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.


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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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