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Spectral analysis approach to the dynamics of air pollutants
~rmospkrxEnvironment Vol.IO,pp.375-379. Pergamon Press 1976. Prmtedm GreatBritam
SPECTRAL ANALYSIS APPROACH TO THE DYNAMICS OF AIR POLLUTANTS S. TRIVIKRAMA
RAO, P. J. SAMSON
and A. R. PEDDADA
Division of Air Resources, New York State Department of Environmental Albany, NY 12233, U.S.A.
Conservation,
(Firsr received 21 August 1975 and in Jim11 form 25 November 1975) Abstract-This paper reports a comparison between the spectral characteristics of sulfur dioxide concentration and the wind speed in the frequency domain on Long Island, New York. The primary results show that, during winter, both spectra have a dominant peak corresponding to the synoptic time scale indicating that the synoptic weather variations are responsible for the long period oscillations of the pollutant. However, during summer, the spectra of the pollutant and the wind speed have significant diurnal and semi-diurnal peaks in addition to the synoptic peak. Directional linear regression indicates an eastward flux of the pollutant from the New YorkkNew Jersey metropolitan area. These results, having a one to one correspondence between the wind velocity and the pollutant concentration, indicate that this type of analysis is a powerful tool to recognize the interrelationships between the pollutants and the weather patterns.
In this paper spectral analysis results for sulfur dioxide data taken at Elmont and Northport, and wind data at Hicksville and Brookhaven, all on Long Island, New York, are presented and their interrelationships discussed. In addition, the behavior of these variables is further examined in light of pollution directional linear regression analysis.
1.INTRODUCTION
Transport of atmospheric pollutants over large distances has gained considerable attention during recent years. Raynor et al. (1974a, 1974b) have presented evidence that sulfur dioxide concentrations measured on Long Island, New York, for the most part originate in the New York City metropolitan complex. The objective of this investigation is to present relationships between the atmospheric pollutants and weather phenomena for their observations. The spectral analysis technique is utilized to distinguish different time scales involved in the pollutant and wind data. This type of analysis has been applied to data for Ottawa, Canada by Tilley and McBean (1973). Although the basic technique used in the present study is similar to theirs, the results reported herein have greater statistical reliability, and the seasonal variation of the various spectral components involved is discussed.
New
2.SOURCE
OF DATA
Data used herein was collected by the Long Island Lighting Company. Hourly values of sulfur dioxide at Ehnont and Northport, New York, and wind data at Brookhaven National Laboratory and Hit ksville, New York (see Fig. 1) for the periods December 196gJanuary 1969, representative of the winter season, and June 1969-July 1969, representative of the summer, are utilized for the time series analysis. Further details on the sampling procedure and the study area can be found in Raynor et al. (1974a, b).
.h
Jersey
‘---
0,55
Scale miles
Fig. 1. Map showing
the general
area
of Long
Island used. 375
and location
of the specific
measurement
sites
S. TRIVIKRAMARAO, P. J. SAMSONand A. R. PEDDAUA
(a)
lb)
I// IO
/
I,,,,
IO
Frequency,
cycles
10 h
Cd)
10 Frequency,
cycles
h
IO‘ Frequency,
cycles
h
10
’
Fig. 2. Power Spectral Density estimates: (a) Spectrum of SO2 concentratton at Elmont, NY. (b) Spectrum of SO2 concentration at Northport, NY. (c) Spectrum of the wind speed at Hicksvillc. NY, and (d) Spectrum of the wind speed at Brookhaven, NY. The frequency, j; along the abscissa is the circular frequency. The solid lines represent spectra during winter and dashed lines during summer. The vertical line near the peak IS the 9OY,, confidence interval, set by a xz distribution for the IO d.,f If S(h) is the true spectral estimate and SI- is the estimated value, then there is a 90”,, confidence (for 10 d,f:) that 0.55 Sk < S(,/J < 2.5 Sk. Note the pronounced diurnal (D) and semidiurnal (SD) peaks during the summer.
3. METHOD OF ANALYSIS
Hinich and Clay (1968) and Gossard and Hooke (1975) have discussed the computational aspects of power spectra. This study employs the fast Fourier transform technique for the spectral analysis. The total length of the data is divided into five non-overlapping segments each consisting of 256 points (N = 256), so that the spectral estimates have 10 d.f: To avoid end effects, all the N points are smoothed out by use of a weighting function of the form 4 (I - cos
the trend is removed 2nn.N), II = I. 2 --2v. In addition, by subtracting a linear function from the data values. This data is then Fourier transformed to compute the complex Fourier coefficients. The power spectra and cross spectra are computed from these Fourier coefficients for each segment, then averaged over all segments. Furthermore, these estimates are Hanned (Blackman and Tukey. 1958) to obtain a smooth spectrum. This technique increases the reliability of the spectral estimates.
311
The dynamics of air pollutants
SD
3.5Days 1
1
Y
)-
I-
s
10-Z
10-I Frequency,
u
100
cycles
IO
h-’
Fig. 3. Variation of coherence between sulfur dioxide at Elmont, NY and wind speed at Hicksville, NY. The 90% confidence interval for 10 d.$ is indicated on the diagram. Note a coherence close to unity during winter, corresponding to a period of 3.5 days (solid line). The only significant coherence occurs at the diurnal oscillation during summer (dashed line).
4. RESULTS
The meteorological variables can be considered control variables and the pollutant a dependent variable. As Tilley and McBean (1973) noted, the dependent variables can be expected to be governed by the control variables much more strongly for certain periods of oscillation. The power spectra for each variable are presented in the next section, and their interrelationships explored in the two sections following. 4.1. The spectra The power spectra of sulfur dioxide at Elmont, NY, and Northport, NY, in winter and summer seasons are presented in Fig. 2 (a and b) respectively. The 90% confidence limits for ten degrees of freedom are shown on the diagrams. It is clear from these diagrams that during winter both stations are characterized by a broad peak at the low frequencies. These peaks reflect the dependence of SO1 on synoptic-scale (approx. 3.5 days) meteorological changes. The spectra do not show any other significant peaks and the power seems to be a decreasing function of increasing frequency in general. There are, however, significant diurnal and semidiurnal peaks during the summer, in addition to a broad peak near the synoptic time periods. The wind spectra for Hicksville, NY, and Brookhaven, NY, shown in Fig. 2 (c and d) respectively, also indicate a dominant peak corresponding to synoptic scale events during winter, and a very significant diurnal peak during summer. From these diagrams, it is evident that both the pollutant and the wind have the same type of oscillations, and, hence, must be related. Cross spectral analysis can be used
to reveal the relationship between those quantities. The results of the cross spectral analysis must be interpreted in terms of coherence and phase relationship. 4.2. Coherence and phase relationships Coherence essentially is a measure of the linear relationship between any two records. It is sometimes stated that coherence is like a correlation function representative of a frequency band in the spectrum. When the coherence is near unity, phase information can be used to derive a relationship between two variables as a function of frequency. Figure 3 is a plot of frequency versus coherence between sulfur dioxide measured at Ehnont, NY, and the wind speed measured at Hicksville, NY for the winter and summer periods. During winter, coherence between these two variables close to unity exists for the oscillation corresponding to a period of 3.5 days. Since atmospheric weather patterns are known to have periods close to 3.5 days, it can be inferred with some confidence that the peak of the sulfur dioxide spectrum at 3.5 days is associated with the synoptic weather variations. During the summer, the overall coherence is much less than that in winter except at a period of one day. This indicates that local meteorology (sea breeze circulation) is responsible for the production of the diurnal peak in the sulfur dioxide spectrum. The phase difference during winter, corresponding to the 3.5 day oscillation is found to be 176” f 4” (90% confidence limits). Tilley and McBean (1973) found that the long period oscillation (3.2 days in their case) has a 270” phase difference; this led them to conclude that the pollutant maximum leads the
S. TKIVIKRAMA RAO. P. J. SAMSON and A. R. P~IxI,zI>.~
378
near IX0 while for 17 and 7.5 h the observed phase difference is close to 270 The phase difference corrcsponding to the diurnal oscillation in summer is found to be 245 f 34 This implies that during summer the pollutant concentration leads the wind speed by about 90 : in other words, there will be roughly a 6-h time difference between pollutant maximum and \n;ind speed maximum. Thus far the relationships between wind speed and SO? level have been presented. The spectral analysis of the wsind direction has not been attempted here since wind direction is a discontinuous function. However, the relationships between pollutant level and wind direction can be examined through a directional regression analysis technique. which is presented in the following section. I S
The wind-rose for Hicksvillc, NY. shown in Fig. 4. indicates that during winter the prevailing wind direction is from W to WNW. the dominant wind direction for the northeast United States (Clirncctic Atlns of U&et/ Stcltes, 196X). On the other hand, during summer the prevailing wind direction is from SSE, a sea breeze type circulation. Directional linear regression, similar to that employed by Samson rt al. (1975). was used to determine relationship between wind direction and pollutant levels. This method breaks down the wind direction into 16 directional
Fig. 4. Wind-rose for Hicksville, NY. The solid lines are for the winter case and dashed lines represent summer case.
wind speed maximum by 90‘. They present a synoptic situation which could illustrate that relationship. In contrast, our results with a phase difference of 180 indicate that a maximum in the pollutant level is associated with a minimum in wind speed. Examination of Fig. 3 indicates that during winter coherence is also high for oscillations of periods 42.6. 12, and 7.5 h. The phase difference for the 42.6 h oscillation is
\
\ \
\
-
0.12
-
0.10
-
0.08
-
0.06
-
0.04
-
0.2 000
6 = s
-
-002
-
-0.04
-
-0.06
--008
I
I
N
NNE
I NE
I
I
I
I
ENE
E
ESE
SE
SSE
I
I
5
SSW
Wind
I
I
SW WSW
I W
I
I
WNW NW
I
I
NNW
N
-
-0.10
-
--0.12 -014
directon
Fig. 5. Diagram illustrating the results of linear regression analysis on the wmd direction, measured at Hicksville, NY, and SO2 measured at Elmont, NY. Also indicated in the diagram is the wind speed-SO, linear regression. The significance at l”/, level (heavy lines) is also shown on the diagram. This means that when the correlation exceeds a critical value of kO.07. the null hypothesis that wind direction and pollutant level has zero correlation is rejected.
379
The dynamics of air pollutants
sectors and calm. Variables representing frequency of occurrence of wind in each sector are correlated with the level of pollutant. Figure 5 shows the results of this analysis between Hicksville wind data and Elmont sulfur dioxide data for both the winter and summer periods. Significance at the 1% level, determined by the F-test, is also shown. This analysis shows that during winter the only significant positive correlation between pollutant level and wind direction occurs for winds from WSW-W. However, during summer in addition to a positive correlation with westerly winds, it is seen that there is a significant negative correlation with SSE winds and a positive correlation with NNW winds. In both seasons, the high positive correlation with westerly winds can be attributed to the synoptic scale variations as revealed by the power spectra. The positive and negative correlations associated with northerly and southerly winds during summer can be attributed to the diurnal oscillation due to the sea breeze circulation, consistent with the diurnal peak in the power spectra. The relationship between wind speed and sulfur dioxide for both seasons is also shown in Fig. 5. There is little variation between seasons. Consequently, it can be generalized that light winds are more often associated with higher pollutant levels, as would be expected. However, it cannot be deduced from this diagram whether this is true for all directions.
ture, is characterized by a coherence of nearly unity and a phase shift of 180”, indicative of a cause and effect relationship between the two variables. During summer, diurnal and semidiurnal oscillations contribute significantly to the total variance of the spectrum. Further, directional linear regression show an eastward flux of pollutant from the New York-New Jersey metropolitan area regardless of season, which may be attributed to the synoptic scale variations. During summer, the sea breeze regime may be responsible for the high positive and negative correlations associated with winds from NNW and SSE directions. Acknowledgements-Thanks are due to Mr. Fred Lipfert of the Long Island Lighting Company for providing us with the necessary data. The authors would also like to thank Dr. John Hawley, Director of Air Resources Research, New York State Department of Environmental Conservation for his helpful comments. Thanks are extended to Mrs. Carol Clas for drafting the diagrams and Mrs. Catherine Cassidy for typing the manuscript. REFERENCES
Blackman R. B. and Tukey J. W. (1958) The Measurement of Power Spectra, 190 pp. Dover, New York. Climatic Atlas of the United States (1968) Published by U.S. Department of Commerce, USI GoGemment Printing Office.. Washineton. DC. 20402. Go&d E. b. and H\okk W. H. (1975) Waves in the Atmosphere, 456 pp. Elsevier, Amsterdam. Hinich M. J. and Clay C. S. (1968) The application of the discrete Fourier transform in the estimation of power spectra, coherence and bispectra of geophysical data. Rev. Geophys. 6, 347-363.
5. SUMMARY
AND CONCLUSIONS
Time series analysis is applied to pollutant and meteorological variables to study the seasonal variation of periods of oscillation involved. The Fourier analysis technique presented here has sufficient number of degrees of freedom to yield high statistical reliability of the spectral estimates. This leads to a clear definition of the relationships between the control (meteorological) and dependent (pollution) variables. It is found that during winter, an oscillation corresponding to a period of 3.5 days, a synoptic fea-
Raynor G. S. et al. (1974a) Temporal and spatial variation in sulfur dioxide concentrations on suburban Long Island, New York. J. Air Pollut. Control Ass. 24, 586-590.
Raynor G. S., Smith M. E. and Singer 1. A. (1974h) Meteorological effects on sulfur dioxide concentrations on Long Island, New York. Atmospheric Environment 8, 1305-1320. Samson P. J. et al. (1975) The transport of suspended particulates as a function of wind direction and atmospheric conditions. J. Air. Pollut. Control. Ass 25, 1232-1237. Tilley M. A. and McBean, G. A. (1973). An application of spectrum analysis to synoptic-pollution data. Atmospheric Environment 7, 79>801.
SPECTRAL ANALYSIS APPROACH TO THE DYNAMICS OF AIR POLLUTANTS S. TRIVIKRAMA
RAO, P. J. SAMSON
and A. R. PEDDADA
Division of Air Resources, New York State Department of Environmental Albany, NY 12233, U.S.A.
Conservation,
(Firsr received 21 August 1975 and in Jim11 form 25 November 1975) Abstract-This paper reports a comparison between the spectral characteristics of sulfur dioxide concentration and the wind speed in the frequency domain on Long Island, New York. The primary results show that, during winter, both spectra have a dominant peak corresponding to the synoptic time scale indicating that the synoptic weather variations are responsible for the long period oscillations of the pollutant. However, during summer, the spectra of the pollutant and the wind speed have significant diurnal and semi-diurnal peaks in addition to the synoptic peak. Directional linear regression indicates an eastward flux of the pollutant from the New YorkkNew Jersey metropolitan area. These results, having a one to one correspondence between the wind velocity and the pollutant concentration, indicate that this type of analysis is a powerful tool to recognize the interrelationships between the pollutants and the weather patterns.
In this paper spectral analysis results for sulfur dioxide data taken at Elmont and Northport, and wind data at Hicksville and Brookhaven, all on Long Island, New York, are presented and their interrelationships discussed. In addition, the behavior of these variables is further examined in light of pollution directional linear regression analysis.
1.INTRODUCTION
Transport of atmospheric pollutants over large distances has gained considerable attention during recent years. Raynor et al. (1974a, 1974b) have presented evidence that sulfur dioxide concentrations measured on Long Island, New York, for the most part originate in the New York City metropolitan complex. The objective of this investigation is to present relationships between the atmospheric pollutants and weather phenomena for their observations. The spectral analysis technique is utilized to distinguish different time scales involved in the pollutant and wind data. This type of analysis has been applied to data for Ottawa, Canada by Tilley and McBean (1973). Although the basic technique used in the present study is similar to theirs, the results reported herein have greater statistical reliability, and the seasonal variation of the various spectral components involved is discussed.
New
2.SOURCE
OF DATA
Data used herein was collected by the Long Island Lighting Company. Hourly values of sulfur dioxide at Ehnont and Northport, New York, and wind data at Brookhaven National Laboratory and Hit ksville, New York (see Fig. 1) for the periods December 196gJanuary 1969, representative of the winter season, and June 1969-July 1969, representative of the summer, are utilized for the time series analysis. Further details on the sampling procedure and the study area can be found in Raynor et al. (1974a, b).
.h
Jersey
‘---
0,55
Scale miles
Fig. 1. Map showing
the general
area
of Long
Island used. 375
and location
of the specific
measurement
sites
S. TRIVIKRAMARAO, P. J. SAMSONand A. R. PEDDAUA
(a)
lb)
I// IO
/
I,,,,
IO
Frequency,
cycles
10 h
Cd)
10 Frequency,
cycles
h
IO‘ Frequency,
cycles
h
10
’
Fig. 2. Power Spectral Density estimates: (a) Spectrum of SO2 concentratton at Elmont, NY. (b) Spectrum of SO2 concentration at Northport, NY. (c) Spectrum of the wind speed at Hicksvillc. NY, and (d) Spectrum of the wind speed at Brookhaven, NY. The frequency, j; along the abscissa is the circular frequency. The solid lines represent spectra during winter and dashed lines during summer. The vertical line near the peak IS the 9OY,, confidence interval, set by a xz distribution for the IO d.,f If S(h) is the true spectral estimate and SI- is the estimated value, then there is a 90”,, confidence (for 10 d,f:) that 0.55 Sk < S(,/J < 2.5 Sk. Note the pronounced diurnal (D) and semidiurnal (SD) peaks during the summer.
3. METHOD OF ANALYSIS
Hinich and Clay (1968) and Gossard and Hooke (1975) have discussed the computational aspects of power spectra. This study employs the fast Fourier transform technique for the spectral analysis. The total length of the data is divided into five non-overlapping segments each consisting of 256 points (N = 256), so that the spectral estimates have 10 d.f: To avoid end effects, all the N points are smoothed out by use of a weighting function of the form 4 (I - cos
the trend is removed 2nn.N), II = I. 2 --2v. In addition, by subtracting a linear function from the data values. This data is then Fourier transformed to compute the complex Fourier coefficients. The power spectra and cross spectra are computed from these Fourier coefficients for each segment, then averaged over all segments. Furthermore, these estimates are Hanned (Blackman and Tukey. 1958) to obtain a smooth spectrum. This technique increases the reliability of the spectral estimates.
311
The dynamics of air pollutants
SD
3.5Days 1
1
Y
)-
I-
s
10-Z
10-I Frequency,
u
100
cycles
IO
h-’
Fig. 3. Variation of coherence between sulfur dioxide at Elmont, NY and wind speed at Hicksville, NY. The 90% confidence interval for 10 d.$ is indicated on the diagram. Note a coherence close to unity during winter, corresponding to a period of 3.5 days (solid line). The only significant coherence occurs at the diurnal oscillation during summer (dashed line).
4. RESULTS
The meteorological variables can be considered control variables and the pollutant a dependent variable. As Tilley and McBean (1973) noted, the dependent variables can be expected to be governed by the control variables much more strongly for certain periods of oscillation. The power spectra for each variable are presented in the next section, and their interrelationships explored in the two sections following. 4.1. The spectra The power spectra of sulfur dioxide at Elmont, NY, and Northport, NY, in winter and summer seasons are presented in Fig. 2 (a and b) respectively. The 90% confidence limits for ten degrees of freedom are shown on the diagrams. It is clear from these diagrams that during winter both stations are characterized by a broad peak at the low frequencies. These peaks reflect the dependence of SO1 on synoptic-scale (approx. 3.5 days) meteorological changes. The spectra do not show any other significant peaks and the power seems to be a decreasing function of increasing frequency in general. There are, however, significant diurnal and semidiurnal peaks during the summer, in addition to a broad peak near the synoptic time periods. The wind spectra for Hicksville, NY, and Brookhaven, NY, shown in Fig. 2 (c and d) respectively, also indicate a dominant peak corresponding to synoptic scale events during winter, and a very significant diurnal peak during summer. From these diagrams, it is evident that both the pollutant and the wind have the same type of oscillations, and, hence, must be related. Cross spectral analysis can be used
to reveal the relationship between those quantities. The results of the cross spectral analysis must be interpreted in terms of coherence and phase relationship. 4.2. Coherence and phase relationships Coherence essentially is a measure of the linear relationship between any two records. It is sometimes stated that coherence is like a correlation function representative of a frequency band in the spectrum. When the coherence is near unity, phase information can be used to derive a relationship between two variables as a function of frequency. Figure 3 is a plot of frequency versus coherence between sulfur dioxide measured at Ehnont, NY, and the wind speed measured at Hicksville, NY for the winter and summer periods. During winter, coherence between these two variables close to unity exists for the oscillation corresponding to a period of 3.5 days. Since atmospheric weather patterns are known to have periods close to 3.5 days, it can be inferred with some confidence that the peak of the sulfur dioxide spectrum at 3.5 days is associated with the synoptic weather variations. During the summer, the overall coherence is much less than that in winter except at a period of one day. This indicates that local meteorology (sea breeze circulation) is responsible for the production of the diurnal peak in the sulfur dioxide spectrum. The phase difference during winter, corresponding to the 3.5 day oscillation is found to be 176” f 4” (90% confidence limits). Tilley and McBean (1973) found that the long period oscillation (3.2 days in their case) has a 270” phase difference; this led them to conclude that the pollutant maximum leads the
S. TKIVIKRAMA RAO. P. J. SAMSON and A. R. P~IxI,zI>.~
378
near IX0 while for 17 and 7.5 h the observed phase difference is close to 270 The phase difference corrcsponding to the diurnal oscillation in summer is found to be 245 f 34 This implies that during summer the pollutant concentration leads the wind speed by about 90 : in other words, there will be roughly a 6-h time difference between pollutant maximum and \n;ind speed maximum. Thus far the relationships between wind speed and SO? level have been presented. The spectral analysis of the wsind direction has not been attempted here since wind direction is a discontinuous function. However, the relationships between pollutant level and wind direction can be examined through a directional regression analysis technique. which is presented in the following section. I S
The wind-rose for Hicksvillc, NY. shown in Fig. 4. indicates that during winter the prevailing wind direction is from W to WNW. the dominant wind direction for the northeast United States (Clirncctic Atlns of U&et/ Stcltes, 196X). On the other hand, during summer the prevailing wind direction is from SSE, a sea breeze type circulation. Directional linear regression, similar to that employed by Samson rt al. (1975). was used to determine relationship between wind direction and pollutant levels. This method breaks down the wind direction into 16 directional
Fig. 4. Wind-rose for Hicksville, NY. The solid lines are for the winter case and dashed lines represent summer case.
wind speed maximum by 90‘. They present a synoptic situation which could illustrate that relationship. In contrast, our results with a phase difference of 180 indicate that a maximum in the pollutant level is associated with a minimum in wind speed. Examination of Fig. 3 indicates that during winter coherence is also high for oscillations of periods 42.6. 12, and 7.5 h. The phase difference for the 42.6 h oscillation is
\
\ \
\
-
0.12
-
0.10
-
0.08
-
0.06
-
0.04
-
0.2 000
6 = s
-
-002
-
-0.04
-
-0.06
--008
I
I
N
NNE
I NE
I
I
I
I
ENE
E
ESE
SE
SSE
I
I
5
SSW
Wind
I
I
SW WSW
I W
I
I
WNW NW
I
I
NNW
N
-
-0.10
-
--0.12 -014
directon
Fig. 5. Diagram illustrating the results of linear regression analysis on the wmd direction, measured at Hicksville, NY, and SO2 measured at Elmont, NY. Also indicated in the diagram is the wind speed-SO, linear regression. The significance at l”/, level (heavy lines) is also shown on the diagram. This means that when the correlation exceeds a critical value of kO.07. the null hypothesis that wind direction and pollutant level has zero correlation is rejected.
379
The dynamics of air pollutants
sectors and calm. Variables representing frequency of occurrence of wind in each sector are correlated with the level of pollutant. Figure 5 shows the results of this analysis between Hicksville wind data and Elmont sulfur dioxide data for both the winter and summer periods. Significance at the 1% level, determined by the F-test, is also shown. This analysis shows that during winter the only significant positive correlation between pollutant level and wind direction occurs for winds from WSW-W. However, during summer in addition to a positive correlation with westerly winds, it is seen that there is a significant negative correlation with SSE winds and a positive correlation with NNW winds. In both seasons, the high positive correlation with westerly winds can be attributed to the synoptic scale variations as revealed by the power spectra. The positive and negative correlations associated with northerly and southerly winds during summer can be attributed to the diurnal oscillation due to the sea breeze circulation, consistent with the diurnal peak in the power spectra. The relationship between wind speed and sulfur dioxide for both seasons is also shown in Fig. 5. There is little variation between seasons. Consequently, it can be generalized that light winds are more often associated with higher pollutant levels, as would be expected. However, it cannot be deduced from this diagram whether this is true for all directions.
ture, is characterized by a coherence of nearly unity and a phase shift of 180”, indicative of a cause and effect relationship between the two variables. During summer, diurnal and semidiurnal oscillations contribute significantly to the total variance of the spectrum. Further, directional linear regression show an eastward flux of pollutant from the New York-New Jersey metropolitan area regardless of season, which may be attributed to the synoptic scale variations. During summer, the sea breeze regime may be responsible for the high positive and negative correlations associated with winds from NNW and SSE directions. Acknowledgements-Thanks are due to Mr. Fred Lipfert of the Long Island Lighting Company for providing us with the necessary data. The authors would also like to thank Dr. John Hawley, Director of Air Resources Research, New York State Department of Environmental Conservation for his helpful comments. Thanks are extended to Mrs. Carol Clas for drafting the diagrams and Mrs. Catherine Cassidy for typing the manuscript. REFERENCES
Blackman R. B. and Tukey J. W. (1958) The Measurement of Power Spectra, 190 pp. Dover, New York. Climatic Atlas of the United States (1968) Published by U.S. Department of Commerce, USI GoGemment Printing Office.. Washineton. DC. 20402. Go&d E. b. and H\okk W. H. (1975) Waves in the Atmosphere, 456 pp. Elsevier, Amsterdam. Hinich M. J. and Clay C. S. (1968) The application of the discrete Fourier transform in the estimation of power spectra, coherence and bispectra of geophysical data. Rev. Geophys. 6, 347-363.
5. SUMMARY
AND CONCLUSIONS
Time series analysis is applied to pollutant and meteorological variables to study the seasonal variation of periods of oscillation involved. The Fourier analysis technique presented here has sufficient number of degrees of freedom to yield high statistical reliability of the spectral estimates. This leads to a clear definition of the relationships between the control (meteorological) and dependent (pollution) variables. It is found that during winter, an oscillation corresponding to a period of 3.5 days, a synoptic fea-
Raynor G. S. et al. (1974a) Temporal and spatial variation in sulfur dioxide concentrations on suburban Long Island, New York. J. Air Pollut. Control Ass. 24, 586-590.
Raynor G. S., Smith M. E. and Singer 1. A. (1974h) Meteorological effects on sulfur dioxide concentrations on Long Island, New York. Atmospheric Environment 8, 1305-1320. Samson P. J. et al. (1975) The transport of suspended particulates as a function of wind direction and atmospheric conditions. J. Air. Pollut. Control. Ass 25, 1232-1237. Tilley M. A. and McBean, G. A. (1973). An application of spectrum analysis to synoptic-pollution data. Atmospheric Environment 7, 79>801.