of the variables was considered isotropic, and "omnidirectional" sample semivariograms were computed (Isaaks e Srivastava, 1989). To the variables studied, spherical semivariograms models were fit defined by:

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ahch

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�

� �

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(3)

where h is the separation distance, c is the sample variance and a is the range or correlation length. The sample semivariograms and models to each variable are shown in Figure 5 and in the Table 03 the model parameters are presented. The iron presented the best spatial correlation, indicated by smaller nugget effect and arsenic showed the largest spatial continuity, due to having the largest range.

Table 03. Summary of fitted semivariogram model parameters Variable Nugget, C0 Sill, C Range, a (km)Arsenic Manganese Iron

0.25 0.27 0.04

0.850.750.92

0.320.180.20

Simulations We used the programs from the GSLIB library (Deustch & Journel, 1992). Fifty conditional simulations of the contaminant concentrations were generated on a regular 35 x 50 grid using the simulated annealing algorithm (Sasim). Figure 06 shows for all variables, the first realization and fitted semivariograms for the five initial realizations. Edge effects may occur by annealing simulation when the univariate distribution is highly skewed. These effects can be avoided by weighting the border pairs (Deustch & Cockerham, 1994) or, alternatively, by a combination of reducing the number of lag vectors used in the objective function, positioning the lag vectors according to anisotropy of the spatial variability model, and supplying a more advanced, realistic initial configuration (Carle, 1997). The edge effects were noticeable in the manganese variable that presented the largest asymmetry. In this case, we used the alternative procedure of reducing the number of lags vectors (4 lags) of the objective function and realistic initial configuration. One can observe a decreasing of the border effects and in the quality of fitted semivariograms (Figure 06, middle graphics). However, the fitted semivariograms of the studied variables can be considered acceptable. Probabilistic summaries of the simulations were obtained using the computer program Postsim. A map is presented of the expected value estimates (E-type) that were obtained by averaging the 50 simulated values for each realization. E-type estimate maps and respective histograms of each variable are presented in Figure 07. The areas with higher levels of arsenic contamination are located in and around the fine refuse basin, while manganese occupied a much larger section, covering almost the entire study area, including a small portion outside the industrial area. Iron concentrations are higher in a southeast portion of industrial areas. Maps showing the probability of exceeding a particular threshold were computed from the set of simulations by counting the number of corresponding pixels across the set of sthocastic images that exceed the stated threshold, converting the sum to a proportion, and presenting the spatially empirical probability in map form. Figure 08 ( on the left)shows the probability maps of each variable considering as cutoff the tolerable maxima of 0.05, 0.1 and 0.3 ppm to arsenic, manganese and iron, respectively. These maps confirmed that manganese is responsible for the largest contamination in the study area. Iron and arsenic occur at larger contamination levels located in small areas. Figure 8 (on the right) shows the estimates of the contamination in the area for the several probability levels, related to the tolerable maxima allowed for each variable. The portion of the area classified as contaminated is relatively insensitive to the choice of a probability cutoff until it reaches about 0.5 for iron and manganese and 0.2 for arsenic. CONCLUSIONS

In this paper the annealing simulation was used to carry out a probabilistic evaluation of arsenic, manganese and iron contamination in the port of Santana, Amapa, Brazil. The probabilistic approach explicitly recognizes the uncertainty in contaminant

concentrations at unsampled locations. Therefore, the area and boundaries of contaminated zones are uncertain. Specific values of these quantities can be obtained through the specification of a target probability or level of risk. The site is discretized into an array of blocks with known size and shape, and a simulated value of contaminant concentration obtained for each block. Fifty realizations were generated of the contaminant concentrations where all matched reasonably to the same statistics (histogram, semivariogram) allowing the assessment of the uncertainty about the spatial distribution of the contaminants. The choice of the probability cutoff was determined by tolerable maxima established by the government agency, however other criteria can be used as the established by searchers, regulatory agencies, etc. The simulated maps can be used as input into transfer functions, as health and remediation costs. REFERENCES Carle, S.F., 1997, Implementation schemes for avoiding artifact discontinuities in simulated annealing: Mathematical Geology, v. 29, n. 2, p. 231-244

CPI - Comissão Parlamentar de Inquérito Informe, maio/98, Assembléia Legislativa do Estado do Amapá. no.01, Macapá-AP, Brazil. Deustch, C. and Cockerham, P., 1994, Practical considerations in the application of simulated annealing to stochastic simulation: Mathematical Geology, Vol. 26, n0. 1, p. 67-82 Deustch, C. and Journel, A. G., 1991, The application of simulated annealing to stacastic reservoir modeling: Soc. Petroleum Engineering, SPE Paper 23565, 30 p. Deustch, C. V., and Journel, A. G., 1992, GSLIB: Geostastical Software Library and user's guide: Oxford Univ. Press, New York, 340 p. Dougherty, D. E., and Marryott, R. A., 1991, Optimal Groundwater Management, 1. Simulated annealing: Water Resources Research, vol. 27, n0. 10, p. 2491-2508. Environmental Protection Agency, January 2001, Drinking water standard for arsenic : Office of Water, 4606, www.epa.gov/water. Fang, J. H. and Wang, P. P., 1997, Random field generation using simulated annealing vs. fractal-based stochastic interpolation: Mathemati-cal Geology, v. 29, n. 6, p. 849-858 Geman, S., and Geman, D., 1984, Stochastic relaxation, Gibbs distributions. And the Bayesian restoration of images: IEEE Trans Pattern Anal. Machine Intell. PAM1. V.6 no. 6, p.721-741 Goovaerts, P., 1977a, Kriging vs. stochastic simulation in soil contamination in Soares, A., Gómez-Hernadez, J., and Froidevaux, R., eds. GeoENV I-Geostatistics for environmental applications: Kluwer Acadaemic Publ. Dordrecht, p. 247-258

Goovaerts, P., 1997, Geostatistics for Natural Resources Evaluation. Oxford Univ. Press, New York, 483 p. Goovaerts, P., 1998, Accounting for estimation optimality oriteria in simulated annealing: Mathematical Geology, Vol. 3, n0. 5, p. 511-534 Gupta-Datta, A., Larry, W.L. and Pope, G.A., 1995, Characterizing hetero-geneuos permeable media with spatial statistics and tracer data using se-quencial simulated annealing: Mathematical Geology, v. 27, n. 6, p. 763-787 IBGE - Instituto Brasileiro de Geografia e Estatística, Brazil, Censo 2000. Isaaks, E. H., and Srivastava, R. M., 1989, Applied Geostatistics. Oxford University Press, New Yprk, NY, 561 pp. Journel, A. G., and Alabert, F., 1990, New method for reservoir mapping: Jour. of Petroleum Technology, p. 212-218 Marryott, R., Dougherty, D. E., and Stollar, R. L., 1993, Optimal Ground-water Management, 2. Applications of simulated annealing to a field-scale contamination site: Water Resources Research, vol. 29, n0. 4, p. 847-860. Relatório JAAKKO PÖYRY ENGENHARIA, Maio/98, Disposição final dos resÍduos da usina de pelotizacao/sinterizacão estocados na área industrial da ICOMI/Santana, AP. Santana, Amapá, Brazil, 66 p. Zheng, C. and Wang, P. P., 1996, Parameter structure identification using tabu search and simulated annealing: Adv. Water Res., v. 19, no. 4, p. 215-224

Amazon River

Lim

it a

rea

ICO

MI 02

Monitoring well

AS-7Subsurface water/effluent

0.1 km

PORT OF SANTANA

SANTANA

N

Tank of combustive

Railroad

basin of fine

rejectsIgarapé

Igarapé

Igarapé

Elesbã

o 1

Elesbã

o 2

Elesbã

o 3

Flow lines

Figure 02 : Industrial area of Santana, used for stacking of the ore, products and insumos (Jakko Pöyry, Report, 1998).

0 50 100 150m

meters10

0

-10

-20

-30

-40

SILTOSA, GRAY,SOFT CLAY ORGANIC

SILTE ARGILLACEOUS, BROWN COLORED

CLAY AVERAGE THICK

FINE SAND, COMPACT

GRAY CLAY CLEAR AND VARIEGADA

CONTAMINATION PLUME

FLOW LINE

STACK OF THE ORE

AMAZON RIVER

PRECIPITATION

PERCOLATING TANKS OF COMBUSTIVE

Figure 03 : Industrial area of Santana. Generalized geologic cross section ( Jakko Pöyry, Report, 1998).

Arsenic data ( % pollut.: 22 )

05

1015202530354045

0 0.05 1 3 5 7 9 11 13 15 17

Concentration (ppm)

Fre

qu

en

cy

0%

20%

40%

60%

80%

100%

Manganese data ( % pollut.: 58 )

0

5

10

15

20

25

0 0.1 1 3 5 7 9 11 13 15 17 >

Concentration (ppm)

Fre

qu

en

cy

0%

20%

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80%

100%

Iron data ( % pollut.: 34 )

0

5

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35

0 0.3 1 3 5 7 9 11 13 15 17 >

Concentration (ppm)

Fre

qu

en

cy

0%

20%

40%

60%

80%

100%

Figure 04. Data locations, histograms and cumulative distribuitions of metal concentrations, arsênic (top), manganese ( middle ) and iron ( bottom ). The proportions of data that exceed the tolerable maxima is represented by the vertical dashed lines.

Sem

ivario

gram

Sem

ivario

gram

Sem

ivario

gram

Distance (km)

Distance (km)

Distance (km)

Arsenic

Manganese

Iron

Figure 05. Experimental omnidirectional semivariograms for Arsenic (top), Manganese (middle) and Iron (bottom). The solid line represents the fitted model.

Figure 06. Conditional Annealing realizations of arsenic (top), manganese (middle) and Iron (bottom) concentrations in ppm (left column). Experimental semivariograms (black lines) for the five initial realizations and the model semivariogram (blue lines) are show on right column.

Figure 07. "E-type" estimate maps of arsenic (top), manganese (middle) and Iron (bottom) concentrations in ppm (left column) derived from postprocessing 50 simulations and respective histograms (right column).

0

0.5

1

1.5

2

2.5

3

3.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Probability Cutoff

Ars

enic

Con

tam

inat

ed A

rea

(Km

2)

0

0.5

1

1.5

2

2.5

3

3.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Probability Cutoff

Man

gane

se C

onta

min

ated

Are

a (K

m2)

0

0.5

1

1.5

2

2.5

3

3.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Probability Cutoff

Iron

Con

tam

inat

ed Á

rea

(Km

2)

Figure 08. Probability maps and total contaminated area of risk cutoff for arsenic (top), manganese (middle) and Iron (bottom) concentrations of exceed tolerable maxima of 0.05, 0.1 and 0.3 ppm, respectively.