1
CRWR Online Report 98-4
An Analysis of
Volunteer Water Quality Data
by
Charles Kaough, M.S. EHE.
and
Dr. David R. Maidment, PhD.
Principal Investigator
May 1998
CENTER FOR RESEARCH IN WATER RESOURCES
Bureau of Engineering Research ? The University of Texas at Austin
J.J. Pickle Research Campus ? Austin, TX 78712-4497
This document is available online via World Wide Web at
http://www.ce.utexas.edu/centers/crwr/reports/online.htm
2
Acknowledgements
I wish to thank Dr. David R. Maidment for supervising and guiding me through this re-
search and Michael Barrett, my reader, who kept me on track with my work. I wish, also
to thank Steven Hubbell, Jason Pinchback, John Wedig and Diane Spinney at the Lower
Colorado River Authority who furnished me with data and much assistance. Also, I wish
to express deep gratitude to my wife, Monica, and children, Maya and Elena, who gave
me support and encouragement throughout graduate school.
3
TABLE OF CONTENTS
1 INTRODUCTION............................................................................................................................... 8
1.1 THE NEED FOR VOLUNTEER WATER QUALITY MONITORING ........................................................... 9
1.2 CREDIBILITY OF VOLUNTEER DATA................................................................................................ 12
1.3 THE GOALS OF THE COLORADO RIVER WATCH NETWORK: ............................................................ 14
2 LITERATURE REVIEW................................................................................................................. 15
3 STATISTICAL ANALYSIS............................................................................................................. 21
3.1 GOALS OF STATISTICAL ANALYSIS ................................................................................................. 22
3.2 DESCRIPTION OF THE STATISTICAL ANALYSIS ................................................................................ 23
3.3 CHOOSING SITES TO ANALYZE......................................................................................................... 28
3.4 PARAMETERS STUDIED AND MEASUREMENT METHODS ................................................................. 32
3.5 PARALLEL MEASUREMENTS ANALYSIS........................................................................................... 34
4 FOURIER ANALYSIS OF WATER QUALITY DATA............................................................... 36
4.1 THEORY .......................................................................................................................................... 36
4.2 SET-UP............................................................................................................................................ 37
4.3 RESULTS.......................................................................................................................................... 41
4.4 CONCLUSION................................................................................................................................... 47
5 STUDY RESULTS ............................................................................................................................ 48
5.1 LAKE AUSTIN.................................................................................................................................. 48
5.2 BASTROP ......................................................................................................................................... 61
5.3 SMITHVILLE .................................................................................................................................... 75
5.4 LAGRANGE ..................................................................................................................................... 88
6 SUMMARIES AND CONCLUSIONS .......................................................................................... 116
7 BIBLIOGRAPHY ........................................................................................................................... 122
APPENDIX................................................................................................................................................ 124
RAW DATA ............................................................................................................................................. 124
4
TABLE OF TABLES
TABLE 3-1 CRITICAL VALUES, PROBABILITY PLOT....................................................................................... 25
TABLE 3-2 SPREADSHEET FOR QUANTILE PLOT............................................................................................ 25
TABLE 3-3 CRWN SEASONAL DATA DISTRIBUTION..................................................................................... 28
TABLE 4-1 RAW DATA EXAMPLE.................................................................................................................. 37
TABLE 4-2 REGRESSION STATISTICS, EXCEL OUTPUT................................................................................... 40
TABLE 4-3 REGRESSION STATISTICS, J=1...................................................................................................... 41
TABLE 4-4 SUMMARY OF MEANS, DO, J=1 AND J=2..................................................................................... 47
TABLE 5-5-1 DESCRIPTIVE STATISTICS, DO- LAKE AUSTIN ......................................................................... 48
TABLE 5-5-2 DESCRIPTIVE STATISTICS COMBINED DATA, DO- LAKE AUSTIN............................................. 49
TABLE 5-5-3 T-TEST RESULTS, DO- LAKE AUSTIN ....................................................................................... 52
TABLE 5-5-4 STANDARD ERROR OF THE MEAN, DO- LAKE AUSTIN............................................................. 53
TABLE 5-5 REGRESSION STATISTICS- LCRA1- LAKE AUSTIN ...................................................................... 55
TABLE 5-6 REGRESSION STATISTICS- CRWN1- LAKE AUSTIN..................................................................... 55
TABLE 5-7 SUMMARY OF MEANS- LAKE AUSTIN.......................................................................................... 56
TABLE 5-8 DESCRIPTIVE STATISTICS, TDS- LAKE AUSTIN........................................................................... 58
TABLE 5-9 RESULT OF THE T-TEST- TDS- LAKE AUSTIN .............................................................................. 59
TABLE 5-10 DESCRIPTIVE STATISTICS, DO- BASTROP................................................................................. 61
TABLE 5-11 DESCRIPTIVE STATS. COMBINED DATA- BASTROP.................................................................... 62
TABLE 5-12 T-TEST RESULTS, DO- BASTROP................................................................................................ 65
TABLE 5-13 STANDARD ERROR OF THE MEAN, DO-BASTROP ...................................................................... 65
TABLE 5-14 REGRESSION STATISTICS, DO-LCRA2...................................................................................... 68
TABLE 5-15 REGRESSION STATISTICS, DO-CRWN2 .................................................................................... 69
TABLE 5-16 SUMMARY OF MEANS, DO- BASTROP ....................................................................................... 70
TABLE 5-17 DESCRIPTIVE STATISTICS, TDS- BASTROP ................................................................................ 71
TABLE 5-18 T-TEST RESULTS, TDS- BASTROP.............................................................................................. 72
TABLE 5-19 DESCRIPTIVE STATISTICS, DO- SMITHVILLE ............................................................................. 75
TABLE 5-20 T-TEST RESULTS, DO- SMITHVILLE........................................................................................... 78
TABLE 5-21 STANDARD ERROR OF THE MEAN, DO- SMITHVILLE................................................................. 78
TABLE 5-22 STANDARD ERROR OF THE MEAN, DO- COMBINED DATA- SMITHVILLE................................... 79
TABLE 5-23 DESCRIPTIVE STATISTICS, DO- COMBINED DATA- SMITHVILLE ............................................... 80
TABLE 5-24 REGRESSION STATISTICS- DO- LCRA3 .................................................................................... 80
TABLE 5-25 REGRESSION STATISTICS- DO- CRWN3 ................................................................................... 81
TABLE 5-26 SUMMARY OF MEANS, DO- SMITHVILLE .................................................................................. 82
TABLE 5-27 DESCRIPTIVE STATISTICS, TDS- SMITHVILLE ........................................................................... 84
TABLE 5-28 T-TEST RESULTS, TDS- SMITHVILLE ......................................................................................... 85
5
TABLE 5-29 DESCRIPTIVE STATISTICS, DO- LAGRANGE .............................................................................. 88
TABLE 5-30 DESCRIPTIVE STATISTICS, COMBINED DATA, DO- LAGRANGE ................................................ 89
TABLE 5-31 T-TEST RESULTS, DO- LAGRANGE............................................................................................ 92
TABLE 5-32 DESCRIPTIVE STATISTICS W/O OUTLIER DATA, DO- LAGRANGE.............................................. 93
TABLE 5-33 STANDARD ERROR OF THE MEAN, DO- LAGRANGE ................................................................. 95
TABLE 5-34 STANDARD ERROR OF THE MEAN W/O OUTLIER DATA, DO- LAGRANGE ................................. 95
TABLE 5-35 REGRESSION STATISTICS, DO- LCRA4..................................................................................... 96
TABLE 5-36 REGRESSION STATISTICS, DO- CRWN4 ................................................................................... 96
TABLE 5-37 SUMMARY OF MEANS, DO- LAGRANGE ................................................................................... 98
TABLE 5-38 DESCRIPTIVE STATISTICS, TDS- LAGRANGE .......................................................................... 100
TABLE 5-39 T-TEST RESULTS, TDS- LAGRANGE ........................................................................................ 101
TABLE 5-40 DESCRIPTIVE STATISTICS, DO- COLUMBUS ............................................................................ 103
TABLE 5-41 DESCRIPTIVE STATISTICS, COMBINED DATA SETS, DO- COLUMBUS ...................................... 104
TABLE 5-42 T-TEST RESULTS, DO- COLUMBUS .......................................................................................... 107
TABLE 5-43 STANDARD ERROR OF THE MEAN, DO- COLUMBUS................................................................ 107
TABLE 5-44 REGRESSION STATISTICS, DO- LCRA5................................................................................... 109
TABLE 5-45 REGRESSION STATISTICS, DO- LCRA5................................................................................... 110
TABLE 5-46 SUMMARY OF MEANS, DO- COLUMBUS.................................................................................. 111
TABLE 5-47 DESCRIPTIVE STATISTICS, TDS- COLUMBUS........................................................................... 112
TABLE 5-48 T-TEST RESULTS, TDS- COLUMBUS ........................................................................................ 113
TABLE 6-1 SUMMARY OF DATA, DO........................................................................................................... 116
TABLE 6-2 SUMMARY OF DATA, TDS......................................................................................................... 117
TABLE 6-3 SUMMARY OF DATA, DO, T-TESTS ............................................................................................ 117
TABLE 6-4 SUMMARY OF DATA, TDS, T-TESTS .......................................................................................... 117
TABLE 6-5 SUMMARY OF DATA, MEANS, DO AND TDS............................................................................. 118
6
TABLE OF FIGURES
FIGURE 1-1 FROM TNRCC?S QAAP DOCUMENT ............................................................................................. 8
FIGURE 1-2 FROM TNRCC?S QAAP DOCUMENT ............................................................................................. 9
FIGURE 3-1 QUANTILE PLOT ......................................................................................................................... 26
FIGURE 3-2 MAP OF MONITORING SITES ....................................................................................................... 29
FIGURE 3-3 PARALLEL TESTING PLOT, DO ................................................................................................... 35
FIGURE 3-4 PARALLEL TESTING PLOT, TDS ................................................................................................. 35
FIGURE 4-1 DO SCATTER PLOT..................................................................................................................... 37
FIGURE 4-2 SPREADSHEET LAYOUT FOR FOURIER ANALYSIS ....................................................................... 38
FIGURE 4-3 SPREADSHEET FORMULAS FOR FOURIER ANALYSIS ................................................................... 38
FIGURE 4-4 EXCEL REGRESSION TOOL.......................................................................................................... 39
FIGURE 4-5 EXCEL REGRESSION TOOL WINDOW .......................................................................................... 39
FIGURE 4-6 PLOT OF REGRESSION RESULTS, J=2 .......................................................................................... 42
FIGURE 4-7 PLOT OF REGRESSION RESULTS, J=1 .......................................................................................... 42
FIGURE 4-8 EXCEL SPREADSHEET, REGRESSION PLOT.................................................................................. 43
FIGURE 4-9 CRWN DO FOURIER PLOTS, J=1 VS. J=2................................................................................... 44
FIGURE 4-10 LCRA DO FOURIER PLOTS, J=1 VS. J=2 .................................................................................. 44
FIGURE 4-11 DO FOURIER PLOT, LCRA VS CRWN, J=1 ............................................................................ 45
FIGURE 4-12 DO FOURIER PLOT, LCRA VS CRWN, J=2 ............................................................................. 46
FIGURE 5-1 QUANTILE PLOT, DO- CRWN1 ................................................................................................. 50
FIGURE 5-2 QUANTILE PLOT, DO- LCRA1................................................................................................... 50
FIGURE 5-3 HISTOGRAMS, DO- LAKE AUSTIN.............................................................................................. 51
FIGURE 5-4 STANDARD ERROR OF THE MEAN, DO- LCRA1 ........................................................................ 53
FIGURE 5-5 STANDARD ERROR OF THE MEAN, DO- CRWN1....................................................................... 54
FIGURE 5-6 FOURIER PLOT- LAKE AUSTIN.................................................................................................... 56
FIGURE 5-7 SCATTER PLOT, TDS- LAKE AUSTIN.......................................................................................... 57
FIGURE 5-8 HISTOGRAMS, TDS- LAKE AUSTIN ............................................................................................ 59
FIGURE 5-9 STANDARD ERROR OF THE MEAN- TDS- LCRA1 ...................................................................... 60
FIGURE 5-10 STANDARD ERROR OF THE MEAN- TDS- CRWN1................................................................... 60
FIGURE 5-11 QUANTILE PLOT, DO- CRWN2 ............................................................................................... 63
FIGURE 5-12 QUANTILE PLOT, DO- LCRA2................................................................................................. 63
FIGURE 5-13 HISTOGRAMS, DO- BASTROP ................................................................................................... 64
FIGURE 5-14 STANDARD ERROR OF THE MEAN, DO- LCRA2 ...................................................................... 66
FIGURE 5-15 STANDARD ERROR OF THE MEAN, DO- CRWN2..................................................................... 67
FIGURE 5-16 SCATTER PLOT, TDS- BASTROP............................................................................................... 68
FIGURE 5-17 FOURIER PLOT, DO- BASTROP ................................................................................................. 69
FIGURE 5-18 SCATTER PLOT, TDS- BASTROP............................................................................................... 71
7
FIGURE 5-19 HISTOGRAMS, TDS- BASTROP ................................................................................................. 72
FIGURE 5-20 STANDARD ERROR OF THE MEAN, TDS- LCRA2 .................................................................... 73
FIGURE 5-21 STANDARD ERROR OF THE MEAN TDS, CRWN2..................................................................... 73
FIGURE 5-22 QUANTILE PLOT, DO- CRWN3 ............................................................................................... 76
FIGURE 5-23 QUANTILE PLOT DO, LCRA3 .................................................................................................. 76
FIGURE 5-24 HISTOGRAMS, DO- SMITHVILLE .............................................................................................. 77
FIGURE 5-25 FOURIER PLOT, DO- SMITHVILLE............................................................................................. 81
FIGURE 5-26 SCATTER PLOT, TDS- SMITHVILLE .......................................................................................... 83
FIGURE 5-27 HISTOGRAMS, TDS- SMITHVILLE............................................................................................. 85
FIGURE 5-28 STANDARD ERROR OF THE MEAN, TDS- CRWN3 ................................................................... 86
FIGURE 5-29 STANDARD ERROR OF THE MEAN, TDS- LCRA3 .................................................................... 86
FIGURE 5-30 HISTOGRAMS, DO- LAGRANGE ............................................................................................... 90
FIGURE 5-31 QUANTILE PLOT, DO- CRWN4 ............................................................................................... 91
FIGURE 5-32 QUANTILE PLOT, DO- LCRA4................................................................................................. 91
FIGURE 5-33 STANDARD ERROR OF THE MEAN, DO- CRWN4..................................................................... 93
FIGURE 5-34 STANDARD ERROR OF THE MEAN, DO- LCRA4 ...................................................................... 94
FIGURE 5-35 CRWN4 FOURIER PLOT, DO WITH DATA ................................................................................ 97
FIGURE 5-36 FOURIER PLOT, DO- LAGRANGE ............................................................................................. 98
FIGURE 5-37 SCATTER PLOT, TDS- LAGRANGE ........................................................................................... 99
FIGURE 5-38 HISTOGRAMS, TDS- LAGRANGE............................................................................................ 100
FIGURE 5-39 STANDARD ERROR OF THE MEAN, TDS- LCRA4 .................................................................. 101
FIGURE 5-40 STANDARD ERROR OF THE MEAN, TDS- CRWN4 ................................................................. 102
FIGURE 5-41 QUANTILE PLOT, DO- CRWN5 ............................................................................................. 105
FIGURE 5-42 QUANTILE PLOT, DO- LCRA5............................................................................................... 105
FIGURE 5-43 HISTOGRAMS, DO- COLUMBUS.............................................................................................. 106
FIGURE 5-44 STANDARD ERROR OF THE MEAN, DO- CRWN5................................................................... 108
FIGURE 5-45 STANDARD ERROR OF THE MEAN, DO- LCRA5 .................................................................... 109
FIGURE 5-46 FOURIER PLOT, DO- COLUMBUS............................................................................................ 110
FIGURE 5-47 SCATTER PLOT, TDS- COLUMBUS ......................................................................................... 111
FIGURE 5-48 HISTOGRAMS, TDS- COLUMBUS............................................................................................ 113
FIGURE 5-49 STANDARD ERROR OF THE MEAN, TDS- LCRA5 .................................................................. 114
FIGURE 5-50 STANDARD ERROR OF THE MEAN, TDS- CRWN5 ................................................................. 114
FIGURE 6-1 DO MEAN VALUES .................................................................................................................. 118
FIGURE 6-2 DO MEAN VALUES, FOURIER METHOD ................................................................................... 119
FIGURE 6-3 MEAN VALUES, TDS................................................................................................................ 119
FIGURE 6-4 LCRA MEAN VALUES, DO- STANDARD VS. FOURIER ............................................................. 120
FIGURE 6-5 CRWN DO MEAN VALUES, STANDARD VS. FOURIER ............................................................. 121
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1 INTRODUCTION
The quality of our lives, indeed, our society is related to the quality of our water.
Water is an essential element for life. With our population growing and more humans
living in urban environments, we are faced with challenges to keep our water quality high
and thus our standard of living high. Only recently have we become aware of how our
lifestyles effect the quality of our water
The scientific community has done much to quantify water quality and develop
methods to preserve and improve it. The government has attempted to use these ad-
vancements in science and technology by developing legislation such as the Clean Water
Act. Designated uses and water quality standards to support these designations have been
set for our streams, lakes, bays and estuaries as mandated by the Clean Water Act. States
adopt EPA-approved standards for their waters that define water quality goals for indi-
vidual waterbodies. Standards consist of designated beneficial uses to be made of the
water, criteria to protect those uses, and antidegradation provisions to protect existing
water quality
1
. States are required by law to systematically assess and report on the qual-
ity of their waters regularly and thoroughly, according to section 305b of the Clean Water
Act.
The task of assessing the quality of all of our bodies of water is a huge task and
requires a immense amount of data. According to the EPA National Water Quality In-
ventory: 1992 Report to Congress only 643,000 miles of the estimated 3.5 million river
miles in the United States have been assessed (Figure 1-1). More than one-fourth of the
1
1972 Clean Water Act (Federal Water Pollution Control Act), Section 305b and 1987 ,
Section 319.
9
assessed water bodies have been found to be pollution impaired waters as shown in Fig-
ure 1-2.
Figure 1-1 from TNRCC?s QAAP document Figure 1-2 from TNRCC?s QAAP docu-
ment
1.1 The Need For Volunteer Water Quality Monitoring
States are faced with both the huge task of assessing the quality of the water in the
state and limited resources, financial and human, to accomplish the task. Volunteer water
quality monitoring programs have the potential to contribute a great deal to both provid-
ing the necessary data and contributing to maintaining or improving the quality of our
waters.
10
Also, volunteer monitoring programs provide a means for citizens to become bet-
ter stewards of the watershed they live in. This quote from the EPA document The Qual-
ity of Our Nations Water describes this:
"The EPA encourages each citizen to become a steward of our precious natural
resources. Complex environmental threats and diminishing funds for pollution
control force us to jointly solve the pollution problems that foul our beaches
and lakes or close our favorite fishing sites. We need to understand these
problems and become a part of their solution. Once we understand these pollu-
tion problems and what is needed to combat them, we will be better able to
prioritize our efforts, devise sound solutions, take appropriate action, monitor
progress after solutions are implemented, and modify behavior that contributes
to the problems.
3
"
In Texas the need for volunteer monitoring is great. According to the Texas
Natural Resource Conservation Commission?s (TNRCC) Texas Watch, which coordinates
state-wide volunteer monitoring programs, four factors create the need for volunteer envi-
ronmental monitoring in Texas:
1) Texas has a large number of water bodies (about 11,247 rivers and streams
large enough to be named) with 191,228 miles of rivers and streams;
2) Texas?s population is projected to increase by 59% through the year 2030;
3) Since 1992 TNRCC funding for surface water quality monitoring has
dropped from approximately $1,108,000 to $800,000 in 1996;
11
4) Senate Bill 818, the Clean Rivers Program, states there is a lack of suffi-
cient water quality data needed for state and local governments to make
environmentally sound decisions
2
.
The scientific community, however, is skeptical about the usefulness of data ob-
tained by citizen monitors. As noted in a master?s report by Fatima Paiva, Volunteer En-
vironmental Monitoring Programs: A Planning Framework, ?Data credibility is the big-
gest threat to the future of volunteer monitoring programs.?
Efforts are being made by citizen monitoring organizations on the national and
state levels to develop methods to insure that this data is valid and useful. The goal of
this report is to assess the credibility of data collected by citizen monitoring organiza-
tions. The data and methods of the state organization, the TNRCC's Texas Watch, and a
regional organization, the Lower Colorado River Authority?s (LCRA) Colorado River
Watch Network will be used as examples.
According to Steven Hubbell, Activity Manager of the Colorado River Watch
Network, there is a need for the methodology of volunteer monitoring organizations to be
scrutinized by the scientific community. This scrutiny will help improve and legitimize
the efforts of these organization. It is the intention of this report to scrutinize the methods
of volunteer monitoring, the Texas Watch and the Colorado River Watch Network, and
determine if the data collected by these organizations is useful to environmental engi-
neers, policy makers and the scientific community.
2
Texas Natural Resource Conservation Commission, Quality Assurance Project Plan,
Texas Watch (Austin, Texas: January 2, 1998)
12
1.2 Credibility of Volunteer Data
The EPA has issued guidelines through its Office of Water for volunteer organiza-
tions to use to insure that its monitoring program is credible. The organization of the
TNRCC?s Texas Watch and the LCRA?s Colorado River Watch Network are based on
these guidelines. The following is the general outline of the recommendations
3
:
1. Establishing a Pilot Program
a) Pick a location
b) Select sampling equipment
c) Design a data collection form
d) Recruit volunteers
e) Train volunteers
f) Conduct ongoing quality control
g) Refine program materials
2. Expand the Program
3. Maintain Volunteer Interest and Motivation
4. Prepare a Quality Assurance Project Plan (QAPP)
a) Project description
b) Project organization and responsibilities
c) Quality Assurance objectives
d) Sampling procedures
3
U.S. Environmental Protection Agency, Volunteer Water Monitoring: A Guide For
State Managers, Office of Water (Washington, D.C.: Government Printing Office,
August 1990)
13
e) Sample custody
f) Calibration procedures and frequency
g) Analytical procedures
h) Data reduction, validation and reporting
i) Internal quality control checks
j) Performance and system audits
k) Preventative maintenance
l) Specific routine procedures used to assess data precision, accuracy and
completeness.
m) Corrective action
n) Quality assurance reports
These guidelines illustrate the thoroughness of the efforts of the Texas Watch and the
Colorado River Watch Network to produce credible data. These projects must adopt
protocols that are straightforward enough for volunteers to master and yet sophisticated
enough to generate data of value to resource managers.
The EPA requires that all volunteer organizations that use EPA funds produce a
Quality Assurance Project Plan (QAPP). It is recommended that organizations that do
not use EPA funds also adopt a QAPP. The first task in this plan is to establish the goals
of the organization. Some of the goals could be:
? primarily education oriented
? collect data that can be used in making water quality management decisions
14
Projects with the second goal might be called primarily data oriented. Data ori-
ented volunteer organizations must show that the measured data is credible. The credi-
bility of the data is indicated by having the following attributes:
? consistent over time and within projects and group members
? collected and analyzed using standardized and acceptable techniques
? comparable to data collected in other assessments using the same methods
1.3 The Goals of the Colorado River Watch Network
4
:
1.Maintain a motivated volunteer monitoring network committed to preserving the
integrity of the Colorado River Watershed.
2.Provide educational opportunities about water quality and the environment to the
communities in the Lower Colorado River Authority (LCRA) service area.
3.Complement and assist the LCRA with its watershed monitoring effort and act as an
early warning system alerting the LCRA to potential water quality threats.
The quality assurance plan:
? details a project?s standard operating procedures in the field and lab,
? outlines project organization,
? address issues such as training requirements, instrument calibration, and internal
checks on how data are collected, analyzed, and reported.
The quality of the CRWN data will be assessed using statistical techniques.
4
Colorado River Watch Network, Technical Instructions, Fifth Edition(Austin, Texas:
May 1996)
15
2 LITERATURE REVIEW
The focus of this report has been on the reliability of volunteer water quality data.
There has been great quantity of material written on water quality monitoring techniques,
water quality modeling and data analysis. There is also a large quantity of material writ-
ten on probability and statistics in general and specifically for hydrologic data. However,
a search of the literature did not uncover any work which was specifically concerning the
comparison of data sets from volunteer and professional monitors except in parallel
studies where the measurements were taken at the same point and time and then com-
pared.
There is wealth of information on quality control and quality assurance of water
quality data collected by volunteer monitors in publications by the U.S. Environmental
Protection Agency, the Texas Natural Resource Conservation Commission, and by indi-
vidual monitoring organizations such as the LCRA?s Colorado River Watch Network. An
example is a detailed discussion of statistical analysis of parallel studies in a series of ar-
ticles in "The Volunteer Monitor" the national newsletter of volunteer water quality
monitoring published by the EPA. This newsletter format is very informative because a
variety of techniques and applications from various monitoring groups around the coun-
try were compiled and discussed. Using the newsletter format of communicating, the
"Volunteer Monitor" was able to first publish a call for articles from its readers on the
specific topic of statistical techniques used to quantify how well monitoring techniques
were working and the accuracy of monitoring methods. A collection of the short articles
was then published in the following publication of the newsletter. Articles detailing spe-
16
cific monitoring techniques, the lab methods, organizational forms, political issues and its
application to water quality issues are all discussed in the newsletters.
The EPA has a number of publications aimed specifically at volunteer water
monitoring and quality assurance. A particularly useful document used in this study is
Volunteer Water Monitoring: A Guide For State Managers. This document provides
guidelines for statewide monitoring programs with emphasis on quality assurance and
quality control. There were some basic statistical techniques discussed and the methods
of analyzing and communicating the information gathered by the monitors.
Another particularly useful document from the EPA is EPA Requirements for
Quality Assurance Project Plans (QAPP) for Environmental Data. The purpose of this
document is to provide volunteer monitoring programs with the information they need to
develop a quality assurance project plan. Specific statistical techniques for assessing data
quality are discussed.
The TNRCC?s Quality Assurance Project Plans is a document intended to provide
guidance for monitoring programs to assure data quality. This document is similar to the
EPA?s QAPP document except that it has the purpose of standardizing the structure and
monitoring techniques of volunteer monitoring programs in Texas in order to integrate
the data into the TNRCC?s data base.
Many of the statistical analysis techniques used for the study came from a class
exercise from Dr. David Maidment?s CE397: Environmental Risk Assessment Class, De-
partment of Civil Engineering, The University of Texas at Austin, Spring 1998. The ex-
ercise covered the use of statistics, using the statistical tools in Microsoft?s Excel, to de-
17
scribe the nature of data sets, distribution analysis, and the properties of the mean of the
data. The methods for interpreting the descriptive statistics is discussed such as:
1. Determining the best form to use for analysis, original or transformed
2. Use of the frequency histogram to visually assess the nature of the distribution of the
data set.
3. Standard Error of the mean to determine if there is a correlation between the number
of data points in the data sets and the precision in the result.
4. The difference in the means of two data sets (t-test) to compare two independently
obtained data sets and when it is appropriate to use this technique.
The exercise contained detailed discussion and examples of the use of these sta-
tistical techniques using environmental data.
Water Quality Monitoring and Water Quality Assessments are books published for
the United Nation?s Environment Program discussing the form of monitoring organiza-
tions and the techniques used to accomplish the stated goals of a monitoring organization.
The technical and organizational structures needed to assure that quality data is collected
is provided.
Water Quality Assessment was particularly useful for this study because it dis-
cussed the use of statistics and their application specifically to water quality data. De-
tailed procedures, examples and interpretations of the results were given. The techniques
used were based on the goals of the sampling techniques utilized and the questions that
one wants to have answered by the statistical analysis. The following topics relevant to
this study were discussed:
18
1. The use of basic statistics to summarize and assess small or large, simple or complex
data sets.
2. The use of descriptive statistics to summarize water quality data sets into simpler and
more understandable forms.
3. How to determine the distribution of the data sets.
4. The construction and interpretation of cumulative distribution plots and histograms.
5. The types of methods to use based on the type of distribution of the data.
6. Standard error of the mean analysis.
7. Hypothesis testing, the t-test.
8. Regression analysis and the use of a trigonometric function.
The author also went into some detail about graphical presentation of the results,
how to most effectively summarize water quality characteristics.
The Handbook of Hydrology has several chapters dedicated to statistical analysis
of hydrologic data. There is a very useful discussion on the basic concepts of statistical
techniques and their application specifically to hydrologic data. Some of the topics cov-
ered included:
1. Histograms and the choice of class intervals utilized for the histogram
2. Quantile plots
3. Hypothesis testing, the t-test and its use for comparing data sets.
4. Multiple regression technique.
Handbook of Hydrology described in detail the use of the sinusoidal function to
describe the periodic functions of a time variable. The basic formula used in this study
19
for the Fourier analysis and the various forms of the function to describe the type of cycle
that is to be modeled is discussed.
Applied Hydrology, a hydrology textbook, provided the information for con-
structing the quantile plots used in the study. The section on probability plotting dis-
cussed the method of transforming the data to a special probability value for accurately
determining whether the data had a normal distribution.
Tips for Statistical Analyses of Parallel Studies, an article by Woodrow Setzer in
"The Volunteer Monitor" examined the statistical methods used for Often the main rea-
son for doing parallel testing is to assure government agencies that the data collected by
volunteers is reliable enough form the agencies to use. The article points out that parallel
testing has been done consistently, resulting in attitude changes toward volunteer data.
Another equally important reason for the parallel testing is for the volunteer programs
own internal use. The results of these tests can point out the program?s strengths and
weaknesses. Problems can be spotted with these tests and ways to make improvements
can be worked out.
These tests are also good for the moral of the volunteer monitors. They appreci-
ate that their efforts as volunteer monitors is being taken seriously and that the quality of
their measurements is being taken into account.
The Handbook of Hydrology has a chapter specifically about statistics and hydrologic
data. Specific information on basic statistics and more sophisticated statistical analysis
can be found there. This chapter examines the difficulty of explaining or predicting hy-
drologic variables and the sources of uncertainty. It is pointed out how the type of infor-
mation used for this study is observational data, rather than experimental. This means
20
that the conditions from which the measured samples are taken can not be duplicated like
one would do in a laboratory experiment. The sources of uncertainty under with hydro-
logic systems are:
1) The inherent randomness of the driving variables and the hydrologic system
2) Sampling error due to the fact that the measured sample is a very small part of large
population.
3) Incorrect understanding of the processes involved. For instance, understanding the
influences on the levels of DO or TDS and how they may vary even over the distance
between where the volunteer monitor takes measurements versus the professional
monitor.
The concept of using statistics to go beyond simply describing the larger population is
examined. The use of statistics to quantify the uncertainty in the knowledge about the
population is explained. Knowledge of the magnitude of the uncertainties is essential to
identifying those areas where it will be worthwhile to collect additional data. In the case
of this study, statistics are used to quantify if the additional data collected by volunteers
can be a valuable addition to the data collected by professional monitors.
Very detailed explanation of statistical methods for water resource data can be
found in Statistical Methods in Water Resources. One particularly useful discussion is in
regards to "outlier data", data points whose values are quite different than others in the
data set. Outlier data was a concern in this study due to the effects it had on the statistical
methods, such as causing larger values of skewness to the data set than if the outlier data
value was not included. This reference also contains detailed discussions of distribution
plots, regression analysis, and histograms.
21
3 STATISTICAL ANALYSIS
Statistics is the science that deals with the collection, tabulation, and analysis of numeri-
cal data. The properties of a population are assessed based on the properties of a sample from
that population. A measure of the uncertainty of the knowledge of this population can be deter-
mined by statistics. One can also determine if independent data sets are statistically different.
Intuitively one can see that uncertainty would decrease by increasing the number of sam-
ples from the population. Statistics provides a way of quantifying this. For this study, statistics
will be used to determine if the increase in the number of water quality samples allowed by vol-
unteer monitoring programs will have a significant effect on decreasing the uncertainty in esti-
mation of population parameters.
This science is particularly important for the task of assessing the quality of a body of
water. Water quality assessment relies heavily on statistics since, typically, the overall quality of
an entire water body is assessed by a set of grab samples taken at one moment and at one or a
few locations on that water body. Natural bodies of water are constantly changing, physically
and chemically. There are many processes, natural and those caused by man, effecting the pa-
rameters used to assess the quality of a water body. The chemical constituents which are meas-
ured to assess water quality are constantly being affected by biological, chemical and physical
processes over varying temporal cycles, daily, seasonal and climatic. Random events such as
storm events have an effect on water quality.
Federal environmental regulations have forced states to define uses for the main water
bodies in the state and the water quality parameters used to determine if the quality of the water
is sufficient for that use. Typically, the quality of a river segment or lake is assessed by small
samples, only millileters in volume, drawn from a few points on the water body. These samples
22
are drawn infrequently, only several times a year for the typical water quality assessment pro-
grams.
In this study basic descriptive statistics and other statistical methods will be used to as-
sess the characteristics of water quality data collected by volunteer monitors. Any statistical
analysis begins by stating the goals of the analysis.
3.1 Goals of Statistical Analysis
1) Determine the nature of the data sets using basic statistical methods.
2) Statistically compare the professional and volunteer data sets collected at the same site or sites
very close to one another. Evaluate which methods are best to compare them.
3) Estimate the increase in confidence that the sample represents the population with the addition
of volunteer data.
4) Compare the water quality data collected at different sites within the same river segment.
5) Determine the increase in data confidence when volunteer data is combined with professional
data (at the same site).
6) Over a given time interval, estimate whether there is a substantial increase confidence in the
data with the increase in data measurements inherent with volunteer data.
23
3.2 Description of the Statistical Analysis
a) Descriptive Statistics: the mean, median, variance, standard deviation, skewness, and range.
These statistics indicate the type of distribution you are dealing with. This information is useful
for making decisions on how to handle the data statistically. For instance, highly skewed data
with a large range may require using the logarithms of the data for the analysis. These basic
statistics were determined using the Descriptive Statistics tool built into Microsoft Excel.
1. What kind of distribution is indicated? It is important to know to what degree the data
follows a normal distribution. Most of the statistical procedures used in this analysis require the
data to be normally distributed to be fully valid.
2. Are the mean, mode and median values close to each other? A normal distribution is
indicated if the mean and median of the data set are nearly equal.
3. How big is the standard deviation? This value gives and indication of the spread of the
data value around the mean. Coupled with the mean, the standard deviation gives a good indica-
tion of the range of values in the data set.
4. What is the skewness and kurtosis values? The skewness is a measure of how asym-
metrically the data are distributed about the mean. The kurtosis measures the extent to which
data are more peaked or more flat-topped than in the normal curve. Values close to zero indicate
normal distribution.
5. Do the Maximum/Minimum values fall within an expected range? This analysis can
be useful for editing bad data out of the data set. They are also useful to describe how much
variability there is in the data set.
b) Histograms: The histogram is useful visual tool for assessing the distribution of the data. If
the histogram resembles the standard, bell shaped curve of a typical normal distribution then it is
24
assumed that the data set has a normal distribution. They cannot be used for more precise
judgements such as depicting individual values.
c) Quantile Plots: Quantile plots also can be used to determine if a data set is normally distrib-
uted.
Quantile plots can be constructed by plotting the data and its probability value on special
log normal plotting paper or the data can be transformed into lognormal values and plotted. The
value of the standard normal variable, z, is used as the horizontal axis to linearize the plot; this is
equivalent to using normal probability plotting paper.
5
The following is the procedure for transforming the data:
i) Arrange the data in descending order
ii) Give each value a rank number, i, .
iii) Calculate the probability value p (Blom, 1958) for each data point:
iv) An intermediate variable w is calculated:
v) The frequency factor for normal distribution, z, is calculated using the following for-
mula:
vi) Plot the data versus the corresponding value of z.
vii) Plot the normal distribution values which correspond to the data set versus the corre-
sponding value of z using the following formula for the predicted value:
where: y is the mean of the data set, ? is the standard deviation of the data set
5
Chow V.T., Maidment D.R. and Mays L.W., "Applied Hydrology", McGraw-Hill, Inc., 1988
25
From the plot a visual inspection of how close to two plots correspond can give an indication of
whether the data is normally distributed and the effects of extreme values. A more accurate
method is to calculate the correlation coefficient of the two lines. This value can be compared to
the values in Table 3-1, which is specifically for p
i
= (i-0.375)/(n+0.25), to determine if the data
is normally distributed.
Table 3-1 Critical Values, Probability Plot
n 0.10 0.05 0.01
10 0.9347 0.9108 0.8804
15 0.9506 0.9383 0.9110
20 0.9600 0.9503 0.9290
30 0.9707 0.9639 0.9490
40 0.9767 0.9715 0.9597
50 0.9807 0.9764 0.9664
60 0.9835 0.9799 0.9710
75 0.9865 0.9835 0.9757
100 0.9893 0.9870 0.9812
300 0.99602 0.99525 0.99354
Significance Level
Probability Plot Correlation Test
Lower Critical Values of the
Statistic for the Normal Distibution.
Just one or a few outlier data points can cause the correlation coefficient to fall beyond the limits
specified in the table. If this is the case a judgement should be made as to whether these values
should be excluded from the calculation. Table 3-2 shows the spreadsheet used to construct the
quantile plot shown in Figure 3-1.
Table 3-2 Spreadsheet For Quantile Plot
I DO (mg/l) p w z DO Desc. y
1 7.1 0.01 3.04 2.27 16.15 12.06
2 7.2 0.03 2.71 1.90 13.40 11.40
3 7.4 0.04 2.52 1.70 10.80 11.04
.. .. .. .. .. .. ..
61 9.65 0.96 0.29 -1.51 5.33 5.26
62 8.10 0.97 0.23 -1.68 4.95 4.95
63 8.00 0.99 0.14 -1.95 4.30 4.46
Col. Riv. @ Beason?s Park- Columbus- Segment 1402
CRWN DATA 1402.0250
26
In this example the two extreme data values (16.15 and 13.4 mg/l) caused the correlation factor
be lower than the lower limit (0.927 vs 0.971) for normal distribution. By eliminating these val-
ues the correlation coefficient value is 0.997.
Quantile Plot- Dissolved Oxygen-- CRWN- Columbus
n=63, Correllation = 0.927
Correllation = 0.991(w/o outliers)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
Standard Normal Variable (z)
DO (m
g/l)
Figure 3-1 Quantile Plot
These results indicate that the data set has a normal distribution.
d) Standard Error of the Mean analysis: This process produces the "mean of the means" and
an estimate of their spread about that mean. The standard deviation of the mean s
x
is known as
the standard error of the mean, with which estimates of the reliability of the data mean can be
made.
How much is the standard deviation of the mean decreased with the addition of volunteer
data? Typical values of n for a calendar year are: professional data, n=6, volunteer data, n>20.
Compare the range of the 95% confidence limit (m+2sd) around the mean for each set of data.
27
e) The t-test: With the t-test one can answer the question: Are the means of the professional
and volunteer data sets statistically different? This can be done by re-stating in the form of hy-
potheses:
Null hypothesis: there is no significant difference in the means of the data sets.
Alternate hypothesis: there is a significant difference in the means of the data sets.
As noted above, it is important that the data sets be nearly normally distributed for this
test to be reliable. The value of t indicates to what degree the means of the two data sets are dif-
ferent. Each unit value of t, positive or negative, is one standard error. An absolute value of 2 for
the t-stat is an estimate of the 95% confidence limit around the mean, so an absolute value of t of
less than two indicates that there is no statistical difference between the means of the two data
sets.
Knowing that both data sets are normally distributed the t-test is used to determine if the
two data sets are statistically different from each other. The t-statistic is determined by the fol-
lowing formula:
m
S
n
S
yx
t
y
x
2
2
+
?
= where x and y are the means of the two data sets, S
2
x
and S
2
y
are the standard deviations and n and m are the number of measurements. Microsoft Excel has
the t-test as part of it?s statistical package. The t-test was done both with the above formula in
the spreadsheet and using the t-test in the software package to confirm the accuracy of the soft-
ware package.
f) Fourier Analysis. The Fourier analysis is used to analyze a data set that displays a cyclical
nature such a diurnal or seasonal cycle. An analysis of the professional and volunteer dissolved
oxygen data sets is done using the Fourier regression technique for several reasons:
28
1. Dissolved oxygen levels in natural waters vary seasonally with the temperature of the water.
The Fourier analysis is used to compare the best-fit lines of the professional and volunteer
data and the mean values for the two data sets determined by the analysis can be compared.
2. Volunteer data sets can have the general characteristic of being inconsistent temporally. This
is shown numerically in Figure 3-4. Six of the seven volunteer data sets used in this study
are from sites being monitored by high school science classes which resulted in a character-
istic of a lack of late spring and summer data for these sites. The Fourier analysis is a
method with which to predict what the measurements may have been at these sites during
these periods.
Table 3-3 CRWN Seasonal Data Distribution
Number of Samples (n)
Site Volunteer Samples
(n) %
Lake Austin 91 65
Bastrop 100 21
Smithville 37 8
LaGrange 33 15
Columbus 60 40
Warm Months (4/1-9/30)
A detailed description of the technique used is examined in the chapter for Fourier analysis
in this report.
3.3 Choosing sites to analyze
The sites for the study were chosen based on the following criteria:
1) Professional and a volunteer monitoring site are at the same location or within close proximity
(about one mile) to each other.
2) The site is on a water body with significant year-round flow.
3) The site is located on river segment identified by the TNRCC
4) At least two years of consistent volunteer monitoring data up to December 1997 are available.
29
The following is a description of the location of the monitoring sites, the location of the
volunteer sites in relation to the professional sites, the site number used for this study, the
TNRCC site number and significant features near the sites.
The sites monitored by professional monitors are called LCRA (Lower Colorado River
Authority) and the volunteer sites are called CRWN (Colorado River Watch Network).
6
Figure 3-2 Map of Monitoring Sites
Lake Austin,
LCRA 1: LCRA Site number 1403.0100 at Tom Miller Dam. This station is located over the
Colorado River thalweg at the deepest portion, a short distance up the reservoir from the dam
outlet.
CRWN 1: CRWN Site number 1403.0100 Colorado River. level 1 site; This site is approxi-
mately 0.4 miles upstream of the LCRA site.
6
Lower Colorado River Authority, The Texas Clean Rivers Program, Technical Report, (Austin,
Texas: October 1, 1996)
30
Bastrop
LCRA 2: LCRA Site number 1434.0600 in Bastrop, Texas at Loop 150. This station is located
approximately on-half mile upstream of the Bastrop wastewater treatment facility discharge.
This provides information for comparison with water quality data from stations upstream and
downstream, and will illustrate the water quality of the river before it receives effluents from
Bastrop.
CRWN 2: CRWN Site 1428.0600 (level 2) located in Bastrop, Texas at the same location as the
LCRA site.
Smithville
LCRA 3: LCRA Site number 1434.0500 (formerly 1402.0505f) in Smithville, Texas at State
Highway 95. This station is located approximately one-quarter mile upstream of the Gazley
Creek confluence. This station will provide data for upstream of the Smithville wastewater
treatment facility discharge. This data is valuable for the analysis of downstream changes in
water quality.
CRWN 3: CRWN Site Number 1402.0505 (level 2), in Smithville, Texas at Highway 71, located
approximately1 mile downstream of the LCRA site. This location is also downstream of the
Gazley Creek confluence and the Smithville wastewater treatment plant, which could be signifi-
cant when comparing the data from this site with the LCRA site which is upstream of the conflu-
ence.
LaGrange
LCRA 4: LCRA Site number 1434.0400 in LaGrange, Texas, located upstream of old HWY 71
bridge and downstream of new HWY 71 bridge. This station is located approximately one-half
mile upstream of the LaGrange wastewater discharge facility discharge. Data from this station is
31
useful for comparison with data collected downstream of the outfall and for analysis of down-
stream water quality changes
CRWN 4: CRWN Site number 1434.0400 (level 2) in LaGrange, Texas located at White Rock
Park. This location is three to four miles downstream of the LCRA site. The wastewater treat-
ment plant discharge is between the two sites.
Columbus
LCRA 5: LCRA Site number 1402.0300 in Columbus, Texas. This site is located approximately
six miles upstream of the Columbus wastewater treatment facility outfall at Business Hwy. 71.
Data from this station is useful for analysis of downstream changes in water quality.
CRWN 5: CRWN Site number 1402.0250(level 2) in Columbus, Texas at Beasons Park. This
site is located 4 miles downstream of the LCRA site. This site is also downstream of the Colum-
bus wastewater treatment plant.
32
3.4 Parameters Studied and Measurement Methods
Dissolved Oxygen (DO) was measured by the volunteer monitors using the Winkler titration
method. This is a widely used and accepted method of measuring dissolved oxygen. The accu-
racy of the volunteer monitor?s field test kit is ?0.5 ppm. A judgement must be made, for one
part of the test, as to whether the color has changed from blue to clear during a titration. One
drop from the titrator is equivalent to 0.3 mg/l on the titrator?s scale. This accounts for the rather
large range in the accuracy. The professional equipment has an accuracy of ?0.2 mg/l.
This particular parameter is subject to a high degree of quality control and was found to
be the most reliable and accurate parameter measured, according to the managers of the River
Watch. Duplicate measurements are made and they must be within 0.6 mg/l of each other for the
results of the test to be valid.
A potential problem with using this parameter is that many conditions can effect the dis-
solved oxygen level such as diurnal variations due to vegetation, temperature and sun light, spa-
tial variations and seasonal variations. One factor that may be relevant is that CRWN monitors
may sample any time between 7:00 a.m. and 7:00 p.m., while LCRA monitors sample between 9
am and noon.
It is important to note whether there is consistency in the time of day that the measure-
ments are taken and that the samples are taken from the same depth in the water body.
Total Dissolved Solids (TDS) is determined by measuring specific conductance using a conduc-
tivity meter. The TDS meter used by the volunteer monitors has an accuracy of ?39.8 mg/l. The
accuracy of the professional instrument is ?1%. This method of measuring TDS is widely used
and accepted.
The CRWN monitors use meters that directly convert the conductivity measurement into
TDS units. The LCRA monitors use a meter that measures conductivity in ?mhos/cm. To com-
33
pare the two data sets the LCRA data was converted into TDS (mg/l) by multiplying the con-
ductance by a conversion factor which varied slightly between the river segments. The conver-
sion factors were obtained from the LCRA.
TDS is a good parameter to study because it is and it is least affected by diurnal varia-
tions in other water parameters.
34
3.5 Parallel Measurements Analysis
The analysis of parallel testing is a way to get some idea as to how well two independent
measurements of the water quality parameters used in this study match in an actual "side by side"
situation, the same place at the same time with two different instruments. The measurements
that are compared in the study were done in a random fashion, at different times and at different
points on the river.
The data used in this analysis were compiled from Quality Assurance/Quality Control
(QA/QC) meetings the staff of the CRWN has with the volunteer monitors. During part of that
meeting the CRWN staff person takes parallel measurements with the volunteer monitor. The
volunteer monitors represented in this analysis are not the same monitors in the study.
Figures 3-3 and 3-4 show the results of the parallel tests. The dashed line originating at the (0,0)
point represents where the points would lie if the two measurements equaled each other. The
solid line is the best-fit line from linear regression. The results show that, when the accuracy of
the instruments is taken into account, the measurements match quite well.
35
Volunteer vs Professional-- Parallel Measurements
Dissolved Oxygen (mg/l)
Dashed Line- x=y
0
2
4
6
8
10
12
14
02468101214
Professional Data DO (mg/l)
Vol
unte
e
r
D
a
ta
Figure 3-3 Parallel Testing Plot, DO
Volunteer vs Professional-- Parallel Measurements
Total Dissolved Solids (mg/l)
Dashed Line- x=y
0
100
200
300
400
500
600
700
800
0 100 200 300 400 500 600 700 800
Professional Data
Vo
l
u
n
t
eer Data
Figure 3-4 Parallel Testing Plot, TDS
36
4 FOURIER ANALYSIS OF WATER QUALITY DATA
4.1 Theory
If it is desired to study the cyclical behavior over time of a water quality variable, fourier
analysis is an effective tool to utilize. The cyclical behavior could be diurnal, seasonal or man-
made. The periodic function may be responding to temperature, sunlight, releases from dams, etc.
This form of analysis can be an effective tool for predicting the behavior of the variable of interest
or it could be used to compare two independent sets of data.
The coefficients of a fourier series can be found by multiple regression analysis. The cycle
is described by a sine function with the general form of:
))2sin()2cos((
1
0
??? +++=
?
=
tjbtjaay
j
J
j
j
where: ? = 2pi/ 365
t = Julian days
y = water quality parameter
a,b = coefficients
The values of j represents the number of cycles within the given time period. In this case the
time period is 365 days over one 2pi (circular) cycle for the sinusoidal function. j=1 would repre-
sent a 12 month cycle, j=2 a 6month cycle, etc..
This is the form that will be used to analyze the variation of dissolved oxygen with the in the
example below. The coefficients for the regression are determined using the regression tool in Mi-
crosoft Excel.
37
4.2 Set-Up
The fourier analysis will now be used to compare two data sets with cyclical behavior and as
a tool for predicting the variable where data is missing. The variable is dissolved oxygen measured
by volunteer monitors (CRWN) and professional monitors (LCRA) at approximately the same lo-
cation on the Colorado River. The raw data has the form shown in Table 4-1.
Table 4-1 Raw Data Example
Date DO (mg/l) Date DO (mg/l)
04/19/93 4.8 04/19/93 8.9
06/21/93 6.2 06/01/93 8.9
06/25/93 7.8 08/11/93 8.2
07/09/93 7.8 10/07/93 7.5
07/16/93 8.3 02/14/94 10.4
07/23/93 6.7 04/27/94 9.2
07/30/93 6.7 06/23/94 9
08/06/93 7.7 08/29/94 7.7
08/13/93 6.7 10/18/94 6.4
08/27/93 7 12/22/94 9
CRWN Data LCRA Data
A scatter plot (Figure 4-1) of the data shows the cyclical nature of the data:
DO Scatter Plot
CRWN Lake Austin
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
0 200 400 600 800 1000 1200 1400 1600 1800
Julian Days
D
O
(
m
g/l)
DO
Figure 4-1 DO Scatter Plot
38
A spreadsheet is developed for each data set. The spreadsheet for j=2 is shown in Figure 4-2 below.
Figure 4-2 Spreadsheet Layout for Fourier Analysis
Column C is used as a reference date used in the formula, yearfrac, for determining the Julian day.
The formulas used in colums D through J are shown in Figure 4-3 below.
Figure 4-3 Spreadsheet Formulas for Fourier Analysis
Now the regression analysis can be performed. The goal is obtain the values for the coefficients a
o
,
a
j
and b
j
in the regression formula and to see how well the calculated curve fits the data. Under the
Tools Menu go to Data Analysis and choose the Regression tool as shown in Figure 4-4 below.
39
Figure 4-4 Excel Regression Tool
The regression tool window is shown in Figure 4-5 below.
Figure 4-5 Excel Regression Tool Window
The Input Y Range is the column with the dissolved oxygen data and the Input X Range is
the field with the values of the sine and cosine functions, for j=1 columns G and H and for j=2
columns G through J. The output of the regression analysis, for j=2, is shown in Table 4-2.
40
Table 4-2 Regression Statistics, Excel Output
SUMMARY OUTPUT- CRWN Lake Austin
j=2
Regression Statistics
Multiple R 0.625
R Square 0.391
Adjusted R Square 0.362
Standard Error 1.304
Observations 90
ANOVA
df SS MS F Significance F
Regression 4 92.748 23.187 13.635 0.000
Residual 85 144.549 1.701
Total 89 237.296
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 8.187 0.141 58.188 0.000 7.907 8.467
X Variable 1 0.959 0.198 4.852 0.000 0.566 1.352
X Variable 2 0.706 0.200 3.526 0.001 0.308 1.104
X Variable 3 0.671 0.190 3.534 0.001 0.294 1.049
X Variable 4 -0.521 0.204 -2.549 0.013 -0.928 -0.115
For this example the coefficients for the regression formula are: a
o
=8.187 mg/l, a
1
=0.959 mg/l,
b
1
=0.706 mg/l, a
2
=0.671 mg/l, b
2
=-0.5212. The a
o
value can be interpreted as being the mean value
of DO as determined by the regression. So the formula for the best-fit line for this set of data is:
365
4
sin5212.0
365
4
cos6712.0
365
2
sin7056.0
365
2
cos9690.01869.8
tttt
y
pipipipi
++++=
The t-stat values for each variable having an absolute value of greater than 2 indicates that each
factor in the equation is contributing significantly to fit of the line. In this case a check into whether
the j=2 expansion gives a better model than the j=1 expansion is appropriate. From the shape of the
data distribution on the scatter plot it appears that the j=1 expansion would be appropriate to fit the
data.
41
4.3 Results
Values of j=1 and j=2 are used in the fourier expansion to determine which one best
represents the water quality data?s seasonal variability. When this is determined the fourier analysis
can be used to compare the volunteer and professional data. The model could also be used to
predict values in time periods when real data is lacking.
Table 4-2, below, show the results for j=1.
Table 4-3 Regression Statistics, j=1
CRWN-Lake Austin-SUMMARY OUTPUT
j=1
Regression Statistics
Multiple R 0.505
R Square 0.255
Adjusted R Square 0.238
Standard Error 1.426
Observations 90
ANOVA
df SS MS F Significance F
Regression 2 60.476 30.238 14.878 0.000
Residual 87 176.820 2.032
Total 89 237.296
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 8.2163 0.1536 53.4992 0.0000 7.9110 8.5215
X Variable 1 0.8892 0.2126 4.1814 0.0001 0.4665 1.3118
X Variable 2 0.7930 0.2174 3.6482 0.0004 0.3610 1.2251
42
Graphically the results have the form shown in Figures 4-6 and 4-7.
DO Scatter Plot with Fourier Series (j=2)
CRWN- Lake Austin, Segment 1403
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
0 200 400 600 800 1000 1200 1400 1600 1800
Julian Days
D
O
(
m
g
/l)
DO
Regression
Figure 4-6 Plot of Regression Results, j=2
DO Scatter Plot with Fourier Series (j=1)
CRWN- Lake Austin
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
0 200 400 600 800 1000 1200 1400 1600 1800
Julian Days
D
O
(
m
g
/l)
DO
Regression
Figure 4-7 Plot of Regression Results, j=1
43
It can be seen how expanding the equation to j=2 resulted in the best-fit line to have larger ex-
tremes, larger maximum and smaller minimum values. A line representing the seasonal variation of
the data may best be represented with values of j=1. The same procedure done to the LCRA data
had the same conclusion.
A smooth best-fit line can now be produced for each data set using uniform time intervals
and the two best-fit lines can be compared graphically. Another Excel spreadsheet was set up with
uniform time intervals (7days in this example). The form of the spreadsheet is shown in Figure 4-8.
Figure 4-8 Excel Spreadsheet, Regression Plot
44
Compare the Expansions (j=1 and j=2)
A plot of the two expansions j=1 and j=2 and the data are shown below in Figures 4-9 and 4-
10.
Regression Analysis (j=1 and j=2))
Dissolved Oxygen- CRWN-Lake Austin
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
0 500 1000 1500 2000
Julian Days
DO (mg/l)
j=1
DO
j=2
Figure 4-9 CRWN DO Fourier Plots, j=1 vs. j=2
Regression Analysis (j=1and j=2)
Dissolved Oxygen LCRA-Lake Austin
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Julian Days
DO (mg
/l)
LCRA (j=1)
DO
j=2
Figure 4-10 LCRA DO Fourier Plots, j=1 vs. j=2
45
Compare the two data sets with j=1 and j=2
The plot of the two best-fit lines (j=1) for the two data sets is shown in Figure 4-11.
LCRA vs CRWN- Lake Austin
Compare Fourier Plots (j=1)
Dissolved Oxygen
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
200 400 600 800 1000 1200 1400 1600 1800
Julian Days
DO (m
g
/
l
)
LCRA (j=1)
CRWN (j=1)
8/23/93
CRWN
8/22/94
7/04 mg/l
LCRA
9/5/94
7.01 mg/l
LCRA
3/14/94
10.20 mg/l
CRWN
2/14/94
9.40 mg/l
Figure 4-11 DO Fourier Plot, LCRA vs CRWN, j=1
The plot of the two best-fit lines (j=2) for the two data sets is shown in Figure 4-12.
46
LCRA vs CRWN- Lake Austin
Compare Fourier Plots (j=2)
Dissolved Oxygen
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
200 400 600 800 1000 1200 1400 1600 1800
Julian Days
D
O
(
m
g
/l)
CRWN Series
LCRA Series
12/27
9.87 mg/l
2/7
10.84 mg/l
Maximum Values
9/5
6.31 mg/l
10/3
6.73 mg/l
Minimum Values
Figure 4-12 DO Fourier Plot, LCRA vs CRWN, j=2
It can be seen that each best-fit line has the same general form but there is a significant
phase shift between the curves and the values of the predicted maximum and minimums. These dif-
ferences are not as pronounced in the j=1 plots. The predicted time and magnitudes of the maxi-
mum and minimums are indicated on the graph.
For these particular data sets there is a significantly larger number of data points in the
CRWN data set (n=90 vs. n=27). The t-test for the two data sets indicated that their means are not
significantly different.
Table 4-4 shows the means of the two data sets determined by standard statistics and the
fourier analysis.
47
Table 4-4 Summary of Means, DO, j=1 and j=2
Method LCRA (n=27)
Mean ? Standard Error
CRWN (n=90)
Mean ? Standard Error
Standard Statistics 8.53 ? 0.30 mg/l 8.05 ? 0.17 mg/l
Fourier Analysis (In-
tercept)
(j=1) 8.70 ? 0.19 mg/l
(j=2) 8.61 ? 0.20 mg/l
(j=1) 8.19 ? 0.14 mg/l
(j=2) 8.21 ? 0.15 mg/l
The mean values for the two methods are in good agreement. The standard error range for both data
sets overlap and with j=1 and j=2 in the fourier analysis.
4.4 Conclusion
?There does not appear to be any advantage to expanding the regression more than j=1 for this
particular type of data set. The best-fit line begins to respond to the daily variability at higher ex-
pansions and distorts the curve from seasonal variations. Also the mean values determined by the
j=1 expansion are within the 95% error range of the j=2 expansion as shown above.
For this study the j=1 expansion will be used.
48
5 STUDY RESULTS
5.1 Lake Austin
Site Analysis- Dissolved Oxygen-- Sites LCRA 1 and CRWN 1
These sites are located on the downstream end of segment 1403 above Tom
Miller Dam. The volunteer (CRWN) site is located about 0.4 miles upstream from the
professional (LCRA) site. The volunteer site is a level 1 site monitored by an employee
of the LCRA, who is not a professional monitor. It is worthwhile to note that the CRWN
data is consistent throughout the year for the entire monitoring period being considered.
A time span of approximately four and a half years was used for the analysis:
CRWN data- 4/19/93 to 9/5/97, n=90
LCRA data- 4/19/93 to 10/13/97, n=27
Descriptive Statistics
Table 5-1 Descriptive Statistics, DO- Lake Austin
CRWN DATA- Lk. Austin LCRA DATA- Lk. Austin
Mean 8.05 Mean 8.53
Standard Error 0.17 Standard Error 0.30
Median 7.95 Median 8.80
Mode 6.70 Mode 9.00
Standard Deviation 1.63 Standard Deviation 1.55
Sample Variance 2.67 Sample Variance 2.40
Kurtosis -0.39 Kurtosis 1.89
Skewness 0.02 Skewness 0.25
Range 7.00 Range 8.00
Minimum 4.60 Minimum 4.80
Maximum 11.60 Maximum 12.80
Sum 724.46 Sum 230.30
Count 90.00 Count 27.00
Confidence Level(95.0%) 0.34 Confidence Level(95.0%) 0.61
49
The mean and median values are very close for both sets of data. There are about
three times more data values for the CRWN site. The skewness and kurtosis values are
very small and both sets of data have about the same range. Essentially, the two data sets
are very similar. The descriptive statistics (Table 5-1) indicate normal distribution of the
data.
Combining the Data Sets
Table 5-2 is the descriptive statistics of the combined data sets.
Table 5-2 Descriptive Statistics Combined Data, DO- Lake Austin
Combined Data Sets
Mean 8.16
Standard Error 0.15
Median 8.1
Mode 6.7
Standard Deviation 1.62
Sample Variance 2.62
Kurtosis -0.01
Skewness 0.04
Range 8.2
Minimum 4.6
Maximum 12.8
Sum 955
Count 117
Lake Austin
The standard error for the combined data sets is lower that either individual data
sets which indicates an improvement in the estimation of the mean.
50
Quantile Plots
Quantile Plot- Dissolved Oxygen-- CRWN- Lake Austin
n=90, Correlation = 0.996
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
Standard Normal Variable (z)
DO
(
m
g
/l)
Figure 5-1 Quantile Plot, DO- CRWN1
Quantile Plot- Dissolved Oxygen-- LCRA- Lake Austin
n= 27, Correlation= 0.971
0
2
4
6
8
10
12
14
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
Standard Normal Variable (z)
DO
(
m
g
/l)
Figure 5-2 Quantile Plot, DO- LCRA1
51
The quantile plots (Figures 5-1 and 5-2) show that both data sets are normally
distributed. Both correlation coefficients are greater than the lower critical value of the
probability plot correlation test statistic for the normal distribution.
Histograms
Histogram
LCRA Data--1403.0100
Lake Austin
0
5
10
15
20
25
30
35
40
0 2 4 6 8
10 1
2
14
More
Bin
Fre
que
nc
y
Frequency
Histogram
CRWN Data--1403.0100
Lake Austin
0
5
10
15
20
25
30
35
40
0 2 4 6 8
1
0
12 1
4
Mo
re
Bin
Fr
e
que
nc
y
Frequency
Figure 5-3 Histograms, DO- Lake Austin
The histograms in Figure 5-3 show a normal distribution also.
t-test
Because the data is normally distributed the t-test is appropriate to compare the
means of the two data sets.
52
Table 5-3 t-test Results, DO- Lake Austin
Calculated t= -1.395
t-Test: Two-Sample Assuming Unequal Variances
CRWN LCRA
Mean 8.050 8.53
Variance 2.666 2.40
Observations 90 27
df 45
t Stat -1.395
P(T<=t) one-tail 0.085
t Critical one-tail 1.679
P(T<=t) two-tail 0.170
t Critical two-tail 2.014
The t-value, shown in Table 5-3, of -1.395 indicates that statistically the means
data sets are not significantly different.
Standard Error of the Mean
Table 5-4 shows that the LCRA data has a much lower standard error than the CRWN
data even though there are fewer measurements. The range for the volunteer data around
the mean for n=90 is 0.69 or the mean DO with 95% confidence is 8.05 ? 0.35 mg/l. The
range for the professional data around the mean for n=27 is 0.11 or the mean DO with
95% confidence is 8.53 ? 0.055 mg/l.
53
Table 5-4 Standard Error of the Mean, DO- Lake Austin
Standard Error of the Mean CRWN Data- Lake Austin
index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
1 4.80 4.80 0.00 4.80 4.80 0.00
2 6.20 5.50 0.70 4.10 6.90 2.80
3 7.80 6.27 0.87 4.53 8.00 3.47
4 7.80 6.65 0.72 5.20 8.10 2.89
5 8.30 6.98 0.65 5.68 8.28 2.60
6 6.70 6.93 0.53 5.87 8.00 2.13
.. .. .. .. .. .. ..
87 7.40 8.09 0.18 7.74 8.45 0.70
88 7.70 8.09 0.17 7.74 8.44 0.69
89 6.30 8.07 0.17 7.72 8.42 0.69
90 6.30 8.05 0.17 7.71 8.39 0.69
Standard Error of the Mean LCRA Data- Lake Austin
index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
1 8.90 8.90 0.00 8.90 8.90 0.00
2 8.90 8.90 0.00 8.90 8.90 0.00
3 8.20 8.67 0.08 8.51 8.82 0.31
4 7.50 8.38 0.12 8.13 8.62 0.50
5 10.40 8.78 0.10 8.58 8.98 0.39
6 9.20 8.85 0.08 8.69 9.01 0.33
.. .. .. .. .. .. ..
24 8.80 8.84 0.03 8.78 8.90 0.12
25 7.00 8.76 0.03 8.71 8.82 0.11
26 4.80 8.61 0.03 8.56 8.67 0.11
27 6.40 8.53 0.03 8.47 8.59 0.11
Figures 5-4 and 5-5 are the graphical representation of the standard error of the mean.
Standard Error of theMean -Dissolved Oxygen
LCRA Lake Austin
4
5
6
7
8
9
10
11
12
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
Number of Samples
DO (mg
/l)
DO
Cum Mean
m-2sd
m+2sd
Figure 5-4 Standard Error of the Mean, DO- LCRA1
54
Mean of Dissolved Oxygen
CRWN 1403.0100 Lake Ausitn
4
5
6
7
8
9
10
11
12
1 4 7
10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88
Number of Samples
DO (mg
/l)
Figure 5-5 Standard Error of the Mean, DO- CRWN1
55
Fourier Analysis--Dissolved Oxygen
The statistics for the regression analysis of the two data sets are shown in Tables
5-5 and 5-6.
Table 5-5 Regression Statistics- LCRA1- Lake Austin
LCRA- Lake Austin SUMMARY OUTPUT
j=1
Regression Statistics
Multiple R 0.763
R Square 0.583
Adjusted R Square 0.548
Standard Error 1.041
Observations 27
ANOVA
df SS MS F Significance F
Regression 2 36.305 18.152 16.761 0.000
Residual 24 25.992 1.083
Total 26 62.296
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 8.609 0.203 42.343 0.000 8.189 9.029
X Variable 1 0.784 0.308 2.548 0.018 0.149 1.419
X Variable 2 1.423 0.267 5.322 0.000 0.871 1.975
Table 5-6 Regression Statistics- CRWN1- Lake Austin
CRWN-Lake Austin-SUMMARY OUTPUT
j=1
Regression Statistics
Multiple R 0.505
R Square 0.255
Adjusted R Square 0.238
Standard Error 1.426
Observations 90
ANOVA
df SS MS F Significance F
Regression 2 60.476 30.238 14.878 0.000
Residual 87 176.820 2.032
Total 89 237.296
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 8.2163 0.1536 53.4992 0.0000 7.9110 8.5215
X Variable 1 0.8892 0.2126 4.1814 0.0001 0.4665 1.3118
X Variable 2 0.7930 0.2174 3.6482 0.0004 0.3610 1.2251
56
The plot of the best fit lines for the two data sets is shown in Figure 5-6.
LCRA vs CRWN- Lake Austin
Compare Fourier Plots (j=1)
Dissolved Oxygen
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
200 400 600 800 1000 1200 1400 1600 1800
Julian Days
DO
(
m
g/l)
LCRA (j=1)
CRWN (j=1)
8/23/93
CRWN
8/22/94
7.04 mg/l
LCRA
9/5/94
7.01 mg/l
LCRA
3/14/94
10.20 mg/l
CRWN
2/14/94
9.40 mg/l
Figure 5-6 Fourier Plot- Lake Austin
Table 5-7 shows the comparison of the means of the two data sets as determined
by the two types of analysis:
Table 5-7 Summary of Means- Lake Austin
Method LCRA (n=27)
Mean ? Standard Error
CRWN (n=90)
Mean ? Standard Error
Standard Statistics 8.53 ? 0.30 mg/l 8.05 ? 0.17 mg/l
Fourier Analysis (Intercept) 8.61 ? 0.20 mg/l 8.22 ? 0.15 mg/l
There is good agreement between the two methods as illustrated above. The mean values
determined by standard statistics and fourier analysis are within the margins of error.
The CRWN data is well distributed temporally with at least one measurement per month
throughout the time period analyzed.
57
Total Dissolved Solids
The same analysis technique will now be used for Total Dissolved Solids. A plot
of the raw data is shown in Figure 5-7.
Total Dissolved Solids
CRWN and LCRA- Lake Austin
0
100
200
300
400
500
600
700
01/31/93 11/27/93 09/23/94 07/20/95 05/15/96 03/11/97 01/05/98
Date
TD
S (m
g/l)
CRWN
LCRA
Figure 5-7 Scatter Plot, TDS- Lake Austin
This plot shows a much wider range and variability in the volunteer data.
58
Descriptive Statistics
Table 5-8 Descriptive Statistics, TDS- Lake Austin
TDS- CRWN TDS- LCRA
Mean 333.96 Mean 327.07
Standard Error 7.79 Standard Error 4.48
Median 340 Median 324.6
Mode 290 Mode 322.8
Standard Deviation 74.28 Standard Deviation 23.26
Sample Variance 5517.51 Sample Variance 540.84
Kurtosis 2.02 Kurtosis 0.43
Skewness 0.12 Skewness -0.35
Range 490 Range 99
Minimum 100 Minimum 275.4
Maximum 590 Maximum 374.4
Sum 30390 Sum 8831
Count 91 Count 27
Confidence Level(95.0%) 15.47 Confidence Level(95.0%) 9.20
The descriptive statistics shown in Figure 5-7, indicate that both data sets show
the signs of normal distribution. The means and medians of the two data sets are rela-
tively close together and they both have small skewness values. The means of the two
data sets are very close also, 334mg/l for CRWN versus 327 mg/l for LCRA. In other
aspects they are quite different. The higher degree of variability of the volunteer data is
shown. The standard deviation is three times larger than the professional data and the
range is almost five times as large. The confidence levels for each data sets are very rea-
sonable for this water quality parameter.
59
Histograms
Histogram LCRA
TDS Lake Austin
0
5
10
15
20
25
30
10
0
2
0
0
3
0
0
40
0
50
0
6
0
0
7
0
0
Bin
Fre
que
nc
y
Frequency
Histogram CRWN
TDS- Lake Austin
0
5
10
15
20
25
30
10
0
2
0
0
3
0
0
40
0
50
0
60
0
7
0
0
Bin
Fre
que
nc
y
Frequency
Figure 5-8 Histograms, TDS- Lake Austin
The histograms (Figure 5-8) show a normal distribution for each data set.
t-test
The result of the t-test are shown in Table 5-9.
Table 5-9 Result of the t-test- TDS- Lake Austin
t-Test: Two-Sample Assuming Unequal Variances
CRWN LCRA
Mean 333.96 327.07
Variance 5517.51 540.84
Observation 91 27
Hypothesiz 0
df 116
t Stat 0.767
P(T<=t) one 0.222
t Critical on 1.658
P(T<=t) two 0.445
t Critical tw 1.981
The t-test indicate that there is no significat difference in the means of the two data sets.
Standard Error of the Mean
The standard error of the mean plots for the two data sets are shown in Figures 5-
9 and 5-10.
60
Cumulative Mean- Total Dissolved Solids
LCRA- Lake Austin
100
150
200
250
300
350
400
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
Number of Samples
T
D
S (
m
g
/l)
TDS
Cum Mean
m-2sd
m+2sd
Figure 5-9 Standard Error of the Mean- TDS- LCRA1
Cumulative Mean- Total Dissolved Solids
CRWN- Lake Austin
0
100
200
300
400
500
600
700
1 5 9
13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89
Number of Samples
T
D
S
(m
g
/l)
Figure 5-10 Standard Error of the Mean- TDS- CRWN1
The plots show that each data set is stable and have a small error interval.
61
5.2 Bastrop
Site Analysis- Dissolved Oxygen-- Sites LCRA 2 and CRWN 2
This site is located in the upstream part of river segment 1434. The LCRA monitors at this site
six times a year and the CRWN has a volunteer site at the same location. The volunteer data lacks
summer month data. Only 21% of the measurements occurred between April1 and October 1.
For the following analysis a time span of approximately four years is used:
LCRA data- 8/23/93 to 10/1/97, n=26
CRWN data- 9/28/93 to 12/16/97, n=104
Descriptive Statistics
The following tables in Figure 5-10 are the descriptive statistics for each site:
Table 5-10 Descriptive Statistics, DO- Bastrop
CRWN Data- Bastrop LCRA DATA- Bastrop
Mean 9.35 Mean 8.96
Standard Error 0.19 Standard Error 0.34
Median 9.45 Median 8.65
Mode 10.00 Mode 7.10
Standard Deviation 1.94 Standard Deviation 1.72
Sample Variance 3.78 Sample Variance 2.96
Kurtosis -0.09 Kurtosis 0.11
Skewness 0.09 Skewness 0.90
Range 10.70 Range 6.30
Minimum 4.10 Minimum 7.00
Maximum 14.80 Maximum 13.30
Sum 972.90 Sum 232.90
Count 104.00 Count 26.00
Note that there are almost four times more CRWN data values than LCRA data values. Both of
the data sets have mean and median values that are very close to each other and relatively small
skewness values. The CRWN skewness value is more than 50% lower than the LCRA values,
probably because of the larger number of data points. The range of the CRWN is substantially higher
than the LCRA
62
range, this being due to the larger number of CRWN measurements. The descriptive statistics indicate
that both sets of data are normally distributed.
Combining the Data Sets
Table 5-11 is the descriptive statistics of the combined data sets.
Table 5-11 Descriptive Statistics Combined Data- Bastrop
Combined Data
Mean 9.28
Standard Error 0.17
Median 9.2
Mode 10
Standard Deviation 1.90
Sample Variance 3.62
Kurtosis -0.14
Skewness 0.23
Range 10.70
Minimum 4.1
Maximum 14.8
Sum 1205.8
Count 130
Bastrop
The standard error for the combined data sets is lower than either individual data sets which indicates
an improvement in the estimation of the mean.
63
Quantile Plot
Figures 5-11 and 5-12 are the cumulative frequency plots and histograms for the two data sets:
Quantile Plot- Dissolved Oxygen-- CRWN- Bastop
n=104, Correlation = 0.996
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
Standard Normal Variable (z)
DO
(
m
g/l)
Figure 5-11 Quantile Plot, DO- CRWN2
Quantile Plot- Dissolved Oxygen-- LCRA- Bastrop
n=26, Correlation= 0.964
0
2
4
6
8
10
12
14
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
Standard Normal Variable (z)
DO
(
m
g/l)
Figure 5-12 Quantile Plot, DO- LCRA2
64
The quantile plots show that both data sets are normally distributed. Both correlation coeffi-
cients are greater than the lower critical value of the probability plot correlation test statistic for the
normal distribution.
Histograms
Histogram- DO Data
CRWN- Bastrop
Segment 1434
0
5
10
15
20
25
4 6 8
10 1
2
1
4
Bin
Fr
e
que
nc
y
Frequency
Histogram- DO Data
LCRA- Bastrop
Segment 1434
0
5
10
15
20
25
4 6 8
1
0
12 14
Bin
Fr
e
que
nc
y
Frequency
Figure 5-13 Histograms, DO- Bastrop
The histogram for the CRWN data has the appearance of a normal distribution, slightly skewed
in the positive direction. The LCRA data appears to be slightly more skewed but there is only a differ-
ence of three data point between the intervals with the highest number of data points.
t-test
The t-test should work well with these data sets since they are normally distributed and the
standard deviations are approximately the same. The t-test was done two ways for this analysis: using
Excel?s built in test and using the above formula in the spreadsheet. The results are in Table 5-12, be-
low.
65
Table 5-12 t-test Results, DO- Bastrop
Calculated t= 1.108
t-Test: Two-Sample Assuming Unequal Variances
CRWN LCRA
Mean 9.401 8.958
Variance 4.371 2.959
Observations 95.000 26
Hypothesized Mean Difference 0.000
df 47.000
t Stat 1.108
P(T<=t) one-tail 0.137
t Critical one-tail 1.678
P(T<=t) two-tail 0.274
t Critical two-tail 2.012
The results using Excel and the formula were the same. The value of t = 1.108 indicates that
the hypothesis there is not a significant difference between the two means cannot be rejected.
Standard Error of the Mean
Table 5-13 Standard Error of the Mean, DO-Bastrop
Standard Error of the Mean CRWN Data- Bastrop
index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
1 7.00 7.00 0 7.000 7.000 0.000
2 9.00 8.00 0.500 7.000 9.000 2.000
3 8.00 8.00 0.333 7.333 8.667 1.333
4 7.60 7.90 0.243 7.414 8.386 0.971
.. .. .. .. .. .. ..
100 10.8 9.29 0.045 9.201 9.381 0.179
101 11.75 9.32 0.044 9.227 9.404 0.178
102 10.45 9.33 0.044 9.239 9.415 0.176
103 9.8 9.33 0.044 9.244 9.418 0.174
104 10.3 9.34 0.043 9.255 9.427 0.172
105 10.8 9.35 0.043 9.269 9.440 0.171
Standard Error of the Mean LCRA Data- Bastrop
index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
1 7.10 7.10 0 7.100 7.100 0.000
2 7.20 7.15 0.025 7.100 7.200 0.100
3 10.70 8.33 0.403 7.527 9.139 1.612
4 11.70 9.18 0.501 8.173 10.177 2.003
.. .. .. .. .. .. ..
21 9.80 9.01 0.150 8.715 9.314 0.599
22 10.20 9.07 0.143 8.783 9.354 0.571
23 9.10 9.07 0.136 8.797 9.343 0.546
24 8.40 9.04 0.131 8.780 9.303 0.523
25 7.60 8.98 0.125 8.733 9.235 0.501
26 8.30 8.96 0.120 8.717 9.199 0.482
66
The results in Figure 5-26, above, indicate that in 95 out of 100 similar measurements the
mean would lie in the approximate range around the mean indicated in the last column. The range for
the volunteer data around the mean for n=105 is 0.171 or the mean DO with 95% confidence is9.35 ?
0.085 mg/l. The range for the professional data around the mean for n=26 is 0.482 or the mean DO
level with 95% confidence is 8.96 ? 0.241 mg/l.
The graphical representation of the above analysis is shown in Figures 5-14 and 5-15:
Standard Error of the Mean-- Dissolved Oxygen
LCRA2- Bastrop
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
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
Number of Samples
D
O
(mg
/l)
DO
Cum Mean
m-2sd
m+2sd
Figure 5-14 Standard Error of the Mean, DO- LCRA2
67
Standard Error of the Mean-- Dissolved Oxygen
CRWN2- Bastrop
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
1 6
11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96
101
Number of Samples
D
O
(mg
/l)
Figure 5-15 Standard Error of the Mean, DO- CRWN2
68
Fourier Analysis-- Dissolved Oxygen
A scatter plot of the data shown in Figure 5-16 illustrates the seasonal variations in the dis-
solved oxygen levels:
DO vs Time
LCRA vs CRWN- Bastop
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
1/
31/
93
8/
1
9/
93
3
/
7/
94
9/
23/
9
4
4/
11
/
95
10
/
2.
.
.
5/
15/
9
6
12/
1/
96
6/
1
9/
97
1
/
5/
98
7/
24/
9
8
Date
DO (mg/l)
CRWN
LCRA
Figure 5-16 Scatter Plot, TDS- Bastrop
The statistics for the regression analysis of the two data sets are shown in Tables 5-14 and 5-15.
Table 5-14 Regression Statistics, DO-LCRA2
LCRA- Bastrop- SUMMARY OUTPUT
j=1
Regression Statistics
Multiple R 0.82
R Square 0.66
Adjusted R Square 0.64
Standard Error 1.04
Observations 26
ANOVA
df SS MS F Significance F
Regression 2 49.18 24.59 22.81 0.00
Residual 23 24.80 1.08
Total 25 73.98
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 9.04 0.20 44.30 0.00 8.62 9.46
X Variable 1 1.58 0.30 5.27 0.00 0.96 2.19
X Variable 2 1.16 0.28 4.16 0.00 0.58 1.73
69
Table 5-15 Regression Statistics, DO-CRWN2
CRWN- Bastrop-SUMMARY OUTPUT
j=1
Regression Statistics
Multiple R 0.57
R Square 0.33
Adjusted R Square 0.32
Standard Error 1.61
Observations 104
ANOVA
df SS MS F Significance F
Regression 2 128.27 64.13 24.83 0.00
Residual 101 260.90 2.58
Total 103 389.17
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 8.47 0.21 39.46 0.00 8.05 8.90
X Variable 1 2.04 0.32 6.30 0.00 1.40 2.69
X Variable 2 0.64 0.21 3.03 0.00 0.22 1.05
The plot of the best fit lines for the two data sets is shown in Figure 5-17.
Fourier Plots DO- Bastop
6.00
7.00
8.00
9.00
10.00
11.00
12.00
200 400 600 800 1000 1200 1400 1600 1800
Julian Days
DO (mg/l)
CRWN Series
LCRA Series
8/23/93
1/24/94
10.8
2/7/94
11.2
6/29/94
6.74
7.3
8/8/4
Figure 5-17 Fourier Plot, DO- Bastrop
70
The fourier plots show a phase shift in the cycles of the two data sets of about 14 days for the
maximums and 40 days for the minimums. It should be kept in mind that the CRWN data set lacked
data points for the summer months, which may account for the phase shift being larger in the summer
period when the minimums occur.
Comparing the mean values determined by standard statistics and fourier analysis is shown in
Table 5-16.
Table 5-16 Summary of Means, DO- Bastrop
Method LCRA (n=27)
Mean ? Standard Error
CRWN (n=90)
Mean ? Standard Error
Standard Statistics 8.96 ? 0.34 mg/l 9.35 ? 0.19 mg/l
Fourier Analysis (Intercept) 9.04 ? 0.21 mg/l 8.55 ? 0.29 mg/l
The means of the LCRA data sets as determined by the two methods are in good agreement,
differing by only 0.08 mg/l. The means CRWN data are considerably different, though, differing by
0.80 mg/l. The mean of the CRWN data set calculated by the fourier method is the lower value and is
more realistic. The CRWN data set lacks summer data. The t-stat for the two data sets is 1.11. So
there is not a significant difference in the means of the data sets.
71
Total Dissolved Solids Analysis-- Bastrop
The scatter plot of TDS data is shown in Figure 5-18.
TDS Scatter Plot
CRWN vs. LCRA Bastrop
0
100
200
300
400
500
600
10/23/92 08/19/93 06/15/94 04/11/95 02/05/96 12/01/96 09/27/97 07/24/98
Date
TDS (
m
g/
l
)
CRWN
LCRA
Figure 5-18 Scatter Plot, TDS- Bastrop
Descriptive Statistics:
Table 5-17 Descriptive Statistics, TDS- Bastrop
CRWN- Bastrop LCRA- Bastop
Mean 368.34 Mean 362.74
Standard Error 7.52 Standard Error 10.25
Median 360 Median 360
Mode 430 Mode 358.2
Standard Deviation 75.17 Standard Deviation 51.25
Sample Variance 5650.61 Sample Variance 2626.35
Kurtosis 1.06 Kurtosis 2.81
Skewness -0.28 Skewness -1.08
Range 420 Range 236.4
Minimum 120 Minimum 202.2
Maximum 540 Maximum 438.6
Sum 36834 Sum 9068.4
Count 100 Count 25
TDS TDS
72
The descriptive statistics, shown in Table 5-17, indicate that the two data sets are very similar.
The median values are exactly the same and the means are close to equal. The main difference is the
greater range and variability of the CRWN data.
Histograms
Histogram- TDS
CRWN- Bastrop
0
5
10
15
20
25
30
35
150 200 250 300 35
0
4
00
4
50
500 550 600 650 700
Mor
e
TDS (mg/l)
Frequency
Histogram- TDS
LCRA- Bastrop
0
5
10
15
20
25
30
35
150 200 2
50
300 350 400 450 5
00
550 600 650 70
0
Mor
e
TDS (mg/l)
Frequency
Figure 5-19 Histograms, TDS- Bastrop
t-test
Table 5-18 t-test Results, TDS- Bastrop
t-Test: Two-Sample Assuming Unequal Variances
CRWN LCRA
Mean 368.34 362.74
Variance 5650.61 2626.35
Observations 100 25
Hypothesized Mean Difference 0
df 53
t Stat 0.44
P(T<=t) one-tail 0.33
t Critical one-tail 1.67
P(T<=t) two-tail 0.66
t Critical two-tail 2.01
73
Standard Error of the Mean Plots
Standard Error of the Mean
Total Dissolved Solids
LCRA -Bastrop
100
150
200
250
300
350
400
450
500
1 2 3 4 5 6 7 8 9 10111213141516171819202122232425
Number of Samples
TDS
(
m
g/
l
)
TDS
Cum Mean
m-2sd
m+2sd
Figure 5-20 Standard Error of the Mean, TDS- LCRA2
Standard Error of the Mean
Total Dissolved Solids
CRWN Bastrop
100
150
200
250
300
350
400
450
500
550
600
1 6
11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96
Number of Samples
TD
S (m
g/l)
Figure 5-21 Standard Error of the Mean TDS, CRWN2
74
Both plots (Figures 5-38 and 5-39) indicate a great degree of stability in the TDS mean values
for both data sets. The 95% confidence interval is very small after only a few measurements.
75
5.3 Smithville
Site Analysis- Dissolved Oxygen-- Sites LCRA 3 and CRWN 3
This site is located in the middle of river segment 1434. The LCRA monitors at this site six
times a year and the CRWN has a volunteer site one mile downstream of the LCRA site. The volunteer
data lacks summer month data. Only 8% of the measurements occurred between April1 and October 1.
For the following analysis a time span of approximately three and a half years is used:
LCRA data- 8/23/93 to 3/20/97, n=23
CRWN data- 8/23/93 to 4/1/97, n=39
Descriptive Statistics
Table 5-19 Descriptive Statistics, DO- Smithville
Mean 7.73 Mean 8.59
Standard Error 0.36 Standard Error 0.32
Median 8.15 Median 8.40
Mode 7.80 Mode 6.90
Standard Deviation 2.24 Standard Deviation 1.55
Sample Variance 5.01 Sample Variance 2.40
Kurtosis 0.86 Kurtosis -0.19
Skewness -1.03 Skewness 0.47
Range 9.50 Range 6.2
Minimum 2 Minimum 5.9
Maximum 11.5 Maximum 12.1
Sum 301 Sum 198
Count 39 Count 23
Confidence Level(95.0%) 0.725 Confidence Level(95.0%) 0.670
LCRA SmithvilleCRWN Smithville
The mean of the volunteer data is lower than the professional data even though volunteer data
is lacking during the period when the DO would be the lowest. The mean and median values are close
to one another for both data sets, but the professional data is closer.
76
Quantile Plots
Quantile Plot- Dissolved Oxygen-- CRWN- Smithville
n=39, Correlation = 0.956
w/o two lowest points, Correl.=0.9602
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
Standard Normal Variable (z)
D
O
(mg
/l)
Figure 5-22 Quantile Plot, DO- CRWN3
Quantile Plot- Dissolved Oxygen-- LCRA- Smithville
n=23, Correlation= 0.987
0
2
4
6
8
10
12
14
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
Standard Normal Variable (z)
D
O
(mg
/l)
Figure 5-23 Quantile Plot DO, LCRA3
77
The quantile plots in Figures 5-22 and 5-23 show that both data sets are normally distributed.
The LCRA correlation coefficient is greater than the lower critical value of the probability plot corre-
lation test statistic for the normal distribution.
The CRWN data set had "outlier" data which caused the correlation coefficients to be less than
the lower critical value of the probability plot correlation test statistic for the normal distribution.
Eliminating just the two lowest values caused the coefficient to be greater than the lower critical value.
Histograms
Histogram- Dissolved Oxygen
CRWN- Smithville
0
1
2
3
4
5
6
7
8
9
10
4 6 8
10 1
2
1
4
16
Bin
Frequency
Frequency
Histogram- Dissolved Oxygen
LCRA- Smithville
0
1
2
3
4
5
6
7
8
9
10
4 6 8
10 1
2
14 1
6
Bin
Frequency
Frequency
Figure 5-24 Histograms, DO- Smithville
The histogram of the volunteer data (Figure 5-24) shows a strong skewness in the negative
direction (skewness=-1.03) and professional data has a good normal distribution.
78
t-test:
Table 5-20 t-test Results, DO- Smithville
-1.777
Smithville
CRWN LCRA
Mean 7.73 8.59
Variance 5.01 2.40
Observations 39 23
df 58
t Stat -1.777
P(T<=t) one-tail 0.040
t Critical one-tail 1.672
P(T<=t) two-tail 0.081
t Critical two-tail 2.002
Calculated t=
The absolute value of the t Stat is less than two but still relatively high, reflecting the differ-
ences in the data sets indicated by the descriptive statistics.
Standard Error of the Mean
Table 5-21 Standard Error of the Mean, DO- Smithville
Standard Error of the Mean CRWN Data- Smithville
index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
1 6.00 6.00 0.00 6.00 6.00 0.00
2 7.80 6.90 0.45 6.00 7.80 1.80
3 2.00 5.27 0.47 4.32 6.21 1.89
4 7.50 5.83 0.34 5.15 6.50 1.36
5 2.00 5.06 0.32 4.41 5.71 1.29
6 4.00 4.88 0.31 4.27 5.49 1.22
.. .. .. .. .. .. ..
36 11.50 7.60 0.14 7.32 7.88 0.56
37 9.60 7.65 0.14 7.37 7.93 0.55
38 9.20 7.69 0.14 7.42 7.97 0.55
39 9.20 7.73 0.14 7.46 8.00 0.55
Standard Error of the Mean LCRA Data- Smithville
index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
1 6.90 6.90 0.00 6.90 6.90 0.00
2 7.50 7.20 0.15 6.90 7.50 0.60
3 10.10 8.17 0.38 7.40 8.93 1.53
4 12.10 9.15 0.51 8.13 10.17 2.04
5 9.70 9.26 0.48 8.29 10.23 1.94
6 7.00 8.88 0.41 8.05 9.71 1.66
.. .. .. .. .. .. ..
20 7.80 8.49 0.13 8.23 8.74 0.51
21 9.30 8.52 0.12 8.28 8.77 0.49
22 9.70 8.58 0.12 8.34 8.81 0.47
23 8.80 8.59 0.11 8.36 8.81 0.45
79
The results in Table 5-21, above, indicate that in 95 out of 100 similar measurements the mean
would lie in the approximate range around the mean indicated in the last column. The range for the
volunteer data around the mean for n=39 is 0.55 or the mean DO with 95% confidence is 7.73 ? 0.275
mg/l. The range for the professional data around the mean for n=23 is 0.45 or the mean DO level with
95% confidence is 8.59 ? 0.225 mg/l.
Combining the Professional and Volunteer Data
Table 5-22 Standard Error of the Mean, DO- Combined Data- Smithville
Date index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
08/23/93 1 6.90 6.90 0.00 6.90 6.90 0.000
09/09/93 2 6.00 6.45 0.22 6.00 6.90 0.900
10/01/93 3 7.80 6.90 0.15 6.60 7.20 0.600
10/07/93 4 2.00 5.68 0.29 5.10 6.25 1.156
10/15/93 5 7.50 6.04 0.24 5.56 6.52 0.962
10/20/93 6 7.50 6.28 0.20 5.89 6.68 0.789
.. .. .. .. .. .. .. ..
12/05/96 55 5.40 7.83 0.10 7.63 8.04 0.409
01/21/97 56 10.20 7.87 0.10 7.67 8.08 0.405
01/31/97 57 11.50 7.94 0.10 7.74 8.14 0.401
02/03/97 58 9.70 7.97 0.10 7.77 8.17 0.397
02/14/97 59 9.60 8.00 0.10 7.80 8.19 0.393
02/27/97 60 9.20 8.02 0.10 7.82 8.21 0.390
03/20/97 61 9.20 8.04 0.10 7.84 8.23 0.386
04/01/97 62 8.80 8.05 0.10 7.86 8.24 0.383
Standard Error of the Mean CRWN Data- Smithville
Combining Volunteer and Professional Data
By combining the two data sets the 95% confidence interval around the mean was reduced to a
value which is less than either data set individually. The standard error of the mean analysis (Table 5-
22) shows that for these particular data sets there is improvement in confidence in the accuracy of the
data.
The descriptive statistics for the combined data sets are shown in Table 5-23 below.
80
Table 5-23 Descriptive Statistics, DO- Combined Data- Smithville
Mean 8.048
Standard Error 0.259
Median 8.350
Mode 7.8
Standard Deviation 2.040
Sample Variance 4.160
Kurtosis 1.523
Skewness -0.947
Range 10.1
Minimum 2
Maximum 12.1
Sum 498.95
Count 62
Confidence Level(95.0%) 0.518
Combined Data-Smithville
Descriptive Statistics
The standard error for the combined data sets is lower than either individual data sets which in-
dicates an improvement in the estimation of the mean. The data is strongly skewed in the negative di-
rection.
Fourier Analysis-- Dissolved Oxygen-- Smithville
The statistics for the regression analysis of the two data sets in shown in Tables 5-24 and 5-25.
Table 5-24 Regression Statistics- DO- LCRA3
LCRA- Smithville-SUMMARY OUTPUT
j=1
Regression Statistics
Multiple R 0.83
R Square 0.68
Adjusted R Square 0.65
Standard Error 0.92
Observations 23
ANOVA
df SS MS F Significance F
Regression 2 36.04 18.02 21.44 0.00
Residual 20 16.81 0.84
Total 22 52.85
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 8.52 0.19 44.48 0.00 8.12 8.92
X Variable 1 1.57 0.28 5.62 0.00 0.98 2.15
X Variable 2 0.87 0.26 3.30 0.00 0.32 1.42
81
Table 5-25 Regression Statistics- DO- CRWN3
CRWN- Smithville-SUMMARY OUTPUT
j=1
Regression Statistics
Multiple R 0.64
R Square 0.41
Adjusted R Square 0.38
Standard Error 1.76
Observations 39
ANOVA
df SS MS F Significance F
Regression 2 78.74 39.37 12.71 0.00
Residual 36 111.55 3.10
Total 38 190.28
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 7.69 0.44 17.41 0.00 6.80 8.59
X Variable 1 0.53 0.68 0.78 0.44 -0.85 1.91
X Variable 2 1.84 0.37 4.93 0.00 1.08 2.59
The plot of the best-fit lines for the two data sets is shown in Figure 5-25 below.
DO Fourier Plots
CRWN vs LCRA Smithville
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
200 400 600 800 1000 1200 1400 1600 1800
Julian Days
D
O
(mg/l)
CRWN Series
LCRA Series
2/7/94
8/23/93
2/6/95
9/12/94
2/28/94
8/1/94
Figure 5-25 Fourier Plot, DO- Smithville
The plots of the best-fit lines for the two data sets indicate that the two data sets are very dis-
similar. The CRWN data set had only 8% of the measurements occurred between April1 and October
1. Also, these data sets had the smallest number of measurement of all the data sets analyzed.
82
Table 5-26 below shows the comparison of the means of the two data sets as determined by the
two types of analysis:
Table 5-26 Summary of Means, DO- Smithville
Method LCRA (n=23)
Mean ? Standard Error
CRWN (n=39)
Mean ? Standard Error
Standard Statistics 8.59? 0.32 mg/l 7.73 ? 0.36 mg/l
Fourier Analysis (Intercept) 8.52 ? 0.20 mg/l 7.69 ? 0.44 mg/l
The mean values determined by the two methods for the data sets are very close. The means
for the LCRA data differ by only 0.07 mg/l and the CRWN data by 0.16 mg/l. The means of the two
data sets also differ from one another by almost 1.0 mg/l using both methods to determine the mean. It
is interesting that the mean of volunteer data set is substantially lower than that of the professional
data set when there is such a lack of summer data in the volunteer data.
83
Total Dissolved Solids Analysis-- Smithville
The scatter plot of the TDS data for the two data sets is shown in Figure 5-26 below.
TDS Scatter Plot
CRWN vs. LCRA Smithville
0
100
200
300
400
500
600
08/19/93 06/15/94 04/11/95 02/05/96 12/01/96 09/27/97
Date
TDS (
m
g/
l
)
CRWN
LCRA
Figure 5-26 Scatter Plot, TDS- Smithville
The scatter plot indicates good agreement between the two data sets with the range and vari-
ability being about the same. The CRWN data set has been manipulated though. In March of 1995
two extremely high values were indicated, 910 and 1130 mg/l. The above plot does not include these
data points and below, the descriptive statistics were done both with and without these values in the
volunteer data set.
84
Descriptive Statistics
Table 5-27 Descriptive Statistics, TDS- Smithville
CRWN- Smithville LCRA- Smithville
Mean 401.75 Mean 370.64
Standard Error 24.94 Standard Error 7.15
Median 380 Median 364.8
Mode 380 Mode 346.8
Standard Deviation 157.75 Standard Deviation 34.28
Sample Variance 24886.60 Sample Variance 1175.15
Kurtosis 13.73 Kurtosis 0.25
Skewness 3.42 Skewness 0.30
Range 950 Range 145.8
Minimum 180 Minimum 297.6
Maximum 1130 Maximum 443.4
Sum 16070 Sum 8524.8
Count 40 Count 23
CRWN- Smithville
Mean 368.38
Standard Error 10.28
Median 370
Mode 380
Standard Deviation 62.52
Sample Variance 3908.41
Kurtosis 0.76
Skewness -0.52
Range 300
Minimum 180
Maximum 480
Sum 13630
Count 37
TDS TDS
TDS w/ outliers deleted
With the extreme data values eliminated the two data sets are very similar as shown in Table 5-
27. The range of the volunteer data set is almost double that of the professional data.
85
Histograms
Histogram- TDS
CRWN- Smithville
0
2
4
6
8
10
12
150 200 250 300 350 400 450 500 550 600 650 700
Mor
e
100
Fr
equency
Histogram- TDS
LCRA Smighville
0
2
4
6
8
10
12
10
0
20
0
30
0
40
0
50
0
60
0
70
0
Bin
Fr
equency
Figure 5-27 Histograms, TDS- Smithville
The histograms in Figure 5-27 indicate that the two data sets are normally distributed.
t-test:
Table 5-28 t-test Results, TDS- Smithville
t-Test: Two-Sample Assuming Unequal Variances
Smithville
CRWN LCRA
Mean 369.21 370.64
Variance 3829.09 1175.15
Observations 38 23
df 59
t Stat -0.12
P(T<=t) one-tail 0.45
t Critical one-tail 1.67
P(T<=t) two-tail 0.91
t Critical two-tail 2.00
The absolute value of the t-stat is very low, indicating that there is no statistical difference in
the means of the two data sets.
86
The Standard Error of the Mean
Standard Error of the Mean
Total Dissolved Solids
CRWN Smithville
100
150
200
250
300
350
400
450
500
550
600
1 3 5 7 9
11 13 15 17 19 21 23 25 27 29 31 33 35 37
Number of Samples
TDS
(mg/l)
Figure 5-28 Standard Error of the Mean, TDS- CRWN3
Standard Error of the Mean
Total Dissolved Solids
LCRA -Smithville
100
150
200
250
300
350
400
450
500
1 2 3 4 5 6 7 8 9 1011121314151617181920212223
Number of Samples
TD
S (
m
g/
l
)
TDS
Cum Mean
m-2sd
m+2sd
Figure 5-29 Standard Error of the Mean, TDS- LCRA3
87
The plots in Figures 5-28 and 5-29 show how both data sets converge at almost the same value
with a very small range in the error around the means.
88
5.4 LaGrange
Site Analysis- Dissolved Oxygen-- Sites LCRA 4 and CRWN 4
These sites are located at the upstream end of river segment 1402. The CRWN site is a
level 2 site monitored by a high school science class downstream of the LCRA site. The CRWN
site lacked data during the period from April to August. 85% of the measurements occurred
between October 1 and March 31. For the following analysis a time span of approximately two
years was used.
CRWN data- 10/19/95 to 10/14/97, n=34.
LCRA data- 10/17/95 to 10/2/97, n=13
Descriptive Statistics
Table 5-29 is the descriptive statistics from each site for dissolved oxygen:
Table 5-29 Descriptive Statistics, DO- LaGrange
Mean 9.44 Mean 8.38
Standard Error 0.40 Standard Error 0.25
Median 9.15 Median 8.40
Mode 9.20 Mode 9.40
Standard Deviation 2.31 Standard Deviation 0.92
Sample Variance 5.34 Sample Variance 0.84
Kurtosis 3.16 Kurtosis -0.78
Skewness 1.36 Skewness -0.09
Range 12.15 Range 3.1
Minimum 5.15 Minimum 6.8
Maximum 17.3 Maximum 9.9
Sum 320.9 Sum 109
Count 34 Count 13
Confidence Level(95.0%) 0.81 Confidence Level(95.0%) 0.56
LCRA DATA- LaGrangeCRWN DATA- LaGrange
The mean and median for both data sets are very close to each other. The CRWN data
has a much higher range (2.5 times more data), a much higher standard deviation and the data is
more skewed. The means of the two data sets differ by 1.0 mg/l. The higher mean dissolved
oxygen level for the CRWN data is at least partially due to the fact that the CRWN data set lacks
89
summer data when, generally, the dissolved oxygen level would normally be at its lowest. This
would also account for the positive skewness.
Combining the Data Sets
Table 5-30 is the descriptive statistics of the combined data sets.
Table 5-30 Descriptive Statistics, Combined Data, DO- LaGrange
Mean 8.97
Standard Error 0.249
Median 8.8
Mode 7.8
Standard Deviation 1.692
Sample Variance 2.863
Kurtosis 1.432
Skewness 0.83
Range 8.95
Minimum 5.15
Maximum 14.1
Sum 412.6
Count 46
Combined Data
LaGrange
The standard error for the combined data sets is lower than either individual data sets
which indicates an improvement in the estimation of the mean.
90
Histograms
The histograms, Figure 5-30, indicate a normal distribution for both data sets:
Histogram
CRWN Data- LaGrange
0
1
2
3
4
5
6
7
8
9
10
4 6 8
1
0
1
2
14 1
6
Bin
Frequency
Frequency
Histogram
LCRA Data- LaGrange
0
1
2
3
4
5
6
7
8
9
10
4 6 8
10 1
2
1
4
1
6
Bin
Frequency
Frequency
Figure 5-30 Histograms, DO- LaGrange
Quantile Plots
The quantile plots, Figures 5-31 and 5-32, show that both data sets are normally distrib-
uted. Both correlation coefficients are greater than the lower critical value of the probability plot
correlation test statistic for the normal distribution.
91
Quantile Plot- Dissolved Oxygen-- CRWN- LaGrange
n=34, Correlation = 0.98
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
Standard Normal Variable (z)
DO
(
mg/l)
Figure 5-31 Quantile Plot, DO- CRWN4
Quantile Plot- Dissolved Oxygen-- LCRA- LaGrange
n=13, Correlation= 0.993
0
2
4
6
8
10
12
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Standard Normal Variable (z)
DO
(
mg/l)
Figure 5-32 Quantile Plot, DO- LCRA4
92
t-test:
Table 5-31 t-test Results, DO- LaGrange
2.236
CRWN LCRA
Mean 9.44 8.38
Variance 5.34 0.84
Observations 34 13
Hypothesized Mean Difference 0
df 45
t Stat 2.236
P(T<=t) one-tail 0.02
t Critical one-tail 1.68
P(T<=t) two-tail 0.03
t Critical two-tail 2.01
calculated t=
The t value for these data sets (Table 5-31) is greater than 2. This is due mainly to the
difference in the mean values of 1.06 mg/l, the largest difference of all of the sites analyzed.
This indicates that the hypothesis that there is not a significant difference between the data sets is
not valid. The CRWN data contained one measurement that was considerably higher than any
other measurement, 17.3 mg/l. Eliminating that data point resulted in the calculated t-value be-
ing 1.969, or slightly less than 2.0. This illustrates the sensitivity of this analysis to "outlier"
data. Also, the gross lack of volunteer data for one half of the year would contribute to the
higher value of t. Table 5-32, below, shows the descriptive statistics of the CRWN site with the
high value eliminated:
93
Table 5-32 Descriptive Statistics w/o Outlier Data, DO- LaGrange
Standard Error of the Mean
Standard Error of the Mean
Dissolved Oxygen
CRWN 4-- LaGrange
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
0 5 10 15 20 25 30 35 40
Number Of Samples (n)
D
O
(mg
/l)
DO
Cum Mean
m-2sd
m+2sd
Figure 5-33 Standard Error of the Mean, DO- CRWN4
94
Standard Error of the Mean
Dissolved Oxygen
LCRA 4-- LaGrange
4
5
6
7
8
9
10
11
12
13
14
02468101214
Number of Samples
DO (mg
/l)
DO
Cum Mean
m-2sd
m+2sd
Figure 5-34 Standard Error of the Mean, DO- LCRA4
The Standard Error of the Mean plots, Figures 5-33 and 5-34, indicate the variability in
the CRWN data set, while the LCRA data sets appears very stable with a very small 95% confi-
dence interval. Below, Table 5-33, is the tabular results of the standard error of the mean
evaluation of the two data sets:
95
Table 5-33 Standard Error of the Mean, DO- LaGrange
Standard Error of the Mean CRWN Data- LaGrange
index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
1 9.2 9.20 0 9.200 9.200 0.000
2 8.3 8.75 0.225 8.300 9.200 0.900
3 8.2 8.57 0.188 8.190 8.943 0.753
4 10.2 8.98 0.137 8.700 9.250 0.549
5 11.7 9.52 0.168 9.185 9.855 0.670
6 12.1 9.95 0.209 9.532 10.368 0.836
.. .. .. .. .. .. ..
31 8.2 9.70 0.140 9.416 9.977 0.561
32 7.05 9.61 0.137 9.340 9.888 0.547
33 8.1 9.57 0.134 9.301 9.836 0.535
34 5.15 9.44 0.131 9.176 9.701 0.525
Standard Error of the Mean LCRA Data- LaGrange
index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
1 8.8 8.80 0 8.800 8.800 0.000
2 8.9 8.85 0.025 8.800 8.900 0.100
3 9.4 9.03 0.071 8.891 9.175 0.284
4 8.3 8.85 0.051 8.747 8.953 0.205
5 7.3 8.54 0.079 8.381 8.699 0.317
6 8.4 8.52 0.082 8.353 8.680 0.327
.. .. .. .. .. .. ..
10 8.7 8.65 0.066 8.519 8.781 0.262
11 7.8 8.57 0.060 8.453 8.693 0.240
12 7.9 8.52 0.056 8.404 8.629 0.224
13 6.8 8.38 0.056 8.274 8.496 0.222
The variability around the mean is significantly higher for the volunteer site despite the
fact that there is more than twice as much data. There is a much more variability in the volunteer
measurements which may warrant taking a closer look at characteristics of the measurements,
such as the consistency in time of day of the measurements and the time span that is missing.
The standard error of the mean for the CRWN data with the high value of 17.3 eliminated is
shown in Table 5-34 below
Table 5-34 Standard Error of the Mean w/o Outlier Data, DO- LaGrange
Standard Error of the Mean CRWN Data- LaGrange
index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
33 5.2 9.20 0.102 8.995 9.405 0.410
The range around the mean has been reduced by 0.115 mg/l by eliminating the one high
value. This, again, illustrates the sensitivity of the analysis to "outlier" data. This also illustrates
96
the need to have a strong quality assurance system in place to prevent erroneous data from
skewing the data.
Fouier Analysis--Dissolved Oxygen
The statistics for the regression analysis of the two data sets are shown in Tables 5-35 and
5-36:
Table 5-35 Regression Statistics, DO- LCRA4
LCRA- LaGrange- SUMMARY OUTPUT
j=1
Regression Statistics
Multiple R 0.78
R Square 0.60
Adjusted R Square 0.53
Standard Error 0.63
Observations 13
ANOVA
df SS MS F Significance F
Regression 2 6.13 3.06 7.63 0.01
Residual 10 4.01 0.40
Total 12 10.14
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 8.41 0.18 47.62 0.00 8.02 8.81
X Variable 1 0.87 0.26 3.30 0.01 0.28 1.45
X Variable 2 0.46 0.24 1.93 0.08 -0.07 0.99
Table 5-36 Regression Statistics, DO- CRWN4
CRWN- LaGrange- SUMMARY OUTPUT
j=1
Regression Statistics
Multiple R 0.65
R Square 0.43
Adjusted R Square 0.39
Standard Error 1.47
Observations 33
ANOVA
df SS MS F Significance F
Regression 2 47.86 23.93 11.10 0.00
Residual 30 64.64 2.15
Total 32 112.50
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 8.16 0.34 23.76 0.00 7.46 8.86
X Variable 1 2.13 0.49 4.36 0.00 1.13 3.13
X Variable 2 1.19 0.38 3.10 0.00 0.41 1.98
97
The plot of the CRWR-LaGrange with the raw data (Figure 5-35):
DO Fourier Plot With Raw Data
CRWN-LaGrange
4.00
6.00
8.00
10.00
12.00
14.00
16.00
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Julian Days
DO (m
g
/l)
j=1
DO
Figure 5-35 CRWN4 Fourier Plot, DO with Data
It is interesting to note that the minimums of the fourier curves are well below all but one
data point. As shown below the two curves match well in time but the minimums differ by
nearly 1.0 mg/l.
98
The plot of the best fit lines for the two data sets is shown in Figure 5-36:
DO Fourier Plot With Raw Data
CRWN vs. LCRA- LaGrange
4.00
6.00
8.00
10.00
12.00
14.00
16.00
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Julian Days
D
O
(m
g/l)
CRWN
LCRA
CRWN Series
LCRA Series
Figure 5-36 Fourier Plot, DO- LaGrange
The results of comparing the means of the two data sets as determined by the two types
of analysis are shown in Table 5-37, below.
Table 5-37 Summary of Means, DO- LaGrange
Method LCRA (n=13)
Mean ? Standard Error
CRWN (n=34)
Mean ? Standard Error
Standard Statistics 8.38 ? 0.25 mg/l 9.44 ? 0.40 mg/l
Fourier Analysis (Intercept) 8.41 ? 0.18 mg/l 8.16 ? 0.34 mg/l
The difference between the means of the two data sets is much lower with the fourier
analysis, 0.25 mg/l, and 1.06 mg/l with standard statistics.
99
Total Dissolved Solids Analysis
The scatter plot for the TDS data, LCRA vs. CRWNis shown in Figure 5-37:
TDS Scatter Plot
CRWN vs. LCRA LaGrange
0
100
200
300
400
500
600
700
800
900
1000
04/11/95 02/05/96 12/01/96 09/27/97 07/24/98
Date
TD
S (mg/
l
)
LCRA
CRWN
Figure 5-37 Scatter Plot, TDS- LaGrange
The two data sets are in good agreement except for 4 "outlier" points in the CRWN data
with values of between 800 and 1000 mg/l. On 2/21/96 both the professional and the volunteer
monitors measured and were in within 50 mg/l of each other that day.
100
Descriptive Statistics for TDS:
Table 5-38 Descriptive Statistics, TDS- LaGrange
CRWN- LaGrange LCRA- LaGrange
Mean 394.85 Mean 347.95
Standard Error 36.61 Standard Error 14.08
Median 330 Median 359.4
Mode 320 Mode #N/A
Standard Deviation 210.31 Standard Deviation 50.77
Sample Variance 44232.01 Sample Variance 2577.09
Kurtosis 3.27 Kurtosis 0.83
Skewness 2.00 Skewness -0.58
Range 850 Range 193.8
Minimum 120 Minimum 238.2
Maximum 970 Maximum 432
Sum 13030 Sum 4523.4
Count 33 Count 13
TDS TDS
The high values in the CRWN data, shown in Figure 5-38, has caused a skewness in the
positive direction. The range in the CRWN data is more than four time the LCRA data.
Histograms
Histogram CRWN-LaGrange
Total Dissolved Solids
0
2
4
6
8
10
12
14
15
0
25
0
35
0
45
0
55
0
65
0
Mo
re
100
Fr
e
que
nc
y
Histogram LCRA- LaGrange
Total Dissolved Solids
0
2
4
6
8
10
12
14
150 200 250 300 350 400 450 500 550 600 650 700
Mor
e
100
Fr
e
que
nc
y
Figure 5-38 Histograms, TDS- LaGrange
The CRWN data show a strong normal distribution except for a few outlier points.
101
t-test
Table 5-39 t-test Results, TDS- LaGrange
Calculated t-stat. 1.196
t-Test: Two-Sample Assuming Unequal Variances
LaGrange
CRWN LCRA
Mean 394.85 347.95
Variance 44232.01 2577.09
Observations 33 13
Hypothesized Mean Difference 0
df 40
t Stat 1.20
P(T<=t) one-tail 0.12
t Critical one-tail 1.68
P(T<=t) two-tail 0.24
t Critical two-tail 2.02
Despite the large differences due to the outlier data points the t-stat remains well below 2 (Table
5-39) which indicates that there is not a significant difference in the means of the data sets.
The Standard Error of the Mean Plots
Standard Error of the Mean
Total Dissolved Solids
LCRA -LaGrange
100
150
200
250
300
350
400
450
1234567891011213
Number of Samples
TD
S
(m
g/l)
TDS
Cum Mean
m-2sd
m+2sd
Figure 5-39 Standard Error of the Mean, TDS- LCRA4
102
Standard Error of the Mean
Total Dissolved Solids
CRWN LaGrange
100
200
300
400
500
600
700
800
900
1000
1 3 5 7 9
11 13 15 17 19 21 23 25 27 29 31 33
Number of Samples
TDS
(mg/l)
Figure 5-40 Standard Error of the Mean, TDS- CRWN4
The standard error of the mean plots, Figures 5-39 and 5-40, show how the two data sets
are converging within 50 mg/l of each other. Without the high values the CRWN data set would
be converging much closer with the professional data set. The two data sets are very similar to
each other except for the few extremely high values in the volunteer data. Both have relatively
small confidence intervals around the mean.
103
Columbus
Site Analysis- Dissolved Oxygen-- Sites LCRA 5 and CRWN 5
These sites are located in the middle of river segment 1402. The LCRA monitors at this site six
times a year upstream from the CRWN site. The site is monitored by a high school science class,
which results in a lack of data in the summer months. There is a higher percentage of measure-
ments from April to September, 40%.
A time span of approximately four years was used for this analysis:
CRWN data- 9/27/93 to 12/10/97, n=63.
LCRA data- 8/24/93 to 10/2/97, n=26.
Descriptive Statistics
Table 5-40 is the descriptive statistics from each site for dissolved oxygen:
Table 5-40 Descriptive Statistics, DO- Columbus
CRWN DATA- Columbus LCRA DATA- Columbus
Mean 7.98 Mean 7.70
Standard Error 0.23 Standard Error 0.21
Median 8.00 Median 7.55
Mode 8.00 Mode 7.00
Standard Deviation 1.80 Standard Deviation 1.08
Sample Variance 3.24 Sample Variance 1.17
Kurtosis 6.84 Kurtosis -0.14
Skewness 1.75 Skewness 0.08
Range 11.85 Range 4.70
Minimum 4.30 Minimum 5.30
Maximum 16.15 Maximum 10.00
Sum 502.65 Sum 200.10
Count 63.00 Count 26.00
Confidence Level(95.0%) 0.45 Confidence Level(95.0%) 0.44
Note that there are about two times more CRWN data values than LCRA data values. Both data
sets have mean and median values that are very close to each other and small skewness values.
The mean of the CRWN data is slightly higher than the LCRA site, probably due to the lack of
summer monitoring data. The LCRA data is less skewed (0.08) than the CRWN data (1.75).
The range of the CRWN data is much higher than the LCRA data (11.85 vs. 4.70). Also the
104
means of each data set are different by almost 0.5 mg/l. The descriptive statistics indicate that
the two data sets are normally distributed.
Combining the Data Sets
Table 5-41 is the descriptive statistics of the combined data sets.
Table 5-41 Descriptive Statistics, Combined Data Sets, DO- Columbus
Mean 7.90
Standard Error 0.17
Median 7.9
Mode 8
Standard Deviation 1.62
Sample Variance 2.63
Kurtosis 7.80
Skewness 1.76
Range 11.85
Minimum 4.3
Maximum 16.15
Sum 702.745
Count 89
Confidence Level(95.0%) 0.34166695
Columbus
Combined Data Sets
The standard error for the combined data sets is lower than either individual data sets
which indicates an improvement in the estimation of the mean.
105
Quantile Plots
Quantile Plot- Dissolved Oxygen-- CRWN- Columbus
n=63, Correlation = 0.927
Correllation = 0.991(w/o outliers)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
Standard Normal Variable (z)
DO
(
mg/l)
Figure 5-41 Quantile Plot, DO- CRWN5
Quantile Plot- Dissolved Oxygen-- LCRA- Columbus
n=26, Correlation= 0.992
0.0
2.0
4.0
6.0
8.0
10.0
12.0
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
Standard Normal Variable (z)
DO
(
mg/l)
Figure 5-42 Quantile Plot, DO- LCRA5
106
The quantile plots in Figures 5-41 and 5-42 show that both data sets are normally distrib-
uted. The LCRA correlation coefficient is greater than the lower critical value of the probability
plot correlation test statistic for the normal distribution. The CRWN data set had "outlier" data
which caused the correlation coefficients to be less than the lower critical value of the probability
plot correlation test statistic for the normal distribution. Eliminating just the two highest values
caused the coefficient to be greater than the lower critical value.
Histograms
The histograms in Figure 5-43 show a good visual indication of the normality of the distribu-
tions.
Histogram
CRWN- Columbus
Segment 1402
0
5
10
15
20
25
2 4 6 8
10 12 14 16
Bin
Fr
e
que
nc
y
Frequency
Histogram
LCRA- Columbus
Segment 1402
0
5
10
15
20
25
2 4 6 8
10 12 1
4
16
Bin
Fr
e
que
nc
y
Frequency
Figure 5-43 Histograms, DO- Columbus
107
t-test
Table 5-42 t-test Results, DO- Columbus
0.909
CRWN LCRA
Mean 7.98 7.70
Variance 3.24 1.17
Observations 63 26
Hypothesized Mean Difference 0.00
df 75.00
t Stat 0.909
P(T<=t) one-tail 0.18
t Critical one-tail 1.67
P(T<=t) two-tail 0.37
t Critical two-tail 1.99
Calculated t=
The t value of 0.909, shown in Table 5-42, indicate that there is no significant difference
between the means of the two data sets.
Standard Error of the Mean
Table 5-43 Standard Error of the Mean, DO- Columbus
Standard Error of the Mean CRWN Data- Columbus
index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
1 7.10 7.10 0.000 7.100 7.100 0.000
2 7.20 7.15 0.025 7.100 7.200 0.100
3 7.40 7.23 0.039 7.156 7.311 0.156
4 8.00 7.43 0.071 7.282 7.568 0.286
.. .. .. .. .. .. ..
58 6.60 7.94 0.043 7.858 8.031 0.173
59 8.00 7.95 0.043 7.860 8.031 0.171
60 8.10 7.95 0.042 7.864 8.032 0.168
61 9.65 7.98 0.041 7.893 8.059 0.166
62 8.10 7.98 0.041 7.896 8.060 0.163
63 8.00 7.98 0.040 7.898 8.059 0.161
Standard Error of the Mean LCRA Data- Columbus
index DO Cum Mean Std Dev/n^0.5 m-2sd m+2sd range
1 7.00 7.00 0.000 7.000 7.000 0.000
2 6.90 6.95 0.025 6.900 7.000 0.100
3 8.90 7.60 0.209 7.182 8.018 0.835
4 10.00 8.20 0.294 7.612 8.788 1.176
.. .. .. .. .. .. ..
21 8.90 7.72 0.066 7.591 7.856 0.265
22 8.50 7.76 0.063 7.633 7.886 0.253
23 8.60 7.80 0.060 7.675 7.917 0.242
24 7.60 7.79 0.058 7.672 7.903 0.231
25 6.80 7.75 0.056 7.637 7.859 0.222
26 6.40 7.70 0.053 7.589 7.803 0.214
108
Table 5-43, above, show that the results indicate that in 95 out of 100 similar measure-
ments the mean would lie in the approximate range around the mean indicated in the last column.
The range around the mean for the volunteer data, n=63, is 0.161 or the mean DO with 95% con-
fidence is 7.98 ?0.08 mg/l. The range around the mean for the professional data, n=26, is 0.214
or the mean DO with 95% confidence is 7.70 ? 0.107 mg/l.
The graphical representation of the above analysis is shown below in Figures 5-44 and 5-
45. Both data sets have very small confidence intervals around the mean.
Standard Error of the Mean
Dissolved Oxygen
CRWN 5- Columbus
4
5
6
7
8
9
10
11
12
13
14
0 10203040506070
Number of Samples
DO
(
m
g/l)
DO
Cum Mean
m-2sd
m+2sd
Figure 5-44 Standard Error of the Mean, DO- CRWN5
109
Stadard Error of the Mean
Dissolved Oxygen
LCRA 5- Columbus
4
5
6
7
8
9
10
11
12
13
14
0 5 10 15 20 25 30
Number of Samples
DO
(
mg/l)
DO
Cum Mean
m-2sd
m+2sd
Figure 5-45 Standard Error of the Mean, DO- LCRA5
Fourier Analysis-- Dissolved Oxygen
The statistics for the regression analysis of the two data sets are shown in Tables 5-44 and
5-45.
Table 5-44 Regression Statistics, DO- LCRA5
LCRA Columbus SUMMARY OUTPUT
j=1
Regression Statistics
Multiple R 0.73
R Square 0.53
Adjusted R Square 0.49
Standard Error 0.78
Observations 26
ANOVA
df SS MS F Significance F
Regression 2 15.46 7.73 12.86 0.00
Residual 23 13.83 0.60
Total 25 29.29
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 7.75 0.15 50.80 0.00 7.44 8.07
X Variable 1 1.00 0.22 4.48 0.00 0.54 1.46
X Variable 2 0.48 0.21 2.33 0.03 0.05 0.91
110
Table 5-45 Regression Statistics, DO- LCRA5
CRWN Columbus SUMMARY OUTPUT
j=1
Regression Statistics
Multiple R 0.41
R Square 0.17
Adjusted R Square 0.14
Standard Error 1.67
Observations 63
ANOVA
df SS MS F Significance F
Regression 2 33.20 16.60 5.95 0.00
Residual 60 167.54 2.79
Total 62 200.75
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 7.73 0.23 33.35 0.00 7.26 8.19
X Variable 1 1.16 0.37 3.16 0.00 0.43 1.90
X Variable 2 0.45 0.27 1.66 0.10 -0.09 1.00
The plot of the best fit lines for the two data sets are shown in Figure 5-46.
DO Fourier Plot
CRWN vs.LCRA- Columbus
5.00
5.50
6.00
6.50
7.00
7.50
8.00
8.50
9.00
9.50
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Julian Days
DO (m
g/l)
LCRA
CRWN
Figure 5-46 Fourier Plot, DO- Columbus
The best-fit lines for these two data sets match up very well in time and in magnitudes.
Table 5-46, below, shows the comparison of the mean values determined by the two methods.
111
Table 5-46 Summary of Means, DO- Columbus
Method LCRA (n=26)
Mean ? Standard Error
CRWN (n=63)
Mean ? Standard Error
Standard Statistics 7.70 ? 0..21 mg/l 7.98 ? 0.23 mg/l
Fourier Analysis (Intercept) 7.75 ? 0.15 mg/l 7.73 ? 0.23 mg/l
The mean values of the two data sets as determined by the two types of analysis are in
good agreement. The two means for each data set are within the error range. The mean for the
CRWN data is lower when calculated by the fourier series method. Again, this is probably due
to the lack of summer data for CRWN data set.
Total Dissolved Solids Analysis- Columbus
The TDS scatter plot for the two data sets is shown in Figure 5-47.
TDS Scatter Plot
CRWN vs. LCRA Columbus
0
100
200
300
400
500
600
10/23/92 08/19/93 06/15/94 04/11/95 02/05/96 12/01/96 09/27/97 07/24/98
Date
TD
S (mg/
l
)
CRWN
LCRA
Figure 5-47 Scatter Plot, TDS- Columbus
112
The scatter plot indicates good agreement between the two data sets in the range and
variability.
Descriptive Statistics:
Table 5-47 Descriptive Statistics, TDS- Columbus
CRWN- Columbus LCRA- Columbus
Mean 326.60 Mean 348.14
Standard Error 11.56 Standard Error 13.31
Median 320 Median 355
Mode 260 Mode 355
Standard Deviation 89.58 Standard Deviation 67.85
Sample Variance 8024.31 Sample Variance 4603.37
Kurtosis -0.46 Kurtosis 4.06
Skewness -0.25 Skewness -1.69
Range 370 Range 310
Minimum 120 Minimum 121
Maximum 490 Maximum 431
Sum 19596 Sum 9052
Count 60 Count 26
TDS TDS
Table 5-47 shows that both of the data set?s statistics indicate normal distribution with the mean
and median values close to one another and low skewness values, though the LCRA data is
slightly skewed in the negative direction. The range and maximum/minimum values are in good
agreement.
113
Histograms
Histogram- TDS
LCRA- Columbus
0
2
4
6
8
10
12
14
16
18
1
00
2
0
0
3
0
0
4
00
5
00
60
0
7
00
Bin
Fr
equency
Histogram- TDS
CRWN- Columbus
0
2
4
6
8
10
12
14
16
18
10
0
20
0
30
0
40
0
5
00
600 700
Bin
Fr
equency
Figure 5-48 Histograms, TDS- Columbus
The histograms, Figure 5-48, show both data sets being skewed in the negative direction.
t-test
Table 5-48 t-test Results, TDS- Columbus
t-Test: Two-Sample Assuming Unequal Variances
Columbus
CRWN LCRA
Mean 326.60 348.14
Variance 8024.31 4603.37
Observations 60 26
df 62
t Stat -1.22
P(T<=t) one-tail 0.11
t Critical one-tail 1.67
P(T<=t) two-tail 0.23
t Critical two-tail 2.00
The absolute value of the t-stat is less than 2 indicating that there is not a significant difference in
the means of the two data sets.
114
The Standard Error of the Means Plots
Standard Error of the Mean
Total Dissolved Solids
LCRA -Columbus
100
150
200
250
300
350
400
450
1234567891011121314151617181920212223242526
Number of Samples
TDS (
m
g/
l
)
TDS
Cum Mean
m-2sd
m+2sd
Figure 5-49 Standard Error of the Mean, TDS- LCRA5
Standard Error of the Mean
Total Dissolved Solids
CRWN Columbus
100
150
200
250
300
350
400
450
500
1 4 7
10 13 16 19 22 25 28 31 34 37 40 43 46 49 53 56 59
Number of Samples
TD
S (
m
g/
l
)
Figure 5-50 Standard Error of the Mean, TDS- CRWN5
115
Both data sets converge close to 350 mg/l with a very small error range around the mean.
The mean of CRWN data appears to be in a steady decline. This trend does not appear in the
LCRA data. It would be interesting to note what happens with trend with future measurements.
116
6 SUMMARIES AND CONCLUSIONS
All of the data sets used in this study were shown to be normally distributed using de-
scriptive statistics, histograms and quantile plots. The quantile plot is the most precise tool to
determine if the data is normally distributed.
The results of the quantile plot analysis for two data sets were distorted by a few "outlier"
data values in the set. The elimination of these outlier data points caused the quantile analysis
correlation value to strongly indicate normal distribution.
Once it was established that all of the data sets were normally distributed the statistical
methods to determine the confidence interval of the mean and to compare the two independent
data sets could be chosen.
The standard error of the mean analysis consistently showed an increase in confidence in
the mean with an increase in the number of measurements in the data set. The volunteer data
consistently had a larger number of data points, a larger range and more variability than the pro-
fessional data sets resulting in a larger standard error of the mean for the volunteer data in some
instances. This may be inherent to simply having a larger number of measurements over a given
time period. The accuracy of the instruments and the measurement methodology can also con-
tribute to this. Tables 6-1 and 6-2 summarize the standard error of the mean analysis of the data
sets for dissolved oxygen and total dissolved solids respectively.
Table 6-1 Summary of Data, DO
Number of Samples (n)
Site Professional Volunteer
(n) (n) Range Mean 95% Range Mean 95%
Lake Austin 27 90 8 8.53 0.06 7 8.05 0.35
Bastrop 26 105 6.3 8.96 0.24 10.7 9.35 0.09
Smithville 23 37 6.2 8.59 0.22 9.5 7.73 0.27
LaGrange 13 34 3.1 8.38 0.11 12.15 9.44 0.26
Columbus 26 63 4.7 7.70 0.17 11.85 7.98 0.08
Summary of Data-- Standard Error of the Mean Results-- Dissolved Oxygen
VolunteerProfessional
117
Table 6-2 Summary of Data, TDS
Number of Samples (n)
Site Professional Volunteer
(n) (n) Range Mean 95% Range Mean 95%
Lake Austin 27 91 99 327 1.6 490 334 15.5
Bastrop 25 101 236 363 2.8 420 368 2.0
Smithville 23 38 146 371 3.1 300 369 3.0
LaGrange 13 33 194 348 8.9 850 395 26.0
Columbus 26 61 310 348 5.4 370 327 5.8
Summary of Data-- Standard Error of the Mean Results-- Total Dissolved Solids
VolunteerProfessional
The t-values shown in Table 6-3 for dissolved oxygen and Table 6-4 for total dissolved
solids are consistently below the value of two which indicates that the means of all of the data
sets compared were not significantly different.
Table 6-3 Summary of Data, DO, t-tests
Sites Professional Volunteer
(n) (n) Range Max. Min. Range Max. Min. t
Lake Austin 27 90 8 12.8 4.8 7 11.6 4.6 1.39
Bastrop 27 90 6.3 13.3 7 10.7 14.8 4.1 1.11
Smithville 23 40 6.2 12.1 5.9 9.5 11.5 2 1.78
LaGrange 13 33 3.1 9.9 6.8 12.15 17.3 5.15 1.97
Columbus 26 63 4.7 10 5.3 11.85 16.15 4.3 0.91
Summary of Data --Descriptive Statististics, t-value
Professional Volunteer
Table 6-4 Summary of Data, TDS, t-tests
Sites Professional Volunteer
(n) (n) Range Max. Min. Range Max. Min. t
Lake Austin 27 91 99 374 275 490 590 100 0.77
Bastrop 25 100 236 439 202 420 540 120 0.44
Smithville 23 37 146 443 298 *300 480 180 1.78
LaGrange 13 33 194 432 238 850 970 120 1.97
Columbus 26 60 310 431 121 370 490 120 1.22
* Outlier Data Removed
Summary of Data --Descriptive Statististics-- Total Dissolved Solids
Professional Volunteer
It should be noted that in some of the cases the professional and volunteer sites were
separated by several river miles and had discharges from creeks and wastewater treatment plants
between them. For instance both Smithville and LaGrange have wastewater treatment discharge
points between the two monitoring sites. This type of situation could be the focus of further
study of the data.
The table in Table 6-5 is a summary of the mean values of dissolved oxygen and total
dissolved solids. The sites are in downstream order.
118
Table 6-5 Summary of Data, Means, DO and TDS
Number of Samples (n)
Site Professional Volunteer Professional Volunteer
(n) (n) Standard Fourier Standard Fourier
Lake Austin 27 90 8.53 8.61 8.05 8.22 327 333
Bastrop 27 90 8.96 9.04 9.35 8.55 363 368
Smithville 23 40 8.59 8.52 7.73 7.69 370 368
LaGrange 13 33 8.38 8.41 9.44 8.16 347 394
Columbus 26 63 7.70 7.75 7.98 7.73 348 326
Professional Volunteer
Dissolved Oxygen (mg/l) Total Dissolved Solids (mg/l)
Mean Values
Table 1. Summary of Data- Mean Values-- Fourier vs. Standard
Mean Values
Three of the four volunteer sites with data lacking during the summer months, when DO
levels would be the lowest, had mean values which were higher than the professional data set.
The exception, Smithville, had several extremely low values which pulled its mean down below
the mean of the corresponding professional data set. The fourier method for determining the
means resulted in these same three volunteer data sets having lower mean values than the profes-
sional data sets. This would be due to the correction for the lack of measurements in the summer
by using the fourier method to determine the mean. Figures 6-1 and 6-2 are the graphical repre-
sentations of the data in Table 6-5.
DO- Mean Values- Standard Method
Professional vs Volunteer
0
1
2
3
4
5
6
7
8
9
10
Lake Austin Bastrop Smithville LaGrange Columbus
Site Names
D
i
s
s
olv
e
d
Ox
y
g
e
n
(
m
g/l)
LCRA
CRWN
Figure 6-1 DO Mean Value
119
DO- Mean Values-- Fourier Analysis
Professional vs Volunteer
0
1
2
3
4
5
6
7
8
9
10
Lake Austin Bastrop Smithville LaGrange Columbus
Site Name
M
ean D
O
(mg/l)
LCRA
CRWN
Figure 6-2 DO Mean Values, Fourier Method
There is no real difference between the professional and volunteer TDS mean values.
This is illustrated in the graph, Figure 6-3, below.
Mean Values-- Total Dissolved Solids
Professional vs Volunteer
0
50
100
150
200
250
300
350
400
450
Lake Austin Bastrop Smithville LaGrange Columbus
Site Name
TDS (m
g/l)
LCRA
CRWN
Figure 6-3 Mean Values, TDS
120
Figures 6-4 and 6-5 illustrate the differences in the mean values of the dissolved oxygen
data sets using the standard method of calculating the mean versus the fourier method. The pro-
fessional (LCRA) mean values, Figure 6-4, were essentially the same using both methods. The
professional data set had a very regular temporal distribution over the time periods studied. This
illustrates how the fourier method is a legitimate way to determine the mean of a data set.
LCRA Data- Di ssol ved Oxygen
Standard Statistics vs Fourier
0
1
2
3
4
5
6
7
8
9
10
Lake Austin Bastrop Smithville LaGrange Columbus
Site Name
Mean
DO
(m
g
Standard
Four ier
Figure 6-4 LCRA Mean Values, DO- Standard vs. Fourier
In contrast the volunteer dissolved oxygen mean values, Figure 6-5, had larger differ-
ences between the means calculated using the standard method and the means determined by the
fourier method. The means determined by the fourier method was consistently lower for those
sites which lacked data during the warmer time of the year when DO values would be lowest.
This illustrates how the fourier method corrected for that lack of data.
121
CRWN- Dissolved Oxygen Mean
Standard Statistics vs Fourier
0
1
2
3
4
5
6
7
8
9
10
Lake Austin Bastrop Smithville LaGrange Columbus
Site Name
M
ean DO (m
g
St an d ar d
Four i er
Figure 6-5 CRWN DO Mean Values, Standard vs. Fourier
This study indicates that there is good statistical agreement between the data col-
lected by volunteer monitors and data collected by professional monitors. The main
weakness of the volunteer monitoring is the lack of consistency temporally.
122
7 BIBLIOGRAPHY
Bartram, Jamie and Balance, Richard. Water Quality Monitoring: A Practical Guide to
the Design and Implementation of Freshwater Quality Studies and Monitoring Pro-
grammes. E & FN Spon, London,1996.
Chapman, D, Water Quality Assessments, E & FN Spon, London, 1996.
Chow V.T., Maidment D.R. and Mays L.W., "Applied Hydrology", McGraw-Hill, Inc.,
1988.
Colorado River Watch Network, Technical Instructions, Fifth Edition(Austin, Texas:
May 1996)
Ely, Eleanor, ed. Building Credibility The Volunteer Monitor, Volume 9, No.1, Spring
1997, pp 19-20.
Ely, Eleanor, ed. Managing and Presenting Your Data. The Volunteer Monitor, Volume
7, number 1, Spring 1995. San Francisco, CA.
Helsel, D.R. and R.M. Hirsch, "Statistical Methods in Water Resources", Elsevier Sci-
ence B.V. 1995
Hubbell, Steven. ?Eyes on the Water: A Framework for Evaluating Volunteer Water
Quality Monitoring Programs.? Master?s Report, The University of Texas at Austin,
May, 1993.
Lower Colorado River Authority, The Texas Clean Rivers Program, Technical Report,
(Austin, Texas: October 1, 1996)
Maidment, David, Assignment #1: Statistical Analysis of Environmental Data, CE 397:
Environmental Risk Assessment, Department of Civil Engineering, The University of
Texas at Austin
Maidment D., Handbook of Hydrology McGraw-Hill, Inc., 1993
Setzer,Woodrow. ?Tips for Statistical Analyses of Parallel Studies", The Volunteer
Monitor, Volume 9, No.1, Spring 1997, pp 19-20.
Setzer, Woodrow, Denise Stoeckel ?Parallel Testing?Volunteers Versus Professionals",
Texas Natural Resource Conservation Commission, Quality Assurance Project Plan,
Texas Watch (Austin, Texas: January 2, 1998)
123
US Environmental Protection Agency, Office of Water, "The Quality of Our Nation?s
Water" Website: http://www.epa.gov/305b/sum1.html#SEC3
U.S. Environmental Protection Agency, National Water Quality Inventory: 1992 Report
to Congress, Office of Water (Washington, D.C.: Government Printing Office, April
1994)
U.S. Environmental Protection Agency, Volunteer Water Monitoring: A Guide For State
Managers, Office of Water (Washington, D.C.: Government Printing Office, August
1990)
U.S. Environmental Protection Agency, Office of Water, Washington, DC. EPA Re-
quirements for Quality Assurance Project Plans (QAPP) for Environmental Data Opera-
tions., EPA/QA/R-5. August 1994. U.S.
U.S Environmental Protection Agency, Office of Research and Development, Washing-
ton, DC., Guidance for Data Quality Assessment. EPA QA/G-9, March 1995. U.S.
124
8 APPENDIX
Raw Data
125
Lake Austin Note: LCRA TDS values are converted from conductivity values
Date CRWN Date LCRA Date CRWN Date LCRA
04/19/93 4.8 04/19/93 8.9 04/19/93 410 4/19/93 317
06/21/93 6.2 06/01/93 8.9 06/21/93 140 6/1/93 323
06/25/93 7.8 08/11/93 8.2 06/25/93 250 8/11/93 332
07/09/93 7.8 10/07/93 7.5 07/09/93 220 10/7/93 317
07/16/93 8.3 02/14/94 10.4 07/16/93 100 2/14/94 335
07/23/93 6.7 04/27/94 9.2 07/23/93 340 4/27/94 333
07/30/93 6.7 06/23/94 9 07/30/93 340 6/23/94 331
08/06/93 7.7 08/29/94 7.7 08/06/93 350 8/29/94 342
08/13/93 6.7 10/18/94 6.4 08/13/93 370 10/18/94 275
08/27/93 7 12/22/94 9 08/27/93 370 12/22/94 338
09/03/93 6.7 02/15/95 12.8 09/03/93 360 2/15/95 374
09/24/93 6.5 04/18/95 8.2 09/24/93 340 4/18/95 364
10/08/93 6.8 06/07/95 9.6 10/08/93 320 6/7/95 350
10/15/93 7 08/17/95 7.9 10/15/93 350 8/17/95 337
10/29/93 8.3 10/25/95 7.9 10/29/93 340 10/25/95 305
11/05/93 8.8 12/14/95 9.3 11/05/93 340 12/14/95 323
11/12/93 8 02/26/96 9.5 11/12/93 320 2/26/96 325
11/19/93 8.2 04/16/96 9.4 11/19/93 400 4/16/96 320
12/13/93 9.6 06/20/96 8.5 12/13/93 400 6/20/96 323
12/16/93 8.6 08/14/96 7.7 12/16/93 340 8/14/96 320
12/17/93 9.4 10/21/96 7.4 12/17/93 350 10/21/96 355
12/30/93 9.2 12/17/96 9 12/30/93 350 12/17/96 352
01/02/94 9.7 03/18/97 10.9 01/02/94 350 3/18/97 344
01/14/94 10.8 04/17/97 8.8 01/14/94 330 4/17/97 313
02/04/94 10.2 06/19/97 7 02/04/94 290 6/19/97 314
02/11/94 10.8 08/27/97 4.8 02/11/94 320 8/27/97 282
02/18/94 7.8 10/13/97 6.4 02/18/94 350 10/13/97 285
03/04/94 8.7 03/04/94 370
03/18/94 7.3 03/18/94 380
03/25/94 9 03/25/94 360
04/01/94 8 04/01/94 350
04/15/94 6.75 04/15/94 340
04/22/94 8.4 04/22/94 370
04/29/94 8.8 04/29/94 360
06/03/94 8.8 06/03/94 360
06/10/94 9.1 06/10/94 380
06/17/94 9.4 06/17/94 380
06/24/94 11 06/24/94 360
07/01/94 7.53 07/01/94 320
07/15/94 5.7 07/15/94 360
07/22/94 6.9 08/05/94 590
08/05/94 6.6 08/12/94 420
08/12/94 5.90 08/19/94 430
08/19/94 4.95 09/16/94 420
09/16/94 5.00 09/23/94 400
09/23/94 6.00 09/30/94 430
09/30/94 4.70 10/06/94 420
10/06/94 4.60 10/14/94 330
10/14/94 5 11/17/94 380
11/17/94 9.20 12/09/94 420
12/09/94 6.6 12/16/94 370
12/16/94 10.60 01/13/95 410
01/13/95 9.4 02/03/95 450
02/03/95 6.5 02/20/95 420
02/20/95 8.7 03/24/95 400
03/24/95 7.5 03/31/95 400
03/31/95 7.77 04/07/95 430
04/28/95 8.7 04/21/95 550
05/12/95 8.1 04/28/95 410
05/19/95 7.2 05/12/95 290
05/26/95 7.9 05/19/95 290
06/02/95 9.6 05/26/95 310
06/09/95 7.6 06/02/95 250
06/16/95 8.1 06/09/95 300
06/22/95 7.4 06/16/95 300
07/21/95 7.4 06/22/95 300
08/25/95 7.9 06/30/95 310
09/08/95 7.5 07/21/95 320
09/14/95 8 08/25/95 290
09/28/95 6.3 09/08/95 290
Total Dissolved Solids (mg/L)Dissolved Oxygen (mg/L)
126
Bastrop Note: LCRA TDS values are converted from conductivity values
Date CRWN Date LCRA Date CRWN Date LCRA
09/28/93 7.00 08/23/93 7.10 10/12/93 390 10/20/93 353
10/05/93 9.00 10/20/93 7.20 10/19/93 420 12/21/93 408
10/12/93 8.00 12/21/93 10.70 10/27/93 370 02/15/94 409
10/19/93 7.60 02/15/94 11.70 11/02/93 300 04/13/94 352
10/27/93 10.00 04/13/94 11.90 11/16/93 530 06/06/94 345
11/02/93 12.00 06/06/94 7.80 11/23/93 360 08/02/94 358
11/16/93 8.90 08/02/94 7.50 11/30/93 330 10/13/94 319
11/23/93 10.00 10/13/94 7.60 12/07/93 360 12/13/94 422
11/30/93 12.20 12/13/94 11.30 12/14/93 420 02/22/95 434
12/07/93 9.20 02/22/95 13.30 12/22/93 490 04/25/95 367
12/14/93 11.00 04/25/95 8.20 12/29/93 390 06/05/95 358
12/22/93 8.50 06/05/95 9.00 01/04/94 340 08/15/95 365
12/29/93 10.00 08/15/95 7.00 01/12/94 390 10/16/95 355
01/04/94 13.40 10/16/95 9.50 01/19/94 400 12/19/95 421
01/12/94 10.50 12/19/95 8.90 01/25/94 410 02/20/96 418
01/19/94 11.30 02/20/96 9.90 02/01/94 430 04/08/96 349
01/25/94 8.80 04/08/96 8.90 02/08/94 370 06/10/96 318
02/01/94 10.00 06/10/96 7.20 02/15/94 360 08/01/96 370
02/08/94 10.00 08/01/96 7.10 02/22/94 350 10/01/96 371
02/15/94 11.00 10/01/96 7.70 03/01/94 370 12/02/96 368
02/22/94 8.80 12/02/96 9.80 03/08/94 430 02/03/97 439
03/01/94 9.50 02/03/97 10.20 03/15/94 370 04/07/97 360
03/08/94 8.00 04/01/97 9.10 03/29/94 350 06/03/97 313
03/15/94 10.00 06/03/97 8.40 04/06/94 130 08/20/97 202
03/29/94 12.50 08/20/97 7.60 04/12/94 290 10/01/97 294
04/06/94 10.50 10/01/97 8.30 04/19/94 320
04/12/94 9.40 04/26/94 420
04/19/94 7.30 05/03/94 380
04/26/94 8.50 05/17/94 330
05/03/94 8.20 05/24/94 390
05/10/94 6.00 10/04/94 370
05/17/94 6.80 10/11/94 320
05/24/94 6.00 10/18/94 120
09/14/94 6.40 10/25/94 410
10/04/94 9.10 11/01/94 360
10/11/94 7.80 11/08/94 250
10/18/94 6.30 11/15/94 430
10/25/94 6.00 11/22/94 430
11/01/94 7.20 12/06/94 430
11/08/94 6.80 12/13/94 430
11/15/94 8.00 12/20/94 340
11/22/94 8.10 12/27/94 460
12/06/94 4.10 01/03/95 330
12/13/94 9.90 01/10/95 380
12/20/94 7.30 01/24/95 420
12/27/94 9.30 01/31/95 390
01/03/95 9.80 02/07/95 489
01/10/95 10.10 02/14/95 430
01/18/95 9.30 02/21/95 420
01/24/95 11.20 02/28/95 460
02/07/95 11.50 03/07/95 460
02/14/95 11.85 03/14/95 220
02/21/95 14.80 09/13/95 320
02/28/95 7.60 09/20/95 300
03/07/95 8.85 10/04/95 300
03/14/95 7.55 10/11/95 290
03/21/95 6.80 11/15/95 300
09/13/95 7.60 12/29/95 290
09/20/95 6.90 01/03/96 350
10/04/95 7.60 01/10/96 320
10/11/95 10.50 01/24/96 310
11/15/95 9.20 01/30/96 315
12/29/95 9.90 02/13/96 280
01/03/96 12.70 02/20/96 280
01/10/96 13.30 02/27/96 340
01/24/96 12.60 03/05/96 310
01/30/96 10.50 09/05/96 420
02/06/96 11.00 09/13/96 430
02/13/96 12.70 09/13/96 430
02/20/96 12.60 09/17/96 490
Dissolved Oxygen (mg/L) Total Dissolved Solids (mg/L)
127
Smithville Note: LCRA TDS values are converted from conductivity values
Date CRWN Date LCRA Date CRWN Date LCRA
09/09/93 6.00 8/23/93 6.90 09/09/93 400 8/23/93 343
10/01/93 7.80 10/20/93 7.50 10/01/93 380 10/20/93 347
10/07/93 2.00 12/21/93 10.10 10/07/93 360 12/21/93 416
10/15/93 7.50 2/15/94 12.10 10/15/93 380 2/15/94 373
10/21/93 2.00 4/13/94 9.70 10/21/93 370 4/13/94 346
11/04/93 4.00 6/6/94 7.00 11/04/93 410 6/6/94 347
11/12/93 9.00 8/2/94 6.90 11/12/93 420 8/2/94 359
11/18/93 3.00 10/13/94 7.60 11/18/93 420 10/13/94 323
12/09/93 7.80 12/13/94 10.50 12/03/93 390 12/13/94 412
01/13/94 9.00 2/22/95 11.30 12/09/93 420 2/22/95 431
01/26/94 6.90 4/26/95 7.80 01/13/94 430 4/26/95 370
12/08/94 7.80 6/5/95 9.00 01/26/94 420 6/5/95 350
12/08/94 7.30 8/15/95 7.00 12/08/94 320 8/15/95 358
01/20/95 8.60 10/16/95 9.40 12/08/94 350 10/16/95 357
03/03/95 9.90 12/19/95 8.40 01/20/95 280 12/19/95 394
03/30/95 9.60 2/20/96 9.10 03/03/95 910 2/20/96 394
04/20/95 8.15 4/8/96 8.40 03/30/95 1130 4/8/96 358
04/28/95 8.10 6/10/96 7.30 04/20/95 350 6/10/96 298
09/20/95 6.30 8/1/96 5.90 04/28/95 380 8/1/96 365
10/05/95 7.00 10/1/96 7.80 09/20/95 340 10/1/96 374
11/08/95 8.90 12/2/96 9.30 10/05/95 320 12/2/96 397
11/17/95 8.50 2/3/97 9.70 11/08/95 310 2/3/97 443
12/07/95 5.60 4/1/97 8.80 11/17/95 330 4/1/97 369
01/19/96 9.90 12/07/95 450
02/08/96 10.15 01/19/96 340
02/15/96 10.10 01/26/96 350
03/08/96 9.80 02/08/96 300
03/22/96 9.40 02/15/96 350
09/28/96 8.45 03/08/96 380
10/18/96 8.30 03/22/96 480
10/24/96 6.00 09/28/96 440
11/22/96 7.10 10/18/96 440
11/26/96 6.40 10/24/96 410
12/05/96 5.40 11/22/96 440
01/21/97 10.20 11/26/96 470
01/31/97 11.50 12/05/96 320
02/14/97 9.60 02/14/97 180
02/27/97 9.20 02/27/97 300
03/20/97 9.20 03/20/97 300
03/26/97 300
Dissolved Oxygen (mg/L) Total Dissolved Solids (mg/L)
128
LaGrange Note: LCRA TDS values are converted from conductivity values
Date CRWN Date LCRA Date CRWN Date LCRA
10/19/95 9.2 10/17/95 8.8 10/19/95 420 10/17/95 361
10/25/95 8.3 12/20/95 8.9 10/25/95 420 12/20/95 238
11/03/95 8.2 02/21/96 9.4 11/03/95 510 02/21/96 410
11/29/95 10.2 04/09/96 8.3 11/15/95 410 04/09/96 355
12/06/95 11.7 06/25/96 7.3 01/17/96 940 06/25/96 337
01/17/96 12.1 08/02/96 8.4 01/31/96 970 08/02/96 362
01/24/96 12.9 10/02/96 7.4 02/07/96 970 10/02/96 370
02/07/96 14.1 12/03/96 9.4 02/21/96 360 12/03/96 377
02/21/96 10.5 02/04/97 9.9 03/01/96 340 02/04/97 432
03/01/96 12.0 04/02/97 8.7 03/07/96 350 04/02/97 359
03/07/96 10.5 06/04/97 7.8 05/22/96 300 06/04/97 306
05/22/96 7.0 08/21/97 7.9 06/08/96 260 08/21/97 286
06/08/96 7.6 10/02/97 6.8 07/07/96 300 10/02/97 330
07/07/96 7.8 11/13/96 320
11/13/96 8.1 11/13/96 330
11/13/96 8.9 11/19/96 330
11/19/96 6.8 11/19/96 320
11/19/96 7.6 12/03/96 210
11/26/96 9.5 12/03/96 310
12/03/96 8.6 12/10/96 320
12/03/96 9.8 12/10/96 310
12/10/96 9.7 01/21/97 220
12/10/96 9.6 02/04/97 380
01/21/97 8.8 02/04/97 380
02/04/97 9.9 02/25/97 320
02/25/97 9.2 02/25/97 310
03/05/97 7.8 03/05/97 790
03/11/97 9.1 03/11/97 290
03/18/97 9.7 03/18/97 260
03/25/97 8.2 03/25/97 330
04/22/97 7.1 10/14/97 120
04/29/97 8.1 10/28/97 270
10/14/97 5.2 11/04/97 360
Dissolved Oxygen (mg/L) Total Dissolved Solids (mg/L)
129
Columbus Note: LCRA TDS values are converted from conductivity values
Date CRWN Date LCRA Date CRWN Date LCRA
04/28/93 7.10 08/24/93 7.00 09/27/93 380 08/24/93 344
09/01/93 7.20 10/21/93 6.90 04/28/93 330 10/21/93 232
09/20/93 7.40 12/08/93 8.90 09/01/93 468 12/08/93 404
09/27/93 8.00 02/16/94 10.00 09/20/93 390 02/16/94 401
10/04/93 6.00 04/14/94 7.20 10/04/93 380 04/14/94 370
10/19/93 7.00 06/07/94 6.60 10/19/93 400 06/07/94 346
11/15/93 9.50 08/03/94 7.10 11/15/93 260 08/03/94 365
12/14/93 7.20 10/13/94 7.80 12/14/93 420 10/13/94 257
01/13/94 8.20 12/14/94 9.00 01/13/94 400 12/14/94 424
01/25/94 8.00 02/23/95 9.40 01/25/94 410 02/23/95 431
03/31/94 8.40 04/26/95 7.90 03/31/94 450 04/26/95 367
04/05/94 6.60 06/06/95 8.30 04/05/94 430 06/06/95 337
04/12/94 8.00 08/16/95 7.00 04/12/94 400 08/16/95 355
04/19/94 8.50 10/17/95 8.40 04/19/94 360 10/17/95 367
04/26/94 6.80 12/20/95 7.50 04/26/94 360 12/20/95 121
05/23/94 6.05 02/21/96 7.30 05/23/94 360 02/21/96 416
06/28/94 6.50 04/09/96 8.10 06/28/94 430 04/09/96 355
08/24/94 7.80 06/25/96 5.30 08/24/94 390 06/25/96 335
09/02/94 8.40 08/02/96 6.30 09/02/94 420 08/02/96 366
09/29/94 8.20 10/02/96 7.30 09/29/94 420 10/02/96 355
11/17/94 8.40 12/03/96 8.90 11/17/94 400 12/03/96 400
01/05/95 8.10 02/04/97 8.50 03/08/95 320 02/04/97 428
01/19/95 7.80 04/02/97 8.60 11/01/95 320 04/02/97 354
01/26/95 9.60 06/04/97 7.60 11/09/95 260 06/04/97 307
02/02/95 8.85 08/21/97 6.80 11/15/95 290 08/21/97 274
03/08/95 8.86 10/02/97 6.40 11/30/95 290 10/02/97 341
11/01/95 7.85 12/01/95 208
11/09/95 8.80 12/13/95 320
11/15/95 16.15 01/01/96 320
11/30/95 10.80 01/11/96 340
12/01/95 7.10 03/14/96 300
12/13/95 7.90 03/21/96 300
01/01/96 5.33 03/28/96 290
01/11/96 9.86 09/03/96 180
03/14/96 10.25 09/09/96 240
03/21/96 13.40 09/12/96 270
03/28/96 9.20 09/18/96 260
09/03/96 5.70 09/20/96 200
09/09/96 6.70 09/24/96 190
09/12/96 6.80 09/30/96 350
09/18/96 6.35 10/08/96 440
09/20/96 4.95 10/21/96 470
09/24/96 4.30 10/29/96 490
09/30/96 6.80 11/14/96 490
10/08/96 7.60 11/26/96 380
10/21/96 7.95 12/11/96 390
10/29/96 6.00 01/11/97 140
11/14/96 9.35 02/13/97 210
11/26/96 8.55 02/21/97 140
12/11/96 7.80 03/07/97 280
01/11/97 9.95 03/20/97 270
02/13/97 8.70 04/10/97 310
02/21/97 6.20 04/17/97 260
03/07/97 7.90 04/21/97 290
04/10/97 8.00 05/15/97 260
04/17/97 8.20 05/20/97 290
04/21/97 7.30 11/05/97 330
05/15/97 6.60 11/19/97 260
05/20/97 8.00 12/03/97 120
11/05/97 8.10 12/10/97 270
11/19/97 9.65
12/03/97 8.10
12/10/97 8.00
Dissolved Oxygen (mg/L) Total Dissolved Solids (mg/L)
130