Statistical analysis of two important chemical features (TDS and (HCO3-) content) in Sudetic therapeutic waters

(1)

Annales Societatis Geologorum Poloniae (1998), vol. 6 8 : 287-294.

STATISTICAL ANALYSIS OF TWO IMPORTANT CHEMICAL FEATURES (TDS AND (HCO;) CONTENT) IN SUDETIC

THERAPEUTIC WATERS

Jacek KOZŁOWSKI

W rocław U niversity o f Technology, D epartm ent o f Geology, D ivision o f G eology a n d M in era l Waters, W ybrzeże S. W yspiańskiego 27, 50-370 W rocław

Kozłowski, J., 1998. Statistical analysis o ftw o im portant chemical features (TDS and ( H C O J ) content) in Sudetic therapeutic waters. Ann. Soc. Geol. Polon., 68: 287-294.

A b stract: Two im portant chem ical features o f therapeutic w aters from 57 intakes in 13 Sudetic health resorts, i.e.

total dissolved solids (TDS) and bicarbonate ion (H C O J ) content, tested w ith the K olm ogorov test at the significance level oc=0.05, during the w hole exploitation period, reveal normal distributions. It bears evidence o f little variability o f these features. Intervals o f the m ost frequent (normal) [H C O 3 ] content values in individual intakes, determ ined using the three standard deviations m ethod (3 a ) are in m ost cases concordant with real values.

These intervals can be used for verification o f m onitoring measurem ents (elim ination o f incorrect determ inations) and/or can indicate sudden changes o f chemical composition o f exploited therapeutic waters.

A b stra k t: Dwie podstaw ow e w łasności w ód leczniczych w 57 ujęciach z 13 m iejscowości uzdrow iskowych Sudetów: suma substancji rozpuszczonych (TDS) i zaw artość jonu wodorowęglanowego (H C O 3 ), przetestowane testem K ołm ogorow a na poziom ie istotności a= 0.05 na przestrzeni całego okresu eksploatacji, w ykazują rozkłady normalne, co św iadczy o ich dużej stałości. W yznaczone m etodą trzech odchyleń standardow ych (3 o ) przedziały w artości najczęściej w ystępujących dla zawartości (H C O 3 ) w poszczególnych ujęciach pokryw ają się zw ykle z wartościami rzeczyw istym i.

Uzyskane przedziały norm alnych zawartości anionu wodorowęglanowego m ogą być w ykorzystyw ane do weryfikacji prow adzonych obserwacji stacjonarnych (elim inow anie błędnych oznaczeń) i/lub sygnalizacji gwał

tow nych zm ian składu chem icznego eksploatowanej w ody leczniczej.

Key w ords: chem ical com position changes, therapeutic waters, Sudetes, statistical analysis.

Manuscript received 13 January 1998, accepted 4 January 1999

INTRODUCTION

According to the Polish geological and mining law, ex

ploitation o f therapeutic waters requires also protection of its deposits, by means a.o. o f a monitoring system. The chemical composition o f water, including TDS (calculated as the sum o f all o f anions and cations indicated in therapeu

tic water), is part o f this system. Once a year a control analy

sis is carried out for health resorts mainly by laboratories of such institutions like ‘Balneoprojekt’ Health Resorts Design and Technical Service Bureau or Department o f Drilling, Petroleum and Gas of the Academy o f Mining and M etal

lurgy in Kraków. Besides, health resorts perform, with vari

ous frequency, their own measurements o f the principal fea

tures o f therapeutic waters, including indicator determina

tions. Since carbonated waters rich in CO2 are the most common ones, bicarbonate ion (H C O3) is most often used as an indicator parameter.

The [ HCO3 ] concentration is an important indicator of environmental changes in the quality o f the water exploited.

On the basis o f rich archival material from the observation

period, exceeding 30 years for most intakes, and in some cases even 100 years (e.g. ‘Em ilia’ intake in Długopole Zdrój or five intakes in Cieplice Śląskie Zdrój), the author determined intervals o f the indicator’s normal (most com

mon) values and compared them with real values observed.

GEOLOGICAL BACKGROUND

Sudetes are an area, where in 13 resorts occur waters declared as therapeutic (at Gorzanow till 1984 only) (Ci?z- kowski, 1990). In most cases there are carbonated waters; in several sites occur thermal waters, radioactive waters and sulphurous waters (Fig. 1).

Fig. 1 shows the occurrence o f these waters on the sche

matic geological map o f the Sudetes (after Oberc, 1952;

Geological Map o f Lower Silesia, 1995). The Sudetes’ bed

rock are igneous and metamorphic rocks, which exhibit common directly on the ground-surface. It concerns spe

cially granitic massifs (Karkonosze massif, Strzegom-So- botka massif, Strzelin massif, K lodzko-Zloty Stok m assif

(2)

Fig. 1. The occurrence o f selected Sudetic mineral waters on the background o f generalized geological setting (after Oberc, 1952; Ciężkowski, 1990; G eological Map o f Lower Silesia, 1995).

a - carbonated waters: 1 - D ługopole Zdrój, 2 - Duszniki Zdrój, 3 - Gorzanów, 4 - Jeleniów, 5 - K udow a Zdrój, 6 - Polanica Zdrój, 7 - Stare Rochowice, 8 - Szczaw ina, 9 - Szczawno Zdrój; b - radon-bearing carbonated w aters: 10 - Czem iaw a Zdrój, 11 - Świeradów Zdrój; c - therm al waters: 12 - Cieplice Zdrój, 13 - Lądek Zdrój; d - sulphurous w aters: 14 - Przerzeczyn Zdrój

a n d K u d o w a m assif) a n d m e ta m o rp h ic z o n e s (Iz e rsk ie M ts., K a c z a w sk ie M ts., S o w ie M ts., B y s trz y c k ie a n d O rlic k ie M ts., Ś n ie ż n ik m a ssif, K ło d z k o m e ta m o rp h ic zo n e a n d N ie m c z a z o n e ), w h e re th e p re d o m in a n t ro c k s are m ic a shists, g n e is se s, p h y llite s a n d g re e n s to n e s. T h e re la tio n sh ip b etw e e n g e o lo g ic a l se ttin g , te c to n ic s a n d fo rm a tio n o f ch e m ic a l c o m p o s itio n o f th e S u d e tic m in e ra l w a te rs w a s p re s e n te d in d e ta il in e.g .: D o w g ia łło (1 9 7 6 ), F is te k (1 9 7 7 ), C ię ż k o w sk i (1 9 8 0 , 1990).

T h e m o s t co m m o n S u d e tic m in e ra l w a te rs are c a rb o n ate d w a te rs , w h ic h o c c u r a lm o s t in a ll h y d ro g e o lo g ic a l u n its an d lith o lo g ic a l ty p e s o f ro c k s . T h e ir o c c u re n c e is a s s o c i

ated w ith d e e p d is lo c a tio n z o n e s, w h ic h fo rm m ig ra tio n p a th w a y s fo r C O 2 o f d e e p o rig in . W ith d e e p fau lts in g ra n ites o f th e K a rk o n o sz e m a s s if a n d in m e ta m o rp h ic ro ck s (m ic a sh ists, g n e isse s) o f th e Ś n ie ż n ik m a s s if is a ss o c ia te d the o c c u re n c e o f th e rm a l w a te rs also . R a d io a c tiv e w a te rs are co m m o n in th e sites, w h e re ig n e o u s o r m e ta m o rp h ic ro ck s a p p e a r on th e g ro u n d -s u rfa c e a n d /o r z o n e s stro n g ly in flu en c e d by te c to n ic s o c c u r (P rz y lib s k i, 1997).

METHOD OF INVESTIGATION

In order to maintain the highest possible homogeneity of the initial material the author used only archival annual control analyses owned by individual health resorts and partly published (Jarocka, 1976). Selection of data resulted in rejection o f results obtained, e.g.: during drilling render

ing the deposit accessible (e.g. intake ‘no 18’ in Kudowa Zdrój - all available analyses, or intake ‘P-300’ in Polanica Zdrój from 27.07.1966 to 23.04.1967), or from periods

Zdrój - analyses from the years 1937, 1954 and 1963, or the

‘Jan’ intake in C zem iaw a Zdrój - analyses from 1928 and 1933) (Jarocka, 1976).

In the statistical analysis results o f determinations being part o f the monitoring system have not been taken into con

sideration. Firstly, because m onitoring is not being carried out in all o f health resorts. Secondly, it is difficult to evalu

ate the accuracy o f these measurements; there are no publi

cations touching this problem.

Apart from therapeutic waters (mineral ones and/or containing specific components and/or o f temperature ex

ceeding 20 °C) also waters present in health resort areas which were not declared as therapeutic (in most cases slightly mineralized common waters) are considered in the paper (Table 1). They present the hydrochemical back

ground for therapeutic waters.

Random samples obtained (Table 1 lists TDS and [H C O3] data from particular intakes) were tested using the Kolmogorov goodness-of-fit test, where two hypotheses were put forward (Davis, 1986):

- Ho : assuming concordance o f distributions o f the gen

eral population, from which the random samples originate, with the normal distribution,

- Hi : opposite to Ho.

All tests were done for the significance level a=0.05.

The most popular goodness-of-fit test, also in hydro

chemical investigations, is the chi-square test (% ) (e.g.

Roszak, 1987). In the present paper, the Kolmogorov test was applied for two reasons. Firstly, it can be used for test

ing samples with the size n>8, and not n>30 as in the %2 test.

Secondly, the y j test is not powerful and it is strongly de

pendent on a small number o f degrees o f freedom (Lusznie- wicz & Słaby, 1996) (i.e. small number o f class intervals in the sample). The Kolmogorov test, on the other hand, may be used for samples not classified into intervals (Davis,

1986). Thus, a decision on acceptance or rejection o f the null hypothesis at the same a significance level is more powerful in the case o f the Kolmogorov test.

RESULTS OF INVESTIGATION

T E ST IN G O F N O R M A L IT Y

Testing o f the TDS distribution concordance with the normal distribution was carried out for 57 intakes from 13 localities (n>8) (Table 1). The results indicate that there is no reason for rejection o f the Ho at the significance level ac

cepted, which means that distributions o f this features in the Sudetic therapeutic waters have a normal character. In spite of the fact that in several tens o f intakes analysed, various chemical water types occur, with a different TDS value, ex

ploited from various depths and in different hydrogeological conditions and with a different fraction o f fresh waters of shallow circulation (calculated using the chemical data;

Ci?zkowski el a l, 1996) no explicit influence o f each of these factors on the TDS distribution is observed. Normal distribution o f TDS is also typical o f shallow, common wa-

(3)

Table 1

SUDETIC THERA PEU TIC W ATERS

289

Basic statistical parameters and [H C O j] values - real and determined using the 3 a method

O rd in a l n u m b e r

o f h e a lth re s o rt

In ta k e n a m e 1-* S a m p le siz e

A r ith m e tic a v e ra g e

X

S ta n d a rd d e v ia tio n

a

S k e w n e s s A x

R e a l v a lu e s o f H C O3 c o n c e n tr a tio n s

N o r m a l v a lu e s o f H C O3 c o n c e n tr a tio n ( - 3 a , + 3 a ) 3)

m in m a x . m in . m a x

m g /d m3 m g /d m3

1 Długopole Z d ró j

Emilia 35 677.2 156.7 +1.06 441.2 1037.0 207.2 1147.2

K azim ierz 31 636.4 112.4 +1.84 483.5 972.7 299.2 973.6

Renata 36 881.6 54.1 -1 .4 9 671.2 983.0 719.2 1043.9

2 Duszniki Zdrój

Jan Kazimierz 34 981.9 142.1 -0 .1 9 701.7 1204.0 555.5 1408.3

Pieniawa Chopina 34 1505.4 105.1 +2.99 1346.0 1993.0 1190.1 1820.7

Agata 2 1 1664.7 313.2 ^- 1050.0 2044.1 725.0 2604.4

B-4 24 1793.0 I S A ^- 1620.0 1952.0 1566.9 2019.1

B-l 14 1709.8 281.4 ^- 1234.6 1998.3 865.5 2554.0

Zim ny Zdrój 7 597.0 49.3 ^- 527.1 671.2 ^- ^-

B-2 11 837.7 267.8 ^- 414.9 1263.1 34.4 1641.0

B-3 30 1309.9 239.3 -0.71 571.2 1760.5 591.9 2027.8

3 Gorzanów

No 1 (Kaczka) 9 268.2 6.9 - 261.0 282.0 247.5 288.9

N o 2 6 497.5 13.8 - 482.6 518.6 - -

No 5 (upper level) 14 679.0 262.5 - 370.7 1214.0 0 1466.6

N o 6 17 745.5 87.8

-

535.6 873.4 482.1 1009.0

No 5 (lower level) 19 1 1 0 2 . 0 35.8 ^- 1049.0 1186.0 994.8 1209.3

4 Jeleniów

No 5 4 116.6 13.4 - 104.6 135.3 ^- ^-

No 8 4 218.6 27.9 - 188.0 254.2 ■ -

No 2 4 239.1 1 2.1 - 226.0 254.1 - -

J -I5 0 45 828.6 155.1 +2.54 517.0 1586.5 363.2 1294.0

Sarenka 11 1381.3 441.9 ^- 335.5 1772.0 55.8 2706.9

P5 15 1572.9 1 2 0 .1 - 1 2 2 1 . 0 1727.4 1 2 1 2 . 6 1933.2

5 Kudowa Zdrój

PI 23 340.2 16.8 - 286.2 365.7 289.7 390.7

No 3 (Nowy M archlew ski) 44 1056.0 175.7 -0 .6 0 695.5 1311.0 528.9 1583.0

P4 23 1206.2 167.8

-

942.0 1579.0 702.6 1709.7

Górne 1 0 1571.1 105.9 - 1370.0 1729.0 1253.3 1888.9

No 26 4 1951.4 88.4

-

1859.0 2062.0 ^- ^-

No 2 (M oniuszko) 46 2187.1 86.7 -0 . 6 8 1952.0 2301.0 1926.9 2447.2

K-200 37 2169.1 29.8 -0 .7 8 2078.0 2226.0 2080.0 2258.4

P 6 2 2 3559.5 160.1 ^- 3363.6 3990.0 3079.2 4039.8

6 Polanica Zdrój

P ie n ia w a J ó ze fa 2 15 609.3 39.4 ^- 545.2 660.9 491.0 727.6

P ie n ia w a J ó z e fa 1 32 797.6 140.2 4 1 .1 4 640.0 1246.0 377.1 1218.1

J ó z e f S tary 5 818.4 40.5 ^- 779.0 885.0 ^- ^-

Ż e laziste 7 1158.7 74.6 ^- 1061.4 1266.0 ^- ^-

W ielka Pieniaw a 37 1197.7 65.1 +1.79 1101.4 1419.0 1002.3 1393.1

P-300 26 1908.0 212.1 ^- 1728.9 2017.8 1271.7 2544.4

7 Stare Rochowice

No 5 9 413.7 39.8 ^- 341.0 457.6 294.3 533.1

No 6 7 1499.2 471.6 ^- 1006.8 2150.9 ^-

No 2 6 2184.4 20.2 ^- 2151.8 2197.3 ^_ ^-

No 1 9 2245.8 321.3 - 1769.5 2616.0 1281.9 3209.8

0 - names o f intakes w here w ater is not regarded at present as therapeutic are written in italics, 2)’ - calculated for samples with size n>30, - calculated for sam ples w ith size n>8. Ordinal numbers o f health resorts as in Fig. 1

(4)

Ordinal number

o f

h e a l t h r e s o r t

Intake n a m e 1J Sample size

Arithmetic average

X

Standard deviation

a

Skewness

A x

Real values o f H C O3

concentrations

N orm al values o f H C O3

concentration

( - 3 o , + 3 a ) 3)

min max. min. max

m g/dm3 m g/dm 3

8 S z c za w in a

S tu d zien n e 17 4 5 2 .6 22 .9 ^- 387.3 49 0 .5 383 .9 521.3

S z c z a w in a -1 8 671 .2 33 3 .2 ^- 343 .9 1418.9 0 1670.7

9 Szczawno Zdrój

No 14 5 2 7 7 .4 10.1 ^- 2 6 8 .0 29 3 .0 ^- ^-

M ie s z k o -14 9 43 3 .5 183.0 ^- 269 .0 701.1 0 98 2 .4

D ą b ró w k a 41 1384.9 30 6 .6 + 0 .0 6 808.5 1980.6 4 6 5 .0 2 3 0 4 .7

M ły n arz 31 1466.9 23 3 .2 +0 .9 5 1079.0 22 4 0 .0 767.3 216 6 .5

M arta 31 1569.6 278.5 + 0 .9 8 1118.0 2 5 0 4 .0 734.1 2 4 0 5 .2

M iesz k o 38 1920.5 27 7 .9 + 0 .7 8 1398.7 26 6 5 .0 1086.8 275 4 .3

10 Czerniaw a Zdrój

R ad o c z y n n e 1 12 7.0 5.1 ^- 0 18.4 0 22.3

R ad o c z y n n e 2 9 7.2 4.4 ^- ___ 3.7 18.1 0 20 .4

N o 1 25 94.3 15.1 ^- 27.7 114.3 4 9 .0 139.6

M aria 10 4 9 3 .0 153.9 ^- 36 4 .9 861.8 31.4 95 4 .6

Jan 24 717.6 209.3 ^- 424.1 1458.0 89 .6 1345.6

N o 4 27 2 0 9 9 .7 136.0 _ 1922.0 24 4 7 .7 1691.6 2 5 0 7 .7

11 Świeradów Zdrój

G ó rn e 1 21 145.9 49.1 ^- 79.7 24 5 .0 0 293.3

G ó rn e 2 21 115.4 72.1 ^- 42 .9 22 8 .8 0 331.7

G ó rn e 3 37 251.8 72.1 + 0 .9 0 159.1 427.1 35 .4 468.1

1A 24 465.1 75 .2 ^- 388.0 61 8 .2 23 9 .3 690.8

Zofia 2 0 680.1 4 2 .0 ^- 587.3 762.7 554.1 806.1

2P 11 1307.5 353 .2 ^- 9 9 9 .0 1872.7 24 8 .0 2 3 6 7 .0

Radoczynne Zbiorcze 13 92 5 .2 168.9 ^- 61 3 .2 1174.6 4 1 8 .4 1432.0

Sancta Maria 4 3869.8 506.3 ^- 31 4 2 .0 4 3 1 7 .0 ^_ ^-

12 Cieplice Zdrój

C ie p lic e 2 25 134.5 8.2 ^- 117.9 145.0 109.8 159.3

C ie p lic e 1 6 134.4 10.8 ^- 120.4 152.2 ^- ^-

N o 4 (N o w e) 37 151.0 14.3 +0.25 123.5 183.2 108.0 193.9

N o 1 (M a ry sień k a ) 36 158.8 20 .4 + 0 .2 0 121.3 197.1 97.7 219 .8

N o 6 (B a se n o w e -M ę sk ie ) 37 139.5 12.1 -0 .0 3 107.3 167.8 103.2 175.8

N o 5 (B a se n o w e -D a m sk ie ) 38 141.6 10.7 + 0 .4 6 122.0 167.0 109.37 173.8

N o 3 (A n to n i-W a c la w ) 37 179.3 25 .8 + 1.36 132.8 27 5 .4 101.7 25 6 .8

N o 2 (S o b iesk i) 32 301 .6 69 .6 -0 .4 1 122.0 415 .6 92.9 510 .4

13 Lądek Zdrój

D ąb ró w k a 36 47.1 12.7 +0 .7 7 11.7 80.8 9.0 85.3

Jerzy 33 49.2 12.7 +0 .9 3 33.1 76.3 11.2 87.2

S k ło d o w sk a -C u rie 34 46 .0 13.3 + 1 .3 8 30.5 83.9 6.0 85.9

W o jciech 36 47 .8 13.3 + 0 .8 9 23.2 83.9 7.8 87.7

C h ro b ry 36 45 .4 13.3 + 1.49 27 .9 80.8 5.4 85.5

L -2 20 41 .4 10.0 ^- 24 .4 66.5 11.3 71.6

Stare 4 63.7 16.3 ^- 42.1 76.3 ^- ^-

14 Przerzeczyn Zdrój

S iarczk o w e 26 267.3 18.4 - 208 .0 305 .0 21 2 .0 32 2 .7

N o IX 15 270.1 9.3 ^_ 25 4 .0 290 .7 242.3 29 8 .0

N o II 8 296 .8 2 8 .4 ^- 269 .7 335.6 211 .6 38 1 .9

No X V 12 375.1 30.3 ^- 307 .4 399.6 284.3 4 6 6 .0

No X III 11 375.5 20.6 ^- 314 .0 386 .0 313.7 43 7 .2

No X I 11 374.6 16.3 ^- 346 .8 394 .0 325 .6 4 2 3 .7

N o V III 14 35 5 .4 23 .9 - 278 .0 381 .4 28 3 .8 427.1

(5)

SUDETIC THERAPEU TIC W ATERS

291

ters and mineral waters not declared as therapeutic, which neighbour the therapeutic waters.

Normality o f distribution is, however, concordant with an often observed phenomenon (Smimow, 1963), that in groundwaters, the normal (symmetrical) distribution is one o f the three most common ones. It occurs in conditions of chemical equilibrium or is a result o f numerous, indepen

dent, anisotropically acting hydrochemical processes. The processes are added but none o f them gains advantage over the other (Macioszczyk, 1977).

The TDS, however, is not an explicit feature for verifi

cation o f the phenomenon described above. In the quantita

tive sense, mineralization o f the Sudetic therapeutic waters and their hydrochemical type is decided most frequently by three, and in many cases even four ionic components, i.e.:

HCO3 and/or SO42', Ca2+, M g2+ and N a+. Therefore, nor

mality o f distribution may (according to Macioszczyk, 1977) result from overlapping o f several independent proc

esses averaging each other. Only the observation o f individ

ual components may bring a more precise solution to the problem o f formation o f the w aters’ chemical character.

The bicarbonate ion comes automatically, as it is pre

sent in waters o f almost all intakes analysed as the principal anion (according to the Shtschukariev-Priklonski classifica

tion as quoted by Macioszczyk, 1987), being second only to the sulphate anion in some intakes. Its major influence on the total mineralization o f the waters is also confirmed by strong correlation relations between the TDS and the [H CO3 ] content in the m ajority o f therapeutic water intakes in the Sudetes (Ciężkowski, 1990; Ciężkowski et al., 1996).

It is also important that m ost o f the waters analysed are car

bonated waters strongly enriched in CO2.

The predominant role o f bicarbonates is typical of w a

ters composition in the upper part o f the earth’s crust, in par

ticular, in the moderate climatic zone, where the composi

tion is formed due to weathering o f primary silicates and aluminosilicates, and leaching o f limestones and dolomites.

Similar conclusions were drawn also in relation to hydrogeological structures o f various types, from comparison of average chemical compositions o f groundwaters from vari

ous parts o f the world (Voigt, 1989).

The result o f testing o f the [H C O3] content in 68 Sudetic therapeutic waters intakes was similar to the TDS distribution. The Kolmogorov test at the significance level oc=0.05 proved that [H C O3 ] content distributions of almost all intakes may be regarded as normal. It means that accept

ing the hypothesis that the samples tested come from a gen

eral population with a normal distribution, one makes an er

ror lower than 5%. The only intake for which there are rea

sons for rejection o f the hypothesis on the normality of [H CO3J distribution at the assumed significance level, is the ‘Górne 2 ’ intake in Świeradów Zdrój. The [H C O3 ] con

tent distributions in waters not declared as therapeutic are of Gauss type.

DETERMINATION OF NORMAL VALUES OF HCO

'3

CONCENTRATION AND HISTOGRAMS

ANALYSIS

Determination o f normal values interval was done using

the three standard deviations method (3a) (e.g. Gawicz et al., 1981; Roszak, 1991). This principle states that the prob

ability o f occurrence o f a value from the interval ( - 3 a , + 3a), whose centre is the expected value (identified in the case o f the normal distribution with the arithmetic average), is close to one and amounts exactly 0.9973. A graphic method, suggested by M acioszczyk (1977) was not applied due to a too small size o f the majority o f the samples. Lower and upper ranges o f the intervals determined are presented in Table 1. In general, it may be noticed that the majority o f the analyses fall within the interval ( - 3 a , + 3 a), and only in less than 20% o f the intakes single values from outside o f this interval were observed.

However, for large samples, i.e. with n>30 (border value for distribution) some analysis of [H C O3 ] concen

tration histograms was carried out. The histograms were plotted for standardized variables, expressing the number o f units o f standard deviation by which the given value devi

ates from the arithmetic average (1) (Fig. 2):

X : — x

z = ^— ---

(

1

)

where:

z: standardized variable, X i: observed value,

x : arithmetic average o f values observed in the sample, a : standard deviation in the sample.

All possible distributions encountered in groundwaters were observed (except for j-shaped), i.e.: symmetrical, asymmetrical with positive skewness and asymmetrical with negative skewness, rarely encountered in groundwaters (Smimow, 1963; Macioszczyk, 1977). In the 28 intakes an

alysed, skewness (asymmetry) coefficients A x were calcu

lated in an unbiased way according to the formula (2) (Luszniewicz & Słaby, op. cit.) (Table 1):

(n — —- l ) ( n - 2 ) ^

X

( X : - X )

(

²

)

where:

n - sample size, other symbols as in (1).

The most common distributions are these with the posi

tive skewness (20 intakes), usually with asymmetry coeffi

cient above +0.5. 8 distributions skewed to the left were ob

served with asymmetry coefficient usually not lower than -1.0. As a rule, similarly as in the TDS distributions, the author did not observe a general dependence o f histogram shapes (including their skewness) on the absolute minerali

zation value, intake depth, or proportion o f common waters component.

In addition, a lot o f the distributions reveal bimodality which eliminates the diagnostic value o f the arithmetic aver

age (Kassyk-Rokicka, 1986) and indicates a heterogeneity o f the sample. Nevertheless, relatively small sample sizes and the lack o f reasons for rejection o f the hypotheses on normality o f general populations distributions, allow the ap

plication o f the statistical method for determination o f nor

mal values. However, in the bimodal samples case, these values, determined with the 3 a method should be treated

(6)

D I %

...

r 2-1

%

^1...,

1

1 0 1 2 3 4 5 1 1 1 1

S ta re

-p zp zi_ ■P S ? )-

B -2

e

« . - 4

£ &n a o-

Z im n y Z d ró j

- . , . .

m ^

...“ ... ,... - -3 -2 -1

^ // \/ / I\I / iy ; J^/A /^ /

0 1

^ Z Z Z ) _

2 3 4

B - l

o 8-4

a)

•3 0'

-3 -2 -1 0

I

1

r -77!

3 4

B -4

S 6 - 0- -

-4 1 6 - |

-2 -1

- n — i— ■— i-

2 3 4

p T p

-1 0 1 . 2 . 3 , 4 5

P ie n ia w a C h o p in a

-4

-2 -1

1 1 I 1 I r

2 3 4 5

.Tan K a z im ie rz

2 3 4

D ą b ró w k a

!----^7T/yŹ>‘/ / / Y ^ Y ^ f11 j frTr-z^-

-1 0

z

Fig. 2. Histograms o f standardized

[HCO

³

]

concentrations in selected Sudetic therapeutic w aters from: A - Czem iaw a Zdrój, B - Długopole Zdrój, C - Duszniki Zdrój, D - Lądek Zdrój, z - standardized

[HCO

³] concentrations w ere calculated according to the formula ( 1) (see text)

(7)

SUDETIC THERAPEU TIC W ATERS

293

w ith c au tio n . In p a rtic u la r, th e in te rv a l b o rd e rs fo r tw o p o p u la tio n s d is tin g u is h e d (c o r re s p o n d in g w ith th e tw o p e a k s) sh o u ld b e d e te rm in e d . T h e n o rm a l v a lu e s w o u ld b e re p re se n te d b y a n in te rv a l re p r e s e n tin g th e la rg e r p o p u la tion; th is w a s, h o w e v e r, a b a n d o n e d b e c a u se o f th e re a s o n s p re s e n te d b efo re.

[ H C O J J d is trib u tio n s in c e rta in in ta k e s d is p la y a sig n ific a n t c o n c e n tra tio n o f a n a ly s e s a ro u n d th e a rith m e tic a v erage (e.g. ‘R a d o c z y n n e 1 ’ a n d ‘R a d o c z y n n e 2 ’ in ta k e s in C z e r-n ia w a Z d ró j a n d ‘S z c z a w in a 1 ’ in S z c z a w in a ) (F ig . 2).

In su ch c a se s n o rm a l v a lu e s in te rv a ls c o u ld b e e x p re s se d m o re p re c ise ly , as e.g. th e ( - 1 .5c,+ 1 .5ct) in te rv a l p ro p o s e d by W eil (1 9 8 1 ).

It is c le a r, th a t th e a c c u ra c y o f th e n o rm a l H C O 3 c o n te n t in te rv a ls in in d iv id u a l in ta k e s w ill be th e h ig h e r th e m o re n ew m e a s u re m e n ts w ill be ta k e n u n d e r c o n sid e ra tio n .

DISCUSSION

It is a ss u m e d , th a t a ll S u d e tic th e ra p e u tic w a te rs are o f in filtra tio n o rig in o r c o n ta in d if fe re n t fra c tio n s o f fresh w a ters o f sh a llo w c irc u la tio n (C ię ż k o w sk i, 1990; C ię ż k o w sk i et al., 1996). T h e ir fin al c h e m ic a l co m p o s itio n re s u lts from m ix in g o f tw o c o m p o n e n ts , i.e. o f th e s tro n g e r m in e ra liz e d c o m p o n e n t o f th e d e e p e r o rig in , a n d th e sh a llo w , slig h tly m in e ra liz e d o n e (C ię ż k o w s k i & S z a rs z e w sk a , 1978; C ię ż k o w sk i, 1990; C ię ż k o w sk i et al., 1996). W h en it co m e s to ch a n g e o f th e se p ro p o rtio n , c o m e s a lso to c h a n g e o f th e m in e ra liz a tio n a n d c h e m ic a l c o m p o s itio n o f m ix tu re .

T he o b se rv e d n o rm a lity o f th e c o n s id e re d c h e m ic a l fe a tu r e s ’ d is trib u tio n in all S u d e tic th e ra p e u tic w a te rs b e a r e v i

d en ce o f th e ir little v a ria b ility d u rin g th e w h o le e x p lo ita tio n p erio d . T h e in flu e n c e o f a n a ly tic a l e rro rs w as re d u c e d to th e m in im u m u sin g rig o ro u s c rite ria o f a n a ly s e s s e le c tio n (see:

M e th o d o f in v e s tig a tio n ). T h e c h e m ic a l a n a ly s e s ta k e n into c o n sid e ra tio n w ere c a rrie d o u t b y th e o n ly tw o la b o ra to rie s a n d in th e sa m e w ay in th e w h o le tim e. M o re o v e r, a ss u m in g a fte r W eil (1 9 8 1 ), th a t v a lu e s o u ts id e th e ( - 5 a , + 5 a ) in te rv a l are false, su ch v alu es are a b s e n t in th e in ta k e s u n d e r c o n s id eration.

It a lso sh o u ld be n o tic e d th a t th e n o rm a lity o f T D S a n d [ H C O J ] d is trib u tio n s is o n ly se e m in g ly in c o n s iste n t w ith resu lts o f p a p e rs c o n c e rn in g d ire c tly o r in d ire c tly th e S u d e tic th e ra p e u tic w a te rs c h e m is try (e.g. C ię ż k o w sk i, 1990;

C ię ż k o w sk i e t al., 1996; K o z ło w sk i, 1997). R esu lts q u o te d in th ese p a p e rs c o n firm c o n s id e ra b le flu c tu a tio n s o f th e p re sent in filtra tio n w aters p ro p o rtio n (b a c k g ro u n d w a te rs ) (C ię ż k o w sk i, 1990) in th e th e ra p e u tic w a te rs e x p lo ite d . It h ap p e n s b e c a u se th e in te rv a ls o f n o rm a l v a lu e s ( - 3 a , + 3 a ) , e x p re s se d in a b so lu te u n its (m g /d m 3), a re o fte n larg e an d reach b e y o n d real v a lu e s (T a b le 1).

L o n g -te rm lin ear tre n d s o f m in e ra liz a tio n d e c re a s e in th e ra p e u tic w aters o f th re e in ta k e s in th e S u d e te s h a v e b e e n o b se rv e d b y P rz y lib sk i e t al. (G ó rn e 1, G ó rn e 2 an d G ó rn e 3 in tak es in Ś w ie ra d ó w Z d ró j - P rz y lib sk i et al., 1998). A s re

su lt o f th e little n u m b e r o f c h e m ic a l a n a ly s e s c o n sid e re d , it is h ard ly to state w h a t p ro c e s s o c c u rs th e re ; w h e th e r ste a d y , irre v e rsib le d e m in e ra liz a tio n o f th e ra p e u tic w a te rs o r lo n g te rm m in e ra liz a tio n v a ria b ility o f sin u o u s ty p e.

T h e n th e re are re a s o n s to a p p ly th e 3 a - m e th o d fo r d e te r m in in g o f n o rm a l v a lu e s in te rv a ls. T h e s e in te rv a ls c a n be u se d fo r th e re s u lts v e rific a tio n o f m o n ito r in g th e S u d e tic th e ra p e u tic w a te rs . T h e o b s e rv e d T D S o r [ H C O J j v a lu e s re a c h in g b e y o n d th e ( - 3 a , + 3 a ) in te rv a l sh o u ld b e re g a rd e d as u n tru s tw o rth y (fa lse ) a n d th e m e a s u re m e n t sh o u ld b e re p e a te d . I f th e n e w m e a s u re m e n t g iv e s th e s a m e re s u lt th e re is a sig n al th a t in c o n c e rn e d th e r a p e u tic w a te r u n d e rw e n t a su d d e n c h a n g e o f its T D S a n d [ H C O 3 ] c o n te n t a n d p ro b ab le a lso o f o th e r c h e m ic a l c o m p o n e n ts.

CONCLUSIONS

A ssu m in g , th a t T D S a n d [ H C O 3 ] c o n c e n tra tio n v a ri

a b ility e x is tin g in th e th e ra p e u tic w a te rs re fle c t n a tu ra l p ro c e sse s ta k in g p la c e in th e sy s te m , it c a n b e c o n c lu d e d :

1) S u d e tic th e ra p e u tic w a te rs a re c h a ra c te riz e d b y a low v a ria b ility o f T D S a n d [ H C O 3 ] c o n te n t in th e w h o le e x p lo i

ta tio n p e rio d ,

2 ) flu c tu a tio n s o f th e s e fe a tu re s h a v e a ra n d o m c h a ra c te r o n ly ; th e ir m o s t fre q u e n t v a lu e s a re c o m p ris e d w ith in a ra n g e o f + 3 a + - 3 a ,

3) d e te rm in e d n o rm a l v a lu e s in te rv a ls c a n b e u s e d fo r v e rific a tio n o f m o n ito rin g m e a s u re m e n ts (th e in d iv id u a lly fa u lty m e a s u re m e n ts e lim in a tio n ) a n d /o r m a y in d ic a te su d d e n c h a n g e s o f c h e m ic a l c o m p o s itio n o f th e e x p lo ite d th e r a p e u tic w aters.

A ck n ow led gem en ts

The author w ishes to thank W. Ciężkow ski and T. A. Przylib

ski for their comm ents and helpful discussion. The thanks are given anonym ous reviewers also. This paper w as prepared under the State Comm ittee for Scientific Research (KBN) G rant No.

9T12B01613.

R E F E R E N C E S

Ciężkowski, W., 1980. H ydrogeologia i hydrochem ia w ód term al

nych Lądka Zdroju. (In Polish only). Probl. Uzdrow., 4: 125—

193.

Ciężkowski, W., 1990. A study o f the hydrogeochem istry o f m in

eral and thermal waters in the Polish Sudety M ountains (SW Poland). (In Polish, English sum mary). Pr. Nauk. Inst. Geo- techn. Polit. W rocl, 60 (19): 1-135.

Ciężkowski, W. & Szarszewska, Z., 1978. O zjawisku mieszania się wód leczniczych z w odam i ich otoczenia na przykładzie uzdrow isk sudeckich. (In Polish only). Probl. Uzdrów., 6 :

167-173.

Ciężkowski, W. et al., 1996. Próba określenia obszarów zasilania wód leczniczych pochodzenia infiltracyjnego w Polsce na podstawie badań izotopowych. (In Polish only). Unpubl., ZBU “Zdroje” , Wrocław.

Davis, J. C., 1986. Statistics and data analysis in geology. John W iley & Sons, N ew York, 646 pp.

Dowgiałło, L, 1976. The Sudetes thermal waters. (In Polish, Eng

lish sum mary). Acta Geol. Pol., 26 (4): 617-643.

Fistek, J., 1977. A cidulous springs o f the K łodzko Basin and Bystrzyckie Mts. (In Polish, English sum mary). Biul. Geol.

UW„ 22: 285-288.

(8)

only). M oskow «U pper School».

Geological Map o f Low er Silesia w ith A djacent Czech and G er

man Territories (w ithout Q uartem ary deposits) 1:100 000, 1995. Polish G eological Institute, Com piled by L. Sawicki, Warsaw.

Jarocka, A., (ed.), 1976. A nalizy fizyko-chem iczne w ód leczni

czych, w ód stołowych, borowin. (In Polish only). Probl.

Uzdrów., 9/12, 474 pp.

Kassyk-Rokicka, H., 1986. Statystyka nie je st trudna 1, M ierniki statystyczne. (In Polish only). PWE, W arszawa, 144 pp.

Kozłowski, J., 1997. Zjawisko m ieszania się w ód na przykładzie wybranych złóż w ód leczniczych w Polsce. (In Polish only).

In: Górski, J. & Liszkow ska, E. (eds.), Współczesne problemy hydrogeologii, W rocław, 8 : 347-352.

Luszniewicz, A. & Słaby, T., 1996. Statystyka stosowana. (In Polish only). PWE, W arszaw a, 342 pp.

M acioszczyk, A., 1977. W yznaczanie tła i anomali hydrochem icz

nych w badaniach hydrogeologicznych. (In Polish, English summary). Biul. Geolog., 21: 67-84.

Macioszczyk, A., 1987. H ydrogeochem ia. (In Polish only). W y

dawnictwa Geologiczne, W arszawa, 475 pp.

Oberc, J., 1952. Budowa geologiczna Polski. Tektonika. Vol. IV, Part 2, (In Polish only). W ydaw nictw a Geologiczne, W ar

szawa, 307 pp.

Przylibski, T.A., 1997. Selected conditions o f radon-222 occur

rence in the Sudety Mts. (In Polish, English summary).

Wroclaw University o f Technology, D epartm ent o f Mining, Institute o f G eotechnics and Hydrotechnics, Report ser. PRE, no 577, W roclaw, 210 pp.

Przylibski, T. A., Kozłowski, J. & Kabat, T., 1998. Selected proc

esses in acidulous w aters from Św ieradów Zdrój in the light o f the results o f chemical analyses over the last thirty years.

Ann. Soc. Geol. Polon., 6 8 : 95-101.

Roszak, W., 1987. Pollution o f underground w ater in W rocław region. Memories. 19th Congress o f International Association o f Hvdrogeologists. Karlovy Vary 8-15.9.1986 Czechoslova

kia. \9 (2): 321-330.

Roszak, W., 1991. The trends o f chemical com position o f the shallow groundwaters in the ice-m arginal valley o f the Odra river near Wroclaw. (In Polish, English summary). Acta Univ.

Wratisl., 1281 (20): 174 pp.

Smimow, S. I., 1963. On the probability-statistical distribution o f the chemical elem ents in natural waters. (In Russian, English summary). Geochimia, 4: 417-424.

Voigt, H.-J., 1989. Hydrogeochemie. (In German only). VEB Deutscher V erlag fur Grundstoffm dustrie, Leipzig, 310 pp.

Weil, W., 1981. Characteristic o f the chemism o f ground w aters occurring within the M esozoic complex o f the W arsaw syn-

Streszczenie

ANALIZA STATYSTYCZNA DWÓCH PODSTAWOWYCH WŁASNOŚCI CHEMICZNYCH

(MINERALIZACJI I ZAWARTOŚCI JONU HCOj) W WODACH LECZNICZYCH SUDETÓW

J a c ek K ozłow ski

W pracy przedstaw iono wyniki analizy statystycznej dwóch podstawow ych własności w ód leczniczych Sudetów: m ineralizacji (TDS) i zawartości jonu w odorow ęglanow ego (H C O J ) w 66 ujęciach z 13 miejscowości uzdrow iskow ych Sudetów (Fig. 1) na podstawie rocznych analiz chem icznych tych wód. Param etry te, przetestowane dla 57 ujęć (n>8) testem K ołm ogorow a na poz

iom ie istotności oc=0.05, w ykazują rozkłady norm alne. W ykorzys

tując m etodę trzech odchyleń standardow ych (3 a ) wyznaczono przedziały w artości najczęściej w ystępujących dla zawartości [H C O 3 ] w poszczególnych ujęciach (Tabela 1). Tylko w około 20% ujęć stwierdzono pojedyncze w artości w ykraczające poza ten przedział.

Dla zmiennych standaryzow anych z w ykreślono histogram y rozkładu zaw artości jo n u [H C O 3 ] oraz przeprowadzono ich ana

lizę (Fig. 2). Zaobserw owano cztery typy rozkładów zawartości H C O 3 : sym etryczne, asym etryczne ze skośnością dodatnią, asy

m etryczne ze skośnością ujem ną oraz histogram y dw uw ierzchoł

kowe (bimodalne). Dla 28 ujęć (n>30) obliczono odciążone w spół

czynniki skośności (asymetrii) Ax. Zdecydow anie dom inują do

datnie w spółczynniki asym etrii (20 ujęć) - najczęściej powyżej +0.5; ujem nych zaobserwow ano tylko 8 (zwykle o wartości nie niższej o d - 1.0).

N ie zaobserwow ano zarówno dla rozkładów TDS ja k i [H C O 3 ] ogólnej zależności kształtu histogram ów oraz charakteru ich skośności od bezwzględnej w artości mineralizacji, głębokości ujęcia oraz udziału składowej w ód zw ykłych.

N orm alność rozkładów TDS oraz zaw artości jo n u [H C O 3 ] w w odach w szystkich przeanalizow anych ujęć świadczy o dużej sta

łości tych param etrów przez cały okres eksploatacji. Obserw o

wane w ahania pow yższych param etrów m ają w yłącznie charakter losowy. Pozwala to na w ykorzystanie uzyskanych przedziałów wartości norm alnych do w eryfikacji w yników obserwacji stacjo

narnych (elim inacji pojedynczych błędnych lub mało praw dopo

dobnych oznaczeń) i/lub sygnalizacji gw ałtow nych zmian składu chemicznego eksploatow anych w ód leczniczych.