COMPARISON OF TWO COMPUTER PROGRAMS FOR VOLUME-WEIGHTED AVERAGING
OF LIMNOLOGICAL DATA
Final Report
on
Interagency Agreement DW89931897-01-0
Submitted To
Great Lakes National Program Office
U.S. Environmental Protection Agency
230 S. Dearborn
Chicago, Illinois 60604
David C. Rockwell, Project Officer
By
Barry M. Lesht
Atmospheric Physics and Chemistry Section
Center for Environmental Research
Biological, Environmental, and Medical Research Division
Argonne National Laboratory
Argonne, Illinois 60439
May 1988
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COMPARISON OF TWO COMPUTER PROGRAMS FOR VOLUME-WEIGHTED AVERAGING
OF LIMNOLOGICAL DATA*
by
Barry M. Lesht
Atmospheric Physics and Chemistry Section
Center for Environmental Research
Biological, Environmental, and Medical Research Division
Argonne National Laboratory, Argonne, IL 60439
*Work supported by the U.S. EPA's Great Lakes National Program Office
under Interagency Agreement DW89931987-01-0.
The submitted manuscript ha been authored
by a contractor of the U.S. Government
under contract No. W-3M09-ENG-38.
Accordingly, the U. S. Government retains *
nonexclusive, royalty-free license to publish
or reproduce the published form of this
contribution, or allow others to do to, for
U. S. Government purposes.
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SUMMARY
This report presents the results of a study in which two computer codes
designed for volume-weighted averaging of I imnological data were evaluated and
compared. Codes such as the two evaluated here, Averaging Lake Data by Regions
(ALDAR) produced by Canada's National Water Research Institute, and Volume-
Weighted Averaging (YWA) produced by the United States Environmental
Protection Agency's Large Lakes Research Station, are most valuable when it is
desirable or necessary to compensate for any spatial bias in sampling that may
affect the calculation of summary statistics. This is often the case in
Iimnological surveys. The report includes a discussion of the basic features
of the codes and their implementation as well as an evaluation of the spatial
interpolation algorithms upon which the codes are based.
Both codes use sample data to estimate the value of the Iimnological
variable in every cell of a gridded representation of the lake of interest.
ALDAR uses a nearest-neighbor interpolation in which the value assigned to
each cell is that of the sampled station nearest the cell. VWA estimates the
value in a cell by using a weighted average of the station data in which the
station weights depend on the distance between the cell and the stations.
Neither of these interpolation techniques is optimal, in the sense that the
expected interpolation error is minimized as a function of the interpolation
parameters. It nay not be possible, however, to devise an optimal
interpolation for Iimnological data without making some assumptions about the
spatial structure of the variable for which interpolation is desired.
Evaluation of alternate methods of spatial interpolation, not represented by
either ALDAR or VWA, is beyond the scope of this study.
Estimates of local interpolation accuracy as a function of the
interpolation parameters can be made by using sample data. Such an evaluation
may be used to decide whether spatial analysis is desirable for analysis of
the data. Local interpolation accuracy depends on the size and configuration
of the sampling network and on the signal-to-noise ratio of the sampled data.
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In most cases the VWA interpolation can be made more accurate than the ALDAR
interpolation by appropriate choice of VWA's distance-weighting parameter. A
simple analysis of the sample data using the VWA algorithm and a range of
interpolation parameters may be used to select a locally best value for the
weighting parameter. This value may vary with the variable to be analyzed.
Several coding errors were noted in ALDAR. These errors result in
mislocation of stations within the bathymetric grid and in Miscalculation of
the volumes associated with specified regions of the lake being analyzed. The
accuracy of the ALDAR method of mass calculation within layers depends on the
assumed vertical structure and may be inaccurate. However, ALDAR, unlike VWA,
is generalized so that it may be applied to any lake and gridding system
without modification. VWA is coded for only one lake (Michigan) and grid
resolution. The measures of variability calculated by VWA are inappropriate
for evaluation of the uncertainty associated with the volume-weighted mean.
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RECOMMENDATIONS
Limnological survey data should be analyzed with the spatial
interpolation algorithm contained in VWA. An initial screening analysis,
involving the sample data only, can be conducted to determine whether the data
exhibit spatial correlation and would benefit from spatial interpolation. If
so, the results of the screening analysis can be used to determine the best
value of the weighting parameter required by VWA.
In general, the VWA code should be used in preference to ALDAR. The major
advantage of ALDAR is its ease of application to different lakes and grids.
The VWA code should be modified so that it too can be applied easily to other
lakes and grids. The VWA code also should be modified along the lines of
ALDAR to accommodate changes in station locations more easily.
Research into the spatial structure of Iimnological variables should be
encouraged. In particular, the application of optimal analysis techniques to
Iimnological data should be investigated. Studies of the factors contributing
to the uncertainty of estimates of volume-weighted means should be conducted
as well. Measures of uncertainty analogous to the standard error would make
it possible to put error ranges or confidence levels on estimates of the
volume-weighted mean. This type of error evaluation is necessary for
comparisons between volume-weighted means.
Sampling designs should be evaluated with the tools of spatial analysis.
Simulations based on historical data can be used to determine the size and
configuration of Iimnological sampling networks. Spatial analysis also can be
used to determine the homogeneity of a sampled region.
IV
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TABLE OF CONTENTS
Summary i i
Recommendations iv
Tab I es v i
Fi gures v i i
Acknow I egments v i i
Section
1. Introduct i on 1
2. Features of Volume-Weighted Averaging Programs 3
3. Implementation of ALDAR and VWA 10
4. General Features of ALDAR and VWA 15
5. Intrinsic Accuracy of the Spatial Interpolation Algorithms 24
6. Cone I us i ons 43
References 45
Appendix A. Input Fi les and Auxi I iary Code Used With ALDAR A-l
Appendix B. Input Files Used With VWA B-l
Append i x C. Examp I e of ALDAR Output C-l
Appendix D. Example of VWA Output D-l
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TABLES
Number Page
1 Properties of bathymetric data ft les 4
2 Comparison of ALDAR and VWA volume calculations with
differing vertical resolutions 18
3 Comparison of ALDAR layer quantity and volume-weighted
concentration calculations with differing vertical
resolutions ig
VI
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FIGURES
Number Page
1 Two-kilometer grid applied to Green Bay, Lake Michigan... 5
2 Normalized error as a function of a for data selected
from a normal distribution 30
3 Station configurations in the square model domain 31
4 Normalized error as a function of a for data selected
from a normal distribution and assigned randomly to
networks of differing configuration 32
5 Deterministic function described by Eq. (15) 33
6 Normalized estimation error as a function of a for data
selected from a deterministic function 34
7 Effect of adding noise to a deterministic signal on the
relationship between normalized estimation error and a
for several network configurations 36
8 Effect of signal-to-noise ratio on the relationship
between normalized estimation error and a for a
random! zed samp I i ng network 36
9 Effect of station density on the relationship between
normalized estimation error and a for a randomized
regular network and a deterministic signal with noise.. 37
10 U.S. Environmental Protection Agency sampling stations
in the southern basin of Lake Michigan during 1977 39
11 Normalized estimation error as a function of a for total
phosphorus and chloride concentrations in southern
Lake Michigan 39
12 Average estimation error for total phosphorus and
chloride concentrations in southern Lake Michigan as a
function of a for five network sizes 40
13 U.S. Environmental Protection Agency sampling stations
in Lake Michigan during 1985 41
14 Normalized estimation error as a function of a for total
phosphorus and chloride concentrations in Lake Michigan
for data collected at stations shown in Fig. 13 42
VI I
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ACKNOWLEGMENTS
This research was sponsored by the Great Lakes National Program Office of
the U.S. Environmental Protection Agency (EPA) through IAG DW89931897-01-0 to
the U.S. Department of Energy. The two computer codes described in this
report were supplied by Mr. Kevin McGunagle and Mr. William Richardson of the
EPA's Large Lakes Research Station (LLRS) in Grosse He, Michigan. The work
was carried out with the advice and guidance of Mr. David C. Rockwell of the
Great Lakes National Program Office, who served as project officer.
VIII
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SECTION 1
INTRODUCTION
Estimation of the mean value of a spatially distributed variable is a
goal common to many limnological sampling programs. This mean value may be
defined as
= V-l / / / c(x,y,z)dxdydz , (1)
in which V is the volume of integration, and c(x,y,z) is the value of the
variable at point x,y,z. If the variable of interest is a mass concentration,
then c(x,y,z) may be thought of as the concentration in a control volume
centered at point x,y,z, and the integration is taken as a summation over all
control volumes. Of course, it is impossible to determine the true mean
exactly. Therefore must be estimated from sample values, usually collected
at discrete locations.
Although the simple average of the sample values is often used to
estimate , this statistic may not be an appropriate estimator of the true
mean value because limnological variables are rarely homogeneous (i.e., their
expected value is not independent of location). When the variable is
nonhomogeneous, for example, the sample average may be biased by the
relationship between the sample locations and the underlying spatial
distribution of the variable, which is, necessarily, unknown.
Methods are available to compensate for this bias, and these have been
incorporated into computer programs that are intended to produce estimates of
that are more appropriate than the simple sample average. The purpose of
the work described in this report was to evaluate and compare two of these
programs, Averaging Lake Data by Regions (ALDAR) produced by the Inland Waters
Directorate of Environment Canada (Neilson et al. 1984), and Volume-Weighted
Averaging (VWA) produced by the Large Lakes Research Station of the U.S.
Environmental Protection Agency (Yui 1978; Griesmer and McGunagle 1984).
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Because software evaluation is a very subjective undertaking, this report
is focused on objective features of the two programs. Included is a
discussion of the approach common to the two, as well as an explicit
explanation of the differences between them. Details of the steps required
to implement and use the codes are discussed. Finally, the absolute accuracy
of the algorithms embodied in the programs is examined by evaluation of their
local accuracy by using sample data and by comparison with analytical results
that may be calculated exactly.
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SECTION 2
FEATURES OF VOLUME-WEIGHTED AVERAGING PROGRAMS
Genera I Strategy
The general strategy used to calculate volume-weighted averages is the
following:
(1) Spatially interpolate the sample data to estimate the value of the
variable of interest at the center of every cell in a gridded
representation of the lake.
(2) Weight each estimate by the relative volume of the cell, where the
relative volume is defined as the volume of the cell divided by the total
volume of the region of interest.
(3) Add the weighted estimates to produce an estimate of the
volume-weighted mean.
ALOAR and VWA share this general strategy along with the ability to
estimate volume-weighted means in predefined subregions of the lake.
Differences exist between the two programs in several key areas, however.
Among them are the ways in which the programs treat the vertical distribution
of the sample data, the methods used for spatial interpolation of the sample
data, the methods used for horizontal integration, and the methods used to
calculate volumes. The basic features of the two programs will be outlined
below.
ALDAR
Grid:
ALDAR is based on an equal-area-gridded representation of the lake. The
grid is made up of square cells typically 2 km, 4 km, or 8 km on a side,
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depending on the lake to be modeled and the resolution desired. The depth in
each cell is given in meters. A 2-km gridded representation of Green Bay,
Lake Michigan, is shown in Fig. 1 as an example. Bathymetric grids with this
(2-km) resolution are readily available (Schwab and Sellers, 1980). Properties
of these grids are listed in Table 1.
Table 1. Properties of bathymetric data files (Schwab and Sellers, 1980)
Lake
Superior
Michigan
Huron
St. Clair
Erie
Ontario
Grid
Size (km)
2.0
2.0
2.0
1.2
2.0
2.0
East-West
Grids
304
160
209
35
209
152
North-South
Grids
147
250
188
36
57
57
Segmentation:
ALDAR allows the user to choose up to 24 separate zones within which
volume-weighted means can be calculated. A "whole-lake" volume-weighted mean
("whole-lake" refers to the sum of the zones actually included in the
calculation) is produced as well. The zones are based on the gridded
representation so that each grid cell is assigned to a zone. Zones may be
excluded, in which case no calculations are done for those zones. Data from
stations within the excluded zones are not used to estimate the parameter
values in the active (i.e., included) zones. The zones are not necessarily
contiguous (e.g., nearshore areas separated by other zones may be designated
as a single zone). Although individual stations may contribute to estimates
in more than one zone, the zones themselves may not overlap.
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GREEN BAY
LAKE MICHIGAN
25 KM
Figure 1. Two-kilometer grid applied to Green Bay, Lake Michigan.
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Vertical Structure:
The user may specify up to 20 "standard depths" in ALDAR. These depths
are used as the basis for the vertical and horizontal interpolation of the
sample data. Data collected at various depths at a station are linearly
interpolated to produce estimated values at the standard depths. For example,
if samples were collected at 10 m and 20 m, their average would be used as the
estimated value of the variable at 15 m if that were a specified standard
depth. If a data point is below the last standard depth, it is ignored. If a
standard depth is deeper than the bottom sounding at a station, and a data
point is located between the next shallower standard depth and the bottom,
that data point too is ignored. Horizontal interpolation in ALDAR is based on
estimates of the variable at the standard depths.
Horizontal Interpolation:
ALDAR uses a nearest-neighbor (Thlessen) horizontal interpolation scheme.
In this method each cell is assigned the value observed at the nearest
station. Thus the horizontal distribution of the interpolated values (at the
surface) resembles a pattern of tiles or polygons, the centers of which are
the station locations. This interpolation holds for each standard depth,
although the station associations for each cell are based on the surface
locations. That is, cells are associated with the nearest station regardless
of the vertical distribution of data at that station. So a deep cell may be
associated with a shallow station and, as a result, there will be no estimated
value (for the cell) at depths below the deepest standard depth at the
station. The area-weighted mean values for each zone are based on summation
of the interpolated estimates at each standard depth.
ResuIts:
ALDAR produces estimates for each selected zone of the surface area and
the area-weighted mean value at each standard depth, estimates of the volume
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and integrated variable values for the layers between standard depths, and
vertically accumulated estimates (from the surface) of the volume and
integrated variable value. These estimates are presented in tabular form.
VWA
Grid:
In contrast to ALDAR, VWA was originally designed to operate on an equal-
angle grid in which each cell was formed by parallels of latitude and
meridians of longitude. Typical cell sizes were 2° and 4°. In the study
reported here, VWA was modified to use the same equal-area grid as was used
for ALDAR. This modification simplified the VWA calculation because the area
of the cells was no longer dependent on latitude and also made comparison
between ALDAR and VWA easier because they could be based on identical
bathymetric grids.
Segmentation:
VWA allows the user to identify 25 zones for which volume-weighted means
will be calculated. Each grid cell is assigned to a zone.
Vertical Structure:
VWA models the vertical structure of the water column as a series of
homogeneous layers. Up to five layers can be specified by the user. Sample
data within each layer are averaged and provided to the program as a station
average. For example, if data were collected at 1 m, 5 m, and 15 m, their
average could be used to represent that station in a layer from the surface to
20 m. Horizontal interpolation in VWA is based on the layering scheme. Each
layer can have its own segmentation scheme, so the number and definitions of
the zones can change with depth.
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Horizontal Interpolation:
VWA uses an inverse distance weighted horizontal interpolation scheme. In
this scheme, the value of the variable z at a point not sampled is given by
z*(x0) =£ wojz'j , (2)
J
in which z* is the estimate at unsampled location xo, the z'j are the sampled
data (j = 1,2,...,N), and the woj are the weights appropriate for position xo.
These weights are given by
*oj = (D0j-a)/(£Doi-tt) , (3)
i
where D;: is the Euclidian distance between points i and j. The weights have
the properties that V wo: = 1 and woj •> 1 as Do: •» 0.
J
Therefore the interpolation is such that the estimated values equal the
observed values at the points of observation. This is termed exact
interpolation.
The parameter a in Equation (3) affects the amount of influence that
distant observations have on the estimated value at a point. The lower this
value, the stronger the influence of distant observations and the smoother the
resultant estimated field will appear between observation points. Since the
interpolation is exact, however, the field will appear spiky at the
observation points. On the other hand, a very high value of a wi 11 cause
nearby observations to have dominant influence on the cell estimates, a
situation that approaches the Theissen interpolation used in ALJDAR.
VWA uses all the sampled points in the interpolation. Thus sample data
collected far away from a point to be estimated will have some influence on
that point. Although the early documentation supplied with VWA (Yui 1978)
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implied that the code has a provision for specifying that sample data used in
the interpolation be restricted to a circular region of specified radius
around each point to be estimated, this feature was not implemented in the
code supplied for this study.
ResuIts:
VWA produces an output listing for each layer. Descriptive statistics
based on sample data are calculated. These include the mean, maximum,
minimum, standard deviation, and standard error of all the vertically averaged
means supplied for the layer. The volume-weighted mean value is calculated
for each zone along with standard error, standard deviation, and confidence
limits defined by the mean plus and minus the standard error and standard
deviation. The maximum and minimum of the estimated values are also calculated
for each zone.
In addition to these results, VWA produces a histogram of the estimated
values for each layer as well as a printer plot contour map showing the
spatial distribution of estimates within the layer. Volume-weighted geometric
statistics also are calculated for each zone.
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. SECTION 3
IMPLEMENTATION OF ALDAR AND VWA
The purpose of this section is to describe the steps required to use the
programs ALDAR and VWA. Because the exact details of implementation will
differ from computer system to computer system, this description is based on
the programs as they were used in this study. In each case it is assumed that
a bathymetric data file containing the gridded depth information for the lake
in question already exists. This discussion is intended to give the reader an
overview of the procedures associated with each program and is not intended to
replace their specific documentation.
ALDAR
Creation of the Zoned Bathymetry File:
The first step in using ALDAR is to create a "zoned bathymetry file" that
contains both the zone assignment and depth for each cell in the grid.
This file is created by using a program called ZONSEL. The user provides the
segmentation scheme to ZONSEL by creating a file that lists the zone number
and the column numbers of the cells beginning each zone for every row of the
bathymetric grid. Each row may include more than one zone (Appendix A). This
information is combined with the bathymetric data contained in another file to
produce the unformatted, zoned bathymetry file that ALDAR requires. A new
zoned bathymetry file is required for every new segmentation scheme. The
effort involved in producing a new segmentation scheme depends on the
complexity of the scheme and the size of the bathymetric grid. This is not a
particularly difficult procedure.
Preparation of the Data File:
In addition to the zoned bathymetry file, ALDAR requires sample data and
run control information. The run control information includes the user's
choice of parameters to be studied, a choice of whether the actual
10
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observations used in the calculation are to be printed, specification of the
number and identity of zones that are to be excluded from the analysis, and
the standard depths at which the observations are to be interpolated. The
sample data are provided for one station at a time (Appendix A). Information
about the station itself (name and location) is also provided to ALDAR in the
data file. One of ALDAR's notable features is its ability to calculate
volume-weighted averages for many variables (up to 50) in one run. A code
(STORET2) has been prepared by the Large Lakes Research Station to create an
ALDAR data file from a STORET-FCF retrieval. This data file contains the
number of stations, the dates of sampling, the station names and locations,
and the sample data for all the variables and depths of interest. A listing of
this code, as modified for use in this study, is also given in Appendix A.
The above three files (zoned bathymetry, data, and control) are all that
is necessary to run ALDAR. ALDAR is sufficiently general so that calculations
can be made for any of the lakes or embayments for which bathymetric data are
available without modification of the code. Sections from a sample output are
shown in Appendix C.
VWA
As supplied, VWA was configured for use with Lake Michigan data on 4°
grid. In contrast to ALDAR, application of VWA to a different lake or grid
would require modification and recompi lation of the code. The basic input
requirements for VWA are similar to those of ALDAR. In VWA the bathymetry,
segmentation scheme, and layering information for a particular run are
contained in a "master file". Control information and the vertically averaged
station data are supplied (in one file) separately for each layer. Only one
variable can be analyzed in each run. The interpolation parameters and
segmentation scheme can vary between layers in the same run. A third input
file containing the segmentation scheme is required for the graphic output.
Just as the ALDAR system consists of several separate codes (ZONSEL, STORET2,
and ALDAR), the VWA system also consists of several separate codes that are
11
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needed to produce the files necessary to run VWA. These will be discussed
below.
Creation of the Master File:
Several steps are required to create a VWA master file. The user must
first decide on a vertical layering scheme. This involves selection of up to
five layers in the water column. The layers are specified by their top
surface depths (starting with 0.0 for layer 1). The bottom depth of the
deepest layer is automatically defined to be the maximum sounding depth in the
grid. The layers must be continuous; that is, there can be no gaps in the
water column. Layers can be ignored, however, when the actual VWA analysis is
conducted.
Once the user has decided on a layering scheme, this information is
combined with the bathymetric information in code CHARLAY to produce a file
that defines the limits of the grid for each layer. These limits show the
transitions between grid cells that are in water and those on land. As the
layers become deeper, for example, those cells bordering the grid in which
the water is shallower than the top of the layer will appear as "land" cells,
and some cells in shallow areas in the lake will appear to be islands. The
file produced by CHARLAY (Appendix 8), which lists the grid columns at which a
transition between land and water occurs for every grid row that has a water
cell, is subsequently used as the basis for the horizontal segmentation
scheme. CHARLAY also produces a printer map of the lake of interest showing
the horizontal extent of the specified layers, and a listing of the geometric
characteristics of these layers including their surface areas and volumes.
Editing of the file produced by CHARLAY to create a segmentation scheme
is similar to the process required by ALDAR. The segmentation is specified by
adding, to each row of the grid, information about the grid columns at which
transitions between segments occur. This information consists of a pair of
numbers (segment number and column number) for each transition in a row. If
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only one segment is used, as would be the case if a direct calculation of the
whole-lake average were desired, the only editing that would be required would
be the insertion of a line after the title line for each layer indicating the
layer number, the number of segments in this layer, and their identification
numbers. This line also would be required for more complicated segmentation
schemes.
Given a segmentation scheme as defined above along with the bathymetric
data, code CORSWAIT is used to produce a raw master file. This file contains,
for each layer, information about the segmentation scheme, including the
volume and area of each segment as well as the location, depth, and relative
weighting for every cell within the segment. The raw master file created by
CORSWAIT is next merged with information describing the stations in code
STARSEG.
One of the differences between VWA and ALDAR is the method by which
information about the sample locations is included in the codes. In ALDAR
this information is provided in the data file along with the sample data. In
VWA, however, the master file contains a prespecified list of all the possible
stations that may be sampled. This list gives a unique number to each of the
potential stations, and this number is used to associate a sample datum with a
particular location. Thus, if sampling is conducted at a new station (i.e.,
one not already included in the master file), a new master file must be
created that includes the description of that station.
Station information required by STARSEG includes the agency designation,
the station name, its latitude and longitude, its coordinates in terms of grid
units, and a station reference number. These data may be produced in the
proper format by using a code STNSC2 (Appendix B) that uses the station
name, agency designation, and geographic position (latitude and longitude)
to calculate the grid position and reference number.
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STARSEG actually has two functions and must be invoked twice in the
process of completing the master file. The first use is to compare the
positions of the potential stations with the bathymetric grid for each layer
and warn the user if a particular station falls on land. This may be the case
if a location has been given incorrectly or if the top of a particular layer
is deeper than the sounding in the cell occupied by a station. STARSEG
produces an output listing that summarizes the station information and, for
each layer, lists the segmentation scheme, prints the number of grid cells in
each segment, prints a map showing the distribution of grid cells and the
locations of the stations, and lists the stations assigned to each segment. In
addition to this listing, STARSEG produces for each layer a data file that
contains the segment assignment for each station that falls in a water cell.
This data file is edited and used as input for the second run of STARSEG, the
purpose of which is to complete the definition of the master file by assigning
stations to particular segments.
Preparation of the Data File:
A separate set of control information and sample data is required for
each layer to be analyzed in VWA. This information is provided to the code
PRNTPNCH as successive FORTRAN files read on input unit 5. That is, an
end-of-file mark serves as a data delimiter for each layer. The control
information required by VWA consists of various descriptive items such as
cruise number and dates and parameter code and name, as well as the number of
the layer to be analyzed and the value of the weighting factor for the spatial
interpolation. Also required are specification of the contour interval to be
used in the output contour maps, and flags as to whether the estimated cell
values are to be printed and plotted. As in ALDAR, the user may select the
number and identity of the segments to be analyzed; however, in contrast to
ALDAR, all the data (including those in segments not analyzed) are used in the
spatial interpolation. The vertically averaged sample data are provided for
each station to be included in the analysis. The stations are identified by
their index number as printed by STARSEG.
14
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SECTION 4
GENERAL FEATURES OF ALDAR AND VWA
The purpose of this section is to point out some features of ALDAR and
VWA that may not be apparent to the end user of the two codes but may have a
significant effect on the interpretation of the results. This discussion does
not include evaluation of the accuracy of the spatial interpolation algorithms,
which will be discussed in detail in Section 5.
ALDAR
ALDAR is fairly easy to use and is sufficiently general so that it can be
applied to the analysis of many different lakes and grids without being
modified or recompiled. This generality is reflected in the simple manner in
which station data are provided to the code via the run time data file.
However, some features of ALDAR are not obvious, and the user should be aware
of these before attempting to use the code.
Location of Stations in Grid Coordinates:
The method used to convert the x and y coordinates of the stations to
grid coordinates in ALDAR is incorrect. If DLAT is the size of the grid in
kilometers and XSTIN and YSTIN are the x and y distances of a station from the
grid origin, also in kilometers, the expression used to calculate IS and JS,
the indices of the grid cell within which the station falls, is given (for IS)
in ALDAR as
IS = (XSTIN + DLAT/2.0)/DLAT .
This will result in an error of one cell whenever the fractional portion of
the quantity XSTIN/DLAT is less than 0.5. This coding problem can be
corrected by changing the code to
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XS = (XSTIN * DLAT/2.0)/DLAT
IS = IFIX (XS «• 0.5) .
Use of Standard Depths to Define Layers:
Vertical layering in ALDAR is based on the definition of standard depths.
At each station, parameter values are estimated at these depths, which are
selected by the user, by linear interpolation of the sample data. If no
sample data are collected at depths equal to or deeper than the standard
depth, no parameter estimate is made for that depth. Similarly, because only
the sample values closest (on either side) to the standard depth are used in
the interpolation, some of the sample data may not be used at all. Thus, the
standard depths must be chosen carefully, and it may be desirable to use as
many as possible to ensure that all of the sample data are included in the
analysis.
If no estimated values exist at the deeper standard depths, these depths
are not used in the subsequent volume calculations. Thus volume-weighted
values are only calculated for layers that are between standard depths for
which estimated values are available.
Stations in Excluded Zones:
The nearest-neighbor interpolation method used in ALDAR assigns to each
grid cell the parameter value of the station closest to the cell only if the
closest station is in an active zone. Thus, data collected at stations that
are in excluded zones are not used at all in the analysis, no matter how close
the stations are to cells in active zones. In order to include data from
these stations, it may be necessary to do calculations in zones that are not
of interest, or to redefine the zones to include the stations of interest.
Because the "whole-lake" estimates calculated by ALDAR are based on all of the
included zones, the first option may result in meaningless "whole-lake"
estimates.
16
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Estimation of Layer Volumes:
ALDAR does not calculate exact volumes for the specified layers. Instead,
layer volumes (in zone J) are approximated by using the code
DELV = (DELC/2.0) * (NHYP(M,J) + NHYP(M-1,J)) ,
in which DELV is the volume of the layer between depths M and M-l, DELC is the
thickness of the layer, NHYP(M,J) is the number of grid cells at standard
depth M, and NHYP(M-1,J) is the number of grid cells at standard depth M-l.
Since this formulation assumes a constant rate of area! decrease with depth,
the accuracy of the approximation will depend on the configuration of the
basin as well as on the selection of the standard depths. The higher the
resolution of the standard depths, the better the approximation will be. This
may be seen by comparison of ALDAR volume calculations for several different
layering schemes with the true layer volumes calculated using VWA (Table 2.)
It also should be noted that the quantity DELV, as defined above, does not
have units of volume. This can be corrected by multiplying the expression by
the square of the grid size, either expressing the units of the layer
thickness in kilometers or the units of the grid size in meters.
Calculation of Layer Quantities:
The total quantity of a substance within a layer is also approximated in
ALDAR. This approximation is written
DELQ = (DELC/3.0) * [(NHYP(M,J)*THS(M,J) + (NHYP(M-1,J)*THS(M-1,J) «•
0.5 * ((NHYP(M,J)*THS(M-1,J) * (NHYP(M-1,J)*THS(M,J))] ,
in which THS(M,J) is the average value of the variable of interest at standard
depth M in segment J, and the NHYP terms are as they were defined above. As
in the case of the volume calculation, the accuracy of this approximation
depends on the configuration of the basin and zone (segment) boundaries as
well as on the selection of the standard depths.
17
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Table 2. Comparison of ALOAR and VWA volume calculations with differing
vertical resolutions. Example from analysis of Green Bay, Lake Michigan
with 2-km grid. Dashed lines indicate layer boundaries.
Depth
0")
0.0
1.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
41.0
Total
Number of
Cells
1128
1128
880
675
523
383
253
105
13
1
Vo 1 ume
Calculated Layer Volume (km^)
9 Layers* 5 Layers 2 Layers
ALDAR ALDAR VWA ALDAR VWA
4.5
16.1
15.6
____
12.0
_
9.1
6.4
3.6
1.2
0.2
68.7
20.1 19.9
15.6 15.1
60.4 55.3
21.2 20.3
— ___ ____ __ — ____
9.8 9.4
„_ IR i in 9
2.3 0.8
69.0 65.5 76.5 65.5
* VWA is limited to five layers, so no comparison is possible.
The quantity THS requires some explanation. This quantity is calculated
by summing all of the individual cell values at a standard depth and within a
zone, and dividing the total by the number of cells at that depth and within
that zone. Thus THS may be considered an areally weighted mean value of the
variable at a single depth. The quantity of the variable within a particular
layer is then approximated by a function of the areally weighted mean values
at the top and bottom of the layer. As was shown above, the approximation
18
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function is not a simple linear one (as is the volume approximation), but one
that includes an adjustment term, the source of which is unclear. The extent
of error in this approximation may be judged by comparing calculations of the
vertically integrated quantity (based on a thick layer) with the sum of
thinner sublayers within the thick layer. Such a comparison is illustrated in
Table 3. Assuming that the approximation based on the thin layers is more
accurate, reducing the vertical resolution results in an underestimate of the
total mass.
Table 3. Comparison of ALDAR layer quantity and volume-weighted
concentration (in parentheses) calculations with differing vertical
resolutions. Example from analysis of Green Bay, Lake Michigan, with
2-km grid. Variable is total phosphorus. Dashed lines indicate layer
boundaries.
Calculated Layer Quantity (Mg)
and Volume-Weighted Concentrations (mg/L)
Depth
(m)
0.0
1.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
AI n
Number of
Cel Is 9 Layers
1128
1128
880
675
523
383
253
105
13
1
61.0
213.0
198.0
157.0
98.6
51.5
29.9
7.8
0.7
(0.0135)
(0.0133)
(0.0128)
(0.0131)
(0.0109)
(0.0081)
(0.0084)
(0.0066)
(0.0040)
5 Layers
267.0 (0.0133)
198.0 (0.0128)
219.0 (0.0103)
77.3 (0.0079)
15.8 (0.0068)
2 Layers
672.0 (0.0111)
105.0 (0.0065)
Total 817.5 (0.0119) 777.1 (0.0113) 777.0 (0.0101)
19
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Presentation of Results:
ALDAR output (Appendix C) consists of a repetition of the input control
information, a listing of the vertically interpolated station data showing the
parameter values estimated at each standard depth at each station, and a
zone-by-zone summary of the volume-weighting calculations. For each active
zone, the summary shows, for each standard depth, the areally weighted mean
value, the area represented by the standard depth, the vertically integrated
quantity from the surface to the standard depth, and the vertically integrated
volume from the surface to the standard depth. As was pointed out above, the
volumes and quantities are approximations and have incorrect units in ALDAR.
As coded, the printed area does not have units of area, but actually is the
number of grid cells at the standard depth. This error can be corrected by
multiplying the listed number by the square of the grid cell length.
In addition to estimates at the standard depths, the zone summary
contains estimates of the volume of and the variable quantity within the
layers defined by the standard depths. The volume-weighted concentration
is also listed for each of these layers. The vertically integrated,
volume-weighted concentration is calculated at each standard depth below the
surface by dividing the integrated quantity by the integrated volume.
The zone summary also contains a listing of the actual observations that
have affected the calculation for that zone. This listing includes the
station number, the depth and value of the observation, and an indicator as to
whether the station is inside the zone. This indicator will be wrong in some
cases because of the error in the original ALDAR code relating station
position to grid location. The calculations, however, will not be affected.
ALDAR produces a 'whole-lake* estimate that is really the combination of
the estimates made for the included zones. The combined data are accumulated
in a phantom zone, number 25. The summary listing for zone 25 follows the
format of the other zone summaries.
20
-------
Finally, ALOAR prints a "summary report" that lists, for each selected
zone and zone 25, the area My weighted mean parameter value at the surface
and, for specified zones and zone 25, the area My weighted mean parameter
value at selected standard depths and the "bottom* or deepest standard depth.
A total integrated quantity of the variable in question is also printed. This
quantity is not the total mass of the variable in the lake (assuming that the
original data are given as concentrations) but is the product of the spatially
averaged, "whole-lake" concentration at the deepest standard depth at which an
estimate has been made, and the estimated volume of the lake. It is not clear
what this number is intended to represent; but unless the code is modified, it
is best ignored.
VWA
YWA is somewhat more cumbersome to use than is ALOAR. A major
shortcoming is its specificity to a single lake. Modifications to the
original code would be required in order to make VWA as general as ALDAR.
Although a new master file is needed for every change in segmentation and
layering, it should be possible to create a library of master files that can
be reused as necessary. This would simplify application of VWA in exploratory
data analysis. Some other features of VWA that require comment are discussed
below.
Use of Vertical Averages to Define Station Data:
VWA is based on analysis of predefined vertical layers. Station data are
provided as a single number representing the mean value for each layer.
Although it is assumed that this mean value is the simple average of sample
data within the layer, this need not be the case. The user can select any
representative value. Thus, the user can correct for any perceived bias in
the vertical location of the station data within the layer. The use of single
values as representatives of the layers tends to reduce the effect of noisy
sample data. There is no implicit assumption (as there is in ALDAR) that the
21
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sample data are exact. However, vertical resolution in VWA is limited to five
layers. It may be desirable to increase the number of vertical layers from the
five currently allowed, but this would increase the complexity of both the
master files and the data files.
Use of All Stations in Horizontal Interpolation:
As currently configured, VWA uses data from all stations to calculate
estimated values at each grid cell. Information from distant stations is
damped, however, by the choice of the smoothing parameter in the
distance-weighting algorithm. The fact that all stations are used may affect
the choice for the value of this parameter. An alternate method would
restrict the selection of stations contributing to the estimate at a cell to
those within some fixed distance of the cell. Although this method is
mentioned in the documentation of VWA, it does not seem to have been
implemented in the production version. Civen the use of all stations,
estimates made outside (e.g., shoreward) of the domain of the sampled
locations will tend toward the arithmetic mean values of the sample data. The
distance at which this will occur depends on the geometry of the sampling
network and on the choice of the smoothing parameter. In no case, however,
will an estimated value be outside the range of the observed values.
Presentation of Results:
The results of a VWA analysis (Appendix D) are produced by three of the
codes that make up the VWA system (CHARLAY, STARSEG, and PRNTPNCH). The basic
geometric conditions of the analysis, including the area and volume of the
zones and layers, are calculated and printed in CHARLAY. CHARLAY also
produces a printer map showing the bathymetric distribution of the selected
layers. Details of the segmentation scheme are printed by STARSEG. This
output includes a cross-referenced listing of the stations in the master file
that shows their reference number, latitude and longitude, and grid
coordinates. Printer maps showing the spatial boundaries of the chosen
22
-------
segments are printed for each layer by STARSEG. These maps also show the
locations of the available stations.
Output from PRNTPNCH is presented by layer. This output consists of a
repetition of the input control data, a listing of the stations actually
selected for the analysis (including the data values used for the layer), a
summary of simple statistics of the input data (mean, high and low values,
standard deviation, and standard error), the volume-weighted statistics (mean,
standard error, standard deviation, and estimated maximum and minimum values),
a histogram of the cell estimates, and a contour map showing the spatial
distribution of the variable.
The measures of dispersion (standard deviation and standard error)
calculated for the volume-weighted statistics are based on the deviations of
the station data from the volume-weighted mean. It is not clear what this
statistic actually represents, however, because the volume-weighted mean is a
complicated function of the basin configuration, station values, and station
locations. These dispersion statistics should not be used as estimates of the
accuracy of the mean value. Because parametric statistical estimators are
inappropriate as measures of the dispersion of the volume-weighted mean, it
may be desirable to use a nonparametric estimator such as that described by
Lesht (1988).
23
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SECTION 5
INTRINSIC ACCURACY OF THE SPATIAL INTERPOLATION ALGORITHMS
Because both ALDAR and VWA depend on spatial interpolation algorithms, it
is of interest to examine these algorithms in terms of accuracy. Two types of
accuracy, which may be termed local (or point) and integrated, may be
considered. Local accuracy is a measure of how well the interpolation
algorithm can be expected to predict the value of a variable at an unsampled
point, and integrated accuracy is a measure of how well the algorithm
reproduces the summed value of the sampled field. Because integration in both
algorithms is based on summation of values estimated at points, this
discussion begins with the question of local accuracy.
Local Accuracy:
For the purposes of this study, local estimation error (ej) is defined as
the difference between the true value of a variable at some point (z;) and the
estimated value at that same point (z*;). Estimators such as the algorithms
used in ALDAR and VWA are termed linear estimators and may be evaluated on the
basis of the average value (bias) and the variance of the errors. Linear
estimators as defined in Eq. (2), repeated below, may be expressed as
2*i =£«ij 2j . (4)
J
where the wjj are the weights appropriate for estimated location i and sample
j. It is easy to see that the spatial interpolation algorthims used in ALDAR
and VWA belong to this class of estimators. In ALDAR the weights wjj are
defined so that wjj = 1 if station j is closest to point i, and wjj = 0
otherwise. Later in this discussion, the value of the variable at station j
closest to point i will be designated zjij.
24
-------
In VWA the weights are defined in Eq. (3) above. If, as is the case for
both ALOAR and VWA,
£>ij =1 ,
J
the estimator is unbiased, because E[z*j] = E[ZJ], and the expected value of
the local estimation error is zero.
A general expression for the variance of the local estimation error (s^e)
when the estimates are based on a weighted average of the sample data can be
written (Tabios and Salas 1985) as
S2e = s2 - 2 £ wjj covCzjZj) + ££ wjjWjk cov(zjzk) , (5)
J J i
where s2 is the variance of the sample data, the wj: are the weights for
location i and sample j, and cov(zjZj) represents the spatial covariance
between Zj and zj.
This expression requires knowledge of the spatial covariance function
which, in general, is unknown. Some methods of spatial interpolation that
have been developed make use of estimates of this function [e.g., Gandin's
(1965) optimal interpolation or Matheron's (1971) Kriging], but these are
beyond the scope of the analysis presented here.
In the case of sampled systems for which the spatial covariance function
is unknown, the bias and variance of an interpolation procedure can be
estimated from the sample data by using all but one of the samples to
interpolate the value at the last point. Thus for a sample network of n
stations, we define the error at station i to be
ej = z; - z*j , (6)
where Zj is the sampled value at the station and z*j is the value estimated
using the interpolation procedure.
25
-------
Given n stations, there will be n values of ej, and the statistics of
these values (e.g., their mean and standard deviation) provide some estimate
of the overall accuracy of the interpolation. If the mean and standard
deviation of the errors are given as
= E[ej] (7)
and
i - 2 + 52^0.5 . (9)
This combination of bias «e» and precision (s2@) will be used as the basic
measure of the accuracy of the local estimates.
Many factors will affect the accuracy of an interpolation procedure.
Among them are the configuration and size of the sampling network and the
structure of the spatial distribution being sampled. For ALDAR and for one
special case of VWA it is possible to derive an analytical expression for the
sample estimates of both the bias [Eq. (7)] and variance [Eq. (8)] of the
errors.
Since, in ALDAR, the estimated value of a variable at location i (written
z*;) is the value observed at location j (zjlj) closest to location i, we can
write
= l/N£(zi - zj,i) (10)
or
:(*iii) • (ii)
26
-------
The first term in Eq. (11) is the simple average of the sample values.
The second term is the simple average of the values at those stations that are
nearest to the sampled stations. Since a station may be nearest to more than
one (or to none) of the other stations, this term, which will be referred to as
z", will not, in general, be equal to .
The expression for the variance of the interpolation errors [Eq. (8)] may
be expanded by using Eq. (11).
(N - 1) S2e = £ (ej -
-------
z*j =£(N - 1)-1 Zj (j t i) (13)
and
= (N)-l [£ zj - ££ (N - 1)"1 2j ] (j t i)
i J '
1 £ *i - E (N - I)'1 ( £ zj) * £
-------
Random Data
We consider first the case in which the sampled variable has no spatial
structure. This case is modeled by drawing samples from a normal distribution
with known mean and variance and assigning them randomly to a preselected
number of locations in a model domain. For the purpose of illustration we
will use a square model domain with sides 100 units long. Although selection
of a domain is arbitrary, the use of a square domain simplifies some of the
following calculations. Since the mean value is the best estimator of sample
values drawn from a normal distribution, we would expect that the VWA
interpolation with parameter a set to zero would result in the lowest RMS
estimation error. This is indeed the case (Fig. 2), with the RMS error
equaIi ng the theoreti caI vaIue
se = [N/(N - 1)] sz
when a is zero.
The RMS error increases as a function of a in this case, approaching the
value obtained by using the ALDAR-type interpolation. This is due to the fact
that as a increases, the influence of nearby stations increases, and VWA
interpolation approaches the nearest-neighbor interpolation used in ALDAR. As
is shown in Eq. (12), the asymptotic value will depend on the configuration of
the stations and on the covariance of the data at the stations and their
nearest neighboring stations.
The configuration of the station locations will influence the
interpolation results. If instead of randomly locating the stations (Fig. 3a)
within the model domain as was done above, we use a regular rectangular grid
of the same number of stations (Fig. 3b), we find that the asymptotic value of
the RMS error is considerably lower than for the purely random case. This is a
result of the regularity of the grid in which each interior station is
equidistant from four other stations. With the distance-weighting algorithm
29
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oc
O
QC
OC
LJJ
Q
LLJ
N
o:
O
ALPHA
Figure 2. Normalized error (RMS error divided by sample standard
deviation) as a function of a for data selected from a normal
distribution and assigned to randomly located stations.
of VWA (and, in its limit, ALDAR), using a regular grid results in a point
estimate that is dominated by the mean of the surrounding stations. This
dominance increases with a. If the grid is made hexagonal (Fig. 3c), then
interior points are equidistant from six other points, and the RMS error is
reduced further at most values of a. At high values of a, small differences
in the calculated distances of the hexagonal grid, resulting from numerical
truncation, tend to dominate. If the grid is regular with some degree of
randomness (Fig. 3d), as is generally the case in limnological sampling, the
RMS errors fall between those of the regular case and the purely random case
(Fig. 4). The proximity of this curve to the extremes (i.e., the random case
and the regular case) depends on the degree of randomness in the grid. Results
from networks based on random spacing of 25%, 50%, and 75% of the grid size
also are shown in Fig. 4.
30
-------
•z.
D
LLJ
O
2
(a)
(b)
80-
60-
40-
H
Q 20
t -
1 1 ' 1 ' 1 ' 1 '
(c)
t 80H
2
D
W 6°^
O
< 40-
I-
D 20-
• • • • •
• • • •
0 20 40 60 80 100
X DISTANCE (UNITS)
• • • • •
• • • • •
• •
• • • •
(d)
• •
• •
•
• •
• •
• • • • •
0 20 40 60 80 100
X DISTANCE (UNITS)
Figure 3. Station configurations in the square model domain with
sides 100 units long, (a) Random network of 49 stations.
(b) Regular rectangular network, (c) Regular hexagonal network.
(d) Regular rectangular network with station positions moved
randomly within a radius of 50% of the grid spacing.
31
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1.6-1
OC
O
OC
CC
UJ
Q
LU
N
OC
O
NETWORK
• RANDOM
D 25% RANDOM
• 50%_R_ANJD_OM_
O 7SX RANDOM
A RECTANGULAR
X HEXAGON
0
Figure 4. Normalized error as a function of a for data selected from a
normal distribution and assigned randomly to networks of differing
configuration.
Deterministic Data
The most important feature of the random data used above is the lack
of spatial correlation. This would be the case if the sampled variable were
homogeneous. The case to be considered next involves variables that have some
deterministic spatial structure. Such a variable can be modeled by any number
of functions. The simple function used here.
z(x»y) = A [sin (xmr/X) sin (yimr/Y)] ,
(15)
in which X and Y are the limits of the domain in the x and y directions, A is
the peak value of the function, and n and n are wave numbers, is shown for one
case (A = 10, m = n = 1, X = Y = 100) in Fig. 5.
32
-------
Figure 5. Deterministic function described by Eq. (15) shown
the model domain.
in
33
-------
Considering again the results of simulated sampling from networks of
differing configurations, we find that the dependence of the estimated RMS
error on the parameter a is opposite that shown in Fig. 6 for the purely
random data. In the case of deterministic data [as represented by the simple
function defined in Eq. (15)], the mean value of the data (i.e., a = 0) is the
poorest estimator of the sample values. When the locations of the stations in
the sampling network are randomly chosen, the minimum RMS error occurs when a
= 5.5. As the station grid becomes more regular, the location of the minimum
error moves toward higher and higher values of a. In the limit of the
rectangular grid, the minimum error is found at the highest value of a tested.
1.2-1
cc
O
cc
cc
UJ
Q
UJ
N
CC
O
NETWORK
• RANDOM
O 26% RANDOM
• 50S_R_AN.P_OM
O 76% RANDOM
A RECTANGULAR
0.2
ALPHA
Figure 6. Normalized error as a function of a for data selected from
the deterministic function described by Eq. (15) at stations defined
by different network configurations.
34
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Deterministic Data With Uncorrelated Noise
The relationship between local RMS error, network configuration, and the
weighting parameter a changes again if noise is added to the deterministic
signal given in Eq. (15). Figure 7 shows the result of simulations in which
the data are given by Eq. (15) plus a random component drawn from a normal
distribution with a mean of zero and a standard deviation of one. Since the
amplitude of the signal ranges from zero to ten, this represents a noise level
of less than 10 percent. As would be expected, the magnitude of the errors is
higher than was the case for the purely regular function. This is a
reflection of the higher variability in the input signal. Similarly, the
relative reduction in the local error is smaller for the case of the noisy
signal than for the case of the regular function. We find that the network in
which the stations are located randomly has its minimum error at a lower
value of the parameter a when the data are noisy and that the minimum error
again occurs at higher values of a as the grid becomes more regular.
Figure 8 shows the effect of the signal-to-noise ratio on the
relationship between the local RMS error and the parameter a for one network
configuration. As the data become more noisy, the optimal value of a
approaches zero. When the data have noise levels similar to those inferred
for limnological variables (between 25 and 50 percent), the RMS error has a
definite minimum between a = 2 and a = 4. This, of course, depends on the
nature of the deterministic signal.
Effects of Network Size
All of the previous examples have been based on a 49-station sampling
network in a domain 10,000 square units in area. This is equivalent to a
sampling density of one station per 200 square units. Typical limnological
sampling networks are more sparse, ranging downward toward one station per
1000 square kilometers. Obviously, reducing the number of stations in a
network will increase the absolute magnitude of the local estimation errors.
35
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1.2 -\
NETWORK
• RANDOM
D26* RANDOM
• BOS .RANDOM
O 76% RANDOM
A RECTANGULAR
0.4
ALPHA
Figure 7. Effect of adding noise (10%) to a deterministic signal
on the relationship between normalized estimation error and a for
for several network configurations.
CC
O
cc
CC
111
N
5
cc
O
1.2-1
1.1-
DATA
SOURCE
• S/N 100:75
D S/N 100:50
• S/N 100:25
0.8
ALPHA
Figure 8. Effect of signal-to-noise ratio on the relationship
between normalized estimation error and a for a randomized
(50%) sampling network.
36
-------
Qualitatively, the dependence of the errors normalized by the sample standard
deviation on the weighting parameter a and the network size (Fig. 9) is
similar to the dependence of the normalized errors on signal-to-noise ratio.
As the number of stations in the network is reduced, the normalized error
curve moves closer to that for the purely random case. This is a result of
the tendency for highly separated stations to have low spatial correlations,
especially when the data have some noise. It should be recalled that the
basis of spatial interpolation is the assumption that some spatial structure
exists in the variable and is reflected in the sample data. Sparse networks
will have some difficulty in representing any spatial structure in the
presence of noise.
1.4-1
0.9
NETWORK
• 49 STATIONS
D 36 STATIONS
• 25 STATIONS
ALPHA
Figure 9. Effect of station density on the relationship between
normalized estimation error and a for a randomized regular network
and a deterministic signal with noise (50%).
37
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Actual Limnological Sampling
Figure 10 shows the location of sampling stations occupied by the U.S.
Environmental Protection Agency in southern Lake Michigan during lakewide
surveys conducted in 1976 and 1977. The network was composed of 39 stations,
and the approximate density was one station per 550 square kilometers. Two of
the variables (total phosphorus and chloride) sampled during one of the 1977
surveys were used for analysis of local estimation errors. These variables
were chosen because they should have similar spatial distributions (with
primary sources along the coasts and at tributaries), but quite different
signal-to-noise ratios; total phosphorus has a much more noisy signal in
general than does chloride. The results of this analysis, shown in Fig. 11,
are consistent with this expectation. Spatial interpolation of both variables
is very dependent on the value of the weighting parameter a. Because the
signal-to-noise ratio is lower (or equivalently the network is more sparse)
for total phosphorus, the lowest normalized error is found at a low value (a =
1) of this parameter. The improvement over the purely random case, however,
is very small. In contrast, local estimation of chloride values is improved
by about 20 percent with the use of the weighting parameter (o = 2). In both
cases the local error calculated by using the weighted averaging algorithm of
VWA is lower than the local error that would be calculated by using the
nearest-neighbor algorithm of ALDAR.
These spatial interpolation procedures may be used to estimate the size
of the smallest network that is not too sparse to resolve any spatial
structure in the sampled variable. This may be done by repeatedly selecting
random subsets of a test sampling network and examining the average dependence
of the local estimation error on a. Fig. 12 shows the results of such an
analysis using the 1977 Lake Michigan southern basin total phosphorus and
chloride data. In this example, randomly selected networks of 26, 21, 16, 11,
and 6 stations were chosen from the original 39 stations, and the average
estimation errors for 1000 realizations were calculated for each. As would be
expected, reducing the number of stations increases the average absolute
38
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43* 30' *
42' 30'
Figure 10. U.S. Environmental Protection Agency sampling stations in
the southern basin of Lake Michigan during 1977.
'•3-1
0.7
Legend
• TOTAL P
O CHLORIDE
Figure 11. Normalized error as a function of a for total phosphorus
and chloride concentrations in southern Lake Michigan. Data are from
39 surface samples collected during the intensive survey of June 1977.
39
-------
estimation error and shifts the optimal value of a. toward zero. In the case
of total phosphorus, information about spatial structure, as evidenced by a
definite minimum error value as a function of a, is lost for networks of less
than 11 stations. Chloride, on the other hand, shows some spatial structure
even when the network size is reduced to six stations.
2.6-1
O)
cc
O
cc
cc
UJ
z
O
I
UJ
2.2-
2.0-
1.8
0.45 n
UJ
0.30
(a) TOTAL PHOSPHORUS
STATIONS
D 21 STATIONS
• 16 STATIONS
O 11 STATIONS
A 6 STATIONS
I
2
(b) CHLORIDE
i
6
8
i
10
4 6
ALPHA
10
Figure 12. Average estimation error for total phosphorus (a) and
chloride (b) as a function of a for five network sizes.
Data are taken from 1977 EPA sampling in southern Lake Michigan.
Each curve shows the average of 1000 realizations, in which stations
for the different-sized networks were chosen at random from the
original 39 stations.
40
-------
In recent years the Environmental Protection Agency has reduced its
sampling network in Lake Michigan to 11 stations. This reduction was
predicated on the assumption that the stations would be located within a
homogeneous region of the lake. The reduced network that has been used since
1985 is shown in Fig. 13. In terms of the surface area of Lake Michigan
(approximately 55,000 km^) this represents an extremely low sampling density
of 1 station per 5000 km^. This value is somewhat misleading because the
network was intended to be representative of the open lake (roughly defined as
waters greater than 90 m deep). Spatial analysis of total phosphorus and
chloride concentrations measured at the surface in June 1976 at these stations
(Fig. 14) showed no spatial structure in total phosphorus, although the
sampling has detected structure in the chloride distribution. This indicates
that, unlike total phosphorus, the scale of the chloride distribution is still
greater than the scale of sampling.
Figure 13. U.S. Environmental Protection Agency sampling stations in
Lake Michigan during 1985.
41
-------
1.7 n
TOTAL PHOSPHORUS
0.9
4 6
ALPHA
Figure 14. Normalized error as a function of a for total phosphorus and
chloride concentrations in Lake Michigan. Data are from surface
samples collected at stations shown in Fig. 13 during intensive the
survey of June 1976.
Although the existence of a minimum estimation error for chloride
concentration (a = 1) implies a spatial dependence, this dependence is weak.
The improvement in the normalized error is less than 10% and does not vary
substantially over the range of a tested. It should be recalled that little
variation exists in chloride concentrations measured in the open waters of
Lake Michigan. In fact, the data that were used in the analysis shown in Fig.
14 ranged from 8.0 mg/L to 7.7 mg/L. Thus, if one were to consider the
hypothetical situation in which the highest and lowest observations were
nearest neighbors, estimation using high values of a, equivalent to the ALDAR
interpolation, would result in an error at either point of only 4 percent.
42
-------
SECTION 6
CONCLUSIONS
Two computer codes for volume-weighted averaging of limnological data
(ALDAR and VWA) have been evaluated in terms of their generality, ease of use,
and accuracy. Although ALDAR is more general than VWA and somewhat easier to
apply and implement, it includes inaccurate algorithms for location of
stations within the numerical grid and for computation of lake volumes and
integrated quantities.
Vertical variations are treated differently in ALDAR and VWA. ALDAR
linearly interpolates between sample values in the water column to produce
estimated values at preselected standard depths. VWA, on the other hand, uses
the average of sample values within preselected layers of the water column to
represent the variable value within that layer. ALDAR allows finer vertical
resolution than does VWA, but this resolution is based on the assumption that
the sampled data are exact, and that the vertical linear interpolation
produces representative variable values at the standard depths. The use of
averages in VWA implicitly accounts for uncertainty in the sample values and
tends to reduce the influence of noisy data on the subsequent calculations.
Both methods require the judgement of the analyst for specification of the
vertical structure.
The spatial interpolation algorithms in both ALDAR and VWA belong to the
family of exact linear interpolators. In ALDAR the weighting function is such
that only the datum from the observation point nearest the point of estimation
is used. VWA uses an inverse-power distance-weighting algorithm involving a
single parameter a that is applied to all of the observed data. The two
weighting functions are equivalent when a is very high and there are no
observation points equidistant from an estimation point. For most cases of
real data the VWA interpolator can be made more accurate than the ALDAR
interpolator by selection of a locally optimal value of a. This selection can
be based on a simple analysis of the sample data.
43
-------
When the data are homogeneous or purely random, the sample mean is the
best estimator of the true mean value for all sampling network configurations.
When the data are purely deterministic, with no noise, the ALDAR interpolation
will produce the best estimator when used with a regular sampling network. If
the data are noisy or the sampling network is irregular, the VWA interpolator
produce the best estimator. The optimum value of the VWA weighting parameter
a will vary with the signal-to-noise ratio of the data and with the
irregularity of the grid. Reducing the density of an irregular sampling
network is roughly equivalent to decreasing the signal-to-noise ratio and has
the effect of limiting the utility of spatial analysis.
Limited simulations using limnological data show that choice of the most
desirable interpolation procedure depends on the variable to be analyzed and
the size and configuration of the sampling network. Spatial analysis, as
provided by ALDAR and VWA, may or may not be beneficial. Exploratory analysis
of sample data using the methods of spatial statistics should be a regular
part of Iimonological surveiI lance programs.
44
-------
REFERENCES
Gandin, L.S. 1965. Objective analysis of meterological fields. Israel
Program for Scientific Translations. Jerusalem, 242 p.
Griesmer, D., and McGunagle, K. 1984. Documentation of VWA programs for Lake
Michigan. Unpublished Manuscript. Large Lakes Research Station, U.S.
Environmental Protection Agency. Grosse lie, MI.
Lesht, 6.M. 1988. Nonparametric evaluation of the size of Iimnological
sampling networks: Application to the design of a survey of Green Bay.
Accepted for publication in the Journal of Great Lakes Research.
Matheron, G. 1971. The theory of regionalized variables and its applications.
Cahiers du Centre de Morphologic Mathematique, Ecole des Mines,
Fountainbleau, France. 211 p.
Neilson, M., Stevens R., and Hodson, J. 1984. Documentation of the Averaging
Lake Data by Regions (ALDAR) Program. Technical Bulletin No. 130. Inland
Waters Directorate, Environment Canada. Burlington, Ontario. 87 p.
Schwab, D.J., and Sellers, D.L. 1980. Computerized bathymetry and shorelines
of the Great Lakes. NOAA Data Report ERL GLERL-16, Great Lakes
Environmental Research Laboratory, Ann Arbor, MI. 13 p.
Tabios, G. Q., and Salas, J.D. 1985. A comparative analysis of techniques for
spatial interpolation of precipitation. Water Resources Bulletin,
21(3):365-380.
Yui, A.K. 1978. The VWA database at the Large Lakes Research Station.
Unpublished Manuscript. Large Lakes Research Station, U.S. Envrionmental
Protection Agency. Grosse, lie, MI.
45
-------
APPENDIX A
INPUT FILES AND AUXILIARY CODE USED WITH ALDAR
Example Segmentation Scheme
In this example the 2-km Lake Michigan grid is segmented into seven
zones. The first two lines of the file contain descriptive information,
and each succeeding line defines the segmentation scheme for a grid row,
starting from the south. Only the first 33 rows are shown.
LAKE MICHIGAN 2KM GRID 7 ZONES 0000
4 250 160 7 2. 0000
3 160 00001
3 160 00002
3 160 00003
3 160 00004
3 160 00005
3 160 00006
3 160 00007
3 160 00008
3 30 1 44 3 160 00009
3 30 1 45 3 160 00010
3 30 1 46 3 160 00011
3 29 1 46 3 160 00012
3 28 1 47 3 160 00013
3 27 1 47 3 160 00014
3 26 1 48 3 160 00015
3 26 1 49 3 160 00016
3 25 1 49 3 160 00017
3 24 1 49 3 160 00018
3 24 1 50 3 160 00019
3 23 1 50 3 160 00020
3 22 1 50 3 160 00021
3 22 1 50 3 160 00022
3 22 1 50 3 160 00023
3 21 1 51 3 160 00024
3 20 1 52 3 160 00025
3 20 1 53 3 160 00026
3 19 1 53 3 160 00027
3 18 1 54 3 160 00028
3 17 1 54 3 160 00029
3 16 1 54 3 160 00030
3 15 1 55 3 160 00031
3 14 1 55 3 160 00032
3 13 1 55 3 160 00033
A-l
-------
Example Input Data File
The following file is an example of an ALDAR input data file. The data
shown here come from 25 stations in Green Bay, Lake Michigan, that were sampled
between 5 October and 8 October 1977. Only one variable (STORET code 665,
Total Phosphorus) is included in this example. Data from five stations are
shown. Sample depths are in feet, and concentrations are in mg/L.
25 771005
01 4554000
NULL
665
665
0
02 4549000
NULL
665
665
665
0
03 4547000
NULL
665
665
665
0
04 4543000
NULL
665
665
665
0
05 4543000
NULL
665
665
665
0
771008
8657000
6 0.200E-01
22 0.230E-01
8703000
6 0.120E-01
22 0.180E-01
32 0.170E-01
8704000
6 0.120E-01
22 0.140E-01
32 0.150E-01
8704000
6 0.110E-01
29 0.800E-02
55 0.700E-02
8702000
6 0.110E-01
19 0.100E-01
32 0.100E-01
A-2
-------
Listing of Code STORET2
The code listed below was written to convert a STORET "Further
Computation File" (FCF) into the form required by the LLRS modification of
ALDAR. This version was written to extract data taken in Green Bay, Lake
Michigan, from the Lake Michigan Intensive Study 1976-1977 database.
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
c c
C STORET2: MODIFICATION OF LLRS CODE STORET2.PGM C
C FOR USE WITH GREEN BAY DATA IN 1976-77 DATABASE C
C C
C PURPOSE: CREATE ALDAR DATA FILE FROM STORET FCF FILE C
C C
C INPUT: CONTROL INFORMATION ON UNIT 5 C
C STORET FCF FILE ON UNIT 8 C
C C
C OUTPUT: PRINTER OUTPUT ON UNIT 6 C
C SCRATCH FILE ON UNIT 9 C
C DATA FILE ON UNIT 10 C
C C
C WRITTEN: BARRY LESHT C
C BEM/CER C
C ARGONNE NATIONAL LAB C
C AUGUST 20, 1987 C
C C
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c c
C VAL IS AN ARRAY OF PARAMETER VALUES
C PCODE IS AN ARRAY OF PARAMETER NAMES
C
REAL*4 VAL(50)
INTEGERS PCODE(50), BDATE,EDATE,SDATE
C
C FORMAT STATEMENTS TO READ ROM STORET FCF
C
1 FORMAT(I2,2I7)
2 FORMAT(2SX,I6,4X,50A4,64X, 15)
3 FORMAT(IS,I10,E10.3)
4 FORMAT(I3,2I8)
5 FORMAT(Al)
C
IZ=0
NST=0
C
C READ IB AND BEGINNING AND ENDING DATE FROM UNIT 5
C WRITE FIRST RECORD TO SCRATCH OUTPUT FILE ON UNIT 9
C
A-3
-------
READ(5,1) IB, BDATE, EDATE
WRITE(9,4) NST, BDATE, EDATE
WRITE(6,4) NST, BDATE, EDATE
C
C IE AND IB REFER TO POSITIONS WITHIN THE STATION NAME STRING
C IN THIS CASE THE NUMBER OF THE STATION
C
IE=IB*2
C
C CODES IS A SUBROUTINE THAT READS THE PARAMETER HEADER RECORD
C FROM THE STORET FCF AND RETURNS THE NUMBER OF PARAMETERS
C AND THEIR ID CODES
C
CALL CODES(PCODE,NCODE)
WRITE(6,420) NCODE
420 FORMATC NOCODE = ',13)
C
C UNIT 8 IS THE STORET FCF - FIRST READ THE DELIMITER RECORD
C BETWEEN THE PARAMETER HEADER CARDS AND THE STATION HEADER
C CARDS
C
READ(8,5) DUMMY
C
C SUBROUTINE STNIFN RETURNS THE STATION NUMBER (NST) AND A
C FLAG ON ENCOUNTERING THE END OF FILE
C
1000 CALL STNINF(NST,IB,IE,IRC,ISFLG)
WRrTE(6,521) NST,ISFLG
521 FORMATC NST.ISFLC = ',214)
C
C FINISH UP IF IRC IS SET
C
IF (IRC.ER.l) GOTO 300
C
C CHECK TO SEE IF THIS IS A GREEN BAY RECORD
C IF NOT SKIP TO DELIMETER AND TRY AGAIN
C
IF (ISFLG.EQ.O) THEN
CALL FNDDEL
GOTO 1000
END IF
C
C START READING DATA RECORDS FROM THE FCF
C
DO 200 INS=1,10000
READ(8,2,END=300) SDATE,VAL,IDEP
C
C CHECK FOR END OF DATA RECORDS
C
IF(SDATE.LT.9999 .OR. SDATE.GT.990000) THEN
A-4
-------
c
C WRITE ZERO AND READ NEXT STATION
C
WRITE(9,3)IZ
CALL STNIFN(NST,IB,IE,IRC,ISFLC)
C
C IF WE'VE HIT THE EOF THEN FINISH UP
C IF WE'RE NO LONGER IN GREEN BAY QUIT
C
IF (IRC.EQ.l .OR. ISFLG.EQ.O) GOTO 300
C
ELSE
C
C SAMPLE IS WITHIN DATE LIMITS - CHECK FOR MISSING DATA
C CHECK FOR PROPER CRUISE DATES
C
IF (SDATE.LT.BDATE. OR. SDATE.GT.EDATE) GOTO 200
C
DO 100 1=1, NCODE
IF (VAL(I).NE.0.1E-20) THEN
WRITE(9,3) PCODE(I),IDEP,VAL(I)
ELSE
C
C DON'T WRITE ANYTHING IF DATA ARE MISSING
C
ENDIF
100 CONTINUE
ENDIF
200 CONTINUE
C
C RESET WRITE DATA ROM SCRATCH FILE TO OUTPUT FILE
C
300 CALL RESET (NST)
STOP
END
C
SUBROUTINE RESET (NST)
CHARACTER*80 LINE
C
C REWIND SCRATCH FILE
C
REWIND 9
C
READ(9,1) 11,12,13
1 FORMAT(I3,2I8)
WRITE(10,1)N,I2,I3
A-5
-------
DO 100 1=1,320000
READ(9,2,END=200)LINE
2 FORMAT(A80)
WRITE(10,2) LINE
100 CONTINUE
200 RETURN
END
SUBROUTINE CODES(PCODE.NCODE)
INTEGER*4 PCODE (50)
CHARACTER*! DUMMY
1 FORMAT(42X,10(5X,15))
2 FORMAT(A!)
3 FORMAT(' NO PARAMETERS RETRIEVED')
DO 200 1=1,5
JE=10*I
JB=JE-9
READ(8,1) (PCODE(J),J=JB,JE)
DO 100 J=l,3
READ(I,2) DUMMY
100 CONTINUE
200 CONTINUE
DO 300 1=50,1,-1
IF(PCODE(I).GT.O) THEN
NCODE=I
RETURN
ELSE
ENDIF
300 CONTINUE
VIRITE(6,3)
STOP
END
C
SUBROUTINE STNINF(N,IB,IE,IRC,ISFLG)
CHARACTER*^ STN
CHARACTER*! DUMMY
CHARACTER*4 GBAY
DATA GBAY/'GBAYV
C
1 FORMAT(A1)
2 FORMAT(8X,A15,67X,3(I2,1X),I1,1
3 FORMAT(A3,I8,I9/'NULL')
IRC=0
C
READ(8,1,END=900)DUMMY
READ(8,2,END=9CO) STN,LT1,LT2,LT3,LT4,LG1,LG2,LG3,LG4
C
DO 100 1=1,7
READ(1,1,END=900)DUMMY
100 CONTINUE
A-6
-------
ISFLG=0
IF (STN (1 : 4) . EQ . GBAY) ISFLG=1
IF (ISaG.EQ.O) RETURN
LAT=((LT1*100+LT2) *100*LT3) *10+LT4
LON=((LG1*100+LG2) *100+LC3) *10+LG4
WRITE(9,3) STN(IB:IE),UT,LON
RETURN
900 IRC=1
RETURN
END
SUBROUTINE FNDOEL
CHARACTER*8 OELIM
CHARACTER*305 RECORD
DATA DELJM/ '99999999 '/
1 READ(8,10,END=99) RECORD
10 FORMAT(A305)
IF(RECORD(24:31).EQ.DEUM) RETURN
GOTO 1
99 fRITE(6,100)
100 FORMAT(» NO DELIMITER FOUND')
STOP
END
A-7
-------
APPENDIX B
INPUT FILES USED WITH VWA
Example of Output of Code CHARLAY
The file listed below shows a simple segmentation scheme for Green Bay,
Lake Michigan, based on a 2-km grid. The first row of the file defines the
layer number (1) and the number of segments in the layer (1). The succeeding
rows identify, for each grid row, the number of transitions and the grid
columns at which a transition from land to water (-1) or from water to land
(1) occurs. The Green Bay grid has 77 rows. Those shown here range from the
most northern (76) to row 46.
1 1
76
75
74
73
72
71
70
69
68
67
66
65
64
63
62
61
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
2
2
4
4
4
4
4
4
4
4
4
4
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-1
-1
-1
-1
-1
i
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
56
55
50
49
38
38
38
38
38
38
37
37
35
33
33
32
32
30
30
30
30
29
29
28
28
28
27
26
25
25
24
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
58
59
52
53
41
42
42
42
42
42
42
42
53
52
52
52
52
54
54
54
53
52
51
50
49
48
47
46
43
43
43
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
55
54
49
49
48
47
46
46
44
43
1
1
1
1
1
1
1
1
1
1
59
59
59
58
57
56
55
55
55
54
B-l
-------
Example of VWA Input Data File
The file listed below is an example of a VWA input file. This example
is for a one-layer analysis of Green Bay, Lake Michigan.
CRUISE=0001
BD=805015
ED=800517
ENDCRUISE=YES
PARMCODE=00076
PARMNAME=TURBIDITY (FTU)
POWER=02.000
LAYER=1
CONTOUR=000.200
MATRIX=NO
PLOTMATRIX=YES
GREEN BAY WHOLE BAY MODEL
1 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
7.2
1.9
6.5
1.2
1.6
3.3
1.95
1.2
1.2
0.6
1.4
1.3
0.9
0.93
0.92
0.75
0.95
0.88
0.78
0.79
0.76
0.68
0.88
0.81
0.67
0.84
0.93
1.2
1.2
0.78
0.82
1.2
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
E+00
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
CONL 2
CONL 3
CONL 4
CONL 5
CONL 6
CONL 7
CONL 8
CONL 9
CONL 10
CONL 11
CONL 12
CONL 13
CONL 14
CONL 15
CONL 16
CONL 17
CONL 18
CONL 19
CONL 20
CONL 21
CONL 22
CONL 23
CONL 24
CONL 25
CONL 26
CONL 27
CONL 28
CONL 29
CONL 30
CONL 31
CONL 32
CONL 33
B-2
-------
Listing of Code STNSC2
The code listed below was written to convert station identification data
into the form required by VWA. This version was written for data collected in
Lake Michigan applied to a 2-km grid.
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
c c
C STNSC2: PRODUCE STATION LISTING COMPATIBLE WITH INPUT FILE C
C REQUIRED BY VWA C
C C
C INPUT: STATION DATA ON UNIT 10 C
C C
C OUTPUT: OUTPUT FILE ON UNIT 8 C
C C
C WRITTEN: BARRY LESHT C
C BEM/CER C
C ARGONNE NATIONAL LAB C
C JULY 14, 1987 C
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c c
CHARACTER*8 AGENCY
CHARACTER*^ NAME
CHARACTER*2 NUM
REAL A (5) , B(S)
C
C PARAMETERS FOR THE LAKE MICHIGAN GRID
C
PHIM=41. 60766
GM=87. 94260
A (1) =83. 1831
A (2) =1.90171
A(3)=-l. 31825
B(l)=-2. 07627
B (4) =0.958685
DLAT=2.0
C
C DATA COME FROM JOHN CONLEY'S THESIS
C
DATA AGENCY/' ANLTEST'/
NAME(1:5)=>CONL '
KNT=0
NAME(8:12)='
B-3
-------
100 REAO(10,1000,END=200)NUM,UTD,ALAMIN,LOND,ALOMIN
1000 FORMAT(A2,2(I3,F6.2))
NAME(6:7)=NUM
C
LAMIN=INT(ALAMIN)
LOMIN=INT(ALOMIN)
C
ALAS=(ALAMIN-LAMIN)*60.0
ALOS=(ALOMIN-LOMIN)*60.0
C
C CONVERT TO GRID COORDINATES
C
XLAT=FLOAT(LATO) +FLOAT (LAMIN) /60. +ALAS/3600.
XLONG=FLOAT(LOND)+FLOAT(LOMIN)/60.+ALOS/3600.
G = GM-XLONG
P = XLAT-PHIM
XSTIN = G*A(1)+P*A(2)+P*G*A(3)
YSTIN = G*B(1)+P*B(2) + (G**2)*B(4)
YSTIN = YSHN-324.
C
BLONG= (XSHN+DUT/2.) /DLAT
BLAT =(YSnN+DLAT/2.)/DLAT
IS=IFIX(BLONG+0.5)
JS=IFIX(BLAT+0.5)
KNT=KNT+1
C
IF(FLOAT(IS) .EQ.BLONG.AND.FLOAT(JS) .EQ.BLAT) THEN
BLONG=BLONG+0.0001
BUT =BLAT+0.0001
END IF
C
C USE FORMAT REQUIRED BY VWA
C
WRITE(8,9100)AGENCY,NAME,LATD,LAMIN,ALAS,LOND,LOMIN,ALOS/
+ BUT,BLONG,JS,IS,KNT
GOTO 100
200 STOP
9100 FORMAT(A8,1X,A12,1X,2(I4,I3,F5.1) ,2(1X,F10.4),3(1X,I3))
END
B-4
-------
APPENDIX C
EXAMPLE OF ALDAR OUTPUT
The following example output is from an ALDAR analysis of total
phosphorus (variable code 665) and turbidity (variable code 76) in Green Bay,
Lake Michigan. The analysis was done by using the 2-km Lake Michigan grid and
a two-layer model of Green Bay, with standard depths at 0 m, 20 m, and 41 m.
Green Bay is identified in the Lake Michigan grid as zone 6. Zone 4 is also
included in the analysis to ensure that stations located outside of, but
close to, zone 6 are included in the calculation. The output in this appendix
is representative of that produced by ALDAR as supplied. Some additional
output has been added in the Argonne version of the code.
Page Description
C-2 First page of ALDAR output showing job parameters. The
station location listing was added to the Argonne version.
C-3 Vertical interpolation of input data at the standard depths.
Shown are station identifiers and values that are used in
the horizontal interpolation.
C-4 Grid nap of Green Bay showing cells and stations that
influence those cells. The grid is 60 columns wide and 77
rows high. Cells with zero values are land. This map was
added to the Argonne version of ALDAR.
C-5 Southern portion of Green Bay grid map.
C-6 ALDAR calculations for the two-layer model in Green Bay
(zone 6).
C-l
-------
ALDAR
NUMBER OP PARAMETER CODES » 2
ACTUAL OBSERVATIONS IN EACH ZONE WILL BE PRINTED
THE FOLLOWING 6 ZONES ARE EXCLUDED: 12367
3 STANDARD DEPTHS:
0.00 20.00 41.00
CRUISE 1
PARAMETER CODES:
666 78
DEPTH NUMBERS FOR ZONE 6 IN SUMMARY REPORT ARE 1
DEPTH NUMBERS FOR ZONE 26 IN SUMMARY REPORT ARE 1
LAKE MICHIGAN(2KM.) IS BEING STUDIED
GEOGRAPHIC AND GRID LOCATIONS
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
STATION
01
02
03
04
06
06
07
08
09
10
11
12
13
14
16
16
17
18
19
20
21
22
23
24
26
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
POSITIONS
46.900
46.817
46.783
46.717
46.717
46.660
46.460
46.600
46.333
46.200
46.133
46.083
46.067
46.033
44.960
44.880
44.883
48.133
46.300
46.460
45.483
46.617
46.633
46.717
46.783
86.960
87.060
87.087
87.087
87.033
87.117
87.133
87.283
87.260
87.487
87.660
87.650
87.617
87.660
87.660
87.683
87.417
87.360
86.967
86.800
86.733
86.700
86.883
86.767
86.650
86
77
76
75
78
71
70
68
61
44
37
37
40
37
37
26
47
63
83
96
101
104
90
.114
.300
.982
.932
.624
.908
.626
.869
.296
.167
.637
.468
.066
.399
.284
.624
.707
.246
.462
.664
.783
.394
.097
99.262
108.348
476.334
466.110
462.417
466.017
456.005
436.639
425.448
431.098
412.672
397.979
390.683
385.132
383.239
379.683
370.333
369.426
362.773
390.466
408.737
426.379
429.091
432.800
434.626
454.984
462.418
43.067
39.150
38.491
38.466
39.762
36.454
35.763
29.929
31.148
22.684
19.269
19.234
20.633
19.199
19.142
13.812
24.364
27.122
42.226
48.782
61.391
62.697
46.648
60.131
64.674
238.167
233.656
231.708
228.008
228.002
218.769
213.224
216.049
206.786
199.490
196.841
193.066
192.120
190.291
186.666
180.213
181.887
196.728
204.868
213.190
215.046
216.900
217.813
227.992
231.709
43
39
38
38
40
36
36
30
31
23
19
19
21
19
19
14
24
27
42
49
51
53
46
60
56
238
234
232
228
228
219
213
216
207
199
196
193
192
190
186
180
182
196
206
213
215
217
218
228
232
C-2
-------
PARAMETER ( MB)
STAM5ARO DEPTHS:
0. 20. 41.
PSN
02 .12E-01
04 .11E-01
05 .11E-01
06 .10E-01
07 .12E-01 .94E-02
08 .10E-01
09 .80E-02 .83E-02
10 .90E-02 .94E-02
11 .10E-01
12 .90E-02
13 .10E-01
14 .1EE-01
16 .16E-01
16 .27E-01
17 .21E-01
18 .16E-01
19 .90E-02 .83E-02
20 .70E-02 .53E-02 .40E-02
21 .60E-02 .60E-02
22 .506-02 .49E-02
23 .70E-02 .60E-02
24 .90E-02
25 .80E-02
C-3
-------
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000000000000000000000000000000000000000000000000000000 023232323 0
0000000000000000000000000000000000000000000000000 02323 0 0 023232323 0
00000000000000000000
00000000000000000000
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000000000000000000000000000 023232323 02323232323 0
000000000000000001110000000 023232323232323232323 0
000000000000000001111000000 0232323232323232323 0 0
00000000000000000111100000 0222223232323232323 000
0000000000000000011130000 0222222222323232323 0000
000000000000000002333000 0222222222222232323 0 0 0 023
000000000000000000000000000000000000002333000 0222222222222222323 0 0 02323
0000000000000000000000000000000000000223330 02222222222222222222323 023232323
0000000000000000000000000000000000000223330 322222222222222222222 0 023232323
0000000000000000000000000000000000022223333 3222222222222222222 0 0 023232323
0000000000000000000000000000000002222223333 32222222222222222 0 0 02223232323
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00000000000000000000000000066666666666666 61818181818181818181919 0000000
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0000000000000000000000000777777777666 61717171717 0 0 01818 000000000000
000000000000000000000000777777777777 6171717171717 0 0 01818 000000000000
00000000000000000000000077777777777 717171717171717 0 0 01717 000000000000
00000000000000000000000077777777777 71717171717171717171717 0000000000000
00000000000000000000000887777777777 717171717171717171717 00000000000000
00000000000000000000008888777777777 7171717171717171717 000000000000000
00000000000000000000088888777777777 71717 0 0 017171717 000000000000000
00000000000000000000088888877777777 71717 0 0 017171717 000000000000000
00000000000000000000888888 81616 77777 71717 0 0 017171717 0000000000000000
0000000000000000000088888 8161616161616 7 7 71717 0 017171717 00000000000000000
00000000000000000998888888 016161616161616161717 017171717 000000000000000000
000000000000000009998888 816 0161616161616161616 0 017171717 000000000000000000
00000000000000009999988 816161616161616 000000 017171717 000000000000000000
0000000000000000999999 81616161616161616 000000 017171717 000000000000000000
000000000000000099999 9111616161616161616 000000 017171717 000000000000000000
0000000000000000 01010101111111616161616161616 000000 017171717 000000000000000000
0000000000000000 01010101111111116161616161616 000000 0161717 0000000000000000000
000000000000000 01010101111111111161616161616 00000 0161616 000000000000000000000
C-4
-------
000000000000000 01212121211111111111616161616 0000 016161616 000000000000000000000
000000000000000 012121212121111111116161616 00000 016161616 000000000000000000000
000000000000000 0121212121212111111111616 00000 016161616 0000000000000000000000
00000000000 0131313131312121212121212111615 00000 016161616 00000000000000000000000
00000000000 0131313131313131313131313161615 00000 016161616 00000000000000000000000
0000000 0141414141413131313131313131313151616 000000 016161616 00000000000000000000000
0000000 0141414141414131313131313131316151616 000000 015161616 00000000000000000000000
0000000 0141414141414141313131313131615161615 0000 01615161615 000000000000000000000000
000000 0141414141414141414131313131315151616 00000 016161515 0000000000000000000000000
000000 0141414141414141414141313131516151615 00000 015161515 0000000000000000000000000
00000 0141414141414141414141414131616 00000000 01516161516 0000000000000000000000000
00000 0141414141414141414141414141616 0000000 01616161616 00000000000000000000000000
0000 0141414141414141414141414 00000000000 016161616 000000000000000000000000000
000 0141414141414141414141414 000000000000 016161616 000000000000000000000000000
000 01414141414141414141414 000000000000 016161616 0000000000000000000000000000
000 01414141414141414141414 00000000000 01615161616 0000000000000000000000000000
0 0 01414141414141414141414 000000000000 01616161616 0000000000000000000000000000
0 01414141414141414141414 000000000000 01616161515 00000000000000000000000000000
0141414141414141414141414 000000000000 01516161616 00000000000000000000000000000
01414141414141414141414 0000000000000 01615161616 00000000000000000000000000000
01414141414141414141414 000000000000 0161615161616 00000000000000000000000000000
014141414141414141414 0000000000000 0161616161616 00000000000000000000000000000
014141414141414141414 000000000000 0161616161616 000000000000000000000000000000
014141414141414 00000000000000 0161616161516 0000000000000000000000000000000
014141414141414 0000000000000 0151516161616 00000000000000000000000000000000
01414141414 000000000000000 0161516161616 00000000000000000000000000000000
014141414 0000000000000000 0151616161616 00000000000000000000000000000000
0141414 0000000000000000 0161616151615 000000000000000000000000000000000
00000000000000000000 0161616161616 000000000000000000000000000000000
C-5
-------
CRUISE 1 ZONE NUMBER 0
PARAMETER ( 666 )
DEPTH AREA WEIGHTED AREA LAYER INTEGRATED LAYER INTEGRATED VOLUME WEIGHTED VALUES
MEAN VALUE QUANTITY QUANTITY VOLUME VOLUME LAYER COLUMN
0.00 0.0136 1128 0.000E+00 0.000E+00
0.672E+03 0.604E+06 0.0111
20.00 0.0077 383 0.6716E403 0.8044E+06 0.0111
0.106E+03 0.161E+06 0.0066
41.00 0.0040 1 0.7784E+03 0.7867E+06 0.0101
C-6
-------
APPENDIX D
EXAMPLE OF VWA OUTPUT
The following example output is from a VWA analysis of turbidity
(parameter code 76) in Green Bay, Lake Michigan. Output from three of the
codes (CHARLAY, STARSEG, arid PRNTPNCH) are shown.
Pages Description
D-2/D-4 Output from CHARLAY for a five-layer model of
Green Bay. CHARLAY produces a printer map of the
grid showing the area! extent of the layers and a
table of layer volumes and areas.
D-5/D-13 Output from STARSEG for a two-layer model of Green
Bay. STARSEG produces a table of station
positions, a listing of the segmentation scheme
for each layer, and printer maps of each layer
showing the areal extent of the segments and the
location of the stations.
D-14/D-21 Output from PRNTPNCH for a two-layer model of
Green Bay (with only one layer printed). PRNTPNCH
lists the control information for the job and
prints a table of the stations that are to be used
in the anIaysis (a subset of those stations listed
by STARSEG). The sample statistics of the data
are printed as well as the volume-weighted
statistics. PRNTPNCH produces histograms of the
interploted values and a printer nap showing the
a real distribution of the interpolated values.
D-l
-------
MAXIMUM DEPTH FOUND FROM BATHYMETRIC DATA IS: 41.00
********************************************
* GREEN BAY VOLUME-WEIGHTED STATISTICS *
********************************************
BATHYMETRIC MAP OF GREEN BAY
GREEN BAY STRATIFIED AT METER-DEPTHS 0.0 5.0 10.0 20.0 30.0 41.0
012
77 o * 0 * 0 *
76 0 * 0 * 0 *
75 o * 0 * 0
74 o * 0 * 0
73 o * 0 * 0
72 0 * 0 * 0
71 0 * 0 * 0
70 0 * 0 * 0
69 0 * 0 * 0
68 0 * 0 * 0
67 0 * 0 * 0
66 0 * 0 * 0
65 0 * 0 * 0
64 0 * 0 * 0
63 0 * 0 * 0
62 0 * 0 * 0
61 0 * 0 * 0
60 0 * 0 * 0
59 0 * 0 * 0
58 0 * 0 * 0
cy A-- -- *_- -- O- * n
56 0 * 0 * 0
55 0 * 0 * 0
54 0 * 0 * 0
53 o * 0 * 0
52 0 * 0 * 0
51 0 * 0 * T0
50 0 * 0 * 0
49 o * 0 * 0
48 0 * 0 * 0
47 o * 0 * 0
46 0 * 0 * 0
45 o * 0 * 0
44 o * 0 * 0
43 o * 0 * 0~ A
42 0 * 0 * 0- AB
41 o * 0 * 0 AAC
40 0 * 0 * 0 ACD
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0— A)
0— Ai
0- AAI
0- ABI
AABO
ABCC
Arrr
ACCC
— ABCDD
— BCDDD
« ACCDDD
— ACDDDD
« BCDDDD
- ACCDDEE
* ABCDDDEE
ABCDDDEDD
ABCDDEDDC
ABCDDDEDCC
ACDDEEEDCC
BCDDEEDDDD
CDDEEEDDDD
CDEEEDDDDD
DEEEDDDDDD
DEDCDDDDCD
4 5
0~ -0 *
0 0 *
0 0
0 AA -
0 AAAA A
AAA AAAAAA
— ABAA AAAAAB
.. ABAA AABBABB
— ABBA - - AABBBBBA
— ABBA - AABBBCBBA
— ABBA - ABCCCCCBA
- ABCBA AAABCCCCBBA
- ABCCA AAABBCCCCBA
AABCCCAAAABBCCCCCA
\AABCDCBABBBBCCCCB -
\BBBCDCBBBBBBCCCCC -
3BBCCDCCCCCCCCCCDC -
3BBCDDCCCCCCCCCDDC -
CCCCDDCCCCCCCCCDDCBA
CCCDEDCCCCDDDDDDDDCA
CCCDEDCCCCODDDDDDCCB
DCCDEDCCCCDDDDDDDCC
DDDDEDCCCDDDDDDDDC -
nnnnFnpffnnnnFFnn —
nnnPFFnnnnnnnFnr —
DDDEEEDDDDDDDFf) -,
DDDEEEEEEEEEEE 0
EEDEEEEEEDDDE -0
EEDEEEEEDBBB 0
DEEEEEEEC 0
DDEEEEEDC 0
DDEEEEEDC 0
DDDEEEEDC 0
DDDDDDDD 0
DEDCCCB -0
EEDBBBA 0
DDDB 0 0
DCBA 0 0
6
0
AA 0
AAAA
AAAA
AAAA
BAAA
BAA 0
AA -0
A —0
— 0
— 0
i — 0
0
0
0
0
0
0
0
0
0
0
0
__A
— o
0
0
0
0
0
0
0
0
0
D-2
-------
OS
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
v
t
0
0
o —
0
o —
o —
0
o —
o —
o —
0
A _.
\j—~~
0
0
0
0
0
0
0
0
0
0
0
k-___O- AAJ
A _* A AAJ
Q
Q
Q_
o —
o —
o —
o —
o —
AAAAARf
AAARRft
ARRRRH
noiuu
RCDDD
CBACCCCCCCBA -0 * 0
- AAACCODDB ACCCBCBBAA -0 * 0
- AABCDDDCB ACCBAAAAA ~0 * 0
AABCCDDDCCBBCCB — * 0 * 0
ABCCDDDDDODCCCB — * 0 * 0
ABCCODDDDODCCCB ~ * 0 * 0
- ACCODDEDDDCCCB ~ * 0 * 0
- ABCCDEEEDDCCBA — * 0 * 0
AABCCDEEEDDCCB — * 0 * 0
ABCCCOEEEDCCBA — * 0 * 0
ABCODDEEEOCBA * 0 * 0
ABCDDDEEDCBA 0 * 0 * 0
\AABCDDDEEDCA -0 * 0 * 0
\AABCDDDDDDBA -0 * 0 * 0
3BBCCDDDDDCB — 0 * 0 * 0
ZCCCODDDDDC
ZCCDDDDCCCE
LA -.-O---.-*---.-/*.-..-..* —.ft.---.
- AABBCCCCDDDDDCCCCA — 0 * 0 * 0
- AABBCCCCDDCCCBBBBA — 0 * 0 * 0
AAABCCCCCCCCCCA —
AABBCCCCCCBBBAA —
AAABBCCCCCBA -0
0 — AAABBCCCCCBA — 0
0 — AABBCCCCCBA — 0
0 — ABBBCCCCBAA — 0
0— AABBCCCCBBA
0- AABBBCCCBBA
0 AAABBBBBBBAA
0 AABBBBBBBBA -
0 AABBBBBBBAA -
0 AABBBBBBBA —
0 ABBBBBBAAA —
0 ABBBBAA 0
0 AABAAAA 0
0 AAAAA — 0
0 AAAA — 0
0 AAA 0
0 * o
0
0
0
0
0
0
0
0
0
0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0
0 * 0 *-- — 0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0
0 * 0 * 0 * 0
0 * 0 * 0 * 0
0 * 0 * 0 * 0
0
0
0
0
0
0
0
0
0
0
0
0
— o
0
0
— o
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
D-3
-------
********************************************
* GREEN BAY VOLUME-WEIGHTED STATISTICS *
********************************************
*****************************************
* GEOMETRICAL CHARACTERISTICS OF LAYERS *
*****************************************
LAYER
NUMBER
MAP
CODE
DEPTH IN METER
TOP BOTTOM
TOP AREA
(KM)**2
LAYER VOLUME
(KM)**3
1
2
3
4
S
A
B
C
D
E
0.0
S.O
10.0
20.0
30.0
5.0
10.0
20.0
30.0
41.0
0.4512E+04
0.3520E+04
0.2700E+04
0.1532E+04
0.4200E+03
0.1990E+02
0.1511E+02
0.2032E+02
0.9432E+01
0.7520E+00
D-4
-------
•««••««*»•«•••»•«*••••«•*•»**••••••«••*••*••
• GREEN BAY VOLUME-WEICHTED STATISTICS *
*»«««»**•»«••«*••••«**•••*•*«*•»•••»*•»»»**•
CROSS REFERENCE LISTING OF ALL STATIONS OF INTEREST
STATION STATION
REFERENCE
NUMBER
1
2
3
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
COORDINATES
DESIGNATION (X)
CONL
COM.
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
CONL
1
2
3
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.87
1.88
2.17
3.56
2.94
4.72
6.20
7.46
9.76
10.13
12.12
13.73
14.78
17.63
20.67
18.87
20.92
22.93
24.96
23.76
26.31
28.35
30.36
32.06
37.18
38.46
42.72
48.17
39.89
40.67
49.76
51.31
54.85
CO
1.27
3.28
5.60
3.46
8.82
7.18
6.32
11.55
16.04
21.10
19.64
18.17
17.66
21.10
24.33
29.68
28.15
26.88
25.25
31.94
42.39
41.66
40.36
40.17
60.22
67.74
63.76
60.63
67.48
72.25
64.46
68.16
68.62
LATITUDE
44
44
44
44
44
44
44
44
44
44
44
44
44
44
44
45
45
45
44
45
45
45
45
45
45
45
45
45
45
45
45
45
45
32
34
37
34
40
38
37
43
48
64
52
60
60
64
67
3
1
0
68
6
17
16
15
16
26
34
29
26
44
49
41
45
45
21.6
33.6
4.2
48.0
34.8
61.0
67.6
39.0
33.6
2.4
30.0
67.0
18.6
12.0
44.4
23.4
62.8
32.4
48.6
1.2
21.0
35.4
12.6
1.2
56.2
3.6
46.8
17.4
36.0
46.6
21.0
20.4
42.6
LONGITUDE
88
87
87
87
87
87
87
87
87
87
87
87
87
87
87
87
87
87
87
87
87
87
87
87
87
87
86
86
87
87
86
86
88
0
68
68
66
67
64
62
60
47
46
43
41
39
35
30
33
30
27
24
26
22
19
16
13
6
3
67
48
1
0
46
44
38
12.6
44.4
21.6
12.0
16.8
32.4
16.2
30.0
7.2
39.6
36.6
7.8
30.6
15.0
40.8
31.2
22.8
17.4
10.2
6.6
22.8
15.0
8.4
32.4
48.6
55.2
20.4
66.4
49.2
39.6
34.2
11.4
43.8
AGENCY
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
TOTAL STATION-COUNT = 33
0-5
-------
********************************************
* GREEN BAY VOLUME-WEIGHTED STATISTICS *
********************************************
SEGMENTATION SCHEME FOR LAYER NO. 1
BETWEEN METER-DEPTHS 0.00 AND 20.00
76
75
74
73
72
71
70
69
68
67
66
65
64
63
62
61
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
2
2
4
4
4
4
4
4
4
4
4
4
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
4
4
2
2
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
56
55
50
49
38
38
38
38
38
38
37
37
35
33
33
32
32
30
30
30
30
29
29
28
28
28
27
26
25
25
24
24
24
23
22
21
21
20
20
17
17
16
16
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
58
59
52 -1 55
53 -1 54
41 -1 49
42 -1 49
42 -1 48
42 -1 47
42 -1 46
42 -1 46
42 -1 44
42 -1 43
53
52
52
52
52
54
54
54
53
52
51
50
49
48
47
46
43
43
43
43
42
41
41
38
38
37
37
26 -1 27
26 -1 27
31
31
1 59
1 59
1 59
1 58
1 57
1 56
1 55
1 55
1 55
1 54
1 37
1 36
D-6
-------
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
_T
-1
-1
-1
-1
-1
-1
16
17
17
16
16
16
16
12
12
8
8
8
7
7
6
6
5
4
4
4
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
31
31
31
30
30
29
28
27
27
26
26
26
25
25
21
21
17
16
15
15
14
13
13
12
12
11
11
8
8
6
5
4
********************************************
* GREEN BAY VOLUME-WEIGHTED STATISTICS *
********************************************
MAP CODE AND SEGMENT GRID-COUNTS FOR LAYER NO. 1
BETWEEN METER-DEPTHS 0.00 AND 20.00
SEGMENT MAP NUMBER OF
NUMBER CODE GRIDS
1128
D-7
-------
********************************************
* GREEN BAY VOLUME-WEIGHTED STATISTICS *
********************************************
STATION t SEGMENTATION MAP FOR LAYER NO.
BETWEEN METER-DEPTHS 0.00 AND 20.00
GREEN BAY MAP NO. 100
77
76
75
74
73
72
71
70
69
68
67
66
65
64
63
62
61
fiO
Vv
59
58
57
56
55
54
53
*MJ
52
51
50
49
48
47
46
45
44
43
42
41
40
0123456
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
o —
o —
o —
o —
0—
o —
0
o —
o —
o —
o —
o —
o —
o —
o —
o —
o —
o —
0
0
0
0
0
0
0
0
0
0
0
0
0
0
— -0-- —
0
0
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0
0
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— -ft-—
^^^^^r
0
— — 0— -
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0
0
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0
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0
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0
0
0
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0
0
0
0
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0
0
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0
0
0
0
0
0
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0
0
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0
0 0 0 * 0
0 0 -0 * AA 0
0 0 0 AAAA
0 0 AA - AAAA
0 0 AAAA AAAAA
n __ AA . AAAAAA
AAAA (
0 AAAA AAAAAAAAA 0
0 AAAA AAAAAAAAA -0
0 - AAAA - - AAAAAAA+A ~0 (
0 AAAA - AAAA+AAAA — 0 I
0 A+AA - AAAAAAAAA — 0 1
0 AAAAA AAAAAAAAAAA — 0
0 AAAAA AAAAAAAAAAA 0
0 AAAAAAAAAAAAAA+AAA 0 (
0~ AAAAAAAAAAAAAAAAAAA 0
0— AAAAAAAAAAAAAAAAAAA 0
0- AAAAAAAAAAAAAAAAAAAA 0
— — ft- AAAAAAAAAAAAAAAAAAAA - -- —ft
— — \J fWWvWWWvWVWWt v
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0 AAAAAAAAAAAAAAAAAA 0
0 AAAAAAAAAAAAAAAAAA 0
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0 — AAAAAAAAAAAAAAAAAAA 0
0 — AAAAAAAAAAAAAAAAAA 0
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0- AAAWUAAAAAAAAAAAAA -0
0 AAAAAAAAAAAAAAAAA 0 0
0 AAAAAAAA+A+AAAAAA 0 0
0
0
A
V
0
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0
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0
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1)
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: i)
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[ i)
C i)
C i)
(2)
(2)
30
33
32
29
31
26
27
28
25
21 22
23 24
D-8
-------
38
37
36
35
34
33
32
31
30
29
28
27
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
o * u
0 * 0
0
0
0
0
0
o —
o —
o —
o —
o —
0.
0_.
o — -
0_ _.
A
o —
o __
o —
o —
0
0
0
,
0
0
0
0
0
0
0
0- AAJ
0- AAj
AAAAAAl
AAAAAAl
AAAAAAl
/wwvwwwwww -u
AAAAAAAAAAAAAAAAA -0
- AAAAAAAAA AAAAAAAAAA -0
- AAAAAAAAA AAAAAAAAA ~ 0
AAAAAAAAAAAAAAA —
AAAAAAAAAAAAAAA —
AAAAAAAAAAAAAAA —
- AAAAAA+AAAAAAA —
- AAAAAAAAAAAAAA —
AA+AAAAAAAAAAA —
AAAAAAAAAAAAAA —
AAAA+AAAA
AAAAAA+AA
AAAA ____
AAA A__
\AAAAAAAAAAAA -0
\AAAAAAAAA+AA -0
\AAAAA+AAAAA ~0
\AAAAAAAAAAA ~0
\AAAAAAAAAAA ~0
- AA+AAAAAAA+AAAAAAA — 0
- AAAA+AAAAAAAAAAAAA _— f»—
AAAAAAAAAAAAAAA 0
AAAAAAA++AAAAAA —
0 AAAAAAAAAAAA -0
0 — AAAAA+AAAAAA ~0
0 — AAAAAAAAAAA — 0
0 — AAAAAAAAAAA — 0
0~ AAAAAAAAAAA
0- AAAAAAAAAAA
0 AAAAAAAAAAAA
0 AAAAAAAAAAA -
0 AAAAAAAAAAA -
0 AAAAAAAAAA ~
0 AAAAAAAAAA —
0 +AAA+AA 0
0 AAAAAAA 0
0 AAAAA — 0 — -
0 +A+A — 0
0 AAA 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 * 0
0 * 0 * 0 * 0
0 1
0
0
0
0
0
0
0
A
A
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
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A
w
0
0
0
0
0
0
0
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0
0
0
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0
0
0
0
0
0
0
0
— — n
0
0
0
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0
0
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0
0
0
0
0 * 0
0 * 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
23456
( 1) 20
( 1) 16
( 1) 17
(1) 18
(1) 19
(1) 15
( 2) 10 14
(1) 11
( 2) 12 13
(1) 9
(1) 8
(1)
(1)
(2)
6
3 7
(2) 2 4
GREEN BAY MAP NO. 100
D-9
-------
********************************************
* GREEN BAY VOLUME-WEIGHTED STATISTICS *
********************************************
SEGMENTATION SCHEME FOR LAYER NO. 2
BETWEEN METER-DEPTHS 20.00 AND 41.00
62
61
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
2
2
2
4
6
4
4
4
4
2
2
2
2
2
2
4
4
4
6
2
2
2
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
39
39
39
38
37
37
37
33
32
31
30
30
30
29
29
28
27
27
26
25
25
24
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
40
40
40
40
40
40
40
40
40
49
49
48
47
43
42
32
32
32
32
37
37
37
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
49
44
44
44
44
43
34
34
34
33
1
1
1
1
1
1
1
1
1
1
51
46 -1 48
51
51
51
50
42
42
42
40 -1 41
1 51
1 42
D-10
-------
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
6
4
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
23
23
22
22
21
21
21
20
20
21
21
21
19
19
19
19
19
18
17
15
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
27 -1
26 -1
25
25
24
24
26
27
27
27
27
26
26
25
25
24
24
24
21
20
29
30
1 32 -1 33 1 35
1 32
********************************************
* GREEN BAY VOLUME-WEIGHTED STATISTICS *
********************************************
MAP CODE AND SEGMENT GRID-COUNTS FOR LAYER NO. 2
BETWEEN METER-DEPTHS 20.00 AND 41.00
SEGMENT MAP NUMBER OF
NUMBER CODE GRIDS
358
D-ll
-------
********************************************
* GREEN BAY VOLUME-WEIGHTED STATISTICS *
********************************************
STATION k SEGMENTATION MAP FOR LAYER NO.
BETWEEN METER-DEPTHS 20.00 AND 41.00
GREEN BAY MAP NO. 101
0
77 o *
76 0 *
75 0
74 o
73 0
79 ft____
If. U— —
71 0
70 0
69 0
68 0
67 0
66 0
65 0
64 0
63 0
62 0
61 0
60 0
59 0
58 0
57 o
56 0
55 0
54 0
«TC ft— -
oo v
*»9 D-—
W& \J—« —
C-l ft....
wj. v —
50 0
AQ n_.__
H\f U~»—
48 0
47 0
46 0
45 o
44 0
43 0
42 0
41 0
40 0
1
0
0
____0
0
0
_ft
— — — — v/— — —
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
____O— —
— — w
__ry____
O-.—
—— — V —
0
_— _- H— - -
—"*— —V — — —
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
_n
— — — — \/
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
_O-
— — — v/—
__O-
A—
—— —\/— »•——
0
—.-O-— .-
"•••••w
0
0
0
0
0
0~
0-
0
0 A
345
0 0 0 *
0 0 0 *
0 0— 0
0 0
— o -o
__o __ ___
0
— o
0
— o
0
0 *-
0 *-
0
0~
0~ A
0- A
0- A
* AA AA
* +AA AA AAA
AAA AAAAAAA
AAA AAAAAAA
AAAAAAA AAAAAAA -
AAAAAAAA AAAAAAA —
AAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAA^. ft —
AAAAAA+AAAAAAAAAA -0
AAAAAAAAAAAAAA __ft -
AAAAAAAAAAAAA 0
AAAA AAAAAAAA 0
AAAAA AAAAAAAA 0
AAAAA AAAAAAAA 0
AAAAAA AAAAAAA A 0
AAAAAAAAAAAA -0
+A+AAAAAAAAA 0
AAAAAAAAAAAAA 0 0
AAA +A+ AA 0 0
6
0
0
0
-0
~0
0
0
0
0
0
0
0
0
0
0
0 ( 1) 26
0
0
0
0
____n
____n
____n / T\ 90
0 ( 1) 25
__ _A
0
o
0
0
0
0
0 ( 2) 21 22
0
0 ( 2) 23 24
D-12
-------
39 0
38 0
37 0
36 0
35 0
34 0
33 0
32 0
31 0
30 0
29 0
28 0
27 0
9fi O__-_
oc O— —
f)A ft --
oo ft____
99 ft-_~_
21 0
20 0
19 0
18 0
0 AAA AA -0 * 0 * 0
0 AAA -0
0 AAA -0
0 AAA ~0
0 AAA
0 AAAAA
0 AAAAAAA
0 *- AAA+AAA
0 *- AAAAAA
0 * AAAAAA
0 * AAAAA
0 * A+AAAAA
0 * AAA+AA 0
_—_ft AAAAAA
A_ AAAAA
A«AAA
k -0
-0
— o
*AAAAA ft
AAAA
— 0
AA+AA 0
0
—
—
17 0 -0
16 0 — ~0
15 0 — 0
14 0 — 0
13 0— 0
12 0- 0
11 0 0
10 0 0
90 0
80 0
70 0
6 0 0 0
5 0 0 0
4 o — 0 0
3 o — -0-— -— 0 — — •
2 0 0 0
1 o * — ~0 — — ____0— -
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0____<
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0 ( 1)
0 * 0
0 * 0
0 * 0
0 * 0 ( 1)
0 * 0 ( 1)
0 * 0
0 * 0
0 * 0 ( 1)
0 * 0
0 * 0 ( 1)
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0 * 0
0123456
20
17
18
15
14
GREEN BAY MAP NO. 101
D-13
-------
********************************************
* GREEN BAY VOLUME-WEIGHTED STATISTICS *
********************************************
********************************************
* SUMMARY OF INPUT DATA FOR USER OPTIONS *
********************************************
CRUISE NO. 1
LAYER NO. 1
PARAMETER CODE
INVERSE POWER=
MAP WANTED USING
DATED: 805015 - 800517
DEFINED BY DEPTHS BETWEEN
76 TURBIDITY (FTU)
2.000
0.200 CONTOUR INCREMENT
0.00 M AND 20.00 M
MATRIX ELEMENTS ARE TO BE PUNCHED
SEGMENT (S) SELECTED BY THE USER FOR THIS LAYER :
1
121-DEC-87 11:32:09
********************************************
* GREEN BAY VOLUME-WEIGHTED STATISTICS *
********************************************
CRUISE NO. 1
LAYER NO. 1
PARAMETER CODE
INVERSE POWER=
DATED: 805015 - 800517
DEFINED BY DEPTHS BETWEEN
76 TURBIDITY (FTU)
2.000
0.00 M AND 20.00 M
D-14
-------
•«••••*•»»•••»•»•«••»•»*••*«•••**»••»••«•«••*•»
* CHARACTERISTICS OF USER-SELECTED STATIONS *
»»•«•*•*«»••»•*•***•*••«*««•••••«•*«»«*««*»**••
STATION
REFERENCE
NUMBER
2
3
4
E
6
7
8
9
10
11
12
13
14
16
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
VERTICALLY
AVERAGED
MEAN
7.200
1.900
6.600
1.200
1.600
3.300
1.960
1.200
1.200
0.6000
1.400
1.300
0.9000
0.9300
0.9200
0.7600
0.9600
0.8800
0.7800
0.7900
0.7600
0.6800
0.8800
0.8100
0.6700
0.8400
0.9300
1.200
1.200
0.7800
COORDINATES SEGMENT
IN UNITS OF GRID
(X) (Y) ASSIGNMENT
1.88
2.17
3.66
2.94
4.72
6.20
7.46
9.76
10.13
12.12
13.73
14.78
17.63
20.67
18.87
20.92
22.93.
24.96
23.76
26.31
28.36
30.36
32.06
37.18
38.46
42.72
48.17
39.89
40.67
49.76
3.28
6.60
3.46
8.82
7.18
6.32
11.66
16.04
21.10
19.64
18.17
17.56
21.10
24.33
29.68
28.16
26.88
26.25
31.94
42.39
41.66
40.36
40.17
50.22
67.74
53.76
50.63
67.48
72.25
64.46
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
STATION
DESIGNATION
CONL 2
CONL 3
CONL 4
CONL 6
CONL 6
CONL 7
CONL 8
CONL 9
CONL 10
CONL 11
CONL 12
CONL 13
CONL 14
CONL 16
CONL 16
CONL 17
CONL 18
CONL 19
CONL 20
CONL 21
CONL 22
CONL 23
CONL 24
CONL 26
CONL 26
CONL 27
CONL 28
CONL 29
CONL 30
CONL 31
AGENCY
CODE
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
ANLTEST
TO BE CONTINUED ON NEXT PAGE
D-15
-------
•*»«•••**•**•****•••***•*•***»•******•**••**
• GREEN BAY VOLUME-WEIGHTED STATISTICS •
«•*«««•«««**•••«»«»•**»•••••••••*••••«*•**«•
CRUISE NO. 1 DATED: 805016 - 800517
LAYER NO. 1 DEFINED BY DEPTHS BETWEEN 0.00 M AND 20.00 M
PARAMETER CODE 78 TURBIDITY (FTU)
INVERSE POWER= 2.000
*****«*****»»****+**********«***»******•*******
* CHARACTERISTICS OF USER-SELECTED STATIONS *
•****•«»»«***«***•«***••»»»»*»*«»»*««•«*•«»»***
STATION
REFERENCE
NUMBER
32
33
VERTICALLY
AVERAGED
MEAN
0.8200
1.200
COORDINATES
IN UNITS OF GRID
00 CO
61.31 68.16
64.85 68.62
SEGMENT
ASSIGNMENT
1
1
STATION
DESIGNATION
COM. 32
CONL 33
AGENCY
CODE
ANLTEST
AMLTEST
TOTAL STATION-COUNT:: 32
D-16
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••••••••»•»*•«*»•*•••»••••*•••«••••••*«**•*»
• CREEN BAY VOLUME-WEIGHTED STATISTICS «
•*••«•••»«»•«*»»«»*«*»»«••»*«•«••**•*»««****
CRUISE NO. 1 DATED: 805015 - 800517
LAYER NO. 1 DEFINED BY DEPTHS BETWEEN 0.00 M AND 20.00 M
PARAMETER CODE 76 TURBIDITY (FTU)
INVERSE POWER= 2.000
GREEN BAY WHOLE BAY MODEL
**«««»•«»»•»»•*«*****»»*»*«»«**#»»*••«*•«»•*«••••»«
* STATISTICS OF VERTICALLY AVERAGED STATION MEANS *
*•*••«*»•**»*«*****«***»*«**«»««***»»**»«*•*»««••»•
STATION AVERAGE OF STANDARD STANDARD
STATION HIGH LOW
COUNT MEANS DEVIATION ERROR
32 1.4694 7.2000 0.60000 1.6056 0.26616
D-17
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a*******************************************
• CREEN BAY VOLUME-WEIGHTED STATISTICS •
*»**»•*»•«**•»••*»•**»»»•**•»*•»••»«•****•*»
CRUISE NO. 1 DATED: 805015 - 800517
LAYER NO. 1 DEFINED BY DEPTHS BETWEEN
PARAMETER CODE 76 TURBIDITY (FTU)
INVERSE POWER= 2.000
0.00 M AND 20.00 M
»«**•*•***«•»»*»**«****»****
• ARITHMETIC STATISTICS *
****************************
SEG STANDARD ERROR
NO. U=MEAN E=ST.ERR. M+E M-E
1 0.9550
0.2817 1.237 0.6733
STANDARD DEVIATION
D=ST.DEV. M+0 M-D
1.694 2.649 -0.6388
SEG GRID STATION PARAMETER ESTIMATED
NO. COUNT COUNT MAXIMUM MINIMUM
1 1128
32
7.042
0.6576
D-18
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••»••••»••»«»••••••••••••«•»•••«»«•••»**••**
• GREEN BAY YOLUME-KCIGHTED STATISTICS •
•••*•*»••*«•»•••«««**•»»»••••»••••••••*••»*•
CRUISE NO. 1 DATED: 805015 - 800517
LAYER NO. 1 DEFINED BY DEPTHS BETWEEN 0.00 M AND 20.00 M
PARAMETER CODE 76 TURBIDITY (FTU)
INVERSE POWER= 2.000
GREEN BAY WHOLE BAY MODEL
HISTOGRAM FOR LAYER NO. 1 AND CONTOUR MAP NO. 100
INTERVAL RAN(
(SYMBOL]
0.0000E+00(A) 0.1
0.8000 (B) 1
1.600 (C) 2
2
3
.400
.200
4.000
4
5
6
.800
.600
.400
0>)
(E)
(F)
(0
(H)
(J)
3
4
4
6
6
7
£ I * I * I *
..I • T * T CFNTFR FREQUENCY
1
3000 .XXX 0.4000 63.00
.600 .XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1.200 9S9.0
.400 .XXX 2.000 71.00
.200
.000
.800
.600
.400
.200
2.800 17.00
3.600 7.000
4.400 1.000
E.200 2.000
6.000 7.000
6.800 1.000
PERCENT
6.69
85.02
6.29
1.51
0.62
0.09
0.18
0.62
0.09
PARAMETER MINIMUM IN THIS LAYER: 0.6576
PARAMETER MAXIMUM IN THIS LAYER: 7.042
D-19
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* GREEN BAY VOLUME-WEIGHTED STATISTICS *
********************************************
CRUISE NO. 1
LAYER NO. 1
PARAMETER CODE
INVERSE POWER=
DATED: 805015 - 800517
DEFINED BY DEPTHS BETWEEN
76 TURBIDITY (FTU)
2.000
GREEN BAY MAP NO. 100
GREEN BAY WHOLE BAY MODEL
0.00 M AND 20.00 M
0123456
77 0
76 0
75 0
74 0
73 0
72 0
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70 0
69 0
68 0
67 0
66 0
65 0
64 0
63 0
62 0
61 0
60 0
59 0
58 0
57 0
56 0
55 o
54 o
53 o
52 0
51 0
50 0
49 0
48 0
47 o
46 0
45 o
0 0 * 0
0 0
0 0
0 0
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BBBBBBBBBBBBBBBBBBBB --O-- 0
0 BBBBBBBBBBBBBBBBBB * 0 0
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D-20
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44 0
43 0
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41 0
40 0
OQ A_ _
OO A_
37 0
36 0
35 0
34 0
33 0
32 0
31 0
30 0
29 0
28 0
27 0
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9Q A
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21 0 BB+BBBBI
20 0 BBBB+BBI
19 o * BBBBBABBI
18 o * BBBBBBB+
17 0 BBBBBBBBBl
16 0 — CCBBB+BBBH
15 0 — CCCBBBBBBB
14 o — CCCCBBBBBB
13 0~ CCCCCCCCBBB
12 0- CCCC+CCCCCC
11 0 CCCCCCCCCCCC
10 0 CCCCCCCCCCC -
9 0 B+CCCCCCCCC -
8 0 CCCCCDDDDC ~
7 0 CCODDDDDD —
6 0 +DDD+OD 0
4 0 HHHFE ~0
3 0 +H+G — 0
2 0 HHG 0
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0
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* 0
* 0
5
0
0
0 ( 2) 21 22
__Q
0 ( 2) 23 24
0
0
0
0
0
0
0 ( 1) 20
— — 0
0 ( 1) 16
— -0
0 ( 1) 17
0 ( 1) 18
0
0 ( 1) 19
Of 1^ m
0
0
0 ( 2) 10 14
0 ( 1) 11
0 ( 2) 12 13
0
0 ( 1) 9
0
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0 (1) 8
0
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0 ( 1) 5
0
0 ( 1) 6
0 ( 2) 3 7
0
0
0 (2) 24
0
— — 0
6
GREEN BAY MAP NO. 100
D-21
U.S Environmental Protection Agency
Region 5 Library
77 W. Jackson Blvd. (PL-16J)
Chicago, IL 60604-3507
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