TRENDS OVER TIME IN ECOLOGICAL RESOURCES OF A REGION

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USES OF POWERIN DESIGNING LONG-TERM
ENVIRONMENTAL SURVEYS

• N. Scott UrquhartDepartment of Statistics
• Colorado State University
• Fort Collins, CO 80523-1877

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OUTLINE FOR TONIGHT

• Long-Term Environmental Surveys
• Agencies involved
• Sorts of Summaries of Interest
• Sources of Variation Major ones
• A Statistical Model
• Superimposed on an Adapted Classical Sampling
  Model
• Calculation of Power Using this Model
• Illustrations
• General
• Specific
• Generalizations - as Time Allows

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LONG-TERM ENVIRONMENTAL SURVEYS

• Objective To Establish
• The Current Status
• Detect Long-Term Trends
• Evaluate Extent of Various Classes
• Of the Resource(s) of Interest
• Usually Ecological or Living Resources
• Agencies Who
• US Environmental Protection Agency (EPA)
• States and Tribes, and Local Jurisdictions
• Response to Legislation Like the Clean Water Act
• Forest Service Forest Health
• National Park Service
• Soil Conservation Service (not the current name)
• National Marine Fisheries Service ( )
• National Wetlands Inventory

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RESPONSES of INTEREST

• EPA
• Variety of Chemical Measures of Water Quality
• Nitrogen to Heavy Metals to Pesticides
• Acid Neutralizing Capacity (ANC)
• Important in Evaluating the Effect of Acid Rain
• Composition of Bugs in the Aquatic Community
• Thought to Contain Better Info on total Effects
  than Individual Chemicals
• Fish Populations Composition, not size
• Clean Water Act Includes Reporting on Temperature
  Pollution

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RESPONSES of INTEREST(continued)

• National Park Service (Eg Olympic NP in WA)
• Vegetation
• Bird Populations
• Composition
• Size of Various Species
• Streams/Rivers
• Fish Populations
• Macroinvertebrate Communities
• Extent of Intermittent Streams
• Health of Glaciers
• Extent Shrinking with Global Warming?
• Composition

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RESPONSES of INTEREST(continued II)

• Grand Canyon National Park
• Erosion Around Archeological Resources
• Near-river Terrestrial Environment (GCMRC)

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SPATIAL EXTENT

• Generally Large Areas
• This is the Way Congress Writes Laws
• Regions can be very large
• 12 Western States
• ND, SC, MT, WY, CO, ID, UT, NV, AZ, WA, OR, CA
• Midatlantic Highlands
• parts of PA, VA, WV, DE, MD
• Individual States
• Lands of Several related Tribes, or Even Only One
• Groups of National Parks
• Groups of Sanitation Districts, or even
• Individual Sanitation Districts

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SUMMARIES of INTEREST

• Extent by Classes
• Track Changes Between Classes
• National Wetlands Inventory
• Major focus
• Has Very Good Graphic Depiction of Class Changes
• Status
• Often is summarized as an Estimated
  Cumulative Distribution Function (cdf)
• Pose some Interesting Statistical Inference
  Problems Due to
• Variable Probability Sampling Almost Always
  Needed
• Spatially Continuous Resources No List Can Exist

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EXAMPLE OF STATUS, SUMMARIZED BY A cdf
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ESTIMATED CUMULATIVE DISTRIBUTION FUNCTION OF
SECCHI DEPTH, EMAP AND DIP-IN
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SUMMARIES of INTEREST(continued)

• Trends
• Directional Changes in Responses
• Reality Detection of Short-Term Cycles is
  Beyond the Resources for the Foreseeable Future
• Great Big Changes Dont Require Surveys
• So Interest Lies in Modest-Sized
  Long-Term Changes in One Direction
• This means Changes the Scale of 1 to 2 Per Year
• Usually a Trend for a Region
• Regional Summaries of Individual Site Trends
• Sometimes how trend varies in relation to other
  things

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IMPORTANT COMPONENTS OF VARIANCE

• POPULATION VARIANCE
• YEAR VARIANCE
• RESIDUAL VARIANCE

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IMPORTANT COMPONENTS OF VARIANCE ( - CONTINUED)

• POPULATION VARIANCE
• VARIATION AMONG VALUES OF AN INDICATOR (RESPONSE)
  ACROSS ALL LAKES IN A REGIONAL POPULATION OR
  SUBPOPULATION

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IMPORTANT COMPONENTS OF VARIANCE ( - CONTINUED II)

• YEAR VARIANCE
• CONCORDANT VARIATION AMONG VALUES OF AN INDICATOR
  (RESPONSE) ACROSS YEARS FOR ALL LAKES IN A
  REGIONAL POPULATION OR SUBPOPULATION
• NOT VARIATION IN AN INDICATOR ACROSS YEARS AT
  A LAKE
• DETRENDED REMAINDER, IF TREND IS PRESENT
• EFFECTIVELY THE DEVIATION AWAY FROM THE TREND
  LINE (OR OTHER CURVE)

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IMPORTANT COMPONENTS OF VARIANCE ( - CONTINUED -
III)

• RESIDUAL COMPONENT OF VARIANCE
• HAS SEVERAL SUBCOMPONENTS
• YEARLAKE INTERACTION
• THIS CONTAINS MOST OF WHAT MOST ECOLOGISTS WOULD
  CALL YEAR TO YEAR VARIATION, I.E. THE LAKE
  SPECIFIC PART
• INDEX VARIATION
• MEASUREMENT ERROR
• CREW-TO-CREW VARIATION
• LOCAL SPATIAL PROTOCOL
• SHORT TERM TEMPORAL

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BIOLOGICAL INDICATORS HAVE SOMEWHAT MORE
VARIABILITY THAN PHYSICAL INDICATORS BUT THIS
VARIES, TOO

• Subsequent slides show the relative amount of
  variability
• Ordered by the amount of residual variability
  least to most (aquatic responses)
• Acid Neutralizing Capacity
• Ln(Conductance)
• Ln(Chloride)
• pH(Closed system)
• Secchi Depth
• Ln(Total Nitrogen)
• Ln(Total Phosphorus)
• Ln(Chlorophyll A)
• Ln( zooplankton taxa)
• Ln( rotifer taxa)
• Maximum Temperature

And others, both aquatic and terrestrial
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SOURCE OF COMPONENTS OF VARIANCE FROM GRAND CANYON

• Grand Canyon Monitoring and Research Center
• Effects of Glen Canyon Dam on the Near-River
  Habitat in the Grand Canyon
• At Various Heights Above the River
• Height Is Measured as the Height of the Rivers
  Water at Various Flow Rates
• Eg 15K cfs, 25K cfs, 35K cfs, 45K cfs 60K
  cfs
• Using First Two Years Data
• Mike Kearsley UNA
• Design Spatially Balanced
• With about 1/3 revisited

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ALL VARIABILITY IS OF INTEREST

• The Site Component of Variance is One of the
  Major Descriptors of the Regional Population
• The Year Component of Variance Often is Small,
  too Small to Estimate. If Present, it is a
  Major Enemy for Detecting Trend Over Time.
• If it has even a moderate size, sample size
  reverts to the number of years.
• In this case, the number of visits and/or number
  of sites has no practical effect.

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ALL VARIABILITY IS OF INTEREST( - CONTINUED)

• Residual Variance Characterizes the Inherent
  Variation in the Response or Indicator.
• But Some of its Subcomponents May Contain Useful
  Management Information
• CREW EFFECTS gt training
• VISIT EFFECTS gt need to reexamine definition
  of index (time) window or evaluation protocol
• MEASUREMENT ERROR gt work on laboratory/measurem
  ent problems

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DESIGN TRADE-OFFS TREND vs STATUS

• How do we Detect Trend in Spite of All of This
  Variation?
• Recall Two Old Statistical Friends.
• Variance of a mean, and
• Blocking

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DESIGN TRADE-OFFS TREND vs STATUS( - CONTINUED)

• VARIANCE OF A MEAN
• Where m members of the associated population
  have been randomly selected and their response
  values averaged.
• Here the mean is a regional average slope, so
  "s2" refers to the variance of an estimated
  slope ---

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DESIGN TRADE-OFFS TREND vs STATUS( - CONTINUED
- II)

• Consequently
• Becomes
• Note that the regional averaging of slopes has
  the same effect as continuing to monitor at one
  site for a much longer time period.

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DESIGN TRADE-OFFS TREND vs STATUS( - CONTINUED
- III)

• Now, s2, in total, is large.
• If we take one regional sample of sites at one
  time, and another at a subsequent time, the site
  component of variance is included in s2.
• Enter the concept of blocking, familiar from
  experimental design.
• Regard a site like a block
• Periodically revisit a site
• The site component of variance vanishes from the
  variance of a slope.

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STATISTICAL MODEL

• CONSIDER A FINITE POPULATION OF SITES
• S1 , S2 , , SN
• and A TIME SERIES OF RESPONSE VALUES AT EACH
  SITE
• A FINITE POPULATION OF TIME SERIES
• TIME IS CONTINUOUS, BUT SUPPOSE
• ONLY A SAMPLE CAN BE OBSERVED IN ANY YEAR, and
• ONLY DURING AN INDEX WINDOW OF, SAY, 10 OF A
  YEAR

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STATISTICAL MODEL -- II
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STATISTICAL MODEL -- III
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STATISTICAL MODEL -- IV

• IF p INDEXES PANELS, THEN
• Sites are nested in panels p ( i ) and
• Years of visit are indicated by panel with npj
  0 or npjgt 0 for panels visited in year j.
• The vector of cell means (of visited cells) has
  a covariance matrix S

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STATISTICAL MODEL -- V

• Now let X denote a regressor matrix containing
  a column of 1s and a column of the numbers of
  the time periods corresponding to the filled
  cells. The second elements of
• contain an estimate of the regional trend and
  its variance.

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TOWARD POWER

• Ability of a panel plan to detect trend can be
  expressed as power.
• We will evaluate power in terms of these ratios
  of variance components
• Power depends on the ratios of variance
  components, the panel plan, and on

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NOW PUT IT ALL TOGETHER

• Question What kind of temporal design should
  you use for Northwest National Parks?
• Well investigate two (families) of recommended
  designs.
• All illustrations will be based on 30 site
  visits per year, a reasonable number given
  resources.
• General relations are uninfluenced by number of
  sites visited per year, but specific performance
  is.
• Well use the panel notation Trent
  McDonald published.

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RECOMMENDATION OF FULLER and BREIDT

• Based on the Natural Resources Inventory (NRI)
• Iowa State US Department of Agriculture
• Oriented toward soil erosion
• Changes in land use
• Their recommendation
• Pure panel 1-0 Always Revisit
• Independent 1-nNever Revisit
• Evaluation context
• No trampling effect remotely sensed data
• No year effects
• Administrative reality of potential variation
  in funding from year to year

MATH RECOME 100 50 0 50
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TEMPORAL LAYOUT OF (1-0), (1-n)
YEAR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1-0 X X X X X X X X X X X X X X X X X X X X
1-n X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
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FIRST TEMPORAL DESIGN FAMILY

• 30 site visits per year

1-0 30 20 10 0
1-n 0 10 20 30
ALWAYS REVISIT NEVER REVISIT
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POWER TO DETECT TRENDFIRST TEMPORAL DESIGN
FAMILY NO YEAR EFFECT
Always Revisit
Never Revisit
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POWER TO DETECT TRENDFIRST TEMPORAL DESIGN
FAMILY, MODEST ( SOME) YEAR EFFECT
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POWER TO DETECT TRENDFIRST TEMPORAL DESIGN
FAMILYBIG ( LOTS) YEAR EFFECT
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SERIALLY ALTERNATING TEMPORAL DESIGN (1-3)4
SOMETIMES USED BY EMAP
YEAR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
FIA X X X
(1-3)4 X X X X X X
X X X X X
X X X X X
X X X X X
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SERIALLY ALTERNATING TEMPORAL DESIGN (1-3)4
SOMETIMES USED BY EMAP
YEAR 1 2 3 4 5 6 7 8 9 10 11
FIA X X
(1-3)4 X X X
X X X
X X X
X X

• Unconnected in an experimental design sense
• Very weak design for estimating year effects, if
  present

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SPLIT PANEL (1-4)5 , ---
YEAR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
FIA X X X
(1-4)5 X X X X X
X X X X
X X X X
X X X X
X X X X

• AGAIN, Unconnected in an experimental design
  sense
• Matches better with FIA
• Still a very weak design for estimating year
  effects, if present

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SPLIT PANEL (1-4)5 ,(2-3)5
YEAR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
FIA X X X
(1-4)5 X X X X X
X X X X
X X X X
X X X X
X X X X
(2-3)5 X X X X X X X X X
X X X X X X X X
X X X X X X X X
X X X X X X X X
X X X X X X X X

• This Temporal Design IS connected
• Has three panels which match up with FIA

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SECOND TEMPORAL DESIGN FAMILY

• 30 site visits per year

1-4 30 20 10 0
2-3 0 5 10 15
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POWER TO DETECT TRENDSECOND TEMPORAL DESIGN
FAMILY NO YEAR EFFECT
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POWER TO DETECT TRENDSECOND TEMPORAL DESIGN
FAMILYSOME YEAR EFFECT
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POWER TO DETECT TRENDSECOND TEMPORAL DESIGN
FAMILYLOTS OF YEAR EFFECT
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COMPARISON OF POWER TO DETECT TRENDDESIGN 1 2
ROWS
YEAR EFFECT NONE
SOME
LOTS
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POWER TO DETECT TRENDVARYING YEAR EFFECT AND
TEMPORAL DESIGN
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STANDARD ERROR OF STATUSTEMPORAL DESIGN 1, NO
YEAR EFFECT
TOTAL OF 30 SITES
110 SITES VISITED BY YEAR 5
410 SITES VISITED BY YEAR 20
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STANDARD ERROR OF STATUSTEMPORAL DESIGN 2, NO
YEAR EFFECT
TOTAL OF 75 SITES
TOTAL OF 150 SITES
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GENERALIZATIONS

• Each site can have its own trend
• These very likely differ
• How should we approach this reality?
• There is a cdf of trends across the region
• Variation in trends can be partitioned
• Components are very similar to those used for
  responses
• Years
• Rivers
• Sites within rivers

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ILLUSTRATION

• Stoddard, J.L., Kahl, J.S., Deviney, F.A.,
  DeWalle, D.R., Driscoll, C.T., Herlihy, A.T.,
  Kellogg, J.H., Murdoch, J.R. Webb, J.R., and
  Webster, K.E. (2003). Response of Surface Water
  Chemistry to the Clean Air Act Amendments of
  1990. EPA/620/R-02/004. US Environmental
  Protection Agency, Washington, DC.

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FUNDING ACKNOWLEDGEMENT
The work reported here today was developed under
the STAR Research Assistance Agreement CR-829095
awarded by the U.S. Environmental Protection
Agency (EPA) to Colorado State University. This
presentation has not been formally reviewed by
EPA.  The views expressed here are solely those
of presenter and STARMAP, the Program he
represents. EPA does not endorse any products or
commercial services mentioned in this
presentation.