EPA-600/3-78-038
April 1978
Ecological Research Series
       TIME  SERIES EXPERIMENTS FOR  STUDYING
         PLANT GROWTH  RESPONSE TO  POLLUTION
                                      Environmental Research Laboratory
                                     Office of Research and Development
                                    U.S. Environmental Protection Agency
                                           Corvallis, Oregon 97330

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                 RESEARCH REPORTING SERIES

Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:

      1.   Environmental Health Effects Research
      2.   Environmental Protection Technology
      3.   Ecological Research
      4.   Environmental Monitoring
      5.   Socioeconomic Environmental Studies
      6.   Scientific  and Technical Assessment Reports (STAR)
      7.   Interagency Energy-Environment Research and Development
      8.   "Special"  Reports
      9.   Miscellaneous Reports

This report has been assigned to the ECOLOGICAL RESEARCH series. This series
describes research on the effects of pollution on humans, plant and animal spe-
cies, and materials.  Problems are assessed for their long- and short-term influ-
ences. Investigations include formation, transport, and pathway studies to deter-
mine the fate of pollutants and their effects. This work provides the technical basis
for setting standards to minimize undesirable changes in living organisms in the
aquatic, terrestrial, and atmospheric environments.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.

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                                           EPA-600/3-78-038
                                           April  1978
  TIME SERIES EXPERIMENTS FOR STUDYING PLANT

        GROWTH RESPONSE TO POLLUTION
                      by
        Larry Male and John VanSickle
  Ecosystem Modeling and Analysis Branch
                     and
                  Ray Wilhour
        Terrestrial Ecosystem Branch
Corvallis Environmental Research Laboratory
          Con/all is, Oregon  97330
 CORVALLIS ENVIRONMENTAL RESEARCH LABORATORY
     OFFICE OF RESEARCH AND DEVELOPMENT
    U.S.  ENVIRONMENTAL PROTECTION AGENCY
          CORVALLIS, OREGON  97330

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                                 DISCLAIMER
     This  report has  been reviewed  by  the Corvallis  Environmental  Research
Laboratory,  U.S. Environmental  Protection  Agency,  and  approved  for  publi-
cation.   Mention of trade  names or  commercial  products does  not constitute
endorsement or recommendation for use.

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                                  FOREWORD

     Effective  regulatory  and   enforcement   actions  by  the  Environmental
Protection Agency would  be  virtually impossible without sound scientific data
on pollutants  and their  impact  on environmental stability  and  human health.
Responsibility for building this  data base has  been  assigned  to EPA's Office
of  Research  and  Development  and  its  15  major  field installations,  one  of
which is the  Corvallis Environmental Research Laboratory (CERL).

     The  primary mission of  the  Corvallis  Laboratory  is  research  on  the
effects  of  environmental  pollutants on  terrestrial, freshwater,  and marine
ecosystems;  the behavior,  effects  and control of pollutants  in  lake systems;
and the  development  of  predictive models on the movement of pollutants in the
biosphere.

     This  report  details research aimed at  establishing  functional relation-
ships  between  agricultural  crop   losses  and  natural  variations  in  S02  air
pollution.
                                                  A.F.  Bartsch
                                                  Director, CERL

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                                  ABSTRACT


     This research  program  was  initiated with the overall objective of defin-
ing  experiments  which  could predict  the  yield  losses  of crops  grown  under
naturally varying sulfur dioxide concentrations.

     A model  for simulating  realistic fluctuations in  S02  air  pollution  was
developed.  This  model  was  used  to design experiments  in  field growth  cham-
bers  for  the purpose  of establishing the  functional  and probabilistic  rela-
tionship  between yield  loss and  median  S02  concentration.  The stochastic
experiments  are  offered as  a  viable alternative  to  traditional  long-term
fixed concentration experiments.

     This  report covers a  period  from April  1974 to September 1977  and  was
completed as of  February 1978.
                                      IV

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                                  CONTENTS


Foreword	   iii

Abstract	    iv

Figures	    vi

     1.   Introduction 	     1
     2.   General Characteristics of Observed Pollutant Levels	     2
     3.   Experimental time series models 	     6

               Stationary Stochastic Models	     6
               Periodic Models	    10

     4.   Discussion	    15

References	    16

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                                    FIGURES
Number                                                                    Page

  1        Daily treatment schedules for S02 ~~ applied continuously
          through growing season 	   11

  2        Periodic S02 treatment schedule — applied continuously
          during growing season  	   12

  3        Five-day sample from concentration time series.  Series
          generated by stochastic process with diurnal periodicity
          in hourly geometric mean concentration  	   14

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                                  SECTION 1

                               INTRODUCTION
     A  fundamental   problem  in  air  pollution-plant  effects  research is  to
predict  the reduction  in  yield of  crops  grown in  areas of  significant  S02
stress.  Within  such areas the  pollutant  concentration at any  point  in  time
is  only  probabilistically predictable,  i.e.,  we can only predict  the proba-
bility that the concentration will fall within a specified interval.  Assuming
the S02  source  strength in an area does not vary over time,  then the fluctua-
tions  in pollutant  concentration are caused primarily by random variations in
wind  speed.   The  time  history  of pollutant concentrations within  an  area is
called  a time  series.   Pollutant time  series  for different  growing  seasons
will appear to  be  considerable different but they will  usually be probabilis-
tically  the same.   Because  of this probabilistical regularity, a model with a
maximum of two or three parameters can simulate certain pollutant time series.
It  is  our purpose  in this paper  to  motivate  the  use of a time series model
for experimentally  studying the  long term effect  on  plant  growth of stochas-
tically (probabilistically) varying pollutant concentrations.

     As  a  first step we might ask "What relationship might  we expect between
crop yield  and a pollutant time  series?"  We  hypothesize that plant growth
rate will  fluctuate in  correspondence with the pollutant time series?  Assume
for the  moment that  growth rate is depressed by  the pollutant.  Plant yield
would  then  be  the  integral, over the  growing  season, of the resulting growth
rate  time  series.    Since  pollutant  time  series within  different  growing
seasons  are probabilistically  the  same,  we would   expect  growth   rate  time
series  to  be  probabilistically  the  same.  Hence  we  would  expect yield in
different  growing  seasons to  be probabilistically the  same.   Ideally, know-
ledge  of the  pollutant  probability  distribution would  allow  one to predict,
for  any  growing  season,  the  probability  that  yield would  be  within  any
specified range.

     The  above model  assumes that  there  is  a  simple  relationship  between
instantaneous  growth rate and pollutant concentration,  but  establishing this
relationship  is not  trivial.   It  is  not practical  to  continuously  monitor
growth  rate  in order to study  its relationship with randomly varying pollu-
tant concentration.   Even  if  it  were possible to monitor growth rate it would
be  an  exceedingly  complex task to correlate it  with  observed fluctuations in

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pollutant  concentration.   In order to achieve  a  desirable precision,  a model
would  have  to consider response time  lags, recovery rate  at different concen-
trations, adaptation,  and of course variation in  other environmental variables
which  affect growth  rate.   Such  a model may eventually  prove  to  be our best
predictive tool but we must wait for further technological  development.

     If  we  cannot construct a model which will predict growth  rate as a func-
tion  of  pollutant concentration  and other  environmental  variables  then  we
might  ask  whether there  exists  a single  summary statistic for  a pollutant
time  series which  would  correlate well  with plant yield.   We cannot answer
this question here, but we  can  suggest  an experimental  approach which can be
used to  define the relationship between  long term growth  response and summary
statistics for a pollutant time series.

     One  experimental  technique  which has been used to estimate the effect of
S02  on crop yield  is  the "long-term fixed concentration  experiment."  Plants
are  subjected to  a fixed S02 concentration  for  an  entire growing season.   A
variation  of  this  experiment  is the  use  of  intermittent exposures  (say,
exposure  every other week).   The  critical assumption underlying this approach
is that  reductions in yield would be  the same as if the  pollutant concentra-
tion  had varied  stochastically  about an  average equal  to the experimentally
fixed  concentration.   Since this  type of  experiment  violates  our hypotheses
concerning  the  interactions  of  growth   rate  and pollutant concentration  we
suggest  abandoning it  in  favor of  experiments which expose plants to a realis-
tic  pollutant concentration  schedule over the  entire  growing season at near-
ambient  environmental  conditions.  The  final  yield of  the  plants would then
be correlated with summary  statistics which characterize  the entire pollutant
regime to which the plants were exposed.

     This  strategy has  led  to at least three different  experimental methods
which  appear  promising.   Oshima  et  al_.  (1976)  conducted growth experiments
based  on environmental gradient analysis.  In  this design,  crops are grown in
identical  field plots  maintained  at  different distances  from  a strong urban
oxidant  source,  thus  providing a natural  gradient in  average concentration
and  dose.   A second  method  is  the zonal  air pollution  system  (ZAPS),  des-
cribed by Lee et  aj.  (1975).  The system employs grids of pipes that dispense
gaseous  pollutants on field  plots.   Source  strength  is  varied  over several
plots  to create a  gradient  of average concentrations, and local variations in
wind speed produce realistic  short-term fluctuations in concentration.

     A third approach, described  here,  uses  closed  field chambers to control
the  S02  regime.   Pollutant concentrations in the chambers are  changed hourly,
thus  plants  are  exposed  to  an  arbitrary,  rapidly  changing  time  series  of
pollutant  concentrations.   This  flexibility  provides  a distinct advantage
over  the natural  gradient and ZAPS methods  which depend on local meteorolo-
gical  conditions for concentration variability.

     These  approaches are sensible only  if  one  can quantitatively summarize
long,  continuously-changing  time   series  of pollutant  concentrations.   For-
tunately,  traditional  statistical  analyses (Larsen, 1971) coupled with advan-
ces  in time  series analysis  techniques  (Box and Jenkins,  1976; Jenkins and
Watts, 1968) have begun to satisfy  this need.

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     When experimental  pollutant  concentrations  are controlled on an hour-by-
hour basis,  as  in the closed field  chambers,  one  must also be able to repro-
duce realistic  time series of pollutants.  This paper  describes  models which
will  generate  such time  series  and  discusses the  design  of  plant  growth
studies based on the models.

     The following  section is  a brief, qualitative description of  the pollu-
tant time series observed in the ambient environment.

     The  final   sections  provide  mathematical  descriptions of observed  time
series and  present  models  which simulate those observations.  We  also discuss
experimental design problems which arise when the  models are used to generate
pollutant exposure schedules.

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                                 SECTION 2

            GENERAL CHARACTERISTICS OF OBSERVED POLLUTANT LEVELS


     The  standard  method of summarizing concentration  levels  observed  over a
long  time  interval   is  to  plot  their relative  frequencies of  occurrence.
Typically  the  data consist of  low  concentrations  with  infrequent occurrences
of  high  concentrations.   Thus,  the frequency curves  can  usually  be described
by  a  lognormal  distribution,  over a broad range of pollutant types and source
configurations  (Larsen,  1971;  Lee  et al_. 1975; Gifford, 1974; and Bencala and
Seinfeld,  1976).   Gifford  (1974)  and  Knox  and  Pollack   (1974)  provide  a
simple theoretical  explanation  of  the observed lognormality.  They argue that
a  pollutant from  several   sources,  as  seen in  urban  areas,  tends to  have
concentration  levels  which are highly correlated  over short time intervals,
and they show how this leads to a lognormal frequency curve.

     If  concentrations  are distributed lognormally, they can be summarized by
a  median  and  shape parameter  as  described  in  Section 3.    In assessing  the
variable  response  of vegetation to ambient  pollution concentration distribu-
tions,  it is  sufficient to correlate  plant response  with  two  parameters of
the distribution, the  median concentration and the shape  parameter.

     A  common  test for  lognormality  is to  see whether the  empirical  distri-
bution  function plots  as  a  straight  line  on  logarithmic-probability  paper.
The Air  Quality Criteria for Sulfur Oxides  (1970) shows the empirical  distri-
bution functions  for  S02 concentration for  six large cities across the United
States (Continuous  Air  Monitoring  Project [CAMP], 1962-1967, one-hour averag-
ing  time).  These  distributions,  plotted  on  logarithmic-probability  paper,
range from slightly curved to approximately  straight  lines.   A general  impres-
sion  is   that  they could  be  approximately modeled  as a family  of parallel
straight  lines.  This  is  equivalent  to  saying  that  the  concentrations  are
lognormally  distributed  with a common shape parameter but with  varying  me-
dians.

     A possible explanation  for  this  phenomenon  is  that the shape parameter
is  determined  by meteorological  factors independently of  source strength of
the pollutant  while  the median is determined  primarily by  source strength.
This  explanation  is   supported empirically by  studies  with  the  Zonal  Air
Pollution Study (Lee et al_. , 1975).

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     Another set of  characteristics  emerges  when pollutant concentrations are
considered as a  time series.   They have regular fluctuations which  can often
be correlated with  human  activity patterns (i.e.,  source strength) as well  as
periodic weather  variables  (Raynor  et  ajL ,  1974;  Holzworth,  1973;  Munn  and
Katz,  1959).   Most  concentration time  series  show  24-hour cycles,  but  the
timing  and  shape  of the diurnal  patterns depend  upon  pollutant  type,  geo-
graphic location, and  season.   Yearly  cycles  as well  usually appear in pollu-
tion data,  but  for  most  cases the  changes  are too slow to be  observed over
the length of a growing season.

     Concentration series are  also  highly correlated over  short  time inter-
vals.   Often  one  can  assume  the time  series  is  stationary  over  a growing
season—that is, the median  and shape parameter of the  concentration distri-
bution  stay  constant.   In  this  case,  the degree  of serial correlation,  or
autocorrelation, exhibited by  a series  can usually be specified  by one para-
meter.   The parameters can be  correlated to the response  of plants when they
are  exposed to  rapidly fluctuating pollutant levels  (low  autocorrelation)  as
opposed to slowly-changing levels  (high autocorrelation).

     These observations provide a basis for simple dynamic models of pollutant
concentrations.   The models are  used to generate exposure schedules for plant
growth  experiments  in closed  field  exposure  chambers.   Several  models  of
different degrees of realism  and complexity are being explored  in an attempt
to  identify  those  features  of  long-term,   continuously-varying  pollutant
concentrations  to  which  plants  are  most  sensitive.   The  following  sections
describe  observed  concentration  time  series  in more  detail and  present  the
models used.

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                                   SECTION 3

                        EXPERIMENTAL  TIME  SERIES MODELS

     To perform  a controlled time series experiment,  a  model  must be used to
generate  exposure schedules.  Varying  levels  of  realism  can  be incorporated
into  this model   by  making  it  more  or less complex.  The  first step in con-
structing  the model is  to decide what features of a  natural  time series are
important for simulation.  We will first deal  with stochastic time series.

STATIONARY STOCHASTIC MODELS

     In the  previous section we  summarized the properties of a  natural pollu-
tant time series.  We must now model these properties with a set of mathemati-
cal  assumptions.  The  criteria  that  we feel  are important for  a pollutant
time series model are:

     (1)   Lognormally distributed concentrations.

     (2)   Stationarity,  i.e., the distribution  of concentration is time
           invariant.

     (3)   Autoregressive,  i.e., future concentrations depend upon past
           behavior.

     (4)   Realistic autocorrelation function, i.e., similar to the natural
           time series  reported in Pollack,  1973,  and Barlow and Singpurwalla,
           1974.

In particular, we will  assume that  the concentration C(t) depends only on the
immediate  past value,  C(t-l),  and a random shock.  Such a  model  is  called a
first-order, autoregressive, stochastic process.

     A preliminary  discussion  of the lognormal distribution and auto/correla-
tion functions will  simplify presentation  of the stochastic model.

     The  lognormal  distribution,  LN(m,  a),  with  median,  m, and  shape  para-
meter, a,  has a distribution function given by

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             l~

LN(c;m,a)  =  f  —]-	exp{-% [ln{(£)1/a}]2}dy                        (D
Decreasing  values  of m cause the probability distribution to concentrate near
zero  while  increasing  values  spread  (instead  of shift)  probability  toward
higher  values.   Decreasing  values of a cause the  probability  distribution to
concentrate  about  the median  while increasing  values  spread  the probability
asymmetrically  about the  median with increasing skewness toward higher values
and increasing pile-up near zero.

     The  mean and variance  of the  lognormal  distribution are  a function of
both m and a:
mean LN(m,o)  = me20
                    2 °2,^2 -M                                       (3)
variance LN(m,a) = me  (ea -1)
The mean  is  always  larger than the median  because  the  distribution is skewed
toward  the  right  and the  difference  between the  mean and median  increases
with a.   The variance of  the lognormal distribution increases with  both  the
median and shape parameter.

     The  natural logarithm  of a lognormal  random variable, with  median m  and
shape parameter a,  has a normal distribution with mean In m (natural  logarithm
of m)  and standard  deviation a, i.e.,  if C ~ LN(m,  a) then In  C   N(ln m,  a).
This property  allows  the parameters  of the lognormal  to be   estimated  from
data  using  standard  statistics  for  the  mean  and  standard  deviation.   The
result  is that the median  of the lognormal distribution  is estimated by  the
geometric mean  of the data and the shape  parameter  is  estimated by the stan-
dard deviation of the  logarithms of the  data.

     Larsen (1971) defined the standard geometric deviation  as the quantity
s = e  .   Probabilities from the lognormal  distribution, LN(m,  a), are related
to the  standard normal distribution, N(0, 1),  by
LN(msz;m,a) = N(z;0,l)

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In  particular,  68%  of  the  probability  lies  between  - and  ms;  95% of  the
probability lies between -2 and ms2.                     s

     The  autocovariance function  of  a stationary stochastic  process,  (C(t),
t =  1,  2, ...}, measures the  covariance  between  occurrences  which are  h time
units apart.   For a given lag time,  h,  it is defined as
Cov(h) = E(C(t)-y)(C(t+h)-y)
(5)
where  n =  EC(t)  is the  mean  value  of  the  stochastic process.  The  auto-
correlation function at lag h, is the covariance function at lag h, normalized
by the variance of the process, i.e.,
 p(h) = Cov(h)/Cov(0)
(6)
     Autocorrelation  functions of  natural  pollutant time  series  are charac-
terized  by high  correlations  for  small  lag times  and  decreasing dependence
with  larger  lag  times.   Certain  periodic  human  activities cause  spikes  at
daily and weekly lag times.

     A  stochastic  model  which  satisfies our  four  conditions  (lognormality-
stationarity  -  autoregressive  - realism) can be expressed in terms of the two
parameters  of the lognormal distribution, m and a,  and a third parameter,  \,
called  the autocorrelation  parameter.   The  concentration at time t is given
in terms of the concentration at time t-1 by
                                                                      (7)
In  this model  Z(t),  t =  1, 2,  '"  are independent, lognormally distributed
random variables with median equal  to one and shape parameter equal to

a/FX2, i.e.,
Z(t) 
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The  parameter,  X,  determines the  degree of  dependence  of C(t)  on previous
concentrations  C(t-l),  C(t-2),   '".   The autocorrelation  function  of  this
stochastic process at lag h is given by
p(h) = (e°x -l)/(eo2-1)   h>o,   |x|
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The procedure  is  to generate a  time  series  from equation (7) using m = 1  and
then multiply  this  series by any  value  of m  .  The resulting series will have
a  median,  m , but  the standard geometric deviation  and correlation function
will not  change.   If several exposure schedules are generated in this manner,
using different medians,  then the  peaks  and valleys in the different schedules
will correspond in time.

     Concentrations  less  than the  median occur half of the time and concentra-
tions higher  than the median occur half the  time,  but the frequency at which
low  and high  concentrations occur is  determined  by the  shape  parameter,  a.
Varying  the median  concentration  corresponds to varying  the source strength
of  a diffuse  source, while  varying the  shape parameter corresponds to varying
meteorological  conditions.   Monitoring  data  taken  from  widely  separated
locations  show surprisingly  small  variation  in the  shape parameter (Larsen,
1971).   However,  small  variations  in a  could be extremely important to plants
because of its effect on the  frequency of high  concentrations.

     Varying  the  correlation parameter,  A.,  changes the time behavior  of  the
process.   With a small  value of  A  a strip  chart  of concentration  vs.  time
would look like  a comb,  while a large value  of \ would cause the strip chart
to  look more  like  hills and valleys.   Two  conflicting hypotheses  about  the
affect  of  X on plant growth seem  reasonable:   1)  a highly correlated (A near
1)  concentration  regime  would reduce growth  more than  an  uncorrelated  regime
(\  near 0) because the highly correlated series would have incidences of high
concentrations which  could last  for several time units; 2) a highly correlated
series  would  reduce  growth  less  than  an uncorrelated series because  plants
possess  adaptive  mechanisms  that  could  operate  efficiently  if the concentra-
tion did not change rapidly.


PERIODIC MODELS

     The  simplest  long-term pollutant  schedule is  a constant  level  applied
night and day throughout the growing  season.   Such  treatments  are  used  for
control  purposes  to  quantify  variablity  within  and  between  experimental
chambers.

     At  the next  level of complexity  are  the exposure schedules of Figure 1.
The  daily, on-off  levels of these  schedules are similar  to those  seen  in
conventional  chronic exposure studies  and provide a  calibration of our  own
experimental  system  with previous studies.   The constant levels are  set  to
occur during morning hours, when  higher S02 levels are usually observed.

     A further increase in realism  is taken with the schedule seen in
Figure  2.   As  we  indicated earlier,  the  shape  of   regular  fluctuations  in
pollutant  strength depends upon  human activity patterns and local meteorologi-
cal conditions.   In the case of  S02, however, some generalization is possible.
A  few available  studies  of  diurnal patterns  in S02 show that urban areas tend
to  have a  bimodal  daytime  concentration curve, with  peaks  at midmorning  and
late afternoon,  followed by  low,  constant nighttime  levels  (Holzworth, 1973;
Munn and Katz, 1959;  and Lee  et al_.  , 1975).
                                      10

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a:

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12 hr
S*






12 4 8 12 4 8 1
A.M. P.M.
                 TIME  OF  DAY
Figure 1.  Daily treatment schedules for S02 -- applied
          continuously throughout growing season.
                    11

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ro
         or  3C
LU
O

O
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LU
            2C
         LU
         o:
         I   .   I  .   I  .   I
I   .  I   .   I  .   I
                                                                 I
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                            5    7

                               A.M.
                                                   5    7

                                                     P.M.
                                        TIME  OF  DAY
                               II     I
            Figure 2.   Periodic S02 treatment schedule — applied continuously during growing season.

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     This pattern  is  the  basis for Figure 2.  Plant responses to schedules in
Figures 1  and 2 can be compared on  the basis of total  dose  received.

     It is  possible that plants  exposed  to  the schedules of  Figures  1  and 2
may become  adapted  to the regular fluctuations.  In the  real  world,  however,
air pollutants are  not so predictable, and hour-to-hour changes in concentra-
tion appear  more  random than periodic.  It is important, therefore, to deter-
mine whether random  shocks  of pollutant stress reduce  growth to  a different
extent  than  do predictable stresses.  The next  model  superimposes stochastic
fluctuations  on periodic  patterns such as the one  in Figure 2.  In this model
we assume that the concentration  at hour i,  i = 1,  2,  ... , 24 of any day is a
lognormally  distributed random variable.   Now let  Figure 2 be a graph of the
median  concentrations,  m, for  every hour of  the   day.   Also  assume  that all
hourly  distributions  have the same shape parameter, a.  Then a time series of
hourly  concentrations  is  generated for  hour  i  of  each day by  choosing a
random  sample from  a distribution which  is LN(m(i), a).   Figure 3  shows a
typical sample time  series  generated by this method.  Bimodal daily peaks can
be discerned in  the  figure,  following the pattern  of Figure 2.  Monte Carlo
studies with this model  have shown that  the  empirical  distribution  function
for all the  hourly  levels taken together is  well fit by a lognormal curve.

     The  time series  in  Figure 3 can  thus  be  summarized  statistically by a
median  and  shape  parameter,  permitting comparison of treatment responses with
those  obtained  from  the  stationary  model,  equation  (7).   Exposure responses
can also  be  compared with those obtained from the purely deterministic treat-
ments  of  Figures  1  and 2 on the basis of total dose or,  in the case of Figure
2, on the  basis of median concentration.
                                      13

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                      TIME  (DAYS)
Figure 3.  Five-day  sample from concentration time series.  Series
          generated by stochastic process with diurnal  periodicity
          in hourly geometric mean concentration.
                        14

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                                   SECTION 4

                                  DISCUSSION


     The  stochastic models  developed  here  are  good descriptors  of natural
concentration  time series from diffuse  sources,  such as urban locations.  It
is  not clear  that the models  are useful in  simulating  levels  from a single
point  source such  as  a power plant in  rural  areas.   There  are  few  long-term
studies of  time series from a  point source.  Gifford  (1974) has suggested, on
empirical grounds,  that a negative exponential provides the best fit to point
source data  and Knox and Pollack  (1974)  argue theoretically that the distri-
bution is Chi  Square with two  degrees  of freedom.   The  most probable concen-
tration  near a point  source is  zero,  and high  levels  of  pollutant are rare
and unpredictable.

     Exposure  schedules  which   simulate a  point  source  raise  problems  of
replication  and prediction  of response.  Imagine a concentration time series,
the  length  of  a  growing season,  which is dominated  by zero levels and has
only two  or three concentration  spikes  high  enough  to  affect  plant growth.
The  problem  is that  the plant  growth  response  to  such a  schedule  may vary
widely,  depending  on  the  timing of  the spikes relative  to each  other and
relative to  the developmental stages of the plant.

     A realistic appraisal of the  effect upon plant growth of an air pollutant
may  be obtained by exposing plants to  simulated ambient fluctuation  in pollu-
tant concentration for  an  entire growing  season.   A gradient  in  pollutant
source  strength,   meteorological   effects  on  the time  series,  and  periodic
changes  in   magnitude  can  be  accomplished  by  varying  the  parameters  of  a
model.   Experiments  currently underway  are  designed  to  test the sensitivity
of plant growth  to both probabilistic  and deterministic variations in concen-
tration time series.   If  plant  growth  does correlate  well  with  parameters of
concentration  frequency  distributions,  then  the output of regional  air pollu-
tion models  can be applied immediately as input  to  plant response models.

     In summary,  stochastic  experiments provide a viable alternative to long-
term fixed concentration  experiments  for predicting crop losses caused by S02
air  pollution.  The probabilistic nature  of S02 time series  are  fairly well
understood and  a  model  which will reasonably simulate realistic exposures has
been  suggested.    Parameters  of  this  model  can be  varied  in  field  growth
chambers to  establish  their  correlation with  crop  yield.   By  designing the
experiment  so  that  a  large  number  of different time  series from  the same
model  are  tested  then relatively precise  probabilistic predictions  of crop
losses  are possible.
                                      15

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                                   REFERENCES


Air Quality Criteria for Sulfur Oxides.  1970.   Nat. Air Poll. Control
     Admin. Pub. AP-50.

Barlow, R.  E.  and N. D. Singpurwalla.  1974.  Averaging Time and Maxima for
     Dependent Observations.  In  Proc. Symp. on Statistical Aspects of Air
     Quality Data.  Env.  Prot.  Agency Report EPA-650.

Bencala, K. E.  and J. H. Seinfeld.  1976.  On Frequency Distributions of Air
     Pollutant Concentrations. Atmos. Env. 10:941-950.

Box, G.  E. .P.  and G.  M.  Jenkins.  1976.   Time Series Analysis:   Forecasting
     and Control.  Holden-Day, San  Francisco.

Gifford,  F.  A.,  Jr.    1974.   The  Form of  the Frequency  Distribution of Air
     Pollution  Concentrations.  In Proc.  Symp.  on  Statistical  Aspects of Air
     Quality Data.  Env.  Prot.  Agency Report EPA-650.

Holzworth, G.  C.   1973.  Variations  of Meteorology,  Pollutant Emissions, and
     Air Quality.   American  Chemical  Society, American  Inst.  of  Aeronautics
     and Astronautics,  American Meteorological  Society,  U.S.  Dept. of Trans-
     portation,  Environmental   Protection  Agency,  Inst.  of  Electrical  and
     Electronic  Engineers,   Instrument  Society  of  America,   National  Aero-
     nautics  and Space Administration, and  National  Oceanographic and Atmos-
     pheric Administration, 2nd  Joint Conf. Sensing Environ. Pollut.,  Washing-
     ton, D.C. , p.  247-255.

Jenkins,  G.  M.  and  D.  G.  Watts.   1968.   Spectral  Analysis  and Its Appli-
     cations.  Holden-Day,  San Francisco.

Knox,  J.   B.  and  R.  I.  Pollack.   1974.    An Investigation  of the  Frequency
     Distribution of  Surface  Air-Pollutant Concentrations.  In Proc.  Symp. on
     Statistical  Aspects of Air Quality Data.   Env.  Prot.  Agency  Report  EPA-
     650.

Larsen,  R.  I.   1971.   A Mathematical Model  for  Relating Air Quality  Measure-
     ments to  Air  Quality  Standards.   Environmental  Protection Agency Report
     AP-89.
                                      16

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Lee, J. J. ,  R.  A.  Lewis, D.  E.  Body.   1975.   A Field Experimental  System  for
     the  Evaluation  of  the  Bioenvironmental  Effects of  Sulfur Dioxide.   Li
     the  Fort Union  Coal  Symposium,  V.  5, W.  C.  Clark,  ed.   Montana  Acad.
     Sci., E.  Mont. Coll., Billings.

Munn,  R.  E.   and  M.  Katz.   1959.  Daily and Seasonal  Pollution Cycles in  the
     Detroit-Windsor Area.   Internat. J. Air Poll.  2:51.

Oshima, R. J. ,  Poe,  M.  P., Braegelmenn, P. K.,  Baldwin, D. W.,  and  VanWay,  V.
     1976.   Ozone  Dosage-Group   Loss  Function  for Alfalfa:   A Standardized
     Method  for  Assessing Crop  Losses  from  Air Pollutants.   APCA Journal
     26:861-865.

Pollack,  R.  I.   1973.  Studies  of Pollutant  Concentration Frequency Distri-
     butions.  Lawrence  Livermore Lab.  UCRL-51459.  Livermore,  CA.

Raynor, G.  S. ,  M.  E.  Smith,  and I.   A.  Singer.  1974.   Temporal and Spatial
     Variation  in  Sulfur Dioxide  Concentrations  on Suburban Long Island,  New
     York.  JAPCA  24:586-590.
                                      17

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                                    TECHNICAL REPORT DATA
                             (Please read Instructions on the reverse before completing/
1. REPORT NO.
     EPA-600/3-78-038
  riTLE AND SUBTITLE
2.
 "Time Series  Experiments  for Studying Plant  Growth
  Response  to  Pollution"
                              3. RECIPIENT'S ACCESSION NO.
                              5. REPORT DATE
                                April  1978
                              6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
                                                            8. PERFORMING ORGANIZATION REPORT NO.
  Larry Male.  John Van Sickle,  and Ray Wilhour
9. PERFORMING ORGANIZATION NAME AND ADDRESS
  Assessment & Criteria Development Division
  Ecosystems Modeling & Analysis Branch
  Corvallis  Environmental  Research Laboratory
  200 S.W.  35th St. -- Corvallis, OR  97330
                              10. PROGRAM ELEMENT NO.

                                1AA602
                              11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
  U.S. Environmental Protection Agency - Corvallis,  OR
  Corvallis  Environmental  Research Center
  200 S.W. 35th St.
  Con/all is,  OR  97330
                              13. TYPE OF REPORT AND PERIOD COVERED
                                Inhouse
                              14. SPONSORING AGENCY CODE
                                EPA/600/02
15. SUPPLEMENTARY NOTES
16. ABSTRACT
   This research program was  initiated with the  overall  objective of defining experi-
   ments which could predict  the yield losses  of crops grown under naturally varying
   sulfur dioxide concentrations.

   A model  for simulating  realistic fluctuations in S02  air pollution  was  developed.
   This model  was used to  design experiments in  field growth chambers  for  the purpose
   of establishing the functional and probabilistic relationship between yield loss
   and median  S02 concentration.  The stochastic experiments are offered as  a viable
   alternative to traditional  long-term fixed  concentration experiments.

   This report covers a period from April 1974 to September 1977 and was completed
   as of February 1978.
17.
                                 KEY WORDS AND DOCUMENT ANALYSIS
                  DESCRIPTORS
                                               b.IDENTIFIERS/OPEN ENDED TERMS
                                            c.  COSATI F-'ield/Group
   Sulfur Dioxide
   Time Series  Analysis
   Experimental  Design
                                            Field  06/F
                                                   06/S
18. DISTRIBUTION STATEMENT
   Release Unlimited
                                               19. SECURITY CLASS (This Report)
                                                  UNCLASSIFIED
                                            21. NO. OF PAGES
                                                 24
                 20. SECURITY CLASS (Thispage)

                    UNCLASSIFIED
                                                                          22. PRICE
EPA Form 2220-1 (Rev. 4-77)   PREVIOUS EDITION is OBSOLETE
                                             18
                                                       6 U.S. GOVERNMENT PRINTING OFCIC6: 1978—796-747/139 REGION 10

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