NPS Temporal Conference # 1 DESIGNING PANEL SURVEYS SPECIFICALLY RELEVANT TO NATIONAL PARKS IN THE NORTHWEST N. Scott Urquhart Senior Research Scientist Department of Statistics Colorado State University Fort Collins, CO 80527-1877 NPS Temporal Conference # 2 INFERENCE PERSPECTIVES Design Based Inferences rest on the probability structure incorporated in the sampling plan Completely defensible; very minimal assumptions Limiting relative to using auxiliary information Model Assisted Uses models to compliment underlying sampling structure Has opportunities for use of auxiliary information Model Based (eg: spatial statistics) Ignores sampling plan Defensibility lies in defense of model NPS Temporal Conference # 3 APPROACH OF THIS PRESENTATION Use tools from the arena of Model assisted and Model based analyses To study the performance of Design based & Model-assisted analyses WHY? Without models, performance evaluations need simulation Before substantial data have been gathered No basis for values to enter into simulation studies NPS Temporal Conference # 4 STATUS & TRENDS OVER TIME IN ECOLOGICAL RESOURCES OF A REGION MAJOR POINTS Regional trend site trend Detection of trend requires substantial elapsed time Regional OR intensive site Almost all indicators have substantial patterns in their variability Design to capitalize on this; don’t fight it. Minimize effect of site variability with planned revisits – specific plans will be illustrated Design tradeoffs: TREND vs STATUS NPS Temporal Conference # 5 REGIONAL TREND SITE TREND The predominant theme of ecology: Ecological processes How does a specific kind of ecosystem function Energy flows Food webs Nutrient cycling Most studies of such functions must be temporally Temporally intensive – What material goes from where to where? Consequently spatially restrictive In this situation: Temporal trend = site trend NPS Temporal Conference # 6 REGIONAL TREND SITE TREND ( - CONTINUED) The predominant theme of ecology versus A Substantial (any) Agency Focus: All of an ecological resource In an area or region Across all of the variability present there Most government regulations Apply to a whole area or region Only a few apply to specific sites The definition of a “region” certainly depends on what agency makes the regulation NPS Temporal Conference # 7 REGIONAL TREND SITE TREND ( - CONTINUED - III) The predominant theme of ecology versus A substantial agency (EPA) focus: An entire region, like Lakes in the Adirondack Mountains All lakes in Northeastern US All (wadeable) streams the mid-Appalachian Mountains Or National Park Service All riparian areas in Olympic National Park All riparian areas in National Parks in the coastal Northwest NPS Temporal Conference # 8 TREND ACROSS TIME - What is it? Any response which changes across time in a generally Increasing or Decreasing Manner shows trend Monotonic change is not essential. If trend of this sort is present, it will be detectable as linear trend. This does NOT mean trend must be linear (examples follow) Any specified form is detectable Time = years, here NPS Temporal Conference # 9 TREND ACROSS TIME - What is it? (continued) TREND = YES TREND = NO; PATTERN = YES 90 90 70 70 50 1989 1991 1993 1995 50 1989 1991 Year 1993 1995 1997 Year TREND = YES, PATTERN = YES TREND = NO; PATTERN = YES 400 350 300 300 CARBON DIOXIDE CONCENTRATION (ppm) CARBON DIOXIDE CONCENTRATION (ppm) 350 250 200 150 100 50 0 1955 1965 1975 1985 YEAR 1995 2005 250 200 150 100 50 0 1955 1965 1975 1985 1995 2005 YEAR NPS Temporal Conference # 10 TREND = NO; PATTERN = YES DETRENDED CARBON DIOXIDE CONCENTRATION (ppm) 350 300 TREND = NO; PATTERN = YES 250 200 150 100 50 0 1955 1965 1975 1985 1995 YEAR NPS Temporal Conference # 11 TREND DETECTION REQUIRES SUBSTANTIAL ELAPSED TIME IT IS NEARLY IMPOSSIBLE TO DETECT TREND IN LESS THAN FIVE YEARS. WHY? var ( ) 2 2 ( t t ) i YEARS 2 ( t t ) i 3 4 5 6 7 8 9 10 2 5 10 17.5 28 42 60 82.5 NPS Temporal Conference # 12 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 NPS Temporal Conference # 13 IMPORTANT COMPONENTS OF VARIANCE POPULATION VARIANCE: 2 ( SITE ) 2 ( YEAR VARIANCE: YEAR ) 2 ( RESIDUAL VARIANCE: RESIDUAL ) NPS Temporal Conference # 14 IMPORTANT COMPONENTS OF VARIANCE ( - CONTINUED) 2 POPULATION VARIANCE: ( SITE ) Variation among values of an indicator (response) across all sites in a park or group of related parks, that is, across a population or subpopulation of sites NPS Temporal Conference # 15 IMPORTANT COMPONENTS OF VARIANCE ( - CONTINUED II) 2 ( YEAR VARIANCE: YEAR ) Concordant variation among values of an indicator (response) across years for ALL sites in a regional population or subpopulation NOT variation in an indicator across years at a single site Detrended remainder, if trend is present Effectively the deviation away from the trend line (or other curve) NPS Temporal Conference # 16 IMPORTANT COMPONENTS OF VARIANCE ( - CONTINUED - III) Residual component of variance Has several contributors Year*Site interaction 2 ( RESIDUAL ) This contains most of what ecologists would call year to year variation, i.e. the site specific part Index variation Measurement error Crew-to-crew variation (minimize with documented protocols and training) Local spatial = protocol variation Short term temporal variation NPS Temporal Conference # 17 SOURCE OF DATA FOR ESTIMATES OF COMPONENTS OF VARIANCE EMAP Surface Waters: Northeast Lakes Pilot 1991 - 1994 About 450 observations Over four years Including about 350 distinct lakes Design allowed estimation of several residual components NPS Temporal Conference # 18 COMPOSITION OF TOTAL VARIANCE - NE LAKES Acid Neutralizing Capacity LAKE COMPONENT OF VARIANCE Ln(Conductance) Ln(Chloride) pH(Closed system) Secchi Depth Ln(Total Nitrogen) Ln(Total Phosphorus) Ln(Chlorophyll A) YEAR Ln( # zooplankton taxa) Ln( # rotifer taxa) Maximum Temperature 0.00 RESIDUAL COMPONENT OF VARIANCE 0.20 0.40 0.60 0.80 1.00 PROPORTION OF VARIANCE NPS Temporal Conference # 19 SOURCE OF COMPONENTS OF VARIANCE FROM NW HABITAT Oregon Department of Fisheries and Wildlife – stream habitat survey GRADIENT: Stream gradient measured on site WIDTH: Wetted stream width ACW: Active Channel ACH: Active Channel Height UNITS100: Number of distinct habitat units per 100 meters of stream length NOPOOLS: Number of pools in the surveyed reach POOLS100: Number of pools per 100 meters PCTPOOL: % of reach length in pools PCTFINES: % stream substrate that is sand or finer particle size PCTGRAVEL: % of stream stubstrate that is gravel sized particles RIFSNDOR: % of riffle stream length that is sand or finer particle size RIFGRAV: % of riffle stream length that is gravel sized particles SHADE: % stream channel shaded LOG(PIECESLWD +0.01): Number of pieces of large woody debris per 100 meters. LOG(VOLUMELWD +0.01): Volume of large woody debris (m^3/100 meters) RESIDPD: Volume of residual pools (pools remaining if streamflow stopped) NPS Temporal Conference # 20 COMPOSITION OF TOTAL VARIANCE NW HABITAT Ln(Conductance) LAKE COMPONENT OF VARIANCE pH(Closed system) LOG(VOLUME L WD) % Shaded % Riffle fine % Fines Pools per 100m UNITS100 YEAR Active Channel Width Gradient RESIDUAL COMPONENT OF VARIANCE 0.00 0.10 PROPORTION OF VARIANCE NPS Temporal Conference # 21 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 NPS Temporal Conference # 22 COMPOSITION OF TOTAL VARIANCE GRAND CANYON -- NEAR RIVER VEGETATION Richness - 60K cfs Richness - 45K cfs SITE COMPONENT OF VARIANCELAKE COMPONENT YEAR RESIDUAL COMPONENT OF VARIANCE Richness - 35K cfs Richness - 25K cfs Richness - 15K cfs Veg - 60K cfs Veg - 45K cfs Veg - 35K cfs Veg - 25K cfs 0.00 0.20 0.40 0.60 0.80 PROPORTION OF VARIANCE 1.00 NPS Temporal Conference # 23 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 to small to estimate. 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. NPS Temporal Conference # 24 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 NPS Temporal Conference # 25 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 NPS Temporal Conference # 26 DESIGN TRADE-OFFS: TREND vs STATUS ( - CONTINUED) VARIANCE OF A MEAN: var (mean) 2 m 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 "2" refers to the variance of an estimated slope --- NPS Temporal Conference # 27 DESIGN TRADE-OFFS: TREND vs STATUS ( - CONTINUED - II) Consequently var (mean) Becomes 2 m 1 2 var (regional mean slope) m ( ti t ) 2 Note that the regional averaging of slopes has the same effect as continuing to monitor at one site for a much longer time period. NPS Temporal Conference # 28 DESIGN TRADE-OFFS: TREND vs STATUS ( - CONTINUED - III) Now, 2, 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 2. 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. NPS Temporal Conference # 29 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, as Andrea recommended. General relations are uninfluenced by number of sites visited per year, but specific performance is. We’ll use the panel notation Trent set out. NPS Temporal Conference # 30 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 MATH RECOME… Pure panel = [1-0] = “Always Revisit” 100% 50% 0% 50% 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 NPS Temporal Conference # 31 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 NPS Temporal Conference # 32 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 NPS Temporal Conference # 33 POWER TO DETECT TREND FIRST TEMPORAL DESIGN FAMILY NO YEAR EFFECT 1 30:0 20:10 10:20 0:30 0.8 POWER Always Revisit 0.6 0.4 0.2 0 0 5 10 15 Never Revisit 20 YEARS NPS Temporal Conference # 34 POWER TO DETECT TREND FIRST TEMPORAL DESIGN FAMILY, MODEST (= SOME) YEAR EFFECT 1 30:0 20:10 10:20 0:30 POWER 0.8 0.6 0.4 0.2 0 0 5 10 15 20 YEARS NPS Temporal Conference # 35 POWER TO DETECT TREND FIRST TEMPORAL DESIGN FAMILY BIG (= LOTS) YEAR EFFECT 1 30:0 20:10 10:20 0:30 POWER 0.8 0.6 0.4 0.2 0 0 5 10 15 20 YEARS NPS Temporal Conference # 36 FOREST INVENTORY ANALYSIS (FIA) HAS A SYSTEMATIC SPATIAL DESIGN WITH [1-9] YEAR 1 FIA X 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 X 21 X Doesn’t match up well with [1-0] and [1-n] We need to investigate alternatives NPS Temporal Conference # 37 SERIALLY ALTERNATING TEMPORAL DESIGN [(1-3)4 ] SOMETIMES USED BY EMAP YEAR 1 FIA X [(1-3)4 ] X 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 X X X X X X X X X X X X X X X 21 X X X X X X NPS Temporal Conference # 38 X SERIALLY ALTERNATING TEMPORAL DESIGN [(1-3)4 ] SOMETIMES USED BY EMAP YEAR 1 FIA X [(1-3)4 ] X 2 3 4 5 6 7 8 9 10 11 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 NPS Temporal Conference # 39 SPLIT PANEL [(1-4)5 , --- ] YEAR 1 FIA X [(1-4)5 ] X 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 X X X X X X X X X X X X X X X X X X X 21 X X AGAIN, Unconnected in an experimental design sense Matches better with FIA Still a very weak design for estimating year effects, if present NPS Temporal Conference # 40 X SPLIT PANEL [(1-4)5 ,(2-3)5 ] YEAR 1 FIA X [(1-4)5 ] X 2 3 4 5 6 7 8 9 X 12 13 14 15 16 17 18 19 20 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 X X X X 21 X X X X 11 X X [(2-3)5 ] 10 X X X X X X X X This Temporal Design IS connected Has three panels which match up with FIA NPS Temporal Conference # 41 X X X SECOND TEMPORAL DESIGN FAMILY 30 site visits per year [1-4] 30 20 10 0 [2-3] 0 5 10 15 NPS Temporal Conference # 42 POWER TO DETECT TREND SECOND TEMPORAL DESIGN FAMILY NO YEAR EFFECT 1 30:0 20:5 10:10 0:15 POWER 0.8 0.6 0.4 0.2 0 0 5 10 YEARS 15 20 NPS Temporal Conference # 43 POWER TO DETECT TREND SECOND TEMPORAL DESIGN FAMILY SOME YEAR EFFECT 1 30:0 20:5 10:10 0:15 POWER 0.8 0.6 0.4 0.2 0 0 5 10 YEARS 15 20 NPS Temporal Conference # 44 POWER TO DETECT TREND SECOND TEMPORAL DESIGN FAMILY LOTS OF YEAR EFFECT 1 30:0 20:5 10:10 0:15 POWER 0.8 0.6 0.4 0.2 0 0 5 10 YEARS 15 20 NPS Temporal Conference # 45 COMPARISON OF POWER TO DETECT TREND DESIGN 1 & 2 = ROWS YEAR EFFECT NONE SOME 1 0.8 0.8 0.6 0.4 POWER 0.8 POWER POWER LOTS 1 1 0.6 0.6 0.4 0.4 0.2 0.2 0.2 0 0 0 5 10 15 20 0 0 YEARS 0 5 10 15 5 10 15 20 15 20 YEARS 20 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.2 POWER 1 POWER POWER YEARS 0.4 0.2 0 0.2 0 0 5 10 YEARS 15 20 0.4 0 0 5 10 YEARS 15 20 0 5 10 YEARS NPS Temporal Conference # 46 POWER TO DETECT TREND VARYING YEAR EFFECT AND TEMPORAL DESIGN 1 TEMPORAL DESIGN 2 0.8 NONE POWER TEMPORAL DESIGN 1 0.6 SOME 0.4 LOTS 0.2 0 0 5 10 15 20 YEARS NPS Temporal Conference # 47 STANDARD ERROR OF STATUS TEMPORAL DESIGN 1, NO YEAR EFFECT 0.5 SE STATUS 0.4 TOTAL OF 30 SITES 0.3 30:0 20:10 10:20 0:30 0.2 110 SITES VISITED BY YEAR 5 0.1 0 0 5 10 410 SITES VISITED BY YEAR 20 15 YEARS NPS Temporal Conference # 48 20 STANDARD ERROR OF STATUS TEMPORAL DESIGN 1, SOME YEAR EFFECT 0.5 30:0 20:10 10:20 0:30 SE STATUS 0.4 0.3 0.2 0.1 0 0 5 10 15 YEARS NPS Temporal Conference # 49 20 STANDARD ERROR OF STATUS TEMPORAL DESIGN 1, LOTS OF YEAR EFFECT 0.5 SE STATUS 0.4 0.3 0.2 30:0 20:10 10:20 0:30 0.1 0 0 5 10 15 YEARS NPS Temporal Conference # 50 20 STANDARD ERROR OF STATUS TEMPORAL DESIGN 2, NO YEAR EFFECT 0.5 SE STATUS 0.4 30:0 20:5 10:10 0:15 TOTAL OF 75 SITES 0.3 0.2 0.1 TOTAL OF 150 SITES 0 0 5 10 15 YEARS NPS Temporal Conference # 51 20 STANDARD ERROR OF STATUS TEMPORAL DESIGN 2, SOME YEAR EFFECT 0.5 30:0 20:5 10:10 0:15 SE STATUS 0.4 0.3 0.2 0.1 0 0 5 10 15 YEARS NPS Temporal Conference # 52 20 STANDARD ERROR OF STATUS TEMPORAL DESIGN 2, LOTS OF YEAR EFFECT 0.5 30:0 20:5 10:10 0:15 SE STATUS 0.4 0.3 0.2 0.1 0 0 5 10 15 YEARS NPS Temporal Conference # 53 20 SO WHAT? Regardless of evaluation circumstances, Trend detection improves the more the same sites are revisited Status estimation improves as the number of distinct sites visited increases Temporal design 2 is better than temporal design 1 in relevant cases Its power is only slightly influenced by split between panels NPS Temporal Conference # 54 METADATA Really important for your successors Like your grandchildrens’ generation I’ll comment about this later in the conference if you want me to NPS Temporal Conference # 55 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. This research is funded by U.S.EPA – Science To Achieve Results (STAR) Program Cooperative # CR - 829095 Agreement NPS Temporal Conference # 56 TEMPORAL DESIGN 1 ALWAYS REVISIT TIME PERIOD ( ex: YEARS) PANEL 1 2 3 4 5 6 7 8 9 10 11 12 13 ... 1 X X X X X X X X X X X X X NPS Temporal Conference # 57 TEMPORAL DESIGN 2: NEVER REVISIT PANEL 1 2 3 4 5 6 7 8 9 1 2 X X TIME PERIOD ( ex: YEARS) 3 4 5 6 7 8 9 10 11 12 13 ... X X X X X X X NPS Temporal Conference # 58 TEMPORAL DESIGN 3: AUGMENTED SERIALLY ALTERNATING TIME PERIOD ( ex: YEARS) PANEL 1 2 3 4 5 6 7 8 9 10 11 12 13 ... 0 X X X X X X X X X X X X X 1 X X X X 2 X X X 3 X X X 4 X X X NPS Temporal Conference # 59 TEMPORAL DESIGN 4: SPLIT PANEL SERIALLY ALTERNATING PLUS SERIALLY ALTERNATING WITH CONSECUTIVE YEAR REVISITS PANEL 1 1A 2 2A 3 3A 4 4A TIME PERIOD ( ex: YEARS) 1 2 3 4 5 6 7 8 9 10 11 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 12 13 ... X X X X X X NPS Temporal Conference # 60 DESIGN EFFECT 1 A POWER for TREND 0.8 0.6 DESIGNS 1, 3, & 4 0.4 DESIGN 2 0.2 0 0 5 10 TIME ( = YEARS ) 15 NPS Temporal Conference # 61 20 LAKE EFFECT; DESIGNS 2 & 4 VAR LAKE = 1, 2, 5 POWER for TREND 1 B 0.8 0.6 DESIGN 4 ALL VARIANCES 0.4 1 2 0.2 DESIGN 2 LAKE VAR = 5 0 0 5 10 15 TIME ( = YEARS ) NPS Temporal Conference # 62 20 YEAR EFFECT - DESIGNS 2 & 4 1 C YEAR EFFECT 0, 0.05, 0.10 TOP CURVES FOR 0.00 POWER for TREND 0.8 0.6 0.4 DESIGN 2 DESIGN 4 0.2 0 0 5 10 15 TIME ( = YEARS ) NPS Temporal Conference # 63 20 STANDARD ERROR (STATUS) STANDARD ERROR OF ESTIMATED STATUS ALL DESIGNS 0.4 D DESIGN 1 0.2 DESIGN 2 DESIGNS 3 & 4 0 0 5 10 15 TIME ( =Years ) NPS Temporal Conference # 64 20 SIZE OF TREND EFFECT: DESIGN 4 1 E POWER for TREND 0.8 l = 0.03 l = 0.02 0.6 l = 0.015 0.4 l = 0.01 0.2 0 0 5 10 15 20 TIME ( = YEARS ) NPS Temporal Conference # 65 SAMPLE SIZE EFFECT - DESIGN 4 1 F POWER for TREND 0.8 n = 240 0.6 n = 120 0.4 n = 60 0.2 0 0 5 10 TIME ( = YEARS ) 15 NPS Temporal Conference # 66 20 SECCHI DEPTH 1.2 A 1 3% PER YEAR 0.8 1% PER YEAR 0.6 0.4 0.2 0 0 5 10 TIME ( = YEARS ) 15 NPS Temporal Conference # 67 ln ( CHLOROPHYLL a ) POWER for TREND 1 A 0.8 3% PER YEAR 0.6 0.4 1% PER YEAR 0.2 0 0 5 10 15 TIME ( = YEARS ) NPS Temporal Conference # 68 20 ln(TOTAL PHOSPHORUS) 1 A POWER for TREND 0.8 0.6 3% PER YEAR 0.4 0.2 1% PER YEAR 0 0 5 10 15 20 TIME ( = YEARS ) NPS Temporal Conference # 69 ln( NUMBER ZOOPLANKTON TAXA) 1 POWER for TREND 0.8 0.6 3% PER YEAR 0.4 0.2 1% PER YEAR 0 0 5 10 15 TIME ( = YEARS ) NPS Temporal Conference # 70 20