<BODY>
<P>
<CENTER>
<H1>Elevation Corrected U.S. PM10 Maps Derived from AIRS and IMPROVE</H1>
<P>
by <A HREF="../../People/SFalke/home.html">Stefan Falke</A>, <A HREF="mailto:stefan@mecf.wustl.edu">stefan@mecf.wustl.edu</A><P>
Center for Air Pollution Impact and Trend Analysis (<A HREF="http://capita.wustl.edu/CAPITA/">CAPITA</A>)<P>
January, 1996<P>
</CENTER>
<HR>
Air pollutants are generally measured at monitoring stations such as those comprising the AIRS (Aerometric
Information Retrieval System) and IMPROVE (Interagency Monitoring of Protected Visual Environments) networks.
In order to determine the concentrations at locations without monitors, some form of extrapolation or interpolation
is required. Generally weighted interpolation is applied where the concentrations at
surrounding sites are weighted dependent on their relative distance from the new concentration location.
This type of interpolation does not account for such concentration dependent factors as
elevation or wind direction. This work incorporates elevation into the interpolation scheme.
Quarterly U.S. PM10 maps are derived using the new interpolation scheme.
<HR>
<P>
<H2><A NAME="content">Contents</A>:</H2>
<UL>
<LI><A href=#rationale>Background and Rationale </A>
<UL>
<LI><A href=#distance>Distance-weighted interpolation</A>
</UL>
<LI><A href=#dataprep>Data Sets</A>
<UL>
<LI><A href=#pm10>PM10</A>
<LI><A href=#elevation>Elevation</A>
<LI><A href=#scalehgt>Scale Height </A>
</UL>
<LI><A href=#method>Methodology </A>
<LI><A href=#results>Results </A>
<UL>
<LI><A href=#bsPM10>Standardized Elevation PM10 </A>
<LI><A href=#adPM10>Elevation Corrected PM10 </A>
<UL>
<LI><A href=#pm10comp>Comparison with Initial PM10</A>
</UL>
</UL>
<LI><A href=#appendixA>Appendix A </A>
<LI><A href=#ref>References </A>
</UL>
<HR>
<BR>
<P>
<A NAME="rationale"><H2>Background and Rationale</H2></A>
<P>
Pollutant concentrations measured at monitors such as those comprising the Aerometric Information
Retrieval System (AIRS) (U.S. EPA, 1994) and the Interagency Monitoring of Protected Visual
Environments (IMPROVE) (Sisler et al., 1993) provide measured concentrations for specific points
across the U.S. Extrapolation or interpolation is required to obtain concentrations at locations
between monitoring sites. A standard interpolation technique averages the monitor values
surrounding a location weighted by the distance between the location and monitor. This type of
averaging does not consider other factors, such as topography, which influence a location's air
pollutant concentration. This can cause considerable inaccuracies in estimated values, particularly
in the rugged terrain of the Western U.S. It is desirable to develop an interpolation technique
which incorporates the varying elevation of the contiguous U.S.
<P>
In general, locations at high altitudes have lower aerosol concentrations than in neighboring valleys
(Dutkiewicz et al., 1987; Husar et al., 1980). Pollutant sources are not normally found on
mountain tops and it can be assumed that the majority of anthropogenic pollutant emissions are
found in low lying areas. In addition, the mixing layer height (the lowest [~1-3km] of the
atmosphere in which surface level pollutants are generally uniformly mixed up to but not above) is
usually below the peaks of mountain ranges resulting in little dispersion of polluted air to higher
altitudes. On the other hand, valleys channel air flow and often "trap" polluted air leading to
high pollutant concentrations. This assumption, namely that at higher elevations pollutant
concentrations are lower than at surrounding lower elevations, is the basis for the application of
elevation in correcting PM10 (particulate matter < 10µm in diameter) concentrations.
<P>
The process of incorporating elevation data with concentration data is referred to as data fusion.
Data fusion is the integration of multiple data sets with varying spatial and temporal resolution.
By reconciling the multiple data inputs onto a common a common spatial and temporal projection, the data can be "fused" to create
a new data set.
<P>
<A NAME="distance"><H3>Distance-weighted Interpolation</H3>
A general technique for the interpolation of point values utilizes weighting known values dependent
upon their respective distances from the desired location. This is illustrated below.
<P>
<CENTER>
<IMG SRC="spatdoc.gif" align=absmiddle width="583" height="616"><P>
</CENTER>
The estimated concentration at j is the sum of the weighted values divided by the sum of the weights. The weighting
factor can also be viewed as a transfer matrix (t<FONT SIZE=1>ij</FONT>) in that it relates the concentration at one location to the
concentrations at surrounding locations. Other factors, such as elevation, can be used as components in the
transfer matrix to increase the accuracy of the interpolation. In the following discussion, the weighting factor, or
transfer matrix, is composed of two components, namely distance and elevation.
<P>
<H2><A NAME="dataprep"><B>Data Sets</B></A></H2>
<P>
Observed PM10 data from the AIRS and IMPROVE networks, U.S. elevation and meteorological scale height data were combined to generate elevation corrected U.S. PM10 maps. Each of the data sets underwent an individual preparation process which ensured consistent spatial and temporal resolutions before being fused in the elevation correction process.
<P>
<H3><A NAME="pm10"><B>PM10</B></A></H3>
<P>
The IMPROVE network has monitoring sites (~40 sites) located mostly in national parks and wilderness areas. The IMPROVE data used in this work were generally collected over a 24 hour period twice weekly from 1988 to June 1993. AIRS monitoring sites (~1600 sites) are mostly located in urban areas although some suburban and non-urban sites are also included. AIRS data were available from 1982 to June 1993, but very little data existed prior to 1985. The AIRS network monitored PM10 approximately every sixth day for 24-hours. The maps below show the location of the AIRS and IMPROVE PM10 stations. The boxes represent AIRS monitoring stations while the circles are IMPROVE sites. The magnitude of the squares and circles are proportional to their respective PM10 concentrations which are shown for quarter 1 (Jan., Feb., Mar.), quarter 2 (Apr., May, Jun.), quarter3 (Jul., Aug., Sep.), and quarter 4 (Oct., Nov., Dec.).
<P>
"Raw" AIRS and IMPROVE daily PM10 data were quarterly aggregated over the time range for which the data existed.
In order for a site to be included in the aggregated data set it had to have at least four months of valid data. The minimum was set at four months of data so that a single quarter from one year
of data was not used in the aggregation over the approximatley five year span. This ensured that each quarterly average was determined from at least two years of data. In the AIRS network has about 5 observations per month so the minimum was set at 20 daily values.
IMPROVE sites required at least 32 daily observations since about 8 observations existed per month.
<B><CENTER>
<IMG SRC="p10flow.gif" align=absmiddle width="500" height="212"><P><Font Size=3>Data flow for the creation of Quarterly PM10 Tables.</FONT><P>
</B></CENTER>
Data quality checking was conducted to remove sites which would bias the resulting elevation corrected PM10 maps. The AIRS site 421010149
Philadelphia was removed because of its anomously high quarterly PM10 values compared to other
Philadelphia sites.<br>
<P>
Four or five high elevation sites (depending on the quarter) were removed because of their extremely high PM10 concentrations which contradicted the assumption used for this work. Their removal was justified since the number of sites removed was small and because the extent of their influence covered large regions thereby making the results in those regions highly biased. The AIRS sites at Mammoth Lakes, Crestline, and Keeler in California
were removed because they displayed high PM10 concentrations at high elevations. In
quarter 1, AIRS site 040051003 Flagstaff was removed for this reason as was AIRS site Lone
Pine in quarter 4, IMPROVE site San Gorgonio in quarters 2, 3, 4 , and IMPROVE site Crater Lake in quarter 3. <P>
After the filtration and aggregation was conducted separately for the AIRS and IMPROVE data, the two sets were combined and then converted into a table format
that was suitable for use with subsequent operators used in the correction process.<P>
<P><CENTER>
<TABLE BORDER>
<TR>
<TH COLSPAN=4><FONT SIZE = 3>INITIAL PM10 Tables (AIRS & IMPROVE)</FONT></TH>
</TR>
<TR>
<TH>Quarter 1</TH>
<TH>Quarter 2</TH>
<TH>Quarter 3</TH>
<TH>Quarter 4</TH>
</TR>
<TR>
<TD><A HREF=INITIALT/TOTAL/gif/impairq1.gif><IMG SRC=INITIALT/TOTAL/gif/impairq1.gif HEIGHT=75></a></TD>
<TD><A HREF=INITIALT/TOTAL/gif/impairq2.gif><IMG SRC=INITIALT/TOTAL/gif/impairq2.gif HEIGHT=75></a></TD>
<TD><A HREF=INITIALT/TOTAL/gif/impairq3.gif><IMG SRC=INITIALT/TOTAL/gif/impairq3.gif HEIGHT=75></a></TD>
<TD><A HREF=INITIALT/TOTAL/gif/impairq4.gif><IMG SRC=INITIALT/TOTAL/gif/impairq4.gif HEIGHT=75></a></TD>
</TR>
</TABLE></CENTER>
<p>
An operator that was frequently used in the elevation correction process was the Contourer. It converts a table of point values to a grid format by distance wieghted spatial interpolation. The inputs consist of the table,
as well as user specified inputs that include a distance weight
function, a radius of influence, a minimum required number of
data points within the radius, a maximum number of data points
used in the calculation of the grid value, and the dimensions
for the output grid. The contouring process is described in more detail in <A href=#appendixA>Appendix A</A>. The contour plots of the observed PM10 data is shown below and will be used later for comparison with the elevation corrected PM10.
<P><CENTER>
<A NAME="intmaps"></A>
<TABLE BORDER>
<TR>
<TH COLSPAN=4><FONT SIZE = 3>INITIAL PM10 Grids</FONT></TH>
</TR>
<TR>
<TH>Quarter 1</TH>
<TH>Quarter 2</TH>
<TH>Quarter 3</TH>
<TH>Quarter 4</TH>
</TR>
<TR>
<TD><A HREF=INITIALG/gif/itp105q1.gif><IMG SRC=INITIALG/gif/itp105q1.gif HEIGHT=75></a></TD>
<TD><A HREF=INITIALG/gif/itp105q2.gif><IMG SRC=INITIALG/gif/itp105q2.gif HEIGHT=75></a></TD>
<TD><A HREF=INITIALG/gif/itp105q3.gif><IMG SRC=INITIALG/gif/itp105q3.gif HEIGHT=75></a></TD>
<TD><A HREF=INITIALG/gif/itp105q4.gif><IMG SRC=INITIALG/gif/itp105q4.gif HEIGHT=75></a></TD>
</TR>
</TABLE></CENTER>
<P>
The contours were obtained by strictly distance weighted interpolation; by averaging a location's
surrounding PM10 values with consideration of distance from the
location. The contouring creates a number of areas with concentrations that
do not represent the area's terrain. For instance, during the winter months
in the western half of the United States many high PM10 concentration
observations in urban areas are spread out over areas which have high moutain peaks. It is known that at these high altitudes, PM10 concentrations are low but the contouring process does not
reflect this understanding.
<P>
<IMG SRC="../../Icons/up3.gif" ALIGN=TOP width="20" height="20">
<A HREF="#content">Back to Contents</A><HR>
<P>
<H3><A NAME="elevation"><B>Elevation</B></A></H3>
<P>
The elevation data originated from NOAA's Terrain Base 30-second resolution digital elevation grid (NOAA, 1995). PM10 concentrations depend on surrounding sources and pollutant transport and therefore are dependent not on absolute elevation but a relative elevation above neighboring valleys containing PM10 sources. An "excess" elevation grid was defined as the absolute elevation of a grid point minus the lowest elevation (base elevation) found an approximately 50 square kilometer area around the grid point, <br>
<CENTER>Excess Elevation = Absolute Elevation - Base Elevation. (1) </CENTER> <BR>
A 50 km2 area was found to be an adequate size to represent a location’s excess elevation. It was small enough to retain the influence of high elevation plateaus but also large enough to account for valleys within mountain ranges. Compared to the original elevation,
the base elevation is much smoother. As expected, the west coast
exhibits the most texture. The Colorado plateau is seen very
clearly and the decreasing elevation as one moves eastward from
the Rockies is seen as a gradual decline in base elevation. The excess elevation map highlights the montain peaks in the west. The excess elevation is similar to a relative elevation used by Loibl et al (1994) in estimating ozone concentrations in complex terrain.
<P>
The derivation of the base elevation exposed some anaomlous values in the NOAA elevation grid.
In the West, a handful of grid cells displayed extremely low
elevations with respect to their neighboring cells. In some instances, a 1kmX1km grid cell with an elevation of approximately 200 meters had
neighboring cells with elevations on the order of 2000 meters. They caused the appearance of "holes" that did not reflect the actual terrain. It was assumed that these low elevation values were erroneous and were adjusted by replacing the very low elevation value with a value of one of the surrounding cells.
<P>
<CENTER>
<IMG SRC="elevate.gif" align=absmiddle width="250" height="93"><P><FontSize=3>Data flow for the creation of Excess Elevation Maps.</FONT SIZE><P>
<TABLE BORDER>
<TR>
<TH COLSPAN=4><FONT SIZE = 3>Elevation Grids</FONT></TH>
</TR>
<TR>
<TH>Elevation</TH>
<TH>Base Elevation</TH>
<TH>Excess Elevation</TH>
</TR>
<TR>
<TD><A HREF=../ELEVATION/gif/elevatn.gif><IMG SRC=../ELEVATION/gif/elevng.gif HEIGHT=75></a></TD>
<TD><A HREF=../ELEVATION/gif/baseelev.gif><IMG SRC=../ELEVATION/gif/bselevng.gif HEIGHT=75></a></TD>
<TD><A HREF=../ELEVATION/gif/exceselv.gif><IMG SRC=../ELEVATION/gif/exelevng.gif HEIGHT=75></a></TD>
</TR>
</TABLE></CENTER>
<P>
The Grand Canyon area is unique in its terrain. The area is relatively flat with the canyon cutting a strip of very low elevation values through it. These characteristics cause the locations neighboring the canyon to have excessively high excess elevation values. Such high excess elevations surrounding the canyon coupled with the extremely low excess elevations in the canyon produce very low elevation corrected PM10 concentrations around the canyon and very high concentrations within the canyon. Given the unique properties of the area, it was desirable to minimize its effect and consequently the Grand Canyon was "filled" so that its elevation resembled that of the surrounding terrain.
<P>
<IMG SRC="../../Icons/up3.gif" ALIGN=TOP width="20" height="20">
<A HREF="#content">Back to Contents</A><HR>
<P>
<H3><A NAME="scalehgt"><B>Scale Height</B></A></H3>
<P>
Estimating a location’s PM10 concentration requires an understanding of the scale height, or the vertical thickness of the atmosphere. The scale height upper boundary is above the mixing layer so it contains the pollutant concentrations in the mixing layer as well as those pollutants which are left above the mixing layer following the nighttime decrease in the mixing layer.
Comparing the scale height of a location with the excess elevation reveals whether or not the particular location is above the height at which most of the pollution exists or whether it is within the layer containing higher PM10 concentrations. The scale height was obtained from the CAPITA Monte Carlo Model (Patterson and Husar, 1981; Schichtel and Husar, 1994) which
simulates pollutant transport via the movement of particles. The scale height was calculated in the model every two hours from the vertical distribution of particles.
The hourly scale height was aggregated and then spatially interpolated using the Contourer to obtain the quarterly averages.
<CENTER>
<IMG SRC="sclhgtf.gif" align=absmiddle width="600" height="98"><P><FontSize=2>Data flow for the creation of Scale Height Maps.</FONT SIZE><P>
<TABLE BORDER>
<TR>
<TH COLSPAN=4><FONT SIZE = 3>Scale Height Grids</FONT></TH>
</TR>
<TR>
<TH>Quarter 1</TH>
<TH>Quarter 2</TH>
<TH>Quarter 3</TH>
<TH>Quarter 4</TH>
</TR>
<TR>
<TD><A HREF=../SCALEHGT/gif/sclhgtq1.gif><IMG SRC=../SCALEHGT/gif/sclhgtq1.gif HEIGHT=75></a></TD>
<TD><A HREF=../SCALEHGT/gif/sclhgtq2.gif><IMG SRC=../SCALEHGT/gif/sclhgtq2.gif HEIGHT=75></a></TD>
<TD><A HREF=../SCALEHGT/gif/sclhgtq3.gif><IMG SRC=../SCALEHGT/gif/sclhgtq3.gif HEIGHT=75></a></TD>
<TD><A HREF=../SCALEHGT/gif/sclhgtq4.gif><IMG SRC=../SCALEHGT/gif/sclhgtq4.gif HEIGHT=75></a></TD>
</TR>
</TABLE></CENTER>
<P>
There are three regions of note: the relatively low heights over much of the West Coast (particularly in California during quarter 1), the higher heights around and just east of the Rockies (particularly in the summer), and the relatively high values over the Appalachian Mountains. The significance of these regions will be illustrated in the maps of elevation corrected concentrations.
<P>
<IMG SRC="../../Icons/up3.gif" ALIGN=TOP width="20" height="20">
<A HREF="#content">Back to Contents</A><HR>
<P>
<A NAME="method"><H2>Methodology</H2></A>
<P>
A two step process was employed to incorporate elevation in the spatial interpolation of PM10 concentrations. The
first consisted of adjusting the measured PM10 concentrations to an identical "base"
elevation and linearly extrapolating these "base"
concentrations. The second step corrected the extrapolated base concentrations
for actual elevation. The figure below outlines the procedure and it components. The rectangles represent the operators which manipulate data. The have inputs and outputs which are designated as ovals in the diagram.
<P>
<B><CENTER>
<IMG SRC="2part.gif" align=absmiddle width="500" height="365"><P><Font Size=2>Two step data flow diagram for the creation of Elevation Corrected PM10 Maps</FONT SIZE><P>
</B></CENTER>
<P>
For each of the AIRS and IMPROVE station locations, an excess elevation and a scale height were extracted from their respective maps. The scale height (S) was used in conjunction with the excess elevation (Ee) to produce a meteorologically normalized height (Nm), <P>
<CENTER>
Nm = Ee / S (2)
</CENTER> <P>
This normalized height serves as an indicator of the mixing layer's influence at a location. A normalized height greater than one indicates that the location is above the scale height and therefore above the higher pollutant concentrations within the mixing layer. <P>
A relation of aerosol concentration as a function of elevation, where the concentrations decreased as the elevation increased, was adapted from Husar et. al. (1980) who mapped the vertical pollutant structure by sampling from aircraft making vertical spiral soundings. This relation <A HREF=corfactr.gif><IMG SRC="corfactr.gif" align=absmiddle HEIGHT=40></A> provided a correction factor (f[Nm]) which was less than or equal to one.<P>
The quarterly aggregated measured PM10 concentration (Ci) at each AIRS and IMPROVE site was divided by f[Nm] to adjust it to a standardized elevation concentration (Co). The <A href="baseflow.gif"> data flow</A> for this procedure consists of obtaining an excess elevation and scale height for each site, calculating a normalized height, and subsequently obtaining a correction factor which was divided by the initial PM10 concentration to get Co.
<CENTER>
Co = Ci / f[Nm] (3)
</CENTER> <P>
The results of equation 3 formed a table of standard elevation concentrations for the AIRS and IMPROVE locations. This adjustment removed the elevational influence of the observed concentrations. The calculated Co values were subsequently mapped out using distance weighted interpolation.
The next step in the method consisted of "elevating" the Co maps to their original elevations. This was achieved using a similar <A href="excsflow.gif">procedure</A> as described above in bringing the concentrations to a standard level except that the factor (f[Nm]) was obtained for each grid cell and was used to <i> multiple</i> the standardized concentration (Co) to obtain the elevation corrected concentrations, (Cc). <P>
<CENTER>
Cc = Co * f[Nm] (4)
</CENTER> <P>
The monitoring stations acted as anchor points in this process. The measured concentrations are retained through the two step method of equations (3) and (4) (Cc=Ci) while their values were applied to the estimation of concentrations at other locations.
<P>
<IMG SRC="../../Icons/up3.gif" ALIGN=TOP width="20" height="20">
<A HREF="#content">Back to Contents</A><HR>
<P>
<H2><A NAME="results"><B>Results</B></A></H2>
<P>
<H3><A NAME="bsPM10"><B>Standardized Elevation PM10</B></A></H3>
<P>
<CENTER>
<TABLE BORDER>
<TR>
<TH COLSPAN=4><FONT SIZE = 3>Standardized Elevation PM10 Concentration Tables</FONT></TH>
</TR>
<TR>
<TH>Quarter 1</TH>
<TH>Quarter 2</TH>
<TH>Quarter 3</TH>
<TH>Quarter 4</TH>
</TR>
<TR>
<TD><A HREF=BASETABL/gif/stdq1t.gif><IMG SRC=BASETABL/gif/stdq1t.gif HEIGHT=75></a></TD>
<TD><A HREF=BASETABL/gif/stdq2t.gif><IMG SRC=BASETABL/gif/stdq2t.gif HEIGHT=75></a></TD>
<TD><A HREF=BASETABL/gif/stdq3t.gif><IMG SRC=BASETABL/gif/stdq3t.gif HEIGHT=75></a></TD>
<TD><A HREF=BASETABL/gif/stdq4t.gif><IMG SRC=BASETABL/gif/stdq4t.gif HEIGHT=75></a></TD>
</TR>
</TABLE></CENTER>
<P>
These tables were processed through the
Contourer to produce standardized PM10 concentration grids.
<A NAME="basemaps"></A>
<CENTER>
<P>
<TABLE BORDER>
<TR>
<TH COLSPAN=4><FONT SIZE = 3>Standardized Elevation PM10 Concentration Maps</FONT></TH>
</TR>
<TR>
<TH>Quarter 1</TH>
<TH>Quarter 2</TH>
<TH>Quarter 3</TH>
<TH>Quarter 4</TH>
</TR>
<TR>
<TD><A HREF=BASEGRID/gif/stdq1g.gif><IMG SRC=BASEGRID/gif/stdq1g.gif HEIGHT=75></a></TD>
<TD><A HREF=BASEGRID/gif/stdq2g.gif><IMG SRC=BASEGRID/gif/stdq2g.gif HEIGHT=75></a></TD>
<TD><A HREF=BASEGRID/gif/stdq3g.gif><IMG SRC=BASEGRID/gif/stdq3g.gif HEIGHT=75></a></TD>
<TD><A HREF=BASEGRID/gif/stdq4g.gif><IMG SRC=BASEGRID/gif/stdq4g.gif HEIGHT=75></a></TD>
</TR>
</TABLE></CENTER>
<P>
West of the Rockies, one notices very little correction of the PM10 concentration
because of the relatively low elevations. The Appalachians
show some adjustment but not much because of the relatively high scale heights in
the region. In the west, the concentrations are increased dramatically in some areas
because of the numerous monitoring stations residing at high elevations
especially in the Sierra Nevada mountains where the scale height
is relatively low.
<P>
<IMG SRC="../../Icons/up3.gif" ALIGN=TOP width="20" height="20">
<A HREF="#content">Back to Contents</A><HR>
<P>
<H3><A NAME="adPM10"><B>Elevation Corrected PM10</B></A></H3>
<P>
<A NAME="adjmaps"></A>
<P><CENTER>
<TABLE BORDER>
<TR>
<TH COLSPAN=4><FONT SIZE = 3>Elevation Corrected PM10 Concentration Maps</FONT></TH>
</TR>
<TR>
<TH>Quarter 1</TH>
<TH>Quarter 2</TH>
<TH>Quarter 3</TH>
<TH>Quarter 4</TH>
</TR>
<TR>
<TD><A HREF=ADJUSTED/gif/corq1.gif><IMG SRC=ADJUSTED/gif/corq1.gif HEIGHT=75></a></TD>
<TD><A HREF=ADJUSTED/gif/corq1.gif><IMG SRC=ADJUSTED/gif/corq2.gif HEIGHT=75></a></TD>
<TD><A HREF=ADJUSTED/gif/corq1.gif><IMG SRC=ADJUSTED/gif/corq3.gif HEIGHT=75></a></TD>
<TD><A HREF=ADJUSTED/gif/corq1.gif><IMG SRC=ADJUSTED/gif/corq4.gif HEIGHT=75></a></TD>
</TR>
</TABLE></CENTER>
<P>
The eastern half of the U.S. shows no elevation correction of the PM10 concentration except for a few areas in the Appalachians and in the mountains of northeastern New York when compared with the strictly distance dependent interpolation maps. In the West, the high elevations of the mountain ranges stand out with low concentrations while the valleys remained essentially uncorrected. Increases by a factor of two are seen in some areas, such as in western Northern California. This is due to the spreading of the standardized elevation concentrations (Co) during the contouring process. In the final correction step, these high Co values were not adjusted to lower Cc values. These areas were also characterized as having no lower elevation sites nearby to offset the spreading of the high Co values into the lower elevation regions. <P>
The influence of the elevation/scale height ratio is noticeable in the corrected maps. The mountainous areas of California with high excess values also are characterized by relatively low scale heights resulting in a large correction. The Appalachians, on the other hand, exhibit a relatively large excess elevation but the relatively high scale heights in the area minimizes PM10 elevation correction.
<P>
<IMG SRC="../../Icons/up3.gif" ALIGN=TOP width="20" height="20">
<A HREF="#content">Back to Contents</A><HR>
<H4><A NAME="pm10comp"><B>Comparison with Initial PM10</B></A></H4>
<P>
<P><CENTER>
<TABLE BORDER>
<TR>
<TH COLSPAN=4><FONT SIZE = 3>PM10 Correction (Corrected PM10/Initial PM10)</FONT></TH>
</TR>
<TR>
<TH>Quarter 1</TH>
<TH>Quarter 2</TH>
<TH>Quarter 3</TH>
<TH>Quarter 4</TH>
</TR>
<TR>
<TD><A HREF=ADJUSTED/ADJ_INT/gif/corintq1.gif><IMG SRC=ADJUSTED/ADJ_INT/gif/corintq1.gif HEIGHT=75></a></TD>
<TD><A HREF=ADJUSTED/ADJ_INT/gif/corintq2.gif><IMG SRC=ADJUSTED/ADJ_INT/gif/corintq2.gif HEIGHT=75></a></TD>
<TD><A HREF=ADJUSTED/ADJ_INT/gif/corintq3.gif><IMG SRC=ADJUSTED/ADJ_INT/gif/corintq3.gif HEIGHT=75></a></TD>
<TD><A HREF=ADJUSTED/ADJ_INT/gif/corintq4.gif><IMG SRC=ADJUSTED/ADJ_INT/gif/corintq4.gif HEIGHT=75></a></TD>
</TR>
</TABLE></CENTER>
<P>
The ratios displayed above represent the overall correction applied to the initial PM10. The Eastern half of the U.S. shows no elevation correction of the PM10 concentration except for a few areas in the Appalachians and in the high peaks of northeastern New York.
In the west, the high elevations of the mountains ranges stick out with low concentrations while the valleys remained essentially uncorrected. Increases on the order
of two are seen in some areas. This is due to the spreading of the standardized elevation corrected concentrations. The sites with initial concentrations were corrected and then contoured, The
contouring was elevation independent and as a result corrected values at high elevation sites were spread out into areas of lower elevation. Subsequently, in the final
correction step, these high values were no adjusted to lower values. These areas were also characterized as having no lower elevation sites nearby to offset the spreading of the high values into the lower elevation regions.
An area that stands out is Montana in the winter seasons. The higher concentrations in Montana is in part caused by low scale heights in quarters 1 and 4. Locations with a high excess elevation are often high above the scale height which results in a correction factor between 5 and 10.
The low station density in parts of Montana allows the highly corrected concentrations to be spread over flat terrain without accounting for the fact that the elevation is lower.
<P>
A property of the elevation correction process is that it leaves the observed data intact. Table 1 presents the regression coefficients and slopes for the correlation between the elevated
corrected values and the observed concentrations. A perfect fit is not seen because when creating a grid (or map) from site specific values, the grid cells are not necessarily centered over the monitoring site locations. Therefore, the grid values will not exactly match those of the monitoring sites. The role of the distance weighted interpolation in causing the lack of perfect correlation is emphasized by the fact that the regression coefficients obtained from strictly distance dependent interpolation is virtually identical to those of the elevation correction process.
<P><CENTER>
<TABLE BORDER>
<TR>
<TH COLSPAN=5><FONT SIZE = 3><B>Correlation parameters for observed PM10 concentrations with elevation corrected concentrations</FONT></B></TH>
</TR>
<TR><TH></TH>
<TH COLSPAN=2><FONT SIZE = 2><b>Elevation Correction</B></TH>
<TH COLSPAN=2><FONT SIZE = 2><b>Distance Weighted</B></TH>
</TR>
<TR><TH></TH>
<TH><FONT SIZE = 2>Slope</TD>
<TH><FONT SIZE = 2>Coer. Coeff.</TD>
<TH><FONT SIZE = 2>Slope</TD>
<TH><FONT SIZE = 2>Coer. Coeff.</TD>
</TR>
<TR><TH>Quarter 1</TH>
<TD><CENTER><FONT SIZE = 2>0.997</TH>
<TD><CENTER><FONT SIZE = 2>0.976</TH>
<TD><CENTER><FONT SIZE = 2>0.997</TH>
<TD><CENTER><FONT SIZE = 2>0.976</TH>
</TR>
<TR><TH>Quarter 2</TH>
<TD><CENTER><FONT SIZE = 2>0.997</TD>
<TD><CENTER><FONT SIZE = 2>0.978</TD>
<TD><CENTER><FONT SIZE = 2>0.997</TD>
<TD><CENTER><FONT SIZE = 2>0.978</TD>
</TR>
<TR><TH>Quarter 3</TH>
<TD><CENTER><FONT SIZE = 2>0.998</TD>
<TD><CENTER><FONT SIZE = 2>0.985</TD>
<TD><CENTER><FONT SIZE = 2>0.998</TD>
<TD><CENTER><FONT SIZE = 2>0.984</TD>
</TR>
<TR><TH>Quarter 4</TH>
<TD><CENTER><FONT SIZE = 2>0.997</TD>
<TD><CENTER><FONT SIZE = 2>0.977</TD>
<TD><CENTER><FONT SIZE = 2>0.997</TD>
<TD><CENTER><FONT SIZE = 2>0.977</TD>
</TR>
</TABLE></CENTER>
<P>
The accuracy of the elevation correction process in estimating PM10 concentrations was tested by randomly removing ten percent of the observed values, running the correction process with the remaining ninety percent, and then comparing the corrected PM10 values with measured concentrations at the locations where the ten percent were removed. The cumulative results for three separate ten percent sets are shown in the table below.
<P><CENTER>
<TABLE BORDER>
<TR>
<TH COLSPAN=7><FONT SIZE = 3><B>Correlation statistics for the interpolation of PM10 Concentrations</FONT></B></TH>
</TR>
<TR><TH></TH>
<TH COLSPAN=3><FONT SIZE = 2><b>Elevation Correction</B></TH>
<TH COLSPAN=3><FONT SIZE = 2><b>Distance Weighted</B></TH>
</TR>
<TR><TH></TH>
<TH><FONT SIZE = 2>Slope</TD>
<TH><FONT SIZE = 2>Offset</TD>
<TH><FONT SIZE = 2>Coer. Coeff.</TD>
<TH><FONT SIZE = 2>Slope</TD>
<TH><FONT SIZE = 2>Offset</TD>
<TH><FONT SIZE = 2>Coer. Coeff.</TD>
</TR>
<TR><TH>Quarter 1</TH>
<TD><CENTER><FONT SIZE = 2>0.54</TH>
<TD><CENTER><FONT SIZE = 2>13.3</TH>
<TD><CENTER><FONT SIZE = 2>0.43</TH>
<TD><CENTER><FONT SIZE = 2>0.52</TH>
<TD><CENTER><FONT SIZE = 2>14.0</TH>
<TD><CENTER><FONT SIZE = 2>0.40</TH>
</TR>
<TR><TH>Quarter 2</TH>
<TD><CENTER><FONT SIZE = 2>0.68</TH>
<TD><CENTER><FONT SIZE = 2>9.6</TH>
<TD><CENTER><FONT SIZE = 2>0.53</TH>
<TD><CENTER><FONT SIZE = 2>0.66</TH>
<TD><CENTER><FONT SIZE = 2>10.3</TH>
<TD><CENTER><FONT SIZE = 2>0.51</TH>
</TR>
<TR><TH>Quarter 3</TH>
<TD><CENTER><FONT SIZE = 2>0.74</TH>
<TD><CENTER><FONT SIZE = 2>9.3</TH>
<TD><CENTER><FONT SIZE = 2>0.59</TH>
<TD><CENTER><FONT SIZE = 2>0.71</TH>
<TD><CENTER><FONT SIZE = 2>10.4</TH>
<TD><CENTER><FONT SIZE = 2>0.57</TH>
</TR>
<TR><TH>Quarter 4</TH>
<TD><CENTER><FONT SIZE = 2>0.65</TH>
<TD><CENTER><FONT SIZE = 2>10.8</TH>
<TD><CENTER><FONT SIZE = 2>0.57</TH>
<TD><CENTER><FONT SIZE = 2>0.62</TH>
<TD><CENTER><FONT SIZE = 2>12.0</TH>
<TD><CENTER><FONT SIZE = 2>0.53</TH>
</TR>
</TABLE></CENTER>
<P>
Quarter 3 shows the best fit. This is likely due to the fact that the third quarter has the least variability in PM10 concentrations over the Western U.S. Table 2 also provides the regression coefficients and slope of the distance dependent interpolation with observed values using the same three 10% sets. The elevation corrected interpolation shows a slightly better correlation but because only a small number of stations are situated at locations where elevation correction occurred, their influence on the regression is limited.
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<A NAME="appendixA"><H2>Appendix A</H2></A>
<P>
An important data transformation processes used in this work is
contouring. Most of the spatial patterns are presented on contour
maps. The contours were derived from the point observations using
a spatial extrapolation scheme. In the first step, the data from
the random locations were projected to a uniform grid that covers the conterminous U.S. The gridding used inverse
distance squared (1/r2) as the station weighing factor. The extrapolations
outside the U.S. boundaries were trimmed to eliminate spurious
values.<P>
<H3>Contourer Pseudocode</H3>
<P>
<PRE>
<b>Contour</b>
Functionality: transform data from table format into grid format
Input: Table - a set of data points
WeightFunc - distance weight function
Radius - distance constraint
MinPoints - minimum required number of data points within Radius
MaxPoints - maximum number of data points used in calculation of a grid cell
Output: Grid - uniformly distributed set of data points
function Contour(out Grid, in Table, in WeightFunc, in Radius, in MinPoints, in MaxPoints)
{
for each Cell in Grid
CalcCell
}
<b>CalcCell</b>
Functionality: calculate value of a grid cell given a table of data points around it
function CalcCell(in out Cell, in Table, in WeightFunc, in Radius, in MinPoints, in MaxPoints)
{
PointList = an empty list of table points
for each point in Table that is not null
if the distance between the point and the cell is less than Radius then
add point to the PointList, sorted by distance
Cell value = Interpolate PointList
}
<b>Interpolate</b>
Functionality: interpolate over a sorted list of data points
function Interpolate(in PointList, in WeightFunc, in MinPoints, in MaxPoints)
{
if number of points in PointList < MinPoints return null value
TotalWeight = 0
Sum = 0
WeightExp = 0 if WeightFunc = 1
1 if WeightFunc = 1/r
2 if WeightFunc = 1/r2, etc
for first MaxPoints in PointList
Dist = point distance from cell
Weight = 1 / (Dist^WeightExp)
TotalWeight = TotalWeight + Weight
Sum = Sum + Weight * point value
if TotalWeight = 0 return null value
Sum = Sum / TotalWeight
return Sum
</PRE>
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<H2><A NAME="ref"><B>References</B></A></H2>
<P><FONT SIZE = 2>
Dutkiewicz V.A., P.P. Parekh,, and L. Husain (1987) An Evaluation of Regional Elemental Signatures Relevant to the Northeastern United States, Atmospheric Environment, 21, 1033-1044. <P>
Husar R.B., D.E. Patterson, D.L. Blumenthal, W.H. White, and T.B. Smith (1980) Three-Dimensional Distribution of Air Pollutants in the Los Angeles Basin in The Character and Origins of Smog Aerosols, John Wiley & Sons, New York.<P>
Loibl W., W. Winiwarter, A. Kopsca, J. Zueger, and R. Baumann, (1994) Estimating the Spatial Distribution of Ozone Concentrations in Complex Terrain, Atmospheric Environment, 28, 2557-2566.<P>
Patterson, D.E., R.B. Husar, W.E. Wilson and L.F. Smith. 1981. Monte Carlo simulation of daily regional sulfur distribution: comparison with SURE data and visibility observations during August 1977. Journal of Applied Meteorology, 20, 404-420.<P>
Schichtel, B.A., R.B. Husar, The Monte Carlo Model: PC-Implementation, Aerosols and Atmospheric Optics: Radiative Balance and Visual Air Quality Proceedings of an A & WMA International specialty Conference held in Snowbird, Utah 29-30 September 1994, 578-599. Pittsburgh, PA: Air and Waste Management Association.<P>
Sisler J.F., D. Huffman, D.A. Latimer, W.C. Malm, and M. Pitchford (1993) Spatial and temporal patterns and the chemical composition of the haze in the United States: An analysis of data from the IMPROVE network, 1988-1991. Report #ISSn No. 0737-5352-26 CIRA, CSU, Fort Collins, CO.<P>
U.S. Environmental Protection Agency (1994) AIRS User’s Guide, Volume AQ1: AQS Data Dictionary. EPA-454/B-94-005.<P>
U.S. National Oceanic and Atmospheric Administration, National Geophysical Data Center (1995) TerrainBase Global Digital Terrain Model, Version 1.0. <P>
</FONT SIZE>
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