Spatial analysis of dissolved oxygen levels using Ordinary Kriging methods near the confluence of Bozeman Creek and the East Gallatin River in Bozeman, Montana

SPATIAL ANALYSIS OF DISSOLVED OXYGEN LEVELS USING ORDINARY
KRIGING METHODS NEAR THE CONFLUENCE OF BOZEMAN CREEK AND THE EAST
GALLATIN RIVER IN BOZEMAN, MT.
by
Jacqueline Lorene Frank
A professional paper submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
in
Environmental Engineering
MONTANA STATE UNIVERSITY
Bozeman, Montana
April, 2015

©COPYRIGHT
by
Jacqueline Lorene Frank
2015
All Rights Reserved

iii
TABLE OF CONTENTS
ABSTRACT......................................................................................................................VI
INTRODUCTION .............................................................................................................. 1
PROJECT BACKGROUND .............................................................................................. 2
DISSOLVED OXYGEN .................................................................................................... 4
DATA COLLECTION METHODS................................................................................... 5
KRIGING METHODS ....................................................................................................... 8
RESULTS ......................................................................................................................... 11
CONCLUSIONS AND RECOMMENDATIONS ........................................................... 21
REFERENCES CITED..................................................................................................... 24
APPENDICES .................................................................................................................. 28
APPENDIX A: SCHEDULE OF WELL OWNERSHIP ................................................. 29
APPENDIX B: ORIGINAL MATLAB CODE FROM DR. KATHRYN PLYMESSER 31
APPENDIX C: MATLAB CODE .................................................................................... 35
APPENDIX D: EXCEL MATLAB DATA...................................................................... 46

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LIST OF TABLES
Table Page
1. A table showing measured Dissolved Oxygen data for the three dates analyzed... 6
2. A subset of predicted DO concentrations and the associated variance, calculated
using data measured on 8.27.2014……………………………................………14

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LIST OF FIGURES
Figure Page
1. A map of the site showing 10 of the 12 water sampling wells. .............................. 7
2. A plot of the semivariogram for DO data collected on 08.27.2014...................... 12
5. A 3-D concentration map showing predicted DO concentrations over the site area
calculated using data measured on 08.27.2014…………………………………..16
8. A map showing the plan view of the site with predicted, scaled DO concentrations
calculated using data measured on 09.02..2014……………………………….....20

vi
ABSTRACT
Spatial prediction methods, including ordinary kriging methods, are used to estimate the
value of a parameter at a location where it is not measured, based on data collected at nearby
locations. For this project dissolved oxygen data are analyzed from 3 different dates, collected at
12 well locations near the confluence of Bozeman Creek and the East Gallatin River in
Bozeman, MT with the goal of gaining a broader understanding of the wetland environment in
that area. Ordinary kriging methods are used to interpolate intermediate dissolved oxygen
concentrations, as well as the variance (error) of the predictions on a fine scale over the site for
each date on which data were collected. The process uses semivariograms to establish the
relationship between distance and spatial weight, but in this case semivariograms presented no
trend. The lack of trend indicates that either there is not enough measured data to accurately
predict unknown concentrations, or that there is indeed no spatial relationship. However, the
measured data gives evidence that the site exhibits characteristics typically described of wetlands
and has the potential to remove nitrogen and organic pollutants from the water, thereby
improving water quality.

1
INTRODUCTION
The confluence of Bozeman Creek and the East Gallatin River in Bozeman Montana
shows signs of a history as a typically classified wetland area. Over time, the land in this area has
been cultivated and filled in by various land owners, and business ventures (Deford, 2014). The
City of Bozeman and the Trust for Public Lands have partnered together to create a public park
at this site, while at the same time aiming to reconstruct and restore the wetland function of the
area, and improve water quality in both the East Gallatin River and Bozeman Creek (Deford,
2014).
Montana State University was brought on as a partner to this project to help understand,
and further study the hydraulics, hydrology, and effects of the project on water quality (Deford,
Stein, Cahoon, Hartshorn, & Ewing, 2014). Project leader Lilly Deford describes the project as
looking specifically at “how, or even if, the restoration efforts will affect surface water quality in
the East Gallatin River” (Deford, 2014). Deford’s project focuses on nitrogen and phosphorous
as water chemistry parameters, but includes other water chemistry parameters including pH and
dissolved oxygen. This paper analyzes a small subset of dissolved oxygen data, providing
additional insight to the overall project. Dissolved oxygen concentrations from three separate
dates over a 15 day period were observed at 12 well locations. The concentrations were
analyzed using ordinary kriging methods with the goal of predicting an interpolated dissolved
oxygen concentration map of the wetland site. Creating and analyzing a predicted dissolved
oxygen surface map is beneficial because dissolved oxygen concentrations can indicate the type

2
of nutrient processes that are expected in the area, specifically denitrification, as well as help
determine if the site is behaving overall as a typical wetland after initial construction efforts.
Ordinary kriging was used as a method of interpolation of unknown points because it has
the advantage of also giving error estimates, or variances, in addition to the predicted values
(Bohling, 2005). Ordinary kriging methods have also been proven to effectively predict
dissolved oxygen concentrations in other settings (Murphy, Curriero, & Ball, 2010).
Semivariograms were first developed, and used to predict dissolved oxygen concentrations and
associated variance values. The predicted concentrations were then used as the basis of
dissolved oxygen surface maps for each date over the area being analyzed.
PROJECT BACKGROUND
The area surrounding the confluence of Bozeman Creek and the East Gallatin
River was historically a wetland setting, but has been significantly altered by different
landowners, mostly as a result of agricultural practices; water has been routed through the area
without interacting with the land long enough to create saturated conditions (Deford, 2014). The
city of Bozeman and the Trust for Public Land are working to create a city park near the
confluence, while restoring the wetland environment at the same time, a project titled The Story
Mill Ecological Restoration Project (City of Bozeman; Trust for Public Land, 2014). “The
restoration will close off the drainage ditches in an attempt to back up the groundwater and
create a more saturated, reducing, wetland like landscape. They will also be removing fill from
some of the floodplain. This is in the hopes of increasing surface water interaction with the
wetland during high flow events, when there will be significant amounts of urban and

3
agricultural runoff” (Deford, Project Goals, 2014). In addition to restoring the historic wetland,
the project will increase public green space and offer “opportunities to connect with nature, our
neighbors, and community”, while also providing educational opportunities for all ages to learn
about this history and science of the site (City of Bozeman; Trust for Public Land, 2014).
Montana State University is assisting with technical and scientific expertise, tasked with
monitoring conditions at the site and helping understand the effects of the restoration project on
surface water quality (Deford, Progress Report, 2014). The multiple objectives of the MSU
component of the study are to:
1. Develop metrics for defining success of wetland restoration efforts,
2. Monitor short- and long-term wetland function,
3. Document progress toward achieving the project restoration objectives,
4. Contribute to public awareness of the importance of wetlands,
5. And help better understand how wetlands influence surface water quality and quantity
(Deford, Progress Report, 2014).
Deford is looking at “how, or even if, the restoration efforts will affect surface water
quality in the East Gallatin River… [and is] tracking surface and groundwater levels and
chemical properties, focusing on the nutrients Nitrogen and Phosphorous” (Deford, Project
Goals, 2014). Due to expected increased interaction of surface water with the wetland, “it is
anticipated that the restoration efforts will improve the watershed’s ability to treat nitrogen and
phosphorous” and therefore decrease nutrient levels in East Gallatin River (Deford, Progress
Report, 2014). Deford developed testing methods including a wetland monitoring matrix
tracking water levels, total nitrogen, total phosphorus, nitrate, nitrite, phosphate, sulfate,
chloride, pH, electrical conductivity and dissolved oxygen (Deford, Progress Report, 2014).

4
Deford installed monitoring equipment and is continuing to collect data, aiming to better
understand and quantify wetland function and nutrient cycling (Deford, Progress Report, 2014).
This paper focuses on analyzing a subset of dissolved oxygen (DO) data collected at the
site, and provides additional insight to the overall project with the goal of gaining a broader
understanding of the wetland function. Dissolved oxygen is a parameter of interest because
“Dissolved oxygen (DO) in water is essential for the biochemical processes which determine the
fate of nitrogen and organic pollutants…in constructed wetlands” (Sewwandi, Weragoda, &
Tanaka, 2010). In addition, dissolved oxygen levels are significantly different in wetlands versus
surface water, therefore DO data can help quantify the extent to which the site is functioning as a
wetland.
DISSOLVED OXYGEN
Dissolved Oxygen (DO) levels differ in wetlands compared to surface waters, because
“DO concentrations in …fresh water will range from 7.56 mg/L at 30 degrees Celsius to 14.62
mg/L at zero degrees Celsius” (Minnesota Pollution Control Agency, 2009) and wetland areas
that can be described as bogs, for example, have DO concentrations ranging from 0-6 ppm or 0-
6mg/l (Mullin, 2011). Therefore dissolved oxygen levels can help provide insight into whether or
not the restoration efforts are promoting a wetland environment.
Dissolved oxygen (DO) levels can be used “to assess the stability of various trace
metals…and organic contaminants in ground water” (Rose & Long, 1988) and can also help
predict the expected microbial processes occurring in a wetland area. Denitrification, for
example, is a process that occurs in anaerobic or anoxic conditions (Faulwetter, et al., 2009), and

5
anoxic groundwater conditions are defined as having “no dissolved oxygen or a very low
concentration of dissolved oxygen (that is, less than 0.5 milligrams per liter)” (USGS, n.d.).
“Respiration and fermentation are the major mechanisms by which microorganisms break down
organically-derived pollutants into assumed harmless substances such as carbon dioxide (CO2),
nitrogen gas (N2) and water (H2O)” (Faulwetter, et al., 2009) and dissolved oxygen
concentrations can help determine which processes are expected to be occurring in the area
(Faulwetter, et al., 2009). It’s also been shown that “lower redox potentials are linked to reduced
conditions” (Faulwetter, et al., 2009), and one of the larger project goals as earlier discussed is
creating a more reducing landscape (Deford, Project Goals, 2014). Dissolved oxygen has a high
redox potential, and is in fact the most biologically reactive oxidant out of naturally occurring
constituents in water (Stumm & Morgan, 1981), and because we expect reducing conditions and
low redox potential (Deford, Project Goals, 2014) we therefore expect DO concentrations to be
low. This can be beneficial because when microbes are starved for oxygen, they select the next
most energetic compound, which is typically nitrate (Ponnamperuma, 1972); therefore when DO
concentrations are low in the anoxic range, it gives evidence that nitrates can be removed from
the water through denitrification (Woltermade, 2000) and contribute to the larger project goal of
improving “the watershed’s ability to treat nitrogen and phosphorous” (Deford, Progress Report,
2014).
DATA COLLECTION METHODS
The dissolved oxygen data shown in Table 1 was analyzed from three different dates,
taken at 12 different groundwater well locations across the site. The location of wells is shown

6
in Figure 1. Figure 1 shows only 10 of the 12 locations, with two well locations not pictured
because they are slightly out of view from the aerial photograph, but are just off the image
on the South side. Data was analyzed from samples collected on August 27th, September 2nd,
and September 11th, 2014. Dissolved oxygen concentrations from these dates were selected for
analyses as the observations were from the time of year which is expected to be representative of
baseline conditions.
Table 1- A table showing measured Dissolved Oxygen data for the three dates analyzed.
Well ID Sample ID DO (mg/l) DO% DO (mg/l) DO% DO (mg/l) DO%
TPL3 1 -- -- 0.81 9.10 1.02 10.80
TPL6 2 1.00 11.40 1.96 23.00 1.38 14.70
TPL8 3 1.83 21.10 2.95 34.00 -- --
TPL10 4 4.58 52.50 0.03 0.30 4.18 45.60
TPL14 5 0.36 3.90 0.84 9.40 4.17 44.80
MSU1 6 0.15 1.70 0.25 2.90 2.98 31.10
MSU2 7 0.09 1.00 0.23 2.60 0.25 2.70
MSU3 8 0.05 0.05 0.27 2.90 0.31 3.20
MSU4 9 0.17 0.17 0.28 3.20 0.56 5.80
MSU6 10 0.31 0.31 1.68 18.30 5.29 55.60
MSU7 11 0.12 1.12 0.30 3.40 0.61 6.30
F5 12 0.42 4.60 0.62 6.90 0.64 6.70
Dissolved Oxygen Concentration Data
8/27/2014 9/2/2014 9/11/2014

7
Figure 1- A map of the site showing 10 of the 12 water sampling wells.
The wells used to collect data were installed by three different entities at different times,
including the Trust for Public Land (listed as TPL wells in Table 1), Hyalite Engineers (well F5
in Table 1), and Montana State University (listed as MSU wells in Table 1). A schedule of well
owners is provided in Appendix A. Montana State University installed “2-inch diameter PVC
wells to a maximum depth of 7 ft. with a 3-inch diameter hand auger. [MSU] wells are slotted for
the deepest two feet, and solid for the remaining length up to, and above the ground surface.
Silica sand was used as a well casing around the slotted portion, and clay removed from the well
hole was used around the solid portion. This allows for groundwater to freely flow into the well,

8
while keeping the well from clogging and surface water from entering” (Deford, Stein, Cahoon,
Hartshorn, & Ewing, 2014). The geo-position of well locations are referenced using the North
American Datum of 1983, and were surveyed using Trimble GPS equipment (Deford, Stein,
Cahoon, Hartshorn, & Ewing, 2014).
Water chemistry data, including the dissolved oxygen observations in Table 1, were
collected by Lilly Deford and research assistants working under her direction, using a Hach LDO
Probe (IntelliCALTM LDO101) (Deford, Stein, Cahoon, Hartshorn, & Ewing, 2014).
Measurements were taken after first pumping wells dry, then reading DO concentrations
immediately after recharge, holding the probe in the center of the water column (Deford, Stein,
Cahoon, Hartshorn, & Ewing, 2014). This method is considered to be “representative of the
surrounding groundwater because the water has had little time to equilibrate with the
atmosphere” (Deford, Stein, Cahoon, Hartshorn, & Ewing, 2014). DO measurements were
recorded after consecutive readings stabilized in time to within 0.2mg/L of each other. (Deford,
Stein, Cahoon, Hartshorn, & Ewing, 2014).
KRIGING METHODS
Ordinary kriging is a method of spatial prediction used to estimate the value of a
parameter in question at a location where it is not measured, based on data collected at nearby
locations (Murphy, Curriero, & Ball, 2010). Data analysis using spatial prediction methods are
used because dissolved oxygen concentration in shallow groundwater have the potential to be
spatially correlated, i.e. the concentration of dissolved oxygen at one location is related to the
concentration at nearby locations.

9
Ordinary kriging has advantages over other spatial prediction methods (Bohling, 2005)
and is a proven method of analyzing and predicting groundwater surface elevations (Varouchakis
& Hristopulos, 2013) (Nikroo, Kompani-Zare, Sepaskhah, & Fallah Shamsi, 2010), as well as
water chemistry properties including dissolved oxygen (Murphy, Curriero, & Ball, 2010). All
interpolation algorithms assume a decreasing weight function with increased separation distance,
but kriging is advantageous because the methods incorporate a data driven weighting function,
rather than an arbitrary function (Bohling, 2005). Kriging has further advantages over other
spatial prediction methods including compensating for data clusters, and giving an error estimate,
i.e. variance, in addition to predicting values at unknown locations (Bohling, 2005).
Ordinary kriging involves two steps; first the degree of similarity between measured data
points is plotted as a function against their separation distance to determine if and how the data is
spatially correlated, and second that relationship is used to interpolate among measured points to
estimate values at unknown locations (Reams, Huso, Vong, & McCollum, 1997). The first step
utilizes the semi-variance statistic (h) defined as “half the expected squared difference between
values a given distance, h, apart:
(ℎ) =
1
2
𝐸[𝑧(𝑥𝑖) − 𝑧(𝑥𝑖 + ℎ)]2
=
1
2𝑁(ℎ)
∑ [𝑧(𝑥𝑖) − 𝑧(𝑥𝑖 + ℎ)]2
𝑁(ℎ)
𝑖−1
where
z(𝑥𝑖) = measured sample value at point 𝑥𝑖 (𝑥𝑖 can be multidimensional),
z(𝑥𝑖 + ℎ) = sample value at a point a distance of h from 𝑥𝑖, and
N(h) = total number of pairs of points within an h of each other” (Reams, Huso, Vong, &
McCollum, 1997). The semi-variance statistic (h) is plotted against the separation distance h;
this plot is called the semivariogram (Reams, Huso, Vong, & McCollum, 1997). If a trend can be

10
determined from the semivariogram and a representative curve can be fit to the data, the
relationship between semi-variance and separation distance is then used to determine weighting
factors utilized in the second step (Reams, Huso, Vong, & McCollum, 1997). Once that
relationship is known, weighting factors are calculated based on the separation distance between
points, giving higher weights to points closer to the point being estimated, and used to “estimate
the value of Z at some unmeasured point 𝑥 𝑜, [as] a linear combination or weighted average of all
the observed variables:
𝑧̂( 𝑥0) = 1
𝑧(𝑥1) + 2
𝑧(𝑥2) + ⋯ +  𝑛
𝑧(𝑥 𝑛),
where
1
= coefficients or weights associated with each of the observed values” (Reams, Huso,
Vong, & McCollum, 1997).
Dissolved oxygen concentrations were analyzed using ordinary kriging methods using a
MATLAB (MATLAB, 2014) program written by Kathryn Plymesser, (Plymesser, 2014). The
code is presented in Appendix B, and uses a linear semi-variance model. This base code was
augmented slightly to use data found in different spreadsheets, and the new code is archived in
Appendix C. The spreadsheet based presentation of the data referenced by the code can be found
in Appendix D.
With the semivariograms established, dissolved oxygen concentrations and the
associated variance were estimated using a range of 1000 meters, and a slope of 1 to ensure over
half of all measured points were used to predict unknown concentrations. DO concentrations
were estimated across the site on a grid pattern with a spacing of 50 meters, starting at
(1579782.07 Easting, 532197.33 Northing) and ending at (1578368.61 Easting, 530821.50
Northing) which is an area roughly 1,413 meters East to West, and 1,375 meters North to South,

11
referenced using the North American Datum of 1983. The code for ordinary Kriging can be
found in Appendix C, and the data referenced in the code can be found in Appendix D. Finally,
predicted DO concentrations were then plotted on a 3-D graph (see figures 5-7 in the results
section) using code found in Appendix C, and data found in Appendix D. The function trisurf
was used (MATLAB, 2014) to plot DO concentrations over the area of interest, and therefore the
automatic color scale for each day analyzed was based on that day’s minimum and maximum
predicted DO value, resulting in color scales that could not be compared across different dates.
This was compensated for by manipulating the kriged DO data output before using that data to
plot the concentration maps, by changing the value at the first point (1578450, 530800) to be
6mg/L DO; this forced the automatic color scale in MATLAB to be a 0-6mg/L DO scale. After
3D DO concentration maps were generated for each date using MATLAB, they were changed to
2D graphs with color representing DO concentration, and overlaid on the map of water wells to
give a plan-view picture of DO concentrations across the site for each date.
RESULTS
The semivariograms for each date analyzed can be seen in Figures 2-4. The
semivariograms do not display any detectable trend in the data, showing there is not enough
measured data, or that the spatial interval is too coarse, or that there is simply no spatial trend.
The outcome is that a spatial trend could not be deduced from the semivariograms using ordinary
kriging methods. Without a spatial trend, a correlation cannot be made between separation
distance and weighting factors, to accurately predict the dissolved oxygen concentration in

12
unknown locations. Therefore, if ordinary kriging methods are used, the variance is expected to
be high, showing that predicted values cannot be trusted as accurate calculations.
Figure 2 – A plot of the semivariogram for DO data collected on 08.27.2014.

13

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In light of the inconclusiveness of the semivariograms, the measured data were used with
ordinary kriging to predict DO values at unknown locations for each data analyzed; a small
sample of the predicted DO values and the associated variance at each point for one date on
08.27.2014 are shown in Table 2, and full results are provided in Appendix D. The variance
values are very high as expected, and are often 2 orders of magnitude higher than the predicted
DO concentration, showing that the error in the predicted value is far greater than the value itself
and that predictions are tenuous at best.
Table 2- A subset of predicted DO concentrations and the associated variance, calculated using
data measured on 08.27.2014.

15
Although predicted DO values at unknown locations have high variances, 3-dimensional
DO concentration maps were generated for each date, which were then compared to see if
general trends could be determined, such as areas of persistent low or high DO concentrations.
The unscaled DO concentration maps for each date are shown in Figures 5-7. As before, the
automatic color scale for each day analyzed was based on that day’s minimum and maximum
predicted DO value, resulting in color scales that could not be compared over different
dates. To compensate for this, the kriged DO data output by MATLAB was manipulated before
using that data to plot the 2-D concentration maps, by changing the value at the first point
(1578450, 530800) to be 6mg/L DO; this forced the automatic color scale to be a 0-6mg/L DO
scale. The concentration maps for each day were then displayed as 2-D contour interval graphs
with color representing DO concentration, and overlaid on the water well map to give a plan-
view picture of DO concentrations across the site for each date. These plan view, scaled DO
concentration maps are shown in Figures 8-10, and are all shown on a scale of 0-6mg/L DO, and
can be compared across dates for general trends. As seen in Figures 8-10, there are no major
trends that carry across all dates, and therefore the predicted DO values combined with their
associated variance values are not accurate enough to contribute additional knowledge about DO
concentrations beyond the measured data. However, the measured data do allow us to draw some
general conclusions, which are discussed in the next section.

16
Figure 5- A 3-D concentration map showing predicted DO concentrations over the site area
calculated using data measured on 08.27.2014.

17
Figure 6 – A 3-D concentration map showing predicted DO concentrations over the site area
calculated using data measured on 09.02.2014

18
Figure 7 – A 3-D concentration map showing predicted DO concentrations over the site area
calculated using data measured on 09.02.2014

19
Figure 8 – A map showing the plan view of the site with predicted, scaled DO concentrations

20

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CONCLUSIONS AND RECOMMENDATIONS
The semivariograms showed no correlation between measured DO concentrations and the
separation distance between points, which in this case likely indicates that the well locations
analyzed were too far apart to correlate DO concentrations with their spatial location. Therefore
no spatial trend could be deduced from the semivariograms using ordinary kriging methods.
Without a spatial trend, accurate weighting factors needed to calculate unknown DO

22
concentrations cannot be predicted based on relative distances, and therefore the variance or
error calculated is often orders of magnitude higher than the predicted DO concentration value.
This shows there is not enough data to accurately predict DO concentrations at unknown
locations across the site using ordinary kriging methods.
However, while accurate concentrations of DO were not able to be predicted using
ordinary kriging methods, other project goals were met. Overall, the maximum measured DO
levels of 5.29 mg/L show that the area is acting as a wetland environment which falls within the
DO concentration range of bogs from 0-6mg/L (Mullin, 2011). In addition, over 50% of
measured DO data is within the anoxic range of 0-0.5mg/L (USGS, n.d.), showing anoxic
microbial processes can be expected. Anoxic environments have potential to reduce nitrates,
thereby removing nutrients from the water through denitrification (Woltermade, 2000). Removal
of nutrients leads to improved surface water quality downstream from the wetland area, which is
one of the overall project goals; therefore there is evidence that the restoration efforts have
potential to increase water quality.
When considering the measured data, shown in Table 1, questions were raised as to why
some DO values on a given day are considerably higher than the other wells measured in the
same day; no definitive conclusions can be made, but potential explanations that have been
speculated include hypothesis that outlier measurements were the result of human error,
subsurface hydrology factors, or other unknown ecological factors. Questions were also raised as
to why average DO concentrations were noticeably higher on September 11, 2014 compared to
the other two dates; again no definitive conclusions can be made as many different factors
influence DO concentrations simultaneously, however it is hypothesized that these
measurements were higher because they were taken later in the day compared to the other days,

23
which would result in higher DO concentrations as plants have access to more sunlight and are
photosynthesizing, giving off dissolved oxygen from respiration at higher rates during the middle
of the day, as demonstrated in the Jackson Bottom Wetlands Preserve, in Hillsboro Oregon
(Hillsboro Parks and Recreation, 2015).
Overall, it was concluded that further analyses of dissolved oxygen data is not warranted
at this time; installing more wells would be required to accurately predict DO concentrations,
and given time, labor, and cost constraints it would not be a reasonable investment of resources
to do so. Additional data analyses of other water chemistry parameters by creating
semivariograms would help determine if well placement and density is adequate to predict other
factors relating to water quality, and is recommended as part of the overall Story Mill Ecological
Restoration Project.

25
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27
Woltermade, C. (2000). Ability of restored wetlands to Reduce Nitrogen and Phosphorus
Concentrations in Agricultural Drainage Water. Journal of Soil and Water Conservation,
55, 303–309.

29
APPENDIX A
SCHEDUE OF WELL OWENERSHIP

31
APPENDIX B
ORIGINAL MATLAB CODE FROM DR. KATHRYN PLYMESSER

32
Appendix B - Original MATLAB Code from Dr. Kathryn Plymesser – Ordinary Kriging
%ordkrig.m
%uses ordinary kriging and a linear semivariance model to predict the
%elevation z0 and its associated variance at a specified location x0,
y0.
data=xlsread('WellsMatlab.xls','MatlabData','B2:D16');
X=data(:,1:3); %select x, y, and ground-surface elevation data
[dtX,b]=detrendsurf(X); %detrend surface
svrange=input('enter the range for the linear semivariance model n fit
to the control data: ');
alpha=input('enter the slope of the linear semivariance model n fit to
the control data: ');
for x0=540300:50:540750
for y0=4851650:50:4852100
mz0=b(1)+b(2)*x0+b(3)*y0;
x=[dtX(:,1);x0];
y=[dtX(:,2);y0];
z=dtX(:,3);
n=length(x);
xx=repmat(x,1,n);
yy=repmat(y,1,n);
dx=xx-xx'; dy=yy-yy';
h=sqrt(dx.^2+dy.^2); %calculating the distances between points
h0=h(end,:); dx0=dx(end,:); dy0=dy(end,:); %distances from the
estimation point
hn=find(h0<svrange); %select points within range to use in
estimate
dxn=dx0(hn); dyn=dy0(hn);
hh=sqrt(dxn.^2+dyn.^2); %distances of selected points from the
estimation point
xi=x(hn); yi=y(hn); m=length(xi);
xxi=repmat(xi,1,m);
yyi=repmat(yi,1,m);
dxxi=xxi-xxi'; dyyi=yyi-yyi';
hhi=sqrt(dxxi.^2+dyyi.^2);
gamh=alpha*hhi; %calculate semivariance
S_top=[gamh(1:m-1,1:m-1) ones(m-1,1)];
S_last=[ones(1,m-1) 0];
S=[S_top;S_last]; %semivariance matrix S
B=[gamh(1:m-1,end);1]; %semivariance vector B
lamv=SB; %lamv are the weights
zi=lamv(1:m-1)'*(z(hn(1:m-1))); %calculate estimated z
z0=zi+mz0;
var0=lamv'*B; %calculate the variance in estimate of z
k=[x0,y0,z0,var0];
dlmwrite('elevation.txt',k,'-append','precision','%.6f')
end
end

33
Appendix B - Original MATLAB Code from Dr. Kathryn Plymesser – Semi-variogram
%semivar.m
data=xlsread('WellsMatlab.xls','MatlabData','B143:D153');
%select x, y, and ground-surface elevation data
dtX=detrendsurf(data); %detrend surface
x=dtX(:,1); y=dtX(:,2); z=dtX(:,3); %read x,y,z values
n=length(x); nn=n*n;
%calculate distance between each pair of points
xx=repmat(x,1,n);
yy=repmat(y,1,n);
zz=repmat(z,1,n);
h=sqrt(dx.^2+dy.^2);
%eliminate duplicate values in the lower triangular part of the matrix
% and sort values by distance
hv=reshape(triu(h),nn,1);
[nr,nc,nhv]=find(hv); %nhv are the nonzero values of hv
[sh,ih]=sort(nhv);
%calculate the squared differences in z values for each pair of points
zvar=(zz-zz').^2; vz=reshape(zvar,nn,1); nvz=vz(nr); sv=nvz(ih);
%only compare distances that are half or less of the largest distance
hmax=max(sh)./2; nm=length(find(sh<=hmax));
nbin=200; hinc=hmax/nbin; %set the number of distance bins to 20
% adjust bin width to be round number
% The values for the magnitude of hinc (10, 100, 1000) may need to be
% adjusted depending on domain size and distance units
if hinc<=10, hinc=floor(hinc);
elseif hinc<=100, hinc=floor(hinc/10)*10;
end;
hvec=0:hinc:nbin*hinc; %vector of bin endpoints
for i=1:nbin-1;
ib=[]; ib=find(sh>hvec(i)&sh<=hvec(i+1)); %find distances falling in
bins
if ~isempty(ib),
ni(i)=length(ib);
gamh(i)=sum(sv(ib))./(2*ni(i)); %calculate semivariance for each
distance bin
else gamh(i)=0; ni(i)=0; %set semivariance to 0 if no data fall in a
bin
end;
end;
hvmn=(hvec(1:nbin-1)+hvec(2:nbin))./2; %find the mid-point of each bin
plot(hvmn,gamh,'bo') %plot the results
xlabel('Distance (ft)')
ylabel('Semivariance')
xlswrite('WellsMatlab.xls',gamh,'MatlabSemi2','A1')
xlswrite('WellsMatlab.xls',hvmn,'MatlabSemi2','A2')

34
Appendix B - Original MATLAB Code from Dr. Kathryn Plymesser – detrendsurf function
function [dtX,b] = detrendsurf(X)
% remove the 1st order trend surface from a data matrix X
% with N rows and 3 columns: values of x, y, and z
[nr,nc] = size(X); % determine no of data (rows)
xew=X(:,1); xns=X(:,2); z=X(:,3);
A=[nr sum(xew) sum(xns);...
sum(xew) sum(xew.^2) sum(xew.*xns);...
sum(xns) sum(xew.*xns) sum(xns.^2)];
rhs=[sum(z);sum(xew.*z);sum(xns.*z)];
b=Arhs; % solution of matrix equation
zhat=b(1)+b(2).*xew+b(3).*xns;
zres=z-zhat; %residuals
dtX=[xew xns zres];

36
Appendix C - MATLAB Code – Ordinary Kriging 08.27.2014
%ordkrig.m
y0.
data=xlsread('DO_MatLab_Data.xlsx','MatLabData08.27.2014','B3:D12');
for x0=530800:50:532200
for y0=1578450:50:1579800
mz0=b(1)+b(2)*x0+b(3)*y0;
x=[dtX(:,1);x0];
y=[dtX(:,2);y0];
z=dtX(:,3);
n=length(x);
xx=repmat(x,1,n);
yy=repmat(y,1,n);
estimation point
estimate
estimation point
xxi=repmat(xi,1,m);
yyi=repmat(yi,1,m);
z0=zi+mz0;
k=[x0,y0,z0,var0];
dlmwrite('elevation_08_27_2014.txt',k,'-
append','precision','%.6f')
end
end

37
%ordkrig.m
y0.
for x0=530800:50:532200
for y0=1578450:50:1579800
mz0=b(1)+b(2)*x0+b(3)*y0;
x=[dtX(:,1);x0];
y=[dtX(:,2);y0];
z=dtX(:,3);
n=length(x);
xx=repmat(x,1,n);
yy=repmat(y,1,n);
estimation point
estimate
estimation point
xxi=repmat(xi,1,m);
yyi=repmat(yi,1,m);
z0=zi+mz0;
k=[x0,y0,z0,var0];
end
end

38
%ordkrig.m
y0.
for x0=530800:50:532200
for y0=1578450:50:1579800
mz0=b(1)+b(2)*x0+b(3)*y0;
x=[dtX(:,1);x0];
y=[dtX(:,2);y0];
z=dtX(:,3);
n=length(x);
xx=repmat(x,1,n);
yy=repmat(y,1,n);
estimation point
estimate
estimation point
xxi=repmat(xi,1,m);
yyi=repmat(yi,1,m);
z0=zi+mz0;
k=[x0,y0,z0,var0];
end
end

39
Appendix C - MATLAB Code – Semi-variogram 08.27.2014
%semivar.m
xx=repmat(x,1,n);
yy=repmat(y,1,n);
zz=repmat(z,1,n);
[sh,ih]=sort(nhv);
end;
for i=1:nbin-1;
bins
if ~isempty(ib),
ni(i)=length(ib);
distance bin
bin
end;
end;

40
%semivar.m
xx=repmat(x,1,n);
yy=repmat(y,1,n);
zz=repmat(z,1,n);
[sh,ih]=sort(nhv);
end;
for i=1:nbin-1;
bins
if ~isempty(ib),
ni(i)=length(ib);
distance bin
bin
end;
end;

41
%semivar.m
xx=repmat(x,1,n);
yy=repmat(y,1,n);
zz=repmat(z,1,n);
[sh,ih]=sort(nhv);
end;
for i=1:nbin-1;
bins
if ~isempty(ib),
ni(i)=length(ib);
distance bin
bin
end;
end;

42
Appendix C - MATLAB Code – function: detrendsurf
function [dtX,b] = detrendsurf(X)
% remove the 1st order trend surface from a data matrix X
% with N rows and 3 columns: values of x, y, and z
[nr,nc] = size(X); % determine no of data (rows)
xew=X(:,1); xns=X(:,2); z=X(:,3);
A=[nr sum(xew) sum(xns);...
sum(xew) sum(xew.^2) sum(xew.*xns);...
sum(xns) sum(xew.*xns) sum(xns.^2)];
rhs=[sum(z);sum(xew.*z);sum(xns.*z)];
b=Arhs; % solution of matrix equation
zhat=b(1)+b(2).*xew+b(3).*xns;
zres=z-zhat; %residuals
dtX=[xew xns zres];

43
Appendix C - MATLAB Code – Plot DO Concentration (Scaled to 6) 08.27.2014
num=xlsread(' DO_Concentration_Data_Scaledto6_08_27_2014.xlsx')
x=num(:,1);
y=num(:,2);
z=num(:,3);
tri = delaunay(x,y);
trisurf(tri,x,y,z);

44
x=num(:,1);
y=num(:,2);
z=num(:,3);
trisurf(tri,x,y,z);

45
x=num(:,1);
y=num(:,2);
z=num(:,3);
trisurf(tri,x,y,z);

46
APPENDIX D
EXCEL MATLAB DATA

47
Appendix D – Excel MATLAB Data
MatLabData08.27.2014

48

49

50
DO_Concentration_Data_Scaledto6_08_27_2014
Northing Easting DO Conc. Variance
530800 1578450 6 700.2728
530800 1578500 0.584658 625.6978
530800 1578550 0.65666 556.8845
530800 1578600 0.735512 495.2222
530800 1578650 0.824191 441.7928
530800 1578700 0.925451 396.6221
530800 1578750 1.040866 357.8864
530800 1578800 1.111849 321.5221
530800 1578850 1.260555 283.0701
530800 1578900 1.423131 237.7072
530800 1578950 1.598201 183.2233
530800 1579000 1.809449 124.9177
530800 1579050 1.944886 98.8082
530800 1579100 2.00765 142.4134
530800 1579150 2.000049 207.3776
530800 1579200 2.06316 270.3473
530800 1579250 2.16345 328.7527
530800 1579300 2.298448 383.5274
530800 1579350 2.460249 435.6183
530800 1579400 2.671907 486.6344
530800 1579450 2.858883 534.957
530800 1579500 3.041788 581.8272
530800 1579550 3.212965 627.7528
530800 1579600 3.366924 673.3654
530800 1579650 3.500382 719.3412
530800 1579700 3.824689 782.9832
530800 1579750 3.919803 832.0083
530800 1579800 3.995268 882.9367
530850 1578450 0.41857 647.4001
530850 1578500 0.479384 568.4699
530850 1578550 0.54334 495.3719
530850 1578600 0.613594 430.3082
530850 1578650 0.694406 375.6638
530850 1578700 0.790258 332.8232
530850 1578750 0.833401 299.9917
530850 1578800 0.963507 272.6443
530850 1578850 1.133019 242.8796
530850 1578900 1.304054 204.0779
530850 1578950 1.46854 150.7533
530850 1579000 1.649883 79.33117
530850 1579050 1.823819 12.21833

51
530850 1579100 1.785594 99.76596
530850 1579150 1.793072 171.3904
530850 1579200 1.851942 232.4918
530850 1579250 1.963822 287.6945
530850 1579300 2.122054 339.8512
530850 1579350 2.313729 390.0514
530850 1579400 2.523637 438.4085
530850 1579450 2.737409 484.8737
530850 1579500 2.943067 529.6672
530850 1579550 3.131508 573.3545
530850 1579600 3.338392 618.418
530850 1579650 3.479016 662.5385
530850 1579700 3.558251 708.6741
530850 1579750 3.884415 771.3712
530850 1579800 3.952945 821.5878
530900 1578450 0.323683 600.4436
530900 1578500 0.376735 516.4056
530900 1578550 0.430753 437.5686
530900 1578600 0.48918 366.9023
530900 1578650 0.557851 308.741
530900 1578700 0.644358 267.4949
530900 1578750 0.702465 243.0511
530900 1578800 0.828703 229.1548
530900 1578850 0.977736 214.5451
530900 1578900 1.115489 190.5434
530900 1578950 1.255775 153.3379
530900 1579000 1.39208 107.5157
530900 1579050 1.491272 83.88791
530900 1579100 1.504219 114.4333
530900 1579150 1.520689 161.0182
530900 1579200 1.591004 207.1459
530900 1579250 1.727899 253.3655
530900 1579300 1.923268 300.729
530900 1579350 2.157636 348.379
530900 1579400 2.40961 394.8493
530900 1579450 2.649119 439.16
530900 1579500 2.884983 481.4982
530900 1579550 3.096224 522.4971
530900 1579600 3.287626 563.3296
530900 1579650 3.432117 604.9383
530900 1579700 3.58533 650.1986

52
530900 1579750 3.63131 697.0296
530900 1579800 3.916025 760.4306
530950 1578450 0.23535 561.3569
530950 1578500 0.280784 471.9564
530950 1578550 0.323922 386.1611
530950 1578600 0.367504 306.981
530950 1578650 0.416767 240.5691
530950 1578700 0.443301 197.2243
530950 1578750 0.547669 183.7019
530950 1578800 0.680256 188.7748
530950 1578850 0.804133 193.9201
530950 1578900 0.922511 188.6019
530950 1578950 1.02782 171.3108
530950 1579000 1.124045 148.6792
530950 1579050 1.166487 135.0848
530950 1579100 1.175493 139.7084
530950 1579150 1.196795 156.9504
530950 1579200 1.280016 183.0076
530950 1579250 1.453141 218.9043
530950 1579300 1.700648 262.5665
530950 1579350 1.990568 308.9936
530950 1579400 2.293586 354.1678
530950 1579450 2.588183 396.3533
530950 1579500 2.858932 435.6319
530950 1579550 3.094851 473.1631
530950 1579600 3.288989 510.5517
530950 1579650 3.438648 549.3562
530950 1579700 3.545403 590.7718
530950 1579750 3.594881 637.4689
530950 1579800 3.809992 697.5659
531000 1578450 0.156921 532.4279
531000 1578500 0.196612 438.5571
531000 1578550 0.230336 346.1184
531000 1578600 0.258973 256.6679
531000 1578650 0.284933 175.291
531000 1578700 0.298652 119.7413
531000 1578750 0.406801 119.9956
531000 1578800 0.531081 152.0993
531000 1578850 0.650143 178.8013
531000 1578900 0.749309 190.3372
531000 1578950 0.83957 187.6793

53
531000 1579000 0.877402 175.9617
531000 1579050 0.876653 161.5953
531000 1579100 0.849889 148.73
531000 1579150 0.844554 140.6169
531000 1579200 0.93285 147.2362
531000 1579250 1.158997 177.5589
531000 1579300 1.483078 223.385
531000 1579350 1.845372 271.966
531000 1579400 2.208983 316.8598
531000 1579450 2.552396 356.4808
531000 1579500 2.860567 391.7319
531000 1579550 3.121956 424.7049
531000 1579600 3.328824 457.848
531000 1579650 3.478588 493.3155
531000 1579700 3.574547 532.5503
531000 1579750 3.592163 576.8363
531000 1579800 3.608911 624.9292
531050 1578450 0.09122 515.612
531050 1578500 0.12912 419.6512
531050 1578550 0.161901 323.6194
531050 1578600 0.1799 227.8887
531050 1578650 0.185376 131.9764
531050 1578700 0.173317 39.81386
531050 1578750 0.280721 65.504
531050 1578800 0.422537 129.6372
531050 1578850 0.537081 171.2994
531050 1578900 0.618361 192.9397
531050 1578950 0.68421 198.2141
531050 1579000 0.684617 190.5494
531050 1579050 0.644782 172.1087
531050 1579100 0.570395 143.3381
531050 1579150 0.497054 107.3157
531050 1579200 0.550555 90.49734
531050 1579250 0.865777 128.7318
531050 1579300 1.294716 186.8407
531050 1579350 1.735709 240.33
531050 1579400 2.159565 284.5798
531050 1579450 2.551164 320.1909
531050 1579500 2.896922 349.6679
531050 1579550 3.183582 376.4617
531050 1579600 3.400802 404.2029

54
531050 1579650 3.545036 435.8365
531050 1579700 3.621786 473.0009
531050 1579750 3.613369 516.5907
531050 1579800 3.598476 565.0165
531100 1578450 0.039447 511.6231
531100 1578500 0.087341 415.8729
531100 1578550 0.119568 322.3683
531100 1578600 0.142972 230.407
531100 1578650 0.103303 142.4263
531100 1578700 0.16044 74.75578
531100 1578750 0.256041 85.84978
531100 1578800 0.380519 135.112
531100 1578850 0.481085 173.2008
531100 1578900 0.56632 195.633
531100 1578950 0.588441 203.6179
531100 1579000 0.569323 197.9
531100 1579050 0.50541 177.5743
531100 1579100 0.399571 139.828
531100 1579150 0.257185 80.29945
531100 1579200 0.14143 9.310357
531100 1579250 0.672661 95.41307
531100 1579300 1.191165 165.7828
531100 1579350 1.687314 219.8522
531100 1579400 2.156599 259.7326
531100 1579450 2.589636 288.2386
531100 1579500 2.971629 309.2135
531100 1579550 3.283869 327.5373
531100 1579600 3.509113 348.4022
531100 1579650 3.640173 375.8366
531100 1579700 3.685653 411.4912
531100 1579750 3.639017 455.3089
531100 1579800 3.581319 504.9516
531150 1578450 0.01122 517.0774
531150 1578500 0.058912 426.4942
531150 1578550 0.102448 338.9637
531150 1578600 0.142856 257.1002
531150 1578650 0.137889 186.7332
531150 1578700 0.205752 142.3455
531150 1578750 0.297711 136.5025
531150 1578800 0.40012 155.8025
531150 1578850 0.484696 178.4175

55
531150 1578900 0.552235 195.3964
531150 1578950 0.564331 203.9391
531150 1579000 0.535474 201.6933
531150 1579050 0.471434 185.8485
531150 1579100 0.384068 154.2079
531150 1579150 0.305306 109.6602
531150 1579200 0.360814 82.91995
531150 1579250 0.721415 118.7625
531150 1579300 1.202009 171.122
531150 1579350 1.699585 213.8984
531150 1579400 2.188781 243.3585
531150 1579450 2.662758 260.861
531150 1579500 3.08102 269.9326
531150 1579550 3.423134 276.7678
531150 1579600 3.656585 288.8734
531150 1579650 3.764387 312.1121
531150 1579700 3.760724 347.6856
531150 1579750 3.658603 393.3716
531150 1579800 3.544865 445.3859
531200 1578450 0 532.9752
531200 1578500 0.043335 446.9542
531200 1578550 0.101676 365.7506
531200 1578600 0.179954 291.7669
531200 1578650 0.168254 231.4337
531200 1578700 0.258895 190.5427
531200 1578750 0.360101 171.6356
531200 1578800 0.460188 169.3524
531200 1578850 0.552541 175.834
531200 1578900 0.597357 186.4085
531200 1578950 0.591624 196.8182
531200 1579000 0.560321 201.7411
531200 1579050 0.510898 196.5024
531200 1579100 0.466529 180.2113
531200 1579150 0.470188 159.2282
531200 1579200 0.594467 150.3055
531200 1579250 0.885017 165.7362
531200 1579300 1.295116 193.9691
531200 1579350 1.762272 219.289
531200 1579400 2.251453 234.3729
531200 1579450 2.739829 237.6682
531200 1579500 3.200098 231.5778

56
531200 1579550 3.587538 223.0349
531200 1579600 3.838656 223.6615
531200 1579650 3.914788 243.5928
531200 1579700 3.833381 282.1944
531200 1579750 3.652115 332.24
531200 1579800 3.46904 387.6997
531250 1578450 0 555.2606
531250 1578500 0.034146 473.1539
531250 1578550 0.107367 396.3742
531250 1578600 0.206643 326.3245
531250 1578650 0.200872 267.5027
531250 1578700 0.312392 221.5041
531250 1578750 0.4308 188.1073
531250 1578800 0.54511 165.9753
531250 1578850 0.642072 156.2879
531250 1578900 0.679453 162.3255
531250 1578950 0.671487 179.5933
531250 1579000 0.637686 196.5803
531250 1579050 0.601775 205.3867
531250 1579100 0.589898 204.9008
531250 1579150 0.635917 199.9814
531250 1579200 0.777742 198.9394
531250 1579250 1.03488 206.6473
531250 1579300 1.392911 219.3816
531250 1579350 1.822122 229.3186
531250 1579400 2.297689 230.2903
531250 1579450 2.800708 219.1695
531250 1579500 3.307967 196.1092
531250 1579550 3.769468 167.127
531250 1579600 4.068423 150.7783
531250 1579650 4.076297 170.3254
531250 1579700 3.853722 218.3576
531250 1579750 3.583269 275.2596
531250 1579800 3.324363 334.0382
531300 1578450 0 581.8843
531300 1578500 0.025314 502.4959
531300 1578550 0.11143 427.9321
531300 1578600 0.228243 358.25
531300 1578650 0.225623 296.4348
531300 1578700 0.35632 241.6058
531300 1578750 0.511499 191.4627

57
531300 1578800 0.645788 146.4918
531300 1578850 0.762264 114.6117
531300 1578900 0.798843 119.0542
531300 1578950 0.771446 152.9491
531300 1579000 0.727985 187.2376
531300 1579050 0.697896 210.7644
531300 1579100 0.702667 223.2717
531300 1579150 0.764765 228.7417
531300 1579200 0.905192 232.1601
531300 1579250 1.134818 236.3022
531300 1579300 1.449735 239.9255
531300 1579350 1.837151 239.0469
531300 1579400 2.284212 229.2875
531300 1579450 2.78157 207.0454
531300 1579500 3.321029 169.7766
531300 1579550 3.882504 117.5137
531300 1579600 4.333631 68.7624
531300 1579650 4.201403 99.08588
531300 1579700 3.782264 165.4853
531300 1579750 3.392398 227.8071
531300 1579800 3.073376 286.5082
531350 1578450 0 611.6771
531350 1578500 0.012088 533.9792
531350 1578550 0.136777 458.4813
531350 1578600 0.238 389.2043
531350 1578650 0.233822 323.2368
531350 1578700 0.407448 258.3839
531350 1578750 0.557313 195.0827
531350 1578800 0.720465 126.8437
531350 1578850 0.890114 54.95453
531350 1578900 0.922417 63.08532
531350 1578950 0.854803 129.5498
531350 1579000 0.799807 180.8076
531350 1579050 0.771879 215.2382
531350 1579100 0.78299 236.0634
531350 1579150 0.846522 247.4157
531350 1579200 0.974563 253.0519
531350 1579250 1.173922 255.0699
531350 1579300 1.444398 253.2831
531350 1579350 1.781051 245.7509
531350 1579400 2.178164 229.8199

58
531350 1579450 2.631717 202.7303
531350 1579500 3.139357 161.6085
531350 1579550 3.697165 103.6055
531350 1579600 4.246587 33.98494
531350 1579650 3.97237 73.67229
531350 1579700 3.456788 139.2753
531350 1579750 3.021838 193.6824
531350 1579800 2.688102 244.9218
531400 1578450 0 644.1629
531400 1578500 0 567.5891
531400 1578550 0.124524 492.1041
531400 1578600 0.231882 421.8228
531400 1578650 0.266297 348.978
531400 1578700 0.40613 282.6957
531400 1578750 0.558159 214.0911
531400 1578800 0.739642 141.033
531400 1578850 0.889472 70.31613
531400 1578900 0.927787 74.49794
531400 1578950 0.874594 135.6041
531400 1579000 0.82878 186.7062
531400 1579050 0.807966 222.5874
531400 1579100 0.821847 245.3943
531400 1579150 0.879414 258.2683
531400 1579200 0.988153 263.963
531400 1579250 1.1524 264.0678
531400 1579300 1.372719 258.796
531400 1579350 1.64685 247.4254
531400 1579400 1.971055 229.0261
531400 1579450 2.339517 202.9252
531400 1579500 2.738301 168.9831
531400 1579550 3.123853 129.7781
531400 1579600 3.354463 100.574
531400 1579650 3.217155 108.0033
531400 1579700 2.840596 136.8103
531400 1579750 2.455744 167.6635
531400 1579800 2.161058 204.4312
531450 1578450 0 679.2183
531450 1578500 0 603.6192
531450 1578550 0.099541 528.3273
531450 1578600 0.263627 450.4009
531450 1578650 0.238799 382.6008

59
531450 1578700 0.373966 317.0184
531450 1578750 0.514163 252.1233
531450 1578800 0.682619 191.0179
531450 1578850 0.789456 146.9421
531450 1578900 0.836893 142.4755
531450 1578950 0.830833 171.1533
531450 1579000 0.811466 205.6667
531450 1579050 0.80354 233.4082
531450 1579100 0.819688 252.0152
531450 1579150 0.867896 262.4547
531450 1579200 0.953374 266.2044
531450 1579250 1.078608 264.0955
531450 1579300 1.243429 256.13
531450 1579350 1.445594 242.0883
531450 1579400 1.681088 222.5025
531450 1579450 1.94183 199.2413
531450 1579500 2.206893 175.0856
531450 1579550 2.425288 153.2912
531450 1579600 2.506192 138.6715
531450 1579650 2.375309 134.1723
531450 1579700 2.078934 134.1526
531450 1579750 1.748601 136.6782
531450 1579800 1.517582 156.5045
531500 1578450 0 716.7924
531500 1578500 0 642.2362
531500 1578550 0.134272 554.4726
531500 1578600 0.237807 486.5273
531500 1578650 0.19257 421.0999
531500 1578700 0.318451 358.8938
531500 1578750 0.442828 300.5174
531500 1578800 0.601509 250.097
531500 1578850 0.688613 215.8026
531500 1578900 0.739998 204.668
531500 1578950 0.75857 213.0996
531500 1579000 0.761641 229.3333
531500 1579050 0.766245 244.35
531500 1579100 0.783812 254.5862
531500 1579150 0.821239 259.6661
531500 1579200 0.882088 260.0454
531500 1579250 0.967081 255.5877
531500 1579300 1.074484 245.3365

60
531500 1579350 1.200843 228.508
531500 1579400 1.341974 206.2647
531500 1579450 1.492644 183.2085
531500 1579500 1.639526 165.9022
531500 1579550 1.745341 156.8026
531500 1579600 1.749055 151.4468
531500 1579650 1.604369 142.3192
531500 1579700 1.321976 121.944
531500 1579750 0.982528 91.77877
531500 1579800 0.801789 93.57294
531550 1578450 0 756.77
531550 1578500 0.001714 659.9271
531550 1578550 0.097001 592.0916
531550 1578600 0.197783 525.607
531550 1578650 0.132929 462.459
531550 1578700 0.248856 403.8869
531550 1578750 0.359631 350.6394
531550 1578800 0.51488 305.7053
531550 1578850 0.592305 273.2987
531550 1578900 0.645733 255.4077
531550 1578950 0.676829 249.5578
531550 1579000 0.693998 249.8595
531550 1579050 0.707329 251.0358
531550 1579100 0.724834 250.6215
531550 1579150 0.751402 248.4733
531550 1579200 0.788831 244.9108
531550 1579250 0.836016 238.8602
531550 1579300 0.889222 227.4788
531550 1579350 0.94283 207.7855
531550 1579400 0.991692 179.6298
531550 1579450 1.037142 149.9676
531550 1579500 1.090039 134.6393
531550 1579550 1.136012 139.5853
531550 1579600 1.113272 147.8317
531550 1579650 0.975181 142.77
531550 1579700 0.709166 114.6513
531550 1579750 0.331923 56.25242
531550 1579800 0.14811 35.68667
531600 1578450 0 776.3342
531600 1578500 0 697.2193
531600 1578550 0.051763 630.8052

61
531600 1578600 0.149166 565.7136
531600 1578650 0.064875 504.5342
531600 1578700 0.172185 448.5789
531600 1578750 0.272934 398.0791
531600 1578800 0.428469 354.6863
531600 1578850 0.500622 320.4408
531600 1578900 0.555193 295.4007
531600 1578950 0.593047 277.6028
531600 1579000 0.618463 263.6364
531600 1579050 0.637042 250.6222
531600 1579100 0.653541 237.8415
531600 1579150 0.670632 226.8745
531600 1579200 0.688402 219.5064
531600 1579250 0.704184 214.1728
531600 1579300 0.712474 204.9521
531600 1579350 0.705065 184.7709
531600 1579400 0.672493 149.1933
531600 1579450 0.613364 101.7138
531600 1579500 0.583678 78.09995
531600 1579550 0.629987 109.3566
531600 1579600 0.628003 139.4143
531600 1579650 0.527797 147.2619
531600 1579700 0.33468 130.88
531600 1579750 0.110916 99.41452
531600 1579800 0.03348 99.54841
531650 1578450 0 814.3003
531650 1578500 0 735.1254
531650 1578550 0.00468 667.9995
531650 1578600 0.094582 605.7844
531650 1578650 0.182091 546.9221
531650 1578700 0.092746 491.174
531650 1578750 0.1866 441.3775
531650 1578800 0.344139 397.0685
531650 1578850 0.413341 359.1382
531650 1578900 0.468765 326.7494
531650 1578950 0.510698 298.1009
531650 1579000 0.541224 270.755
531650 1579050 0.563193 242.9689
531650 1579100 0.57897 215.4474
531650 1579150 0.58943 192.8335
531650 1579200 0.593384 181.717

62
531650 1579250 0.587376 181.5307
531650 1579300 0.565513 180.7665
531650 1579350 0.519119 166.7729
531650 1579400 0.436627 131.7401
531650 1579450 0.304298 71.47305
531650 1579500 0.179616 19.79311
531650 1579550 0.284808 93.70925
531650 1579600 0.308408 139.2995
531650 1579650 0.258288 159.9894
531650 1579700 0.147221 161.8886
531650 1579750 0.038161 158.0992
531650 1579800 0.013814 171.6923
531700 1578450 0 854.0211
531700 1578500 0 774.3454
531700 1578550 0 706.6318
531700 1578600 0.035996 645.1472
531700 1578650 0.119732 586.8483
531700 1578700 0.012928 531.1044
531700 1578750 0.102271 480.5962
531700 1578800 0.262503 434.0222
531700 1578850 0.330248 391.6695
531700 1578900 0.386675 352.2202
531700 1578950 0.431668 313.8389
531700 1579000 0.466062 274.2415
531700 1579050 0.491073 231.5823
531700 1579100 0.507549 186.2973
531700 1579150 0.515237 145.5724
531700 1579200 0.512228 128.5053
531700 1579250 0.495172 141.5393
531700 1579300 0.45977 157.7868
531700 1579350 0.400605 157.4397
531700 1579400 0.313322 136.0676
531700 1579450 0.205532 101.1947
531700 1579500 0.133416 85.86382
531700 1579550 0.141136 115.0704
531700 1579600 0.147981 151.5556
531700 1579650 0.114125 177.7311
531700 1579700 0.055031 193.8807
531700 1579750 0.006421 207.8907
531700 1579800 0.007654 231.5667
531750 1578450 0 892.8112

63
531750 1578500 0 812.4678
531750 1578550 0 745.9776
531750 1578600 0.050459 684.6874
531750 1578650 0.055744 625.0966
531750 1578700 0.131866 569.7184
531750 1578750 0.020523 516.4815
531750 1578800 0.099742 467.3802
531750 1578850 0.251071 420.3375
531750 1578900 0.308941 374.7306
531750 1578950 0.356894 328.4251
531750 1579000 0.395054 279.0873
531750 1579050 0.423708 224.1894
531750 1579100 0.442879 161.661
531750 1579150 0.451897 93.03087
531750 1579200 0.44858 56.68393
531750 1579250 0.429653 102.5198
531750 1579300 0.394201 141.091
531750 1579350 0.34098 154.3294
531750 1579400 0.272033 146.0639
531750 1579450 0.196209 128.4292
531750 1579500 0.143829 120.9678
531750 1579550 0.115649 135.4362
531750 1579600 0.092851 163.6938
531750 1579650 0.060077 193.7904
531750 1579700 0.023141 221.1542
531750 1579750 0.000774 248.2155
531750 1579800 0.041 281.1629
531800 1578450 0 970.2186
531800 1578500 0 864.7455
531800 1578550 0 783.6919
531800 1578600 0 722.1347
531800 1578650 0.066024 663.0214
531800 1578700 0.138252 606.3795
531800 1578750 0 549.9957
531800 1578800 0.020287 498.0366
531800 1578850 0.175398 447.1053
531800 1578900 0.235291 396.7
531800 1578950 0.286569 344.9373
531800 1579000 0.328972 289.8969
531800 1579050 0.362275 229.4427
531800 1579100 0.38605 161.5155

64
531800 1579150 0.399463 85.78098
531800 1579200 0.400617 40.169
531800 1579250 0.386799 96.78578
531800 1579300 0.359566 139.068
531800 1579350 0.320444 154.8328
531800 1579400 0.27336 148.4733
531800 1579450 0.226245 130.2602
531800 1579500 0.183452 118.3609
531800 1579550 0.141792 130.5562
531800 1579600 0.09928 163.7195
531800 1579650 0.058851 203.5411
531800 1579700 0.026752 242.7317
531800 1579750 0.012653 281.2716
531800 1579800 0.058906 322.8506
531850 1578450 0 1010.177
531850 1578500 0 940.6139
531850 1578550 0 821.01
531850 1578600 0 758.8478
531850 1578650 0.000841 698.7439
531850 1578700 0.072156 640.6254
531850 1578750 0.137465 584.2925
531850 1578800 0 528.1293
531850 1578850 0.145011 473.8759
531850 1578900 0.203036 419.9474
531850 1578950 0.253019 364.9843
531850 1579000 0.294539 308.0511
531850 1579050 0.327157 248.756
531850 1579100 0.350342 188.6248
531850 1579150 0.363631 135.6636
531850 1579200 0.367203 112.7752
531850 1579250 0.36123 129.081
531850 1579300 0.345221 151.3299
531850 1579350 0.319798 158.0086
531850 1579400 0.29285 143.7614
531850 1579450 0.269203 110.77
531850 1579500 0.244663 78.27623
531850 1579550 0.193787 98.55394
531850 1579600 0.132502 153.4353
531850 1579650 0.081891 209.6561
531850 1579700 0.047494 261.6053
531850 1579750 0.064976 310.9483

65
531850 1579800 0.080944 360.0997
531900 1578450 0 1050.104
531900 1578500 0 980.3138
531900 1578550 0 873.4949
531900 1578600 0 795.1771
531900 1578650 0 733.8835
531900 1578700 0.005932 674.1678
531900 1578750 0.071646 615.811
531900 1578800 0 557.1299
531900 1578850 0.07378 500.2646
531900 1578900 0.134822 443.8834
531900 1578950 0.189121 387.2405
531900 1579000 0.236289 330.3995
531900 1579050 0.275891 274.4741
531900 1579100 0.307382 222.772
531900 1579150 0.330131 182.2391
531900 1579200 0.343527 161.5875
531900 1579250 0.347071 160.5998
531900 1579300 0.340725 165.8111
531900 1579350 0.327247 162.7138
531900 1579400 0.312707 141.7711
531900 1579450 0.304081 96.57789
531900 1579500 0.307805 21.84885
531900 1579550 0.239777 72.65619
531900 1579600 0.164596 152.8851
531900 1579650 0.10835 222.0846
531900 1579700 0.071709 283.5375
531900 1579750 0.090771 340.822
531900 1579800 0.103007 396.2239
531950 1578450 0 1090.151
531950 1578500 0 1019.97
531950 1578550 0 910.9317
531950 1578600 0 845.4466
531950 1578650 0 781.2787
531950 1578700 0 707.6221
531950 1578750 0.005871 647.3177
531950 1578800 0.067314 587.7882
531950 1578850 0 527.5313
531950 1578900 0.06833 468.716
531950 1578950 0.127362 410.6053
531950 1579000 0.180721 353.4699

66
531950 1579050 0.228073 298.921
531950 1579100 0.268871 250.0457
531950 1579150 0.302171 211.3174
531950 1579200 0.329498 186.661
531950 1579250 0.341237 175.5582
531950 1579300 0.342039 171.8649
531950 1579350 0.333952 166.2196
531950 1579400 0.321638 149.9176
531950 1579450 0.308935 119.606
531950 1579500 0.28919 92.31176
531950 1579550 0.239965 118.5053
531950 1579600 0.177909 182.1614
531950 1579650 0.126002 249.4554
531950 1579700 0.123121 313.775
531950 1579750 0 375.7898
531950 1579800 0 435.3112
532000 1578450 0 1130.529
532000 1578500 0 1059.854
532000 1578550 0 962.8779
532000 1578600 0 882.3881
532000 1578650 0 816.9605
532000 1578700 0 752.4548
532000 1578750 0 688.7157
532000 1578800 0.002878 617.8239
532000 1578850 0.061531 556.6091
532000 1578900 0.002243 494.3332
532000 1578950 0.06605 434.2042
532000 1579000 0.125666 375.2388
532000 1579050 0.180959 318.7712
532000 1579100 0.241153 267.3004
532000 1579150 0.282572 222.9118
532000 1579200 0.316401 189.3802
532000 1579250 0.338526 169.2949
532000 1579300 0.345129 162.5224
532000 1579350 0.337107 162.9882
532000 1579400 0.319882 161.7215
532000 1579450 0.297211 156.2088
532000 1579500 0.266616 157.4325
532000 1579550 0.22392 182.6557
532000 1579600 0.175281 231.3503
532000 1579650 0.050369 291.6224

67
532000 1579700 0.005515 353.5379
532000 1579750 0 415.1575
532000 1579800 0 476.3561
532050 1578450 0 1193.106
532050 1578500 0 1117.399
532050 1578550 0 1016.505
532050 1578600 0 920.2379
532050 1578650 0 853.6089
532050 1578700 0 787.6569
532050 1578750 0 722.2305
532050 1578800 0 657.177
532050 1578850 0 592.3769
532050 1578900 0.094097 526.1128
532050 1578950 0.028534 460.6268
532050 1579000 0.088432 397.5502
532050 1579050 0.146314 335.9587
532050 1579100 0.202117 276.7885
532050 1579150 0.255128 221.5067
532050 1579200 0.302766 173.1622
532050 1579250 0.3379 139.5567
532050 1579300 0.34915 132.5135
532050 1579350 0.335907 148.2615
532050 1579400 0.310008 168.9654
532050 1579450 0.278827 187.3605
532050 1579500 0.243442 208.3559
532050 1579550 0.168738 240.1907
532050 1579600 0.118993 285.05
532050 1579650 0.037288 340.2311
532050 1579700 0 399.0188
532050 1579750 0 459.602
532050 1579800 0 521.0268
532100 1578450 0 1233.039
532100 1578500 0 1157.254
532100 1578550 0 1055.824
532100 1578600 0 983.343
532100 1578650 0 900.7221
532100 1578700 0 831.0597
532100 1578750 0 762.2094
532100 1578800 0 693.9603
532100 1578850 0 626.1018
532100 1578900 0 558.4501

68
532100 1578950 0.052783 489.1809
532100 1579000 0 421.0681
532100 1579050 0 353.8795
532100 1579100 0.080428 286.2788
532100 1579150 0.219002 217.7319
532100 1579200 0.281298 149.0715
532100 1579250 0.336399 87.99208
532100 1579300 0.346028 79.84829
532100 1579350 0.314219 126.63
532100 1579400 0.270874 174.1929
532100 1579450 0.226267 214.1865
532100 1579500 0.181193 251.264
532100 1579550 0.13598 291.4328
532100 1579600 0.057045 338.9869
532100 1579650 0.015176 391.7137
532100 1579700 0 448.6379
532100 1579750 0 508.0845
532100 1579800 0 569.1291
532150 1578450 0 1274.39
532150 1578500 0 1198.531
532150 1578550 0 1096.894
532150 1578600 0 1023.987
532150 1578650 0 940.4796
532150 1578700 0 869.983
532150 1578750 0 800.0804
532150 1578800 0 730.5554
532150 1578850 0 661.1742
532150 1578900 0 591.6881
532150 1578950 0 521.822
532150 1579000 0.044727 450.0031
532150 1579050 0 377.8383
532150 1579100 0.018787 304.5212
532150 1579150 0.107244 227.8625
532150 1579200 0.198778 146.0872
532150 1579250 0.293078 57.65526
532150 1579300 0.324735 44.51689
532150 1579350 0.274172 125.0766
532150 1579400 0.225816 190.7665
532150 1579450 0.180123 245.0708
532150 1579500 0.107288 294.1663
532150 1579550 0.062009 341.7548

69
532150 1579600 0.020553 391.5884
532150 1579650 0 444.7831
532150 1579700 0 501.0797
532150 1579750 0 559.7826
532150 1579800 0 620.3259
532200 1578450 0 1317.381
532200 1578500 0 1241.506
532200 1578550 0 1166.473
532200 1578600 0 1066.874
532200 1578650 0 994.436
532200 1578700 0 911.7409
532200 1578750 0 841.1702
532200 1578800 0 770.8539
532200 1578850 0 700.5664
532200 1578900 0 630.0606
532200 1578950 0 559.0593
532200 1579000 0 487.242
532200 1579050 0.035003 413.4964
532200 1579100 0.090477 339.2728
532200 1579150 0.027442 263.3029
532200 1579200 0.111384 188.8893
532200 1579250 0.182592 128.561
532200 1579300 0.210506 121.7876
532200 1579350 0.190987 170.5228
532200 1579400 0.155826 230.7915
532200 1579450 0.094161 288.3576
532200 1579500 0.051632 341.7734
532200 1579550 0.01214 393.542
532200 1579600 0 445.839
532200 1579650 0 499.9089
532200 1579700 0 556.1208
532200 1579750 0 614.365
532200 1579800 0 674.4114

70
530800 1578450 6 158.5898
530800 1578500 0.95398 107.8811
530800 1578550 0.991507 125.6566
530800 1578600 1.064331 173.3408
530800 1578650 1.167337 214.599
530800 1578700 1.303267 242.591
530800 1578750 1.4745 257.1312
530800 1578800 1.684571 258.2257
530800 1578850 1.919191 245.1042
530800 1578900 2.174802 216.5583
530800 1578950 2.439817 172.8043
530800 1579000 2.686455 120.7051
530800 1579050 2.7866 97.25586
530800 1579100 2.625717 141.4347
530800 1579150 2.380011 206.4319
530800 1579200 2.133688 269.312
530800 1579250 1.912198 327.5878
530800 1579300 1.720249 382.2247
530800 1579350 1.556618 434.1844
530800 1579400 1.40784 485.1356
530800 1579450 1.288588 533.3594
530800 1579500 1.18615 580.1427
530800 1579550 1.119046 627.7528
530800 1579600 1.041856 673.3654
530800 1579650 0.973827 719.3412
530800 1579700 0.93587 782.9832
530800 1579750 0.884998 832.0083
530800 1579800 0.839009 882.9367
530850 1578450 0.857517 115.7645
530850 1578500 0.824672 18.41355
530850 1578550 0.858032 75.05459
530850 1578600 0.921073 139.9951
530850 1578650 1.011945 183.7427
530850 1578700 1.140309 211.2168
530850 1578750 1.318413 226.1445
530850 1578800 1.53361 229.541
530850 1578850 1.787153 219.1651
530850 1578900 2.060972 192.4249
530850 1578950 2.35349 146.2131
530850 1579000 2.662542 78.40799
530850 1579050 2.904142 12.21822

71
530850 1579100 2.561925 99.74075
530850 1579150 2.251353 171.2886
530850 1579200 1.979409 232.2678
530850 1579250 1.749179 287.3224
530850 1579300 1.558822 339.3248
530850 1579350 1.402785 389.3775
530850 1579400 1.274247 437.599
530850 1579450 1.166986 483.9414
530850 1579500 1.076116 528.6237
530850 1579550 1.015317 573.3545
530850 1579600 0.935711 618.418
530850 1579650 0.876169 662.5385
530850 1579700 0.727958 708.6741
530850 1579750 0.791981 771.3712
530850 1579800 0.75318 821.5878
530900 1578450 0.786443 139.8029
530900 1578500 0.750218 83.27781
530900 1578550 0.750105 97.5643
530900 1578600 0.781743 136.0631
530900 1578650 0.845094 164.7046
530900 1578700 0.953878 183.4179
530900 1578750 1.129722 196.4966
530900 1578800 1.348529 204.4077
530900 1578850 1.600916 202.2985
530900 1578900 1.868094 185.3489
530900 1578950 2.132691 151.8205
530900 1579000 2.363121 107.3952
530900 1579050 2.440824 83.84643
530900 1579100 2.258035 114.3734
530900 1579150 1.988691 161.0112
530900 1579200 1.734143 207.1351
530900 1579250 1.52057 253.2913
530900 1579300 1.350219 300.5595
530900 1579350 1.215586 348.1037
530900 1579400 1.107364 394.4679
530900 1579450 0.99677 438.6753
530900 1579500 0.920441 480.9149
530900 1579550 0.869013 522.4971
530900 1579600 0.835148 563.3296
530900 1579650 0.786304 604.9383
530900 1579700 0.730266 650.1986

72
530900 1579750 0.595039 697.0296
530900 1579800 0.667501 760.4306
530950 1578450 0.738902 194.546
530950 1578500 0.692151 152.3145
530950 1578550 0.662315 141.302
530950 1578600 0.65293 145.1187
530950 1578650 0.675787 147.6292
530950 1578700 0.754122 150.0943
530950 1578750 0.91135 161.2699
530950 1578800 1.13588 178.3364
530950 1578850 1.387403 189.4195
530950 1578900 1.631899 187.0763
530950 1578950 1.841514 171.0566
530950 1579000 1.977269 148.6758
530950 1579050 1.986274 134.9451
530950 1579100 1.848491 139.5386
530950 1579150 1.630925 156.8722
530950 1579200 1.407508 182.9978
530950 1579250 1.226629 218.9
530950 1579300 1.090281 262.5266
530950 1579350 0.98696 308.899
530950 1579400 0.905045 354.0091
530950 1579450 0.837215 396.1249
530950 1579500 0.779519 435.3304
530950 1579550 0.739862 473.1631
530950 1579600 0.698205 510.5517
530950 1579650 0.662727 549.3562
530950 1579700 0.63279 590.7718
530950 1579750 0.468954 637.4689
530950 1579800 0.505076 697.5659
531000 1578450 0.71176 248.79
531000 1578500 0.652949 205.7681
531000 1578550 0.598239 177.0921
531000 1578600 0.546016 153.0426
531000 1578650 0.511335 125.0456
531000 1578700 0.530007 101.7023
531000 1578750 0.682012 114.0662
531000 1578800 0.931294 149.8752
531000 1578850 1.185692 178.0776
531000 1578900 1.403938 190.228
531000 1578950 1.559498 187.6703

73
531000 1579000 1.62994 175.8048
531000 1579050 1.590944 161.3111
531000 1579100 1.442869 148.4822
531000 1579150 1.235738 140.4975
531000 1579200 1.040101 147.2082
531000 1579250 0.906182 177.5582
531000 1579300 0.823815 223.3795
531000 1579350 0.766031 271.9413
531000 1579400 0.718602 316.8054
531000 1579450 0.676463 356.3876
531000 1579500 0.644374 391.7319
531000 1579550 0.611289 424.7049
531000 1579600 0.58249 457.848
531000 1579650 0.558192 493.3155
531000 1579700 0.538311 532.5503
531000 1579750 0.43044 576.8363
531000 1579800 0.419726 624.9292
531050 1578450 0.708477 297.5962
531050 1578500 0.643238 249.9221
531050 1578550 0.565287 207.6772
531050 1578600 0.492804 163.7004
531050 1578650 0.407761 108.2033
531050 1578700 0.314694 37.38611
531050 1578750 0.495659 65.40636
531050 1578800 0.792718 129.6269
531050 1578850 1.043064 171.2831
531050 1578900 1.230664 192.8122
531050 1578950 1.339144 197.9121
531050 1579000 1.352179 190.1108
531050 1579050 1.270786 171.6685
531050 1579100 1.094014 143.0425
531050 1579150 0.854581 107.205
531050 1579200 0.649319 90.4805
531050 1579250 0.581145 128.7301
531050 1579300 0.569054 186.8407
531050 1579350 0.559571 240.3273
531050 1579400 0.544692 284.5681
531050 1579450 0.525475 320.1622
531050 1579500 0.508154 349.6679
531050 1579550 0.488559 376.4617
531050 1579600 0.471236 404.2029

74
531050 1579650 0.457292 435.8365
531050 1579700 0.447083 473.0009
531050 1579750 0.353989 516.5907
531050 1579800 0.351134 565.0165
531100 1578450 0.731561 342.5832
531100 1578500 0.651598 289.6004
531100 1578550 0.58941 240.332
531100 1578600 0.520864 188.0826
531100 1578650 0.451295 128.8464
531100 1578700 0.404115 73.73885
531100 1578750 0.541801 85.78701
531100 1578800 0.784537 134.838
531100 1578850 0.995457 172.7644
531100 1578900 1.139342 195.0427
531100 1578950 1.196282 202.9186
531100 1579000 1.171244 197.1929
531100 1579050 1.054146 176.9963
531100 1579100 0.848513 139.4866
531100 1579150 0.564975 80.19892
531100 1579200 0.254929 9.310294
531100 1579250 0.328334 95.41045
531100 1579300 0.373277 165.7795
531100 1579350 0.394282 219.8509
531100 1579400 0.399296 259.7325
531100 1579450 0.394451 288.235
531100 1579500 0.386487 309.2135
531100 1579550 0.376339 327.5373
531100 1579600 0.367817 348.4022
531100 1579650 0.362646 375.8366
531100 1579700 0.361321 411.4912
531100 1579750 0.285234 455.3089
531100 1579800 0.289748 504.9516
531150 1578450 0.751369 383.1868
531150 1578500 0.705667 329.3798
531150 1578550 0.660703 277.3625
531150 1578600 0.619551 225.5285
531150 1578650 0.599614 175.7604
531150 1578700 0.619746 140.577
531150 1578750 0.72723 136.4972
531150 1578800 0.892494 155.5364
531150 1578850 1.038822 177.803

75
531150 1578900 1.133071 194.5623
531150 1578950 1.151003 203.021
531150 1579000 1.087826 200.8302
531150 1579050 0.94674 185.1688
531150 1579100 0.73835 153.7897
531150 1579150 0.48885 109.4873
531150 1579200 0.293525 82.87452
531150 1579250 0.258059 118.7383
531150 1579300 0.277922 171.1025
531150 1579350 0.294254 213.8857
531150 1579400 0.300229 243.3534
531150 1579450 0.290001 260.8601
531150 1579500 0.283966 269.9326
531150 1579550 0.277913 276.7678
531150 1579600 0.274666 288.8734
531150 1579650 0.276306 312.1121
531150 1579700 0.283004 347.6856
531150 1579750 0.225784 393.3716
531150 1579800 0.237064 445.3859
531200 1578450 0.811487 424.3078
531200 1578500 0.783238 369.1793
531200 1578550 0.762119 316.4172
531200 1578600 0.757425 265.8469
531200 1578650 0.777885 221.0363
531200 1578700 0.832438 187.9218
531200 1578750 0.934862 171.4289
531200 1578800 1.061865 169.2841
531200 1578850 1.167686 175.3969
531200 1578900 1.215672 185.6579
531200 1578950 1.196248 195.9388
531200 1579000 1.098211 200.8843
531200 1579050 0.939794 195.7965
531200 1579100 0.740385 179.7236
531200 1579150 0.532626 158.948
531200 1579200 0.368943 150.1589
531200 1579250 0.284415 165.65
531200 1579300 0.253776 193.9107
531200 1579350 0.241835 219.2503
531200 1579400 0.23275 234.351
531200 1579450 0.220755 237.6682
531200 1579500 0.210068 231.5778

76
531200 1579550 0.201168 223.0349
531200 1579600 0.198149 223.6615
531200 1579650 0.199689 243.5928
531200 1579700 0.213989 282.1944
531200 1579750 0.177156 332.24
531200 1579800 0.194536 387.6997
531250 1578450 0.882075 464.6133
531250 1578500 0.872398 408.3813
531250 1578550 0.87495 354.6674
531250 1578600 0.900016 303.3563
531250 1578650 0.95297 257.1038
531250 1578700 1.032135 218.0378
531250 1578750 1.149589 187.4727
531250 1578800 1.266172 165.9728
531250 1578850 1.35417 156.1043
531250 1578900 1.3697 161.8315
531250 1578950 1.29867 178.8956
531250 1579000 1.162019 195.8314
531250 1579050 0.98441 204.7134
531250 1579100 0.788004 204.3759
531250 1579150 0.597926 199.616
531250 1579200 0.441434 198.6996
531250 1579250 0.333696 206.4883
531250 1579300 0.267677 219.2733
531250 1579350 0.226451 229.2461
531250 1579400 0.197009 230.2459
531250 1579450 0.170351 219.1695
531250 1579500 0.149841 196.1092
531250 1579550 0.13346 167.127
531250 1579600 0.126887 150.7783
531250 1579650 0.136805 170.3254
531250 1579700 0.121587 218.3576
531250 1579750 0.140979 275.2596
531250 1579800 0.16365 334.0382
531300 1578450 0.95532 504.276
531300 1578500 0.962255 446.6978
531300 1578550 0.984529 391.1996
531300 1578600 1.032473 337.0299
531300 1578650 1.108879 285.8307
531300 1578700 1.207451 237.3328
531300 1578750 1.330549 190.3075

77
531300 1578800 1.471602 146.3736
531300 1578850 1.577746 114.583
531300 1578900 1.56565 118.8074
531300 1578950 1.434914 152.4874
531300 1579000 1.25235 186.6647
531300 1579050 1.052043 210.1893
531300 1579100 0.851206 222.7701
531300 1579150 0.665003 228.3453
531300 1579200 0.507288 231.8654
531300 1579250 0.385315 236.0895
531300 1579300 0.296581 239.7748
531300 1579350 0.232546 238.9439
531300 1579400 0.184424 229.2221
531300 1579450 0.142977 207.0454
531300 1579500 0.111356 169.7766
531300 1579550 0.084128 117.5137
531300 1579600 0.066696 68.7624
531300 1579650 0.083261 99.08588
531300 1579700 0.093671 165.4853
531300 1579750 0.12127 227.8071
531300 1579800 0.146984 286.5082
531350 1578450 1.024711 543.6797
531350 1578500 1.044515 484.566
531350 1578550 1.087039 425.6623
531350 1578600 1.143768 369.0792
531350 1578650 1.234274 312.3439
531350 1578700 1.335687 253.5057
531350 1578750 1.476371 193.3302
531350 1578800 1.64232 126.4621
531350 1578850 1.812879 54.94723
531350 1578900 1.771741 63.00961
531350 1578950 1.552988 129.305
531350 1579000 1.329225 180.4289
531350 1579050 1.112207 214.8011
531350 1579100 0.907584 235.6363
531350 1579150 0.722239 247.0416
531350 1579200 0.562705 252.7478
531350 1579250 0.432292 254.8353
531350 1579300 0.329658 253.1099
531350 1579350 0.250084 245.6295
531350 1579400 0.183656 229.8199

78
531350 1579450 0.13536 202.7303
531350 1579500 0.09621 161.6085
531350 1579550 0.063435 103.6055
531350 1579600 0.03757 33.98494
531350 1579650 0.060151 73.67229
531350 1579700 0.08608 139.2753
531350 1579750 0.115654 193.6824
531350 1579800 0.142976 244.9218
531400 1578450 1.085617 583.3966
531400 1578500 1.113823 522.8533
531400 1578550 1.164872 461.716
531400 1578600 1.22784 402.405
531400 1578650 1.309875 338.134
531400 1578700 1.418457 277.1565
531400 1578750 1.550621 211.7182
531400 1578800 1.701815 140.2799
531400 1578850 1.842184 70.20067
531400 1578900 1.793461 74.49628
531400 1578950 1.581423 135.5177
531400 1579000 1.358404 186.501
531400 1579050 1.143956 222.2972
531400 1579100 0.94393 245.0705
531400 1579150 0.763037 257.9546
531400 1579200 0.605054 263.6869
531400 1579250 0.47168 263.842
531400 1579300 0.362037 258.6228
531400 1579350 0.267955 247.4254
531400 1579400 0.198176 229.0261
531400 1579450 0.143682 202.9252
531400 1579500 0.102716 168.9831
531400 1579550 0.074697 129.7781
531400 1579600 0.063601 100.574
531400 1579650 0.077388 108.0033
531400 1579700 0.100531 136.8103
531400 1579750 0.127977 167.6635
531400 1579800 0.154313 204.4312
531450 1578450 1.135366 624.0045
531450 1578500 1.167578 562.4014
531450 1578550 1.221409 499.7205
531450 1578600 1.319239 432.0347
531450 1578650 1.357415 371.5044

79
531450 1578700 1.451038 310.8706
531450 1578750 1.555596 249.1299
531450 1578800 1.657476 189.8182
531450 1578850 1.715144 146.6015
531450 1578900 1.668482 142.4383
531450 1578950 1.521987 171.1454
531450 1579000 1.335043 205.5879
531450 1579050 1.141595 233.2476
531450 1579100 0.955918 251.7996
531450 1579150 0.785287 262.2196
531450 1579200 0.633756 265.9798
531450 1579250 0.502887 263.901
531450 1579300 0.392144 255.9755
531450 1579350 0.294683 242.0883
531450 1579400 0.220485 222.5025
531450 1579450 0.163391 199.2413
531450 1579500 0.124261 175.0856
531450 1579550 0.103475 153.2912
531450 1579600 0.100608 138.6715
531450 1579650 0.111844 134.1723
531450 1579700 0.133912 134.1526
531450 1579750 0.157355 136.6782
531450 1579800 0.180719 156.5045
531500 1578450 1.173013 665.925
531500 1578500 1.205473 603.7266
531500 1578550 1.304764 528.1357
531500 1578600 1.29202 468.6926
531500 1578650 1.373585 409.7624
531500 1578700 1.44607 352.1913
531500 1578750 1.518455 296.9245
531500 1578800 1.57693 248.4159
531500 1578850 1.592696 215.1598
531500 1578900 1.543631 204.5012
531500 1578950 1.430956 213.0877
531500 1579000 1.279126 229.3216
531500 1579050 1.112369 244.2841
531500 1579100 0.946441 254.4648
531500 1579150 0.790715 259.5101
531500 1579200 0.650363 259.8808
531500 1579250 0.527289 255.4361
531500 1579300 0.415461 245.3365

80
531500 1579350 0.324952 228.508
531500 1579400 0.249196 206.2647
531500 1579450 0.190888 183.2085
531500 1579500 0.155107 165.9022
531500 1579550 0.143223 156.8026
531500 1579600 0.149493 151.4468
531500 1579650 0.165013 142.3192
531500 1579700 0.185126 121.944
531500 1579750 0.203093 91.77877
531500 1579800 0.221645 93.57294
531550 1578450 1.198929 709.3657
531550 1578500 1.296667 625.6188
531550 1578550 1.330856 566.9057
531550 1578600 1.299624 508.0949
531550 1578650 1.367457 450.9009
531550 1578700 1.418487 396.686
531550 1578750 1.463066 346.4839
531550 1578800 1.491333 303.5382
531550 1578850 1.484019 272.3099
531550 1578900 1.432444 255.0443
531550 1578950 1.337266 249.4719
531550 1579000 1.210443 249.8562
531550 1579050 1.067479 251.0229
531550 1579100 0.921784 250.5691
531550 1579150 0.783197 248.3846
531550 1579200 0.65781 244.8029
531550 1579250 0.542689 238.8602
531550 1579300 0.446933 227.4788
531550 1579350 0.362199 207.7855
531550 1579400 0.286722 179.6298
531550 1579450 0.225346 149.9676
531550 1579500 0.192622 134.6393
531550 1579550 0.194766 139.5853
531550 1579600 0.213052 147.8317
531550 1579650 0.23817 142.77
531550 1579700 0.257164 114.6513
531550 1579750 0.268261 56.25242
531550 1579800 0.271895 35.68667
531600 1578450 1.268766 732.6749
531600 1578500 1.31629 664.7632
531600 1578550 1.34365 606.5576

81
531600 1578600 1.293079 548.4621
531600 1578650 1.347467 492.7816
531600 1578700 1.379683 440.9362
531600 1578750 1.402692 393.4068
531600 1578800 1.410554 352.0479
531600 1578850 1.389216 319.0875
531600 1578900 1.3357 294.7979
531600 1578950 1.250566 277.3903
531600 1579000 1.140643 263.5913
531600 1579050 1.016237 250.6216
531600 1579100 0.888306 237.829
531600 1579150 0.766823 226.8342
531600 1579200 0.655308 219.5064
531600 1579250 0.563678 214.1728
531600 1579300 0.485473 204.9521
531600 1579350 0.414 184.7709
531600 1579400 0.34287 149.1933
531600 1579450 0.272524 101.7138
531600 1579500 0.236634 78.09995
531600 1579550 0.267026 109.3566
531600 1579600 0.307065 139.4143
531600 1579650 0.337142 147.2619
531600 1579700 0.353791 130.88
531600 1579750 0.368578 99.41452
531600 1579800 0.361537 99.54841
531650 1578450 1.28254 773.0415
531650 1578500 1.326672 704.2112
531650 1578550 1.253601 644.749
531650 1578600 1.277526 588.7532
531650 1578650 1.300763 534.9219
531650 1578700 1.336929 483.1443
531650 1578750 1.343869 436.2378
531650 1578800 1.33788 393.985
531650 1578850 1.307638 357.4193
531650 1578900 1.252962 325.884
531650 1578950 1.174335 297.726
531650 1579000 1.076064 270.6296
531650 1579050 0.965327 242.9461
531650 1579100 0.85125 215.4474
531650 1579150 0.742971 192.8335
531650 1579200 0.65356 181.717

82
531650 1579250 0.586907 181.5307
531650 1579300 0.536266 180.7665
531650 1579350 0.4903 166.7729
531650 1579400 0.43802 131.7401
531650 1579450 0.369644 71.47305
531650 1579500 0.314758 19.79311
531650 1579550 0.391458 93.70925
531650 1579600 0.441165 139.2995
531650 1579650 0.480291 159.9894
531650 1579700 0.486481 161.8886
531650 1579750 0.478396 158.0992
531650 1579800 0.461574 171.6923
531700 1578450 1.650526 820.2921
531700 1578500 1.655119 749.1058
531700 1578550 1.242549 684.0642
531700 1578600 1.256972 628.3107
531700 1578650 1.26907 574.7049
531700 1578700 1.294534 522.7391
531700 1578750 1.289759 475.0387
531700 1578800 1.274415 430.5264
531700 1578850 1.238642 389.5958
531700 1578900 1.183787 351.0836
531700 1578950 1.110235 313.2799
531700 1579000 1.020775 274.0086
531700 1579050 0.924423 231.5823
531700 1579100 0.817349 186.2973
531700 1579150 0.718405 145.5724
531700 1579200 0.647023 128.5053
531700 1579250 0.613765 141.5393
531700 1579300 0.602343 157.7868
531700 1579350 0.59589 157.4397
531700 1579400 0.584459 136.0676
531700 1579450 0.565591 101.1947
531700 1579500 0.561053 85.86382
531700 1579550 0.594926 115.0704
531700 1579600 0.62905 151.5556
531700 1579650 0.635805 177.7311
531700 1579700 0.623665 193.8807
531700 1579750 0.599354 207.8907
531700 1579800 0.568183 231.5667
531750 1578450 1.653658 860.7503

83
531750 1578500 1.654057 788.3017
531750 1578550 1.528744 727.6088
531750 1578600 1.514828 671.0129
531750 1578650 1.237413 612.8373
531750 1578700 1.234694 560.9915
531750 1578750 1.241824 510.5532
531750 1578800 1.217041 463.492
531750 1578850 1.181562 417.9273
531750 1578900 1.127715 373.3245
531750 1578950 1.059187 327.6715
531750 1579000 0.987112 279.0873
531750 1579050 0.892679 224.1894
531750 1579100 0.793439 161.661
531750 1579150 0.696106 93.03087
531750 1579200 0.633132 56.68393
531750 1579250 0.648617 102.5198
531750 1579300 0.684425 141.091
531750 1579350 0.724652 154.3294
531750 1579400 0.7645 146.0639
531750 1579450 0.793178 128.4292
531750 1579500 0.828443 120.9678
531750 1579550 0.844543 135.4362
531750 1579600 0.838411 163.6938
531750 1579650 0.811472 193.7904
531750 1579700 0.771506 221.1542
531750 1579750 0.72513 248.2155
531750 1579800 0.710109 281.1629
531800 1578450 1.513829 944.0417
531800 1578500 1.637746 840.2828
531800 1578550 1.513008 765.8229
531800 1578600 1.492994 708.6275
531800 1578650 1.468176 653.1028
531800 1578700 1.436774 599.3284
531800 1578750 1.200581 543.74
531800 1578800 1.171977 493.8048
531800 1578850 1.161056 447.1053
531800 1578900 1.103914 396.7
531800 1578950 1.036277 344.9373
531800 1579000 0.959811 289.8969
531800 1579050 0.877175 229.4427
531800 1579100 0.791895 161.5155

Spatial analysis of dissolved oxygen levels using Ordinary Kriging methods near the confluence of Bozeman Creek and the East Gallatin River in Bozeman, Montana

Spatial analysis of dissolved oxygen levels using Ordinary Kriging methods near the confluence of Bozeman Creek and the East Gallatin River in Bozeman, Montana

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Spatial analysis of dissolved oxygen levels using Ordinary Kriging methods near the confluence of Bozeman Creek and the East Gallatin River in Bozeman, Montana