J. of Balkan Ecology, vol. 6, No. 1, 5-14, 2003.

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Spatial Distribution and Statistical Analysis of Mineral Waters in Bulgaria ALEXANDER N. SADOVSKI, LUBOMIR A. SADOVSKY Abstract: Statistical methods including Quadrat analysis, Cluster analysis, Factor analysis, Descriptive statistics and Geographic Information Systems are used to study spatial distribution and to summarize data about physical and chemical characteristics of the mineral water sources in Bulgaria. Besides their terapeutical significance some of the springs of mineral water could be considered as sources of geothermal energy and to be of interest for Bulgarian energetics. Key words: Mineral water, statistical methods, geothermal energy.

INTRODUCTION

Since ancient times the healing properties of mineral waters have been known to the people.

Romans and ancient Bulgarians have builded-up baths and have used mineral springs on the

territory of Bulgaria. Only in the first half of 20th century studies of mineral waters’ properties and

classification of the sources have been initiated (Petrov, 1930). Attempt to create a genetic

classification (systematics) of Bulgarian mineral waters uses their genesis and complex

characteristics without considering the balneotherapeutical applications (Shterev, 1971). A new

classification based on physical-chemical characteristics and healing properties of mineral waters is

developed by D. Karakolev (Karakolev, 1976).

Mineral waters are well known as means for health improvement and treatment of different

complaints and diseases. Besides their terapeutical significance some of the springs of mineral water

could be considered as sources of geothermal energy and could be of interest for Bulgarian

energetics. The rational use of Bulgarian thermal wealth could make contribution for development

of ecological tourism and prosperity of the locations where it is situated.

The paper is aimed at establishing the spatial distribution of natural mineral water sources

over Bulgarian territory and the statistical characteristics related to some of their properties. It will

help for better understanding of their qualities and more rational and many-sided use in the future.

CONCEPT AND METHODS

We consider: (a) interest in areal distribution; (b) interest in spatial structure; and (c) concern

with the explanation of areal variation. Since spatial data are neither the outcome of controlled

J. of Balkan Ecology, vol. 6, No. 1, 5-14, 2003.

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experiments, nor do they result from random samples, it is clear that beyond mapping and informal

inference from patterns, specific spatial statistical methods are required.

The concept, which is used in this study, is that of “randomness”. In mathematical terms a

random spatial point pattern is defined as an geographical disposition of points on a plane, generated

by a realization of a spatial point process, that satisfies the conditions of equal probability and

independence. If N points are located randomly in a planar region, then the probability distribution

of this random spatial point pattern follows the Poisson law. An observed frequency distribution,

which does not conform to the expected from a random point process, leads to rejection of the

hypothesis of randomness in favor of the alternative - more regular or more clustered, than the

random model.

The method applied for study spatial distribution of mineral waters’ springs in Bulgaria is

called “Quadrat analysis” (Rogers, 1974). In the quadrat method a planar study region is divided

into a grid with cells of equal size, called “quadrats”, and the number of points in each cell is

counted. A regular point process generates a large number of quadrats containing only a single

point, some empty quadrats and a very few quadrats with more than one point in them. Conversely,

a clustered point process is expected to produce a very large number of empty quadrats, a few

quadrats with one or two points, and several quadrats with many points in them. Analyses have

shown that the Poisson distribution

(1) P x aax

xX

1 0 1 2( ) exp( )( )

!, ( , , ,...)= − =λ λ

corresponds to random spatial dispersion.

The Binomial distribution

(2) P xn

xp px n x

2 1( ) ( )=������ − −

is connected with regular spatial pattern,

and the Negative binomial distribution

(3) P xk x

xp pk x

3

11( ) ( )=

+ −���

��� −

corresponds to clustered spatial dispersion.

It is known that the following inequalities exist (Kendall et al., 1958):

Binomial distribution Variance < Mean

Poisson distribution Variance = Mean

J. of Balkan Ecology, vol. 6, No. 1, 5-14, 2003.

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Negative binomial distribution Variance > Mean

They could give indication about the type of statistical distribution and corresponding point

process.

If the hypotheses of randomness and regularity are rejected, that it is convenient to apply

some method of cluster analysis. For our purposes we select the minimal dispersion method (Ward,

1963) and Euclidean distance, calculated from standardized data. This transformation of data is

imposed by the fact that various characteristics of mineral waters are measured with different units.

Since the characteristics under study are not mutually independent, factor analysis with Varimax

rotation will help to extract groups of variables, which are almost orthogonal and are able to

describe a great part of the total variance.

Statistical analysis of mineral waters aims to describe and summarize data about their

physical and chemical characteristics, and to reveal natural groups (clusters) of mineral water

sources. Data from 106 sources (natural springs) are object of the analysis (Karakolev, 1984). We

intentionally omit data from other 119 sources, which extract mineral water by drilling, in order to

study only the sources resulting from natural processes. The following physical and chemical

characteristics have been analyzed: Capacity (l/s), Temperature (°C), Acidity (pH), Hardness (H°),

Mineralization (g/l), Chemical composition - HCO3+CO3, SO4, Cl, Na+K, Ca, Mg, Si, F (g/l) and

Rn (nCi/l). Such set of data is sufficient for reliable inferences and conclusions.

SPATIAL DISTRIBUTION OF MINERAL WATERS

A digitized map of Bulgaria with scale 1:500 000 is used as a base map. The mineral springs

with their longitude/latitude coordinates have been overlaid on this base map. The whole area is

divided into a grid with cells of equal size (quadrats 0.5o longitude by 0.5o latitude) and the pattern

is shown on Figure 1. The number of points in each cell on the Bulgarian territory is counted and

sample statistics are calculated. To make conclusion about the character of observed spatial point

pattern, three statistical distributions are fitted to the data: Binomial, Poisson and Negative binomial

distribution. Results are presented in Table 1.

Two statistical tests are applied: Chi-square goodness of fit test

and variance-mean ratio test

������ ��χ ν2

2

1

= −=�

( ),

O EE

i i

ii

k

������ �� t

mm

N

* ,=−

−

2

1

1

21

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where:

Oi are observed frequencies, Ei are expected frequencies and ν - degrees of freedom;

m1 is Mean, m2 is Variance and N - number of observations.

It is evident that values of χ2 for Binomial and Poisson distributions exceed the critical value

from chi-square table (22.46), which lead to rejection of the null hypothesis of regularness and

randomness of spatial pattern. Only χ2 value for Negative binomial distribution is less than the

critical value and shows a clustered point process.

The results from variance-mean ratio test are:

m1 = 1.9273, m2 = 4.513, m2/m1 = 2.342,

t* = 6.971, ν = 54, p < 0.001,

which confirms that the observed spatial dispersion is significantly different from the random

Poisson model.

SPATIAL STRUCTURE OF MINERAL WATER SPRINGS

Relationships between 106 natural springs of mineral water are examined by the method of

cluster analysis. Ward's method belongs to the so-called hierarchical grouping. Its application gives

a dendrogram, presented on Figure 2. Eleven clusters are found and their members are listed in

Table 2.

To facilitate the interpretation of results, clusters' means are given in Table 3.

It is interesting to notice that clusters 4, 7, 8, 9, 10 and 11, consist of one or a few members

as they have very specific properties. Cluster 4 (Momin prohod and Narechen) is with highest values

of Rn and H2SiO3. Cluster 7 (Dlagnevo, Inzovo and Shipkovo) has well balanced content of

hydrocarbonates, sulfates and other compositions. Boianovo is with highest values of

mineralization, hydrocarbonates, sulfates, chlorides, Na + K and Ca. Cluster 9 (Breznik, Gorno uino

and Pelovo) is characterized with lowest values of pH, absence of hydrocarbonates and Rn. Water of

Devenci has high mineralization and content of Mg, sulfates and hydrocarbonates. Cluster 11

(Harmanli, Merichleri and Mihalkovo) is with highest level of hydrocarbonates. Interpretation of the

characteristics of other clusters is possible to be done based on the same table.

J. of Balkan Ecology, vol. 6, No. 1, 5-14, 2003.

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DESCRIPTIVE STATISTICS OF MINERAL WATERS

Basic descriptive statistics for the characteristics of all 106 mineral waters are calculated,

namely: mean, median, minimal and maximal values, standard deviation, skewness and kurtosis.

They are given in Table 4.

It is evident that the characteristics of Bulgarian mineral waters vary in very wide limits.

This determines their application for treatment of a very broad range of disorders and diseases.

Distributions of the mineral waters in this study according their capacity, temperature,

mineralization, hardness, acidity and Radon content are presented on Tables 5 - 10. They give a

right idea about the possibilities for the many-sided utilization of Bulgarian mineral waters.

Table 10 shows that almost half of the mineral springs total capacity (48.07%) are Radon's

waters. They stimulate and regulate cell's functions and have prophylactic and healing effect for

large number of illnesses.

Here is the place to stress the importance of some mineral waters for Bulgarian energetics. In

a study on the possibilities of using renewable energy sources in Bulgaria (ENERGOPROJECT,

1996), it is indicated that the total quantity of geothermal energy is unknown and it is less than

0.01% from the reserve energy potential for this country. Nevertheless the results of present study

indicate much more perspectives for geothermal energy from mineral water sources. From Table 6 it

is evident that hyperthermal waters include considerable part - 68.88% and the very hot waters with

temperature above 50oC are 34.05% from the total capacity of mineral springs. It confirms that the

significance of geothermal energy from mineral waters in Bulgaria is underestimated.

CONCLUSIONS

Use of several statistical methods such as Quadrat analysis, Cluster analysis, Factor analysis,

Descriptive statistics and Geographic Information Systems has allowed revealing spatial distribution

and spatial structure of mineral waters sources in Bulgaria. The study rejects the hypothesis of

random dispersion of mineral springs over the country's territory in favor of the alternative - more

clustered, than the random model. Cluster analysis allocates all 106 sources into 11 clusters with

distinct properties. Tables 2 - 10 give bases for more profound interpretation.

J. of Balkan Ecology, vol. 6, No. 1, 5-14, 2003.

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The descriptive statistical analysis shows that Bulgarian mineral waters vary in very wide

limits. This determines their application for treatment of a very broad range of disorders and

diseases.

The result of present study indicates more perspectives for geothermal energy from mineral

water sources. It confirms that the significance of geothermal energy from mineral waters in

Bulgaria is underestimated.

REFERENCES

ENERGOPROJECT. 1996. Study for Bulgaria directed to the global problems of climate change.

General final report, ENERGOPROJECT, Sofia.

Karakolev D. 1976. Bulgarian health resorts, 299-340. Medicine and Sport, Sofia.

Karakolev D. (Ed.). 1984. Fundamentals of Balneotherapy. Medicine and Sport, Sofia.

Karakolev D. 1990. Medical guide for Bulgarian mineral waters. Medicine and Sport, Sofia.

Kendall M., A Stuart. 1958. The Advanced Theory of Statistics, Vol. I. Ch. Griffin, London.

Petrov T. 1930. Mineral Waters in Bulgaria. Department of Health. State Printing Office, Sofia, p.

69.

Rogers A. 1974. Statistical analysis of spatial dispersion: The Quadrat method. Pion Ltd., London.

Shterev K. 1971. Atlas “Resorts regioning of Bulgaria”, 22-23. Ministry of Health, Sofia.

Ward J. H. Jr. 1963. Hierarchical Grouping to optimize an Objective Function. Amer. Stat. Assoc.

Journal, vol. 58, 236-244.

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Table 1. Observed and expected distributions of the mineral water springs

No.of Observed Binomial Poisson Neg.binom. points frequ-

per ency n = 106 λa = w = 1.9273 cell p = 0.01818 1.9273 k = 1.4366

0 20 7.86 8.00 16.20 1 7 15.44 15.43 13.33 2 11 15.01 14.87 9.31 3 6 9.63 9.55 6.11 4 5 4.59 4.60 3.88 5 2 1.74 1.77 2.42 6 1 0.54 0.57 1.49 7 1 0.14 0.16 0.90 8 2 0.03 0.04 0.55 9 0 0.01 0.01 0.33

10+ 0 0.48

χ2 - 40.821 38.546 5.006 df - 6 6 7

P0.001 - 22.46 22.46 24.32 - p < 0.001 p < 0.001 p < 0.659

Table 2. Clusters and their members

Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 Cluster 6 Aitos Bachevo Beden Momin prohod Alexandrovo Boliarovo Bania (Bg) Bania (Pz) Blagoevgrad Narechen Banichan Chukovec Bania (Bs) Bankia (Sf) Dolna bania Bankia (Pk) Granitovo Bania (Pd) Bracigovo Dolno Osenovo Bansko Krichim Belchin Elenov dol Draginovo Belovo Nova Varbovka Dobrinishte Gorna bania Gradeshnica Beronovo Ovcha kupel Eleshnica Jeleznica Haskovski bani Bogatovo Pchelarovo Hisaria Kniajevo Kiustendil Chukovo Pravo burdo Klisura Ladja - Banite Korten Dolni Rakovec Radomirci Kostenec Pancharevo Marikostino Dolno Botevo Salmanovo Krasnovo Rudarci Oshtava Enchevci Seslav Miromir Sofia CB Ovoshtnik Jeravna Slivenski bani Ognianovo Spanchevci Pavel bania Kirkovo Stefan Karadjovo Pravdino Staro Jelezare Pchelinski bani Musomishte Voneshta voda Stoletovo Starozagorski bani Sandanski Oriahovica Yambol Strelcha Varshec Sapareva bania Sindel Velingrad-Chepino Simitli Slivek Velingrad-Ludjene Varvara Smochan

Velingrad-Kamenica Starosel Yagoda Triavna Varbica Vardun Vlahovo

J. of Balkan Ecology, vol. 6, No. 1, 5-14, 2003.

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Zlatna Panega

Cluster 7 Cluster 8 Cluster 9 Cluster 10 Cluster 11 Dlagnevo Boianovo Breznik Devenci Harmanli Inzovo Gorno uino Merichleri Shipkovo Pelovo Mihalkovo

Table 4. Descriptive statistics of mineral waters (N=106)

Variable Mean Median Min Max Std.Dev. Skew. Kurt. Capacity 13.19 8.00 1.0 80.0 16.389 2.169 5.362 to 34.97 30.50 8.0 94.0 20.580 0.919 0.168 pH 7.89 7.75 2.6 10.0 1.236 -1.267 4.010 H° 20.53 3.85 0.2 273.0 41.223 3.659 16.376 Mineralization 1183.99 651.50 119.0 11271.0 1555.849 3.767 18.434 HCO3 + CO3 324.74 194.00 0.0 2075.0 344.939 2.609 9.753 SO4 351.16 82.50 5.0 4444.0 750.016 3.757 15.056 Cl 95.16 19.00 2.0 3499.0 354.369 8.697 82.900 Na + K 193.90 133.00 2.0 2004.0 296.556 4.638 24.357 Ca 80.42 22.00 1.0 885.0 140.766 3.154 12.223 Mg 40.56 2.20 0.0 741.0 108.540 4.724 25.297 H2SiO3 45.25 41.00 1.0 115.0 27.940 0.562 -0.565 F 4.38 3.05 0.0 24.0 4.669 1.511 2.587 Rn 3.85 0.00 0.0 110.0 12.692 6.494 49.387

Table 5. Distribution by capacity

Group Sources Capacity Part of total (number) (l/s) capacity

(%) < 5 l/s 43 58 4.15

5 - 15 l/s 24 210 15.02 15 - 25 l/s 22 401 28.68 25 - 50 l/s 12 377 26.97

> 50 l/s 5 352 25.18

Table 6. Distribution by temperature

Type Temperature Sources Capacity Part of total (oC) (number) (l/s) capacity (%)

Cold < 20 33 40 2.86 Hypothermal 20 - 34 26 368 26.32 Homothermal 34 - 37 3 27 1.93 Hyperthermal little hot 37 - 42 7 125 8.94 moderately hot 42 - 50 16 362 25.89 very hot > 50 21 476 34.05

J. of Balkan Ecology, vol. 6, No. 1, 5-14, 2003.

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Table 7. Distribution by mineralization

Type Mineralization Sources Capacity Part of total (g/l) (number) (l/s) capacity (%)

Weakly mineralized < 1 70 1225 87.63 Lightly " 1 - 5 32 158 11.30 Moderately " 5 - 10 3 14 1.00 Highly " > 10 1 1 0.07

Table 8. Distribution by hardness

Hardness Sources Capacity Part of total (H°) (number) (l/s) capacity (%) < 1 36 721 51.57

1 - 5 20 199 14.23 5 - 10 10 69 4.94 10 - 25 19 348 24.89

> 25 21 61 4.36

Table 9. Distribution by acidity

Type Acidity Sources Capacity Part of total (pH) (number) (l/s) capacity (%)

Acid < 6.5 6 32 2.29 Neutral 6.5 - 7.5 36 417 29.83 Alkaline > 7.5 64 949 67.88

Table 10. Distribution by Radon content

Radon Sources Capacity Part of total (nCi/l) (number) (l/s) capacity (%) 1 - 5 23 384 27.47

5 - 10 6 85 6.08 10 - 20 5 130 9.30 20 - 50 3 53 3.79

> 50 2 20 1.43

12

Fig.

1

13

Tabl

e 3

Clu

ster

s mea

ns

Var

iabl

eC

lust

er 1

Clu

ster

2C

lust

er 3

Clu

ster

4C

lust

er 5

Clu

ster

6C

lust

er 7

Clu

ster

8C

lust

er 9

Clu

ster

10

Clu

ster

11

Cap

acity

25.4

11.6

19.0

10.0

10.1

5.1

1.0

1.0

1.0

1.0

10.0

to43

.035

.466

.145

.517

.721

.616

.312

.014

.015

.029

.7pH

9.2

8.4

8.2

7.5

7.8

7.0

6.9

7.3

3.3

8.0

6.9

H°

0.9

4.0

3.0

10.6

8.6

47.0

96.3

273.

088

.720

1.0

24.6

Min

eral

izat

ion

319.

939

3.7

762.

612

61.0

773.

516

69.9

2798

.711

271.

041

05.7

5928

.047

16.0

HC

O3 +

CO

387

.813

4.3

200.

426

5.5

403.

463

3.9

422.

341

5.0

0.0

839.

014

81.0

SO4

58.7

92.3

230.

650

1.0

75.5

234.

813

25.3

3797

.028

87.7

3542

.012

54.7

Cl

18.1

14.9

22.1

40.5

64.6

124.

217

6.0

3499

.024

.712

8.0

452.

7N

a +

K86

.778

.819

3.9

292.

016

7.2

127.

523

0.0

2004

.011

3.7

444.

012

89.0

Ca

4.4

21.8

19.4

57.5

38.2

179.

347

7.7

885.

035

7.0

213.

012

7.7

Mg

1.3

4.5

1.4

11.7

14.1

96.8

129.

364

7.0

166.

774

1.0

29.0

H2S

iO3

55.8

45.1

78.2

85.5

14.9

33.6

28.0

20.0

66.3

15.0

52.3

F5.

51.

311

.38.

02.

51.

11.

81.

00.

50.

06.

2R

n6.

60.

94.

983

.00.

10.

40.

00.

00.

00.

01.

3

14

Fig.

2