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USES OF POWER IN DESIGNING LONG-TERM ENVIRONMENTAL SURVEYS

USES OF POWER IN DESIGNING LONG-TERM ENVIRONMENTAL SURVEYS. N. Scott Urquhart Department of Statistics Colorado State University Fort Collins, CO 80523-1877. OUTLINE FOR TONIGHT. Long-Term Environmental Surveys Agencies involved Sorts of Summaries of Interest

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USES OF POWER IN DESIGNING LONG-TERM ENVIRONMENTAL SURVEYS

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  1. USES OF POWERIN DESIGNING LONG-TERM ENVIRONMENTAL SURVEYS N. Scott UrquhartDepartment of Statistics Colorado State University Fort Collins, CO 80523-1877

  2. 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

  3. 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

  4. 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

  5. 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

  6. RESPONSES of INTEREST(continued II) • Grand Canyon National Park • Erosion Around Archeological Resources • Near-river Terrestrial Environment (GCMRC)

  7. 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*

  8. 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

  9. EXAMPLE OF STATUS, SUMMARIZED BY A cdf

  10. ESTIMATED CUMULATIVE DISTRIBUTION FUNCTION OF SECCHI DEPTH, EMAP AND “DIP-IN”

  11. 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 Don’t 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

  12. IMPORTANT COMPONENTS OF VARIANCE • POPULATION VARIANCE: • YEAR VARIANCE: • RESIDUAL VARIANCE:

  13. IMPORTANT COMPONENTS OF VARIANCE ( - CONTINUED) • POPULATION VARIANCE: • VARIATION AMONG VALUES OF AN INDICATOR (RESPONSE) ACROSS ALL LAKES IN A REGIONAL POPULATION OR SUBPOPULATION

  14. 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 • NOTVARIATION 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)

  15. IMPORTANT COMPONENTS OF VARIANCE ( - CONTINUED - III) • RESIDUAL COMPONENT OF VARIANCE • HAS SEVERAL SUBCOMPONENTS • YEAR*LAKE 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

  16. 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

  17. 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 River’s 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

  18. 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.

  19. 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 ===> training • VISIT EFFECTS ===> need to reexamine definition of index (time) window or evaluation protocol • MEASUREMENT ERROR ===> work on laboratory/measurement problems

  20. 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

  21. 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 ---

  22. 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.

  23. 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.

  24. 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

  25. STATISTICAL MODEL -- II

  26. STATISTICAL MODEL -- III

  27. 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 npj> 0 for panels visited in year j. • The vector of cell means (of visited cells) has a covariance matrix S :

  28. 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.

  29. 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

  30. NOW PUT IT ALL TOGETHER • Question: “ What kind of temporal design should you use for Northwest National Parks? • We’ll 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. • We’ll use the panel notation Trent McDonald published.

  31. 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-n]=“Never 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%

  32. TEMPORAL LAYOUT OF [(1-0), (1-n)]

  33. FIRST TEMPORAL DESIGN FAMILY • 30 site visits per year

  34. POWER TO DETECT TRENDFIRST TEMPORAL DESIGN FAMILY NO YEAR EFFECT Always Revisit Never Revisit

  35. POWER TO DETECT TRENDFIRST TEMPORAL DESIGN FAMILY, MODEST (= SOME) YEAR EFFECT

  36. POWER TO DETECT TRENDFIRST TEMPORAL DESIGN FAMILYBIG (= LOTS) YEAR EFFECT

  37. SERIALLY ALTERNATING TEMPORAL DESIGN [(1-3)4 ] SOMETIMES USED BY EMAP

  38. SERIALLY ALTERNATING TEMPORAL DESIGN [(1-3)4 ] SOMETIMES USED BY EMAP • Unconnected in an experimental design sense • Very weak design for estimating year effects, if present

  39. SPLIT PANEL [(1-4)5 , ---] • AGAIN, Unconnected in an experimental design sense • Matches better with FIA • Still a very weak design for estimating year effects, if present

  40. SPLIT PANEL [(1-4)5 ,(2-3)5 ] • This Temporal Design IS connected • Has three panels which match up with FIA

  41. SECOND TEMPORAL DESIGN FAMILY • 30 site visits per year

  42. POWER TO DETECT TRENDSECOND TEMPORAL DESIGN FAMILY NO YEAR EFFECT

  43. POWER TO DETECT TRENDSECOND TEMPORAL DESIGN FAMILYSOME YEAR EFFECT

  44. POWER TO DETECT TRENDSECOND TEMPORAL DESIGN FAMILYLOTS OF YEAR EFFECT

  45. COMPARISON OF POWER TO DETECT TRENDDESIGN 1 & 2 = ROWS YEAR EFFECT NONE SOME LOTS

  46. POWER TO DETECT TRENDVARYING YEAR EFFECT AND TEMPORAL DESIGN

  47. 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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