United States
Environmental Protection
Agency
Environmental
Research Laboratory
Corvallis OR 97333
Research and Development
EPA/600/S3-89/037 Sept. 1989
Project Summary
An Evaluation of Trend
Detection Techniques for
Use in Water Quality
Monitoring Programs
J.C. Loftis, R.C. Ward, R.D. Phillips, and C.H. Taylor
Goals for a long-term water quality
monitoring program designed to
measure the impacts of acid precipi-
tation were identified using the Acid
Precipitation Act of 1980 (PL 96-294,
Title VII) as a basis. These goals were
refined to obtain statistical hypoth-
eses concerning trends in water
quality that could be statistically
tested.
Seven statistical tests were iden-
tified as capable of providing the
desired information regarding trends
in individual systems. The tests were
evaluated under various conditions
(distribution shape, seasonality, and
serial correlation) in order to deter-
mine how well they might perform. A
Monte Carlo simulation approach was
used to evaluate the tests.
For annual sampling, the Kendall-
tau test is recommended. For sea-
sonal sampling, either the Seasonal
Kendall test or the analysis of
covariance (ANOCOV) on ranks test
is recommended.
This Project Summary was devel-
oped by EPA's Environmental Re-
search Laboratory, Corvallis, OR, to
announce key findings of the research
protect that is fully documented in a
separate report of the same title (see
Project Report ordering information at
back).
Introduction
One of the major goals of the Acid
Precipitation Act of 1980 (PL 96-294, Title
VII) is the evaluation of the environmental
effects of acid precipitation. To accom-
plish this purpose, we must be able to
detect trends in water quality related to
acid precipitation and understand the
nature of these trends.
In this report, the authors examine the
statistical characteristics of the water
quality variables most pertinent to acidi-
fication (ANC, pH, and S042-) and use
these characteristics to estimate the abil-
ity of seven statistical tests to detect tem-
poral trends of varying magnitudes. The
report focuses strictly on populations of
lakes and streams sensitive to acidifica-
tion. It is concerned only with detecting
trends over time and does not deal
directly with cause and effect.
Trend Detection Tests—
Description and Evaluation
The goal most relevant to detecting
long-term trends is the estimation of
regional trends in surface water acidifica-
tion or recovery. Further refinement of
this goal into a statistically meaningful
statement around which a statistically
sound monitoring system can be de-
signed is required. This refinement in-
volves stating the goal as a hypothesis
that can be tested using the data as they
are collected. The null hypothesis can be
stated as: there are no long-term regional
trends in the acidification or recovery of
surface waters. The alternate hypothesis
is that a trend exists.
The available tests for this null hypoth-
esis were evaluated using a univariate
time series approach. The single variable
can be the concentration of a water
quality constituent, the ratio of concen-
trations of two constituents, or the
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weighted average of concentrations over
a group of lakes or streams.
Statistical characteristics of concern
are distribution shape (normality versus
non-normality), seasonal variation, and
serial correlation. There was no attempt
to incorporate the effects of hydrologic
variables such as rainfall or acidic depo-
sition into recommended trend analysis
procedures, although the usefulness of
doing so is discussed.
In order to select statistical tests that
are well matched to both the goals and
anticipated data attributes, background
data from several sources were studied.
Data sources included the U.S. EPA's
Long-term Monitoring (LTM) data set,
data from Environment Canada for
Clearwater Lake, Ontario, and data from
the U.S. Bureau of Reclamation for Twin
Lakes, Colorado. From these data, gener-
alizations were made regarding the level
of seasonal behavior, serial correlation,
and non-normality to be anticipated.
Seven candidate tests for trend detec-
tion, including parametric and nonpara-
metric approaches, were selected for
evaluation. Several options for dealing
with seasonality were included, and one
test included a correction for serial corre-
lation. The candidate trend tests were as
follows:
• Analysis of covariance (ANOCOV)
• Modified "t"
• Kendall-t.au, following removal of sea-
son means
• Seasonal Kendall with serial correla-
tion correction
• Seasonal Kendall
• ANOCOV on ranks
• Modified "t" on ranks
The candidate tests were evaluated by
comparing their performances under a
Monte Carlo simulation study designed to
reproduce the anticipated data character-
istics. The performance indices were (1)
actual significance level and (2) power of
trend detection. Based on Monte Carlo
results, a single trend test was selected
for annual data and two tests are recom-
mended for seasonal data.
Recommendations
For annual sampling, the recom-
mended test is the Kendall-tau, also
called the Mann-Kendall test for trend.
The Mann-Kendall test is nonparametric
and is a member of the class of tests
called rank correlation methods, meaning
that the test checks for a correlation
between the ranks of data and time. The
test does not account for seasonal
variation. Since, however, it is recom-
mended for use with annual data only, no
prior removal of seasonal means is
necessary.
For seasonal (generally quarterly) sam-
pling, two alternative tests are recom-
mended: (1) analysis of covariance
(ANOCOV) on ranks or (2) the Seasonal
Kendall test. Both tests are non-
parametric and both tests performed very
well under most of the conditions studied
in the Monte Carlo analysis (i.e., seasonal
variation and both non-normal and log-
normal error).
Justification of
Recommend ations
The approach taken to compare alter-
nate trend tests was to conduct a
simulation of water quality variables
under varying trend magnitudes and as-
sumed behavioral characteristics. Rec-
ommendations were formulated based on
a comparison of empirical significance
levels and power of candidate tests.
Comparison of trend testing methods
was achieved through Monte Carlo
testing. In a Monte Carlo evaluation, the
significance level of a test is determined
by generating a large number of se-
quences of data with known character-
istics and no trend. The test is applied to
each sequence with the significance level
being the fraction of trials in which a
trend is falsely detected. The power of a
given test is determined the same way,
except that a trend of known magnitude
is added to each synthetic data se-
quence. The power is then the fraction of
sequences in which the trend is correctly
detected.
A total of 3,024 simulations were
conducted covering different ranges of
seasonality, trend magnitude, underlying
distribution, and serial correlation. Results
showed that the most powerful tests over
the range of conditions studied were the
Seasonal Kendall test and ANOCOV on
ranks, although as expected, no single
test performed best under all conditions.
Both of these tests performed as well as
the parametric tests, when the data were
normal, and both outperformed (were
more powerful than) the parametric tests
when the underlying distribution was log-
normal. In a few cases, the Kendall-tau
on deseasonalized data was more power-
ful, but it did not generally preserve the
nominal significance level as well as the
other tests. The modified "t" test on
ranks performed well, but was in most
cases slightly less powerful than
ANOCOV on ranks. All tests, except the
corrected Seasonal Kendall, suffered
from inflated significance levels undei
serial correlation. The corrected test
however, was much less powerful thar
the other tests, except for very larg«
trend magnitudes and/or long dat;
records.
Expected Performance of
Monitoring-Power of Trend
Detection
The actual ability of monitoring anc
data analysis to detect trends in wate
quality depends upon data charac
teristics, especially temporal variance
and upon the shape or functional forn
and magnitude of the trend that actualh
occurs. Thus trend detection power:
cannot really be predicted in advance. I
is informative, however, to assume ;
reasonable set of data characteristics am
trend characteristics and then to calculate
detectable trend magnitudes over variou;
time horizons. The adequacy of a pro
posed monitoring network design cai
thus be evaluated in objective terms.
Theoretical curves depicting the powe
of trend detection for individual system
versus time for quarterly and annul
sampling were constructed and com
pared to simulation results. Comparabl
curves were developed for multiple lake
for the problem of detecting changes i
regional means. The Kendall an<
ANOCOV tests were also applied t
historical data from Clearwater Lake
Ontario, and Twin Lakes, Colorado.
Specialized Procedures
Specialized techniques, in which th
interrelationships among multiple wate
quality variables and/or local watershe
conditions are considered, are likely to b
more powerful for detecting trend!
These techniques include adjustment f<
hydrologic factors, such as stream flo'
and precipitation, use of water qualit
indices, multivariate trend tests, an
analysis of water quality or watershe
model output. Possible implementation <
these techniques is discussed in th
report.
References
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Dinius, S. H. 1987. Design of an index of
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J. C. Loftis, R. C. Ward, R. D. Phillips, and C. H. Taylor are with Colorado State
University, Fort Collins, CO 80523.
D. H. Landers is the EPA Project Officer (see below).
The complete report, entitled "An Evaluation of Trend Detection Techniques for
Use in Water Quality Monitoring Programs," (Order No. PB 90-100 058/AS; Cost:
$21.95, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Environmental Research Laboratory
U.S. Environmental Protection Agency
Corvallis, OR 97333
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use $300
EPA/600/S3-89/037
C00085833
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