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Statistical analysis of nephelometer regional field data
Afmosphenc Enuironmem Vol. IS. No. 6. p. 1243-1244. Pcrpmon Press Ltd. Prmted m Great Bntam
1984
DISCUSSIONS STATISTICAL ANALYSIS OF NEPHELOMETER REGIONAL FIELD DATA*
DESIGN METHODOLOGY FOR OPTIMUM DOSAGE AIR MONITORING SITE SELECTION-t
For an ambient air quality network to be useful, the monitors must be dense enough that occurrences of the larger concentrations may be either detectable or estimable yet sparse enough to be affordable. In their recent paper No11 and Mitsutomi present an interesting approach for meeting a useful compromise between these two, often divergent, goals. The authors develop a routine for the identification of receptor points at which monitors would consistently measure most of the concentrations above a prescribed threshold value. The authors claim that their procedure defines an area which an efficient station can cover and results in an expansion of an arca covered by a monitor beyond that of the original grid size used in the diffusion model. Redundant monitors are thereby avoided. The method proposed by the authors may well accomplish these objectives to some degree. but the question of how to measure its success is not answered satisfactorily. Their network efficiency isan intuitivemeasure; one defined with a statistical essence would be preferable and more rigorous. The general scope of the problem addressed here is defined by three questions. What is the error associated with assigning r n rfl7;) r(5 Y.) a measured (or computed) value to a nearby point or points where no ,monitor exists? What improvements in this error 0.288 0.372 0.772 46 can be expected with the addition of another monitor to the 0.232 0.302 0.044 70 network? How can measured or calculated concentrations be 0.239 0.311 0.263 66 interpolated toestimatcconcentrationsat intermediaterecep tor points? I take this opportunity to comment on a general approach, already developed in other fields, that should It would be helpful if the authors gave a reference for afford a powerful means for answering these important Equation (1) and the definition of m. questions. Otherwise, the paper is a good discussion of point and path Theconcentration of an air pollutant may be considered to visibility measurements during periods of local or regional be a regionalized random variable 2(x, r) so named because it haze. Not surprisingly, the information in the paper suggests is defined over a region of space as well as in time. Here x is to the value of monitoring visibility with multiple methods be interpreted as a vector locating the point of observation in including nephelometry, multiple-path teleradiometry and three-dimensional space. Generally the outcomes of Z(x, t) photography. Such a combination allows the strengths of will be correlated in space and time. Correlation of outcomes each methodology to cover each method’s weaknesses. at neighboring receptors implies that one receptor can take the place of several with less error than would be possible otherwise. REFERENCE The importance of spatial correlations among air quality monitors has been recognized and considered in an evaluKennedy J. B. and Neville A. M. (1974) Basic Stotisticul ation of an operating air quality network (Handscombe and Methods (2nd Edition). Harper and Row, New York. Elsom, 1982). The mathematical apparatus used by Handscombe and Elsom is well known, easy to use. and Lockheed Engineering and Manugement ERIC G. WALTHER produces results easily graphed for visual analysis. It should Services Company, 1nc. be entirely adequate as a baais for designing a rational air P.O. Box 15027 quality network from theoretically calculated pollutant conLas Vegas, NV 89114, U.S.A. centrations as well as from measured concentrations. In their estimations of ore reserves, mining geologists have long recognized the importance of accounting for spatial correlations. In the field of geostatisttcal ore reserve estimation. the grades of equally sized samples and the thickness of the deposit are important regionalized random variables. The theory of regional random processes has been extensively developed and applied to ore reserve estimation (David,
In Babson ec al., 1982,* the authors present three correlation coefficients of 0.772,0.044 and 0.263, representing a regional haze period, forest-fire period and clear-background period respectively. Later in the paper they refer to a correlation coefficient of 0.338 as “poor” and 0.263 as “fairly low”. The poorness or goodness of any correlation coefficient depends on the number of data pairs included in the computation. The significance of a correlation coefficient depends on exceeding a threshold value. below which the correlation could result from random chance. For example, if the reader of the paper counts the number of points in Figs 4(a), (b) and (c), then the threshold correlation coefhcients for 5 per cent and 1percent chance of random correlation are as follows: (Kennedy and Neville, 1974) With this additional information, the reader can judge that 0.772 is a significant correlation, 0.044 is insignificant at both levels and 0.263 is only significant at the 5 per cent level.
lBabson B. L., Bergstrom R. W., Samuelson M. A. and Seigneur C. (1982) Armospherir Enl;ironmenr 16, 2335-2346.
t No11 K. E. and Mitsutomi Etwironmem
1243
17, 2583-2590.
S. (1983) Armospheric
1984
DISCUSSIONS STATISTICAL ANALYSIS OF NEPHELOMETER REGIONAL FIELD DATA*
DESIGN METHODOLOGY FOR OPTIMUM DOSAGE AIR MONITORING SITE SELECTION-t
For an ambient air quality network to be useful, the monitors must be dense enough that occurrences of the larger concentrations may be either detectable or estimable yet sparse enough to be affordable. In their recent paper No11 and Mitsutomi present an interesting approach for meeting a useful compromise between these two, often divergent, goals. The authors develop a routine for the identification of receptor points at which monitors would consistently measure most of the concentrations above a prescribed threshold value. The authors claim that their procedure defines an area which an efficient station can cover and results in an expansion of an arca covered by a monitor beyond that of the original grid size used in the diffusion model. Redundant monitors are thereby avoided. The method proposed by the authors may well accomplish these objectives to some degree. but the question of how to measure its success is not answered satisfactorily. Their network efficiency isan intuitivemeasure; one defined with a statistical essence would be preferable and more rigorous. The general scope of the problem addressed here is defined by three questions. What is the error associated with assigning r n rfl7;) r(5 Y.) a measured (or computed) value to a nearby point or points where no ,monitor exists? What improvements in this error 0.288 0.372 0.772 46 can be expected with the addition of another monitor to the 0.232 0.302 0.044 70 network? How can measured or calculated concentrations be 0.239 0.311 0.263 66 interpolated toestimatcconcentrationsat intermediaterecep tor points? I take this opportunity to comment on a general approach, already developed in other fields, that should It would be helpful if the authors gave a reference for afford a powerful means for answering these important Equation (1) and the definition of m. questions. Otherwise, the paper is a good discussion of point and path Theconcentration of an air pollutant may be considered to visibility measurements during periods of local or regional be a regionalized random variable 2(x, r) so named because it haze. Not surprisingly, the information in the paper suggests is defined over a region of space as well as in time. Here x is to the value of monitoring visibility with multiple methods be interpreted as a vector locating the point of observation in including nephelometry, multiple-path teleradiometry and three-dimensional space. Generally the outcomes of Z(x, t) photography. Such a combination allows the strengths of will be correlated in space and time. Correlation of outcomes each methodology to cover each method’s weaknesses. at neighboring receptors implies that one receptor can take the place of several with less error than would be possible otherwise. REFERENCE The importance of spatial correlations among air quality monitors has been recognized and considered in an evaluKennedy J. B. and Neville A. M. (1974) Basic Stotisticul ation of an operating air quality network (Handscombe and Methods (2nd Edition). Harper and Row, New York. Elsom, 1982). The mathematical apparatus used by Handscombe and Elsom is well known, easy to use. and Lockheed Engineering and Manugement ERIC G. WALTHER produces results easily graphed for visual analysis. It should Services Company, 1nc. be entirely adequate as a baais for designing a rational air P.O. Box 15027 quality network from theoretically calculated pollutant conLas Vegas, NV 89114, U.S.A. centrations as well as from measured concentrations. In their estimations of ore reserves, mining geologists have long recognized the importance of accounting for spatial correlations. In the field of geostatisttcal ore reserve estimation. the grades of equally sized samples and the thickness of the deposit are important regionalized random variables. The theory of regional random processes has been extensively developed and applied to ore reserve estimation (David,
In Babson ec al., 1982,* the authors present three correlation coefficients of 0.772,0.044 and 0.263, representing a regional haze period, forest-fire period and clear-background period respectively. Later in the paper they refer to a correlation coefficient of 0.338 as “poor” and 0.263 as “fairly low”. The poorness or goodness of any correlation coefficient depends on the number of data pairs included in the computation. The significance of a correlation coefficient depends on exceeding a threshold value. below which the correlation could result from random chance. For example, if the reader of the paper counts the number of points in Figs 4(a), (b) and (c), then the threshold correlation coefhcients for 5 per cent and 1percent chance of random correlation are as follows: (Kennedy and Neville, 1974) With this additional information, the reader can judge that 0.772 is a significant correlation, 0.044 is insignificant at both levels and 0.263 is only significant at the 5 per cent level.
lBabson B. L., Bergstrom R. W., Samuelson M. A. and Seigneur C. (1982) Armospherir Enl;ironmenr 16, 2335-2346.
t No11 K. E. and Mitsutomi Etwironmem
1243
17, 2583-2590.
S. (1983) Armospheric