Evaluation of Sources of Acidity in Rainwater Using a Constrained

Environ. Sci. Techno/. 1995, 29, 1638- 1645

Evaluation of Sources of Acidity in Raiawater Using a Constrailted we Rotational Factor Analysis

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on September 1, 2015 | http://pubs.acs.org Publication Date: June 1, 1995 | doi: 10.1021/es00006a030

TORU OZEKI,*st K U N I C H I K A K O I D E , t AND TAKASHI K I M O T O i Hyogo University of Teacher Education, Shimokume 942-1, Yashiro-cho, Kato-gun, Hyogo 673-14,Japan, and Research Institute of OceanoChemistry, Funahashi-cho 5-19, Tennoji-ku, Osaka 543, Japan

Acidity (or basicity) of sources of rainwater pollutants, whether they work as acids, bases, or neutral substances, is not easily evaluated by using conventional multivariate analysis such as the principal component analysis (PCA) or that with the Varimax rotation. W e examined the application of an oblique rotational factor analysis in this work based on the nonnegative constraint as to the ion concentrations except hydrogen ion and to the contributions of pollutant sources in rainwater. The method is as follows: (1) the PCA, (2) the Varimax rotation, and (3) the oblique rotation with partially nonnegative constraint. The method and its validity are demonstrated by using analytical data for 391 rainwater samples collected at Hyogo prefecture in Japan during 1991-1992. As a result, four predominant pollutant sources were extracted; they were a source with sea salt origin, a source acidifying rainwater, a source basifying rainwater, and a source specific to potassium ion. At most, six pollutant sources were extracted and were reasonably interpreted from the chemical, biological, geographical, and meteorological points of view.

Introduction Acid rain is one of the major concerns on the environmental problems in Japan ( 1 ) . This phenomenon was widely recognized when drizzling injured people’s eyes and caused skin irritation during the rainy seasons from 1973 to 1975 in Tokyo and its surrounding prefectures. According to a report analyzing the rainwater samples during 1984-1986 by the Japan Environment Agency, the annual mean value of the pH ranged from 4.5 to 5.1 with an overall mean of 4.7 (1). However, the value of the pH of each rain changes widely event by event (for example, see Figure 3); the presence of a couple of sources polluting rainwater is likely. Identification of the pollutant sources and evaluation of their chemical compositions are required in order to understand the contamination process of rainwater. One of the approaches to achieve this objective is a multivariate analysis such as principal component analysis (PCA)or factor analysis (2-11). A conventional approach follows: (1)an estimation ofthe number of sources (factors) polluting rainwater using the PCA and (2) an evaluation of the chemical compositions of the sources by the Varimax orthogonal rotation. The numbers of the factors proposed by such studies were two (2-41, three (5-7), or four (8111, probably reflecting the difference in the sampling locations, sampling methods, etc. The extracted factors have been interpreted with some of the following sources: (1) a source with sea salt origin, (2) an anthropogenic source containing hydrogen ion acidifying rainwater, (3) a source originating to soil dust or agricultural activities, and others. A noticeable characteristic of the rains in Japan is a high contribution of sea salt because the land is surrounded by seas as shown in Figure 1. If the polluting mechanisms are examined in detail, however, a much more precise grouping of the pollutant sources is necessary: for example, nitrogen oxide and sulfur oxide should have different histories from their generations to precipitation; the same is true between soil dust and ammonia. For the purpose of making groupings of these pollutant sources precise, the combination of the PCAwith the Varimaxmethod has limited ability because the Varimax method assumes the orthogonal relationship for chemical compositions of pollutant sources, although they need not be orthogonal in fact. This method has another shortcoming that some loadings of the factors become negative. Thus, the degree of acidity of pollutant source cannot be estimated, especially related to whether it works as a base or is neutral. In this study, we have applied a kind of constrained factor analysis to the analysis of rainwater that utilizes the nature of rainwater effectively. Namely, ion concentrations should not be negative in rainwater, and contributions of any pollutant sources to each rainwater should not be negative. Using a nonnegative constraint, the bases of the factor axes for the score (contribution) matrix R and for the loading (composition) matrix C obtained by the PCA have been rotated. A remarkable feature of this work is that the nonnegative constraint is excluded from the hydrogen ion in order to evaluate the contribution of hydroxide ion. This approach enables the evaluation of acidity (and basicity) +

Hyogo University of Teacher Education.

* Research Institute of OceanoChemistry. 1638 m ENVIRONMENTAL SCIENCE &TECHNOLOGY / VOL. 29, NO. 6, 1995

0013-936W95/0929-1638$09.00/0

@ 1995 American Chemical Sociew

I

Japan

t"'

Y : Yashiro

I

fl

Am: Amagasaki

-3 k40.N

Sea of Japan


log,o(

2 0 / 20)

FIGURE 2 Distribution plat of the ionic balance [Z-LZ+) of 624 rainwater samples. The 391 data set correspondingtu the shaded panwas used forthe analysis. Abscissavaluesof +O.Olland -0.08 correspond to 1.2 and 0.83 of the ionic balance ratio, respectively.

I

I

30"

TABLE 1

Statistical Iluantities of Ions

FIGURE 1. Locations of sampling places.

of pollutant sources. We report here the method and its validity by using data for rainwater samples collected by us.

Experimental Section Sampling of Rainwaters. Locations of the two sampling places are shown as Y and Am in Figure 1. The location Am is Amagasaki, a populated sea-side city, including industrial areas. The sampling point was chosen on the roof of the Amagasaki-kita High School. The location Y is Yashiro, a town where the Hyogo University of Teacher Education lies. Five sampling points (Yl-Y5) were chosen within a 5 km area from the university. The locations Y and Am are about 40 km apart; the former is typical urban, but the latter is rural. Both areas are however ascribed to the same climate group; thus, there is no difference in metheorological nature. We collected rainwater samples for 1 year from October 1991 to September 1992. Sampling methods were two different kinds: A-rain, all rainwater was collected by an event; B-rain, rainwater correspondingto an initial (beginning) 1 mm height was collected. In the latter case, we used a 100-mLpolyethylene bottle connected to a 300 mm diameter funnel in which a ball made of polystyrene foam was included. When rainwater corresponding to an initial 1 mm height is collected (about 70 mL), the ball floats up and shuts up the inlet of the botde; thus, any successive rain flows out without entering in the bottle. Chemical Analysis. Water used for chemical analysis was distilledtwice afterbeingdeionizedusingionexchange resin. Analytical-gradechemicalswere utilized. Analytical methods and items were as follows: (1) an amount of rainwater from its volume; (2) a pH meter with a glasselectrode (HoribaM-8L): pH to be converted into [H+];(3) a specific conductance meter (Horiba DS-7): EC; (4) ion chromatography (Yokokawa-Hokusbin IC-100): IC1-1, [NOs-], and [S042-1;(5) atomic absorption spectrophotometry (Hitachi 180-301: INa+l. lK+l, lMg2+1,and lCa2+l;

PH EC b S cmPl amount (mml ICI-1 (/rmol dm-'I [NOS-] @mol dm-')

[SO& bmol dm+) [Caz+l @mol dm+) [Mgz+l bmol d w 3 ) [NHl+l (#mol dm+I

lK+l bmol dm-? lNa+l (#mol dm-? lH+l (Ilmol dm-3)

mean.

SD

max

min

4.69 59.80 8.83 108.45 70.26 84.16 46.56 14.53 74.52 18.06 83.12 58.09

0.77 41.97 12.75 112.05 65.88 66.44 50.08 14.31 86.95 21.43 71.57 71.72

7.01 285.00 50.00 615.30 425.40 389.50 338.90 107.10 493.00 178.00 311.40 346.74

3.46 3.89 1.00 2.90 1.20 4.80 0.00 0.00 0.00 0.00 0.00 0.10

'Mean is the simple arithmetic mean as to rainwater sampleswith

no weight.

(6) ultraviolet/visible absorption spectrophotometry (Sbimadzu W-210): INHI+] (indophenol method). The procedures suggested by the Japan Environment Agency were carried out for the above listed chemical analyses. Details have been described elsewhere (12).

Computational Procedures In order to check the quality of the data obtained by the chemical analysis, the sum of the equivalents (products of molar concentration with charge) of anions and that of cations were calculated and compared. The ratio should be unity to fulfill ionic balance if the majority of ions are correctly analyzed. In the present case, total 624 rainwater samples gave a distribution plot of the ionic balance (ZE+) shown in Figure 2. A 391 data set (62.796) corresponding to a shaded part with the ionic balance from 1.2 to0.83 (wi~20%error)wasusedforthefollo~ganalysis. Abscissa values f0.08 and -0.08 of Figure 2 correspond to 1.2 and 0.83 of the ionic balance ratio, respectively. The data set contains Amagasaki A-rain (38) and B-rain (25) andYashiro A-rain (151) andB-rain (177). These rawdata are presented in the supporting information, and some statistical quantitiesarelistedinTable1. Ionconcentrations used for the factor analysis were the following: (1) ICI-I, (2) [NOS-1,(3) lSO~z-l,(41 lCa2+l,(5) lMg2+1,(6) ["4+1. (7) K+I, (8) lNa+l. and (9) lH+l. VOL. 29. NO. 6,1995 I ENVIRONMENTAL SCIENCE &TECHNOLOGY m 1639

:1

TABLE 2

Ei~envaluesand Variances 1 2 3 4 5 6 7 8 9

3t

eigenvalues

YO of variance

1 257 248.125 247759.750 100566.859 30804.012 20614.602 16 460.299 11 046.292 5 941.405 1 440.687

74.31 14.64 5.94 1.82 1.22 0.97 0.65 0.35 0.09

(cumulative YOvariance) (74.31) (88.95) (94.90) (96.72) (97.94) (98.91) (99.56) (99.911 (100.00)

-

d . . . 10 . I ~ " 20. I ~ ~30. " " "40 ' " ' ' 50' ~ ' ~60. '

Amount I m m FIGURE 3. Dependence of pH values of the 391 rainwater samples used in the present analysis upon their precipitation amounts.

3 factors

4 factors

CI-


NOj'

The electrical conductivity (EC)data were not used for the following analysis because it was not an independent variable. The distribution of the pH values of the rainwater samples used here is shown in Figure 3 against the amount of rainwater. Figure 3 shows that the variation of the pH is large as the amount is small, and it comes to converge at the overall mean value of the domestic rains in Japan as the amount increases. Analysis Using Principal Component Analysis (PCA). Step I: Normalization by a Mean Concentration for Each Zon. Among the ions contained in the rainwaters in Japan, the predominant ones are chloride and sodium ions because Japan is surrounded by seas. In contrast with sodium or chloride ions, concentrations of some ions such as magnesium and potassium are relatively low. If the raw data are used for the analysis, the ions of high concentrations affect the principal component analysis (PCA) too greatly as compared with the ones of low concentrations, because the treatment of the PCA analysis work in evaluating the magnitude of the element of a data matrix. In this study, the normalized concentrations were calculated by dividing the measured ones with a mean concentration for each ion. The nine normalized concentrations of the nine ions were aligned as row elements of a data matrix D for each rainwater sample. The data matrix D of 391 rows and nine columns was consequently obtained. The mean concentrations used here are listed in the Table 1. Step 2 Calculation of Eigenvalues and Eigenvectors (13, 14). From the data matrix D,a covariance matrix Z was calculated:

z = 'D-D where a matrix 'D is a transposed matrix of D. Here, an eigenvalue matrix E and an eigenvector matrix Q were obtained by applying the Jacobi method. The relation among E,Q,and Z is expressed as follows:

z = Q-E.'Q A list of the eigenvalues, the fractions of the variance of

each factor to the total variance, and the cumulative values of the variance fractions are listed in Table 2. In the present case, the first three eigenvalues represent 94.90% of the total variance. It means that the rainwaters used here were contaminated by the three predominant pollutant sources. However, the concentrations of potassium ion in the rainwaters, which were reproduced by using these three factors, show apparent deviations from the 1640 ENVIRONMENTAL SCIENCE 81 TECHNOLOGY / VOL. 29, NO. 6.1995

so42. p I

I

I

1

MgZ+ NHq+

K+

I I FIGURE 4. Plots of differences between the original concentrations of ions (in the matrix D) and their reproduced ones (in the matrix product R-C) using a given number of factors.

measured ones, as shown in the left panel of Figure 4.The perpendicular axis of Figure 4 shows the difference of the measured concentration from the reproduced one using a given number of factors for each rainwater. These deviations were however improved when the first four factors were used as shown in the right panel of Figure 4. The fourth factor is stronglyrelated to the potassium ion. About the source of potassium ion, some authors have suggested plants with high potassium contents (9),biomass burning of vegetation, local farms, and forest fires (10). Thus, the first four factors were chosen here. Step 3: Chemical Compositions and Contributions of the Factor Sources. From the eigenvector matrix Q obtained above, the eigenvectors corresponding to the four largest eigenvalues were extracted, and a composition matrix C was obtained that describes the chemical compositions (loadings)of the factors (pollutant sources). On the other hand, a contribution matrix R describing the contributions (scores) of the factors to each rainwater was obtained as follows:

R = D.'C

(3)

The obtained compositionmatrix C and the contribution matrix R are shown in Figure 5. The first factor obtained by the Jacobi method represents the total contamination. Thus, the four factors described in Figure 5 do not explain chemical characters of the four independent pollutant sources. In order to get them, the bases of both the matrixes C and R have to be rotated. One way to accomplish this is by using the Varimax method. Analysis Using the Varimax Method. The Varimax method is one of the orthogonal rotational methods, which gathers the ion variables and the rainwater points close to

'g

3 @


uE

10 11 12

Ions

2

1

3

4

5

6

7

8

9

Month ( 1991-1992)

FIGURE 5. Result of the principal component analysis; left panels: the chemical compositions of four factors (A-D); right panels: seasonal changes of the contributions of the factors in the rainwater samples.

any one of the factor axes while keeping the orthogonal relationships among factors (1.516). As aresult, eachfactor comes to load a similar amount of variance. The product of the matrixes R and C becomes the data matrix D:

D = ROC

(4)

Here, a rotation matrix T is introduced:

D = (R*T-') (T-C) = R'*C'

(5)

For a newly obtained composition matrix C , the following quantity a

m

u r n

called the Varimax criterion is defined. m is the number of ion variables, 9, and p is the number of factors, 4. The rotation matrix T is now determined so that the Varimax criterion Vcomes to have the largest value. The details of the algorithm can be found elsewhere (16). We programmed the Varimax method used here. The result of the Varimax method is shown in Figure 6. The left panels show the chemical compositions of the four pollutant sources after the Varimax rotation. It is easily understood that the four pollutant sources correspond to (1) a source with sea salt origin, (2) a source acidifying rainwater, (3) a source coming from soil dust or agricultural origins, and (4) a source specific to potassium ion.

However, the chemical compositions of the pollutant sources need not be orthogonal as mathematical vectors. In fact, the concentrations of some ions (NOs- of the factor A, CaZt of the factor B, K+ of the factor C, NH4+and C1- of the factor D, etc.) are negative, which are meaningless as concentrations. These negative values are yielded from the requirement that these factor compositions have to be orthogonal as vectors. In most articles on the acid rain treated by the above treatment, less than four factors have been proposed; it is because these negative values make the interpretation of the chemical characteristics of factors very difficult when the number of the factors is increased (11). The fact that some ion concentrations are negative causes another shortcoming that the degree of acidity of pollutant source cannot be correctly estimated, especially related to whether it works as a base or a neutral substance. So next the oblique rotational method has been introduced. Analysis Using Oblique Rotation with Partially Nonnegative Constraint. Algorithm To Accomplish a Nonnegative Constraint. The constraints used here are that any ion (excepthydrogen ion, as is mentioned later) should not have negative concentration in pollutant source and any rain sample should not have negative contribution from the pollutant source. Now suppose that some elements of the matrix R and C are negative. Here, a rotation matrix T is introduced again (see eq 5). The rotation matrix T giving the new R' and C' in which all elements are not negative can be obtained as follows: VOL. 29, NO. 6,1995 I ENVIRONMENTAL SCIENCE &TECHNOLOGY

1641

I

I

A


B

D

Ions

Month ( 1991-1992)

FIGURE 6. Result of the Varimax orthogonal rotation; left penels: the chemical compositions of four factors (A-D); right panels: seasonal changes of the contributions of the factors in the rainwater samples.

Step 1. AU negative elements of the composition matrix C are replaced by zero; and this matrix is denoted as C*. Step 2. Aleast square solution of T optimizing a relation

C* = T-C

(7)

is calculated by using (Moore-Penrose's) generalized inverse matrix:

T = C*.tC.(C.'C)-'

(8)

A better choice of the composition matrix C than the original C is

C' = T-C

(9)

Step 3. A new matrix R corresponding to this C is calculated using the T matrix:

R" = R.T-~

(10)

Step 4 . All negative elements of the R are replaced by zero, and this matrix is denoted as R*. Step5 Aleast square solution of another rotation matrix S optimizing a relation:

R* = R*S

(11)

is calculated by using a generalized inverse matrix:

s = ('R-R)-~('R-R*)

(12)

A better choice of the contribution matrix R' than the

original matrix R is

R' = R*S

(13)

and the corresponding better choice of the composition matrix C is 1042 ENVIRONMENTAL SCIENCE &TECHNOLOGY I VOL. 29, NO. 6,1995

While this matrix C still has the negative elements, the process is returned to step 1 by using this C in place of C to make another C*.As the loop is repeated, the negative elements decrease. When the sum of the squares of the negative elements in C' becomes smaller than a proper limitingvalue, the process stops. As a result, a set of R' and C having few negative elements is obtained. According to a study on the requirements to obtain unique rotation result by nonnegative constraint, the set of R' and C thus obtained is unfortunately not always the unique solution; sometimes, there are several sets ( 17). It is up to the nature (and quality) of the rainwater data; however, it should be emphasized that any set of R' and C obtained by this oblique rotation is at least better than the one obtained by the Varimax method because no orthogonal requirement is assumed among factors. Another point to be emphasized here is that the rotation using the Varimax method is not always necessary, although the use of the Varimaxrotation prior to this oblique rotation shortens the iteration time, but the rotation based on the nonnegative constraint can be applied directly to the result of the PCA. Similar approaches to get reliable loadings and scores based on given constraints, such as nonnegative constraint, have been proposed by several researchers in order to analyze chromatographicdata, spectroscopicdata, etc. (1820).

Partially Nonnegative Constraint. In this stage, an additional feature is introduced to account for how to treat the hydroxide ion. Hydrogen ion and hydroxide ion react to give a water molecule:

A I


C

I

D Ions

Month ( 1991-1992)

FIGURE 7. Result of the oblique rotation with partially nonnegative constraint left panels: the chemical compositions of four factors (A-D); right panels: seasonal changes of the contributions of the factors in the rainwater samples.

The concentrations of these ions in pure water are lo-’ mol dm-3; this amount is negligible as compared with the concentrations of the other ions in rainwater (see Table 1). Any pollutant source containing a hydrogen ion concentration larger than this amount can be regarded as acid and that containing a hydroxide ion concentration larger than this amount can be regarded as base. Thus, we exclude the nonnegative constraint from the hydrogen ion, and the resultant positive value of the hydrogen ion is taken as the hydrogen concentration itself, but the negative value is taken as the hydroxide ion concentration using its absolute value:

[OH-] = -[H+]

(16)

It enables the evaluation of the acidity and basicity of the pollutant source. We have named this method the “obliquerotational factor analysis with partially nonnegative constraint”.

Discussion Compositional Characters of Four Independent Pollutant Sources Obtained by Oblique Method. The result of the

application of this oblique method is shown in Figure 7. The left panels show the chemical compositions of the four pollutant sources (A-D); The right panels show the seasonal changes of their contributions to rainwater. Pollutant Source A of Sea Salt Origin. Major ions belonging to this source are chloride, sodium, and magnesium ions. From the average sea salt composition reported elsewhere (21),the order of the normalized concentrationscontributing to the sea salt factor is expected to be Na+ C1- > Mgz+3 K+ > S042- Ca2+. This order agreeswith the factorA extracted in Figure 7. Participations of H+ ion and NH4+ ion are also observed, but they are not

-

-

explained for the sea salt; they seem to be incorporated as particles of the source A are flying to sampling points. The seasonal change of this source to each rainwater shows that the contribution is small in summer (from May to August) and is large in the other seasons. Even in the summer, some rains categorized into a typhoon (a kind of tropical cyclone) have high content. Typical rains precipitating in the Japanese summer are typhoons and showers (sometimesaccompanied by thunderstorms). Usually in a Japanese summer, we have only a little rain because the stable Ogasawara high atmospheric pressure system existing in the Pacific Ocean covers the Japan islands. In the evening of such clear hot days, a moist air rises to grow a cumulo-nimbus cloud and is cooled down at the upper air to cause a sudden rain shower. This process of precipitation occurs locally, thus the inclusion of sea salt particles can not be expected. On the other hand, typhoons are born in the tropical zone of the Pacific Ocean and move to the north. Some of them approach the Japan islands, land there, and drop a lot of rainwater containing sea salt particles. The precipitation water amounts due to typhoons are vast, but the number of such events is few. In the other seasons except summer, many rain clouds are coming over the seas from west to east or from north to south. This is the reason why this source A of sea salt origin contributes to rainwaters little in summer (except typhoon) but much in autumn (fall),winter, and spring. Pollutant Source B AcidifjlingRainwater. This source B contains nitrate ion, sulfate ion, ammonium ion, and a remarkable amount of hydrogen ion. It means this source is the one acidifying rainwater. In contrast with the pollutant source A, the contribution of this source to rainwater is high in summer. Nitrogen oxide gas (NOx) VOL. 29. NO. 6, 1995 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

1643


and sulfur oxide gas (SOZ)are exhausted from chimneys of factories and from automobiles; They are transformed to nitric acid and sulfuric acid through photochemical reactions. Intense sunlight of the summer promotes this reaction. The resultant acids seem to be absorbed by moving clouds (rain-out process) and by precipitating raindrops (wash-out process) to acid@ rainwater. Another characteristic point of this source is to contain appreciable amounts of ammonium ion. Probably the reason is that the ammonia gas in air is easily absorbed by acidic clouds. Pollutant Source C Basihing Rainwater. Major ions belonging to this source C are calcium, ammonium, and nitrate. Here, hydrogen ion concentration has a negative value, meaning that this source works as a base. There is no clear seasonal change observed; the up-and-down pattern seen in the right panel C of Figure 7 mainly relates to the precipitation amounts. The contribution of source C is bigger for the B-rains (the initial 1mm rains). It means that pollution by this source proceeds through the washout process. Soil dust consisting of calcium oxide or calcium bicarbonate seems to be the origin of the calcium content. In addition, the generation of ammonia gas from agricultural activity is expected because many of the sampling points are located in the suburbs. Pollutant Source D ContainingPotassium Ion as a Major Cation. Source D is unique because its predominant cation is potassium ion. The other ions contained in this source are sulfate and magnesium ions. This source has a negative amount of hydrogen ion; thus, this source seems to work as a base to rainwater. No distinctive seasonal change can be observed; rather some peak-shape contributions are seen. These characters of source D may indicate that this source is of fertilizer origin or biomass burning. The latter possibility has been suggested by some researchers ( 6 , I O ) . Changes of Pollutant Source Compositions When the Number of Factors Is Increased. When many factors are adopted in the PCA or the Varimax method, the interpretation of the character of the factor becomes difficult. Our method however enables the interpretation of the characters of the factors of pretty large numbers. In Figure 8, changes of chemical compositions of the factors as increasing number of factors are shown. When only one factor was assumed, the chemical composition (1A) obtained was corresponding to the averaged composition in all rainwater samples. In the case that two factors were assumed, one (2B) showed a positive hydrogen ion concentration (net acidic source) and the other (2A) showed a negative hydrogen ion concentration (net basic source); 2B was close to the pollutant source B of Figure 7 acidifying rainwater, and 2A was close to the sum of the other sources (A, C, and D). In the case that three factors were assumed, the source corresponding to the sea salt origin (3A), the source acidifymgrainwater (3B), and the source baslfylng rainwater (3C) were extracted. The source specific to the potassium ion was extracted when the four factors were assumed, as already mentioned. In the case that five factors were assumed, a new pollutant source (5E) was separated mainly from the one of sea salt origin (4A) and partially from the source (4C). This source (5E) consists of calcium, magnesium, sulfate, and chloride ions; its acidity is essentially neutral. It is a kind of mixture of sea salt, enriched sulfate, and calcium. It has a high contribution in the spring. In the Japanese 1644 1 ENVIRONMENTAL SCIENCE &TECHNOLOGY / VOL. 29, NO. 6, 1995

q $4 c

N

pq


winter and spring, especially spring, an Asian long-range eolian dust, referred to as “kosa” in Japan, comes from China; its origin is the Gobi Desert. This source (5E) may be the eolian dust absorbing sulfuric acid and sea salt substances on the way to Japan. In the case that six factors were assumed, the factor basifying rainwater (5C)was divided into two independent factors; one (6C)was calcium-rich and the other (6D)was ammonium-rich. An interesting point is the difference of distributions of these sources in geographical pattern; the calcium-rich factor (6C)has high contributions at an urban area and the areas close to highway roads, probably because the construction of buildings and road soil dust are related to this source. On the other hand, the ammonium-rich factor (6D)has high contributions at surburban areas close to agricultural activity points. Another interesting point related to these factors (6C and 6D) is that the major anions are hydroxide and nitrate ions not sulfate ion. In domestic Japan, the exhaustion of sulfur oxide gas has been strongly regulated; thus, a great amount of domestic yielding of sulfate ion from anthropogenic activity is not expected. However,the automobiles moving in the current Japan are exhausting large amounts of nitrogen oxide gas. As a local acid source relating to the wash-out process, nitric acid seems to be predominant rather than sulfuric acid. In contrast with this, the acidic source (6B) mainly consisted of sulfateion. This source has higher contribution to the A-rains (the rains collected by an event) rather than the B-rains (the initial 1 mm); the former rainwaters are strongly correlated to the rain-out process when the precipitation amounts are large. It means that sulfuric acid is related to the long-range atmospheric transport. In the case that seven factors were assumed, a new factor (7G) specific to the nitrate and magnesium ions was given. Now the origin of this factor cannot be explained adequately. It is important to know what the differences are in the interpretation when more factors are used. Certainly, there is no simple answer for how many factors are really reliable. Taking seven factors may be a lot for the present data set consisting of nine variables. However, we think that the six pollutant sources taken in the above discussion are fully reliable because they can be reasonably interpreted from the chemical, biological geographical, and meteorological points of view.

Conclusions As a result, the oblique rotational factor analysis with partially nonnegative constraint was applied to the chemical data of the rainwater samples during 1991-1992 and was demonstrated to give much reasonable and useful information on the pollutant sources and polluting processes of rainwater.

Acknowledgments The authors thank Dr. Kunishige Higashi and Dr. Shin-ichi Wakida for letting us use an ion chromatograph of the

Government Industrial Research Institute of Osaka and for giving us good advices in terms of chemical analysis of rainwater. We also thank the students and teachers of the Amagasaki-kita High School for their cooperation in collecting rainwater samples.

Supplementary Material Available Data for Amagasaki A-rain and B-rain and Yashiro A-rain and B-rain (6pp) will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supporting information from this paper or microfiche (105 x 148 mm, 24x reduction, negatives) may be obtained from MicroformsOffice, American Chemical Society, 1155 16th St. NW, Washington, DC 20036. Full bibliographic citation (journal,title of article,names of authors,inclusivepagination, volume number, and issue number) and prepayment, check or money order for $16.50 for photocopy ($18.50 foreign) or $12.00for microfiche ($13.00foreign),are required. Canadian residents should add 7% GST.

literature Cited (1) Hara, H.; Ito, E.; Katou, T.; Kitamura,Y.; Komeiji, T.; Oohara, M.; Okita, T.; Sekiguchi, K.; Taguchi, K.; Tamaki, M.; Yamanaka, Y.; Yoshimura, K. Bull. Chem. SOC.Jpn. 1990, 63, 2691. (2) Matsumoto, M.; Itano, T. J. Jpn. SOC.Air Pollut. 1985, 20, 12. (3) Matsumoto, M.; Ueda, N.; Itano, T. 1.Jpn. SOC.Air Pollut. 1985, 20, 218. (4) Vong, R. J.; Hansson, HX.; Ross, H. B.; Covert, D. S.; Charlson, R. J. J. Geophys. Res. 1988, 93, 1625. (5) Finzi, G.; Novo, A.;Viarengo, S.Environ. Monit.Assess. 1991,17, 273. (6) Bridgman, H. A. Atmos. Environ. 1992, 26A, 2401. (7) Zhang, P.; Dudley, N.; Ure, A. M.; Littlejohn, D.AnaZ. Chim.Acta 1992, 258, 1. (8) Gatz, D. F. Atmos. Environ. 1984, 18, 1895. (9) Romero, F.; Elejalde,C.; Gomez, G. Tonicol. Environ. Chem. 1988, 17, 117. (lo) Khwaja, H. A.; Husain, L. Atmos. Environ. 1990, 24A,1869. (11) Kessler, C. J.; Porter, T. H.; Firth, D.; Sager, T. W.; Hemphill, M. W. Atmos. Environ. 1992, 26A, 1137. (12) JEA. A Mannual for Acid Precipitation Monitoring, 1990, 2nd ed.; Japan Environment Agency: Tokyo, 1990. (13) Ozeki, T.; Kihara, H.; Hikime, S. Anal. Chem. 1987, 59, 945. (14) Ozeki, T.; Kihara, H.; Ikeda, S. Anal. Chem. 1988, 60, 2055. (15) Malinowski, E. R.; Howery, D. G. Factor Analysis in Chemistry, 1st ed.; Wiley: New York, 1980; p 49. (16) Nakatani, K. Multivariate Analysis; Shin-yosha: Tokyo, 1981;p 50 (in Japanese). (17) Ozeki, T.; Kihara, H.; Hikime, S.; Ikeda, S. Anal. Sci. 1987,3,285. (18) Vandeginste, B. G. M.; Derks, W.; Kateman, G.Anal. Chim. Acta 1985, 173, 253. (19) Karjalainen, E. J. Chemom. Intell. Lab. Syst. 1989, 7, 31. (20) Karjalainen, E. J.; Karjalainen, U. P. Anal. Chim.Acta 1991,250, 169. (21) Drever,J. I. TheGeochemistryofNaturalWaters,2nded.; Prentice Hall: Englewood Cliffs, NJ, 1988; p 266, Table 12-1.

Received for review October 26, 1994. Revised manuscript received February 20, 1995. Accepted March 6, 1995.*

ES940661U Abstract published in Advance ACS Abstracts, April 15, 1995.

VOL. 29, NO. 6 , 1 9 9 5 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

1

1646

Evaluation of Sources of Acidity in Rainwater Using a Constrained

Recommend Documents