uses of power in designing long-term environmental surveys
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Wageningen 2004 # 1
Wageningen 2004 # 2
USES OF POWERUSES OF POWERIN DESIGNING IN DESIGNING LONG-TERM LONG-TERM
ENVIRONMENTAL SURVEYSENVIRONMENTAL SURVEYS
N. Scott UrquhartN. Scott UrquhartDepartment of Statistics Department of Statistics
Colorado State UniversityColorado State University
Fort Collins, CO 80523-1877Fort Collins, CO 80523-1877
Wageningen 2004 # 3
OUTLINE FOR TONIGHTOUTLINE FOR TONIGHT
Long-Term Environmental SurveysLong-Term Environmental Surveys Agencies involved
Sorts of Summaries of InterestSorts of Summaries of InterestSources of Variation – Major onesSources of Variation – Major onesA Statistical ModelA Statistical Model
Superimposed on an Adapted Classical Sampling Model
Calculation of Power Using this Model Illustrations
General Specific
Generalizations - as Time AllowsGeneralizations - as Time Allows
Wageningen 2004 # 4
LONG-TERM ENVIRONMENTAL SURVEYSLONG-TERM ENVIRONMENTAL SURVEYS
Objective: To Establish 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 = WhoAgencies = 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
Wageningen 2004 # 5
RESPONSES of INTERESTRESPONSES of INTEREST
EPAEPA 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
thanIndividual Chemicals
Fish Populations – Composition, not size Clean Water Act Includes Reporting on
Temperature Pollution
Wageningen 2004 # 6
RESPONSES of INTERESTRESPONSES of INTEREST(continued)(continued)
National Park Service (Eg: Olympic NP in National Park Service (Eg: Olympic NP in WA)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
Wageningen 2004 # 7
RESPONSES of INTERESTRESPONSES of INTEREST(continued II)(continued II)
Grand Canyon National Park Erosion Around Archeological Resources Near-river Terrestrial Environment (GCMRC)
Wageningen 2004 # 8
SPATIAL EXTENTSPATIAL EXTENT
Generally Large AreasGenerally Large Areas This is the Way Congress Writes Laws
Regions can be very large 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*
Wageningen 2004 # 9
SUMMARIES of INTERESTSUMMARIES of INTEREST
Extent by ClassesExtent by Classes Track Changes Between Classes
National Wetlands Inventory Major focus Has Very Good Graphic Depiction of Class
Changes
““Status”Status” Often is summarized as an Estimated
CumulativeDistribution Function (cdf)
Pose some Interesting Statistical Inference Problems Due to Variable Probability Sampling – Almost Always
Needed Spatially Continuous Resources – No List Can Exist
Wageningen 2004 # 10
EXAMPLE OF STATUS,
SUMMARIZED BY A cdf
Wageningen 2004 # 11
ESTIMATED CUMULATIVE DISTRIBUTION ESTIMATED CUMULATIVE DISTRIBUTION FUNCTION OF SECCHI DEPTH, EMAP AND “DIP-IN”FUNCTION OF SECCHI DEPTH, EMAP AND “DIP-IN”
Wageningen 2004 # 12
SUMMARIES of INTERESTSUMMARIES of INTEREST(continued)(continued)
TrendsTrends 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 Regional Summaries of Individual Site TrendsTrends Sometimes how trend varies in relation to other
things
Wageningen 2004 # 13
POPULATION VARIANCE: POPULATION VARIANCE:
YEAR VARIANCE:YEAR VARIANCE:
RESIDUAL VARIANCE:RESIDUAL VARIANCE:
( ) LAKE
2
( ) YEAR2
IMPORTANT COMPONENTS OF VARIANCEIMPORTANT COMPONENTS OF VARIANCE
( ) RESIDUAL
2
Wageningen 2004 # 14
POPULATION VARIANCE: POPULATION VARIANCE:
VARIATION AMONG VALUES OF AN INDICATOR (RESPONSE) ACROSS ALL LAKES IN A REGIONAL POPULATION OR SUBPOPULATION
( ) LAKE
2
IMPORTANT COMPONENTS OF VARIANCEIMPORTANT COMPONENTS OF VARIANCE( - CONTINUED)( - CONTINUED)
Wageningen 2004 # 15
YEAR VARIANCE: 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)
( ) YEAR2
IMPORTANT COMPONENTS OF VARIANCEIMPORTANT COMPONENTS OF VARIANCE( - CONTINUED II)( - CONTINUED II)
Wageningen 2004 # 16
RESIDUAL COMPONENT OF VARIANCERESIDUAL 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
IMPORTANT COMPONENTS OF VARIANCEIMPORTANT COMPONENTS OF VARIANCE( - CONTINUED - III)( - CONTINUED - III)
( ) RESIDUAL
2
Wageningen 2004 # 17
BIOLOGICAL INDICATORS HAVE SOMEWHAT MORE BIOLOGICAL INDICATORS HAVE SOMEWHAT MORE VARIABILITY THAN PHYSICAL INDICATORS – BUT THIS VARIES, VARIABILITY THAN PHYSICAL INDICATORS – BUT THIS VARIES,
TOOTOO Subsequent slides show the relative Subsequent slides show the relative
amount of variability amount of variability Ordered by the amount of residual
variability: least to most (aquatic responses) Acid Neutralizing CapacityAcid Neutralizing Capacity Ln(Conductance)Ln(Conductance) Ln(Chloride)Ln(Chloride) pH(Closed system)pH(Closed system) Secchi DepthSecchi Depth Ln(Total Nitrogen)Ln(Total Nitrogen) Ln(Total Phosphorus)Ln(Total Phosphorus) Ln(Chlorophyll A)Ln(Chlorophyll A) Ln( # zooplankton taxa)Ln( # zooplankton taxa) Ln( # rotifer taxa)Ln( # rotifer taxa) Maximum TemperatureMaximum Temperature
And others, both aquatic and terrestrial
Wageningen 2004 # 18
COMPOSITION OF TOTAL VARIANCE
0.00 0.20 0.40 0.60 0.80 1.00
Maximum Temperature
Ln( # rotifer taxa)
Ln( # zooplankton taxa)
Ln(Chlorophyll A)
Ln(Total Phosphorus)
Ln(Total Nitrogen)
Secchi Depth
pH(Closed system)
Ln(Chloride)
Ln(Conductance)
Acid Neutralizing Capacity
PROPORTION OF VARIANCE
RESIDUAL COMPONENT OF VARIANCE
LAKE COMPONENT OF VARIANCE
YEAR
Wageningen 2004 # 19
SOURCE OF COMPONENTS OF SOURCE OF COMPONENTS OF VARIANCE FROM GRAND CANYONVARIANCE FROM GRAND CANYON
Grand Canyon Monitoring and Research Grand Canyon Monitoring and Research CenterCenter
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’ DataUsing First Two Years’ Data Mike Kearsley – UNA
Design = Spatially BalancedDesign = Spatially Balanced With about 1/3 revisited
Wageningen 2004 # 20
COMPOSITION OF TOTAL VARIANCEGRAND CANYON -- NEAR RIVER VEGETATION
0.00 0.20 0.40 0.60 0.80 1.00
Veg - 25K cfs
Veg - 35K cfs
Veg - 45K cfs
Veg - 60K cfs
Richness - 15K cfs
Richness - 25K cfs
Richness - 35K cfs
Richness - 45K cfs
Richness - 60K cfs
PROPORTION OF VARIANCE
RESIDUAL COMPONENT OF VARIANCE
SITE COMPONENT OF VARIANCELAKE COMPONENT
YEAR
Wageningen 2004 # 21
ALL VARIABILITY IS OF INTERESTALL VARIABILITY IS OF INTEREST
The Site Component of Variance is One of The Site Component of Variance is One of the Major Descriptors of the Regional the Major Descriptors of the Regional PopulationPopulation
The Year Component of Variance Often is The Year Component of Variance Often is Small, too Small to Estimate. If Small, too Small to Estimate. If
Present,Present,it is a Major Enemy for Detecting Trendit is a Major Enemy for Detecting TrendOver Time.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.
Wageningen 2004 # 22
ALL VARIABILITY IS OF INTERESTALL VARIABILITY IS OF INTEREST( - CONTINUED)( - CONTINUED)
Residual Variance Characterizes the Residual Variance Characterizes the Inherent Variation in the Response or Inherent Variation in the Response or Indicator.Indicator.
But Some of its Subcomponents May But Some of its Subcomponents May Contain Useful Management InformationContain 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
Wageningen 2004 # 23
DESIGN TRADE-OFFS: TREND DESIGN TRADE-OFFS: TREND vs vs STATUSSTATUS
How do we Detect Trend in Spite of All How do we Detect Trend in Spite of All of This Variation?of This Variation?
Recall Two Old Statistical “Friends.”Recall Two Old Statistical “Friends.” Variance of a mean, and Blocking
Wageningen 2004 # 24
DESIGN TRADE-OFFS: TREND DESIGN TRADE-OFFS: TREND vs vs STATUSSTATUS( - CONTINUED)( - CONTINUED)
VARIANCE OF A MEAN: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 "2" refers to the variance of an estimated slope ---
var meanm
( ) 2
Wageningen 2004 # 25
DESIGN TRADE-OFFS: TREND DESIGN TRADE-OFFS: TREND vs vs STATUSSTATUS( - CONTINUED - II)( - CONTINUED - II)
ConsequentlyConsequently
BecomesBecomes
Note that the regional averaging of Note that the regional averaging of slopes has the same effect as slopes has the same effect as continuing to monitor at one site for a continuing to monitor at one site for a much longer time period.much longer time period.
var meanm
( ) 2
var regional mean slopem t ti
( )( )
1 2
2
Wageningen 2004 # 26
DESIGN TRADE-OFFS: TREND DESIGN TRADE-OFFS: TREND vs vs STATUSSTATUS( - CONTINUED - III)( - CONTINUED - III)
Now, Now, 22, in total, is large., in total, is large.
If we take one regional sample of sites If we take one regional sample of sites at one time, and another at a at one time, and another at a subsequent time, the site component of subsequent time, the site component of variance is included in variance is included in 22..
Enter the concept of blocking, familiar Enter the concept of blocking, familiar from experimental design.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.
Wageningen 2004 # 27
STATISTICAL MODELSTATISTICAL MODEL
CONSIDER A FINITE POPULATION OF CONSIDER A FINITE POPULATION OF SITESSITES {S1 , S2 , … , SN }
and A TIME SERIES OF RESPONSE and A TIME SERIES OF RESPONSE VALUES AT EACH SITE: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
{ ( ), ( ), , ( )} ( )Y t Y t Y t Y tN1 2 and their average:
Wageningen 2004 # 28
STATISTICAL MODEL -- IISTATISTICAL MODEL -- IIAGAIN CONSIDER THE UNDERLYING TIME SERIES
DURING AN INDEX WINDOW
and their averages: and
= var{
{ ( ), ( ), , ( )}
( ), ( ), ( ).
( )},
var{ ( )}
var{ ( ) ( ) ( ) ( )}
Y t Y t Y t
Y Y t Y
Y
Y t
Y t Y Y t Y
N
i
SITE i
YEAR
RESIDUAL i i
1 2
2
2
2
Wageningen 2004 # 29
STATISTICAL MODEL -- IIISTATISTICAL MODEL -- III
{ ( )} { }
( ) ( ) ( )
~ ( , ), ~ ( , ), ~ ( , ),
Y t Yi
j
Y Y Y Y Y Y Y Y Y Y
Y S T E
S T E
i ij
ij i j ij i j
i j ij
i SITE j YEAR ij RESIDUAL
RST
where indexes sites
indexes "years"
and and
with these random variables otherwise uncorrelated.
0 0 02 2 2
Wageningen 2004 # 30
STATISTICAL MODEL -- IVSTATISTICAL MODEL -- IV
IF IF pp INDEXES PANELS, THEN 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
cov ( , , , )Y npj SITE YEAR RESIDUAL pjc h 2 2 2
Wageningen 2004 # 31
STATISTICAL MODEL -- VSTATISTICAL MODEL -- V
Now let X denote a regressor matrixNow let X denote a regressor matrixcontaining a column of 1s and a column containing a column of 1s and a column
ofofthe numbers of the time periodsthe numbers of the time periodscorresponding to the filled cells. Thecorresponding to the filled cells. Thesecond elements ofsecond elements of
contain an estimate of the regional trendcontain an estimate of the regional trendand its variance.and its variance.
and ( ' ) ' ,
cov( ) ( ' )
X X X Y
X X
1 1
1
1
1
Wageningen 2004 # 32
Ability of a panel plan to detect trend Ability of a panel plan to detect trend can be can be expressed as power.expressed as power.
We will evaluate power in terms of theseWe will evaluate power in terms of theseratios of variance components ratios of variance components
Power depends on the ratios of variance Power depends on the ratios of variance components, the panel plan, and oncomponents, the panel plan, and on
TOWARD POWERTOWARD POWER
0 2; approximately, ˆˆ/ ~ ( , )RESI DUAL N
SITE RESIDUAL YEAR RESIDUAL2 2 2 2/ / and
Wageningen 2004 # 33
NOW PUT IT ALL TOGETHERNOW PUT IT ALL TOGETHER
Question: “ What kind of temporal design Question: “ What kind of temporal design should you use for Northwest National should you use for Northwest National Parks?Parks?
We’ll investigate two (families) of We’ll investigate two (families) of recommended designs.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 We’ll use the panel notation Trent McDonaldMcDonald
published.published.
Wageningen 2004 # 34
RECOMMENDATION OF RECOMMENDATION OF FULLER and BREIDTFULLER and BREIDT
Based on the Natural Resources Based on the Natural Resources Inventory (NRI)Inventory (NRI) Iowa State & US Department of Agriculture
Oriented toward soil erosion & Changes in land use
Their recommendationTheir recommendation Pure panel =[1-0] =“Always Revisit” Independent =[1-n]=“Never Revisit”
Evaluation contextEvaluation context No trampling effect – remotely sensed data No year effects
Administrative reality of potential Administrative reality of potential variation invariation in
funding from year to yearfunding from year to year
MATH RECOME 100% 50% 0% 50%
Wageningen 2004 # 35
TEMPORAL LAYOUT OF [(1-0), (1-n)]TEMPORAL LAYOUT OF [(1-0), (1-n)]YEARYEAR 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020
[1-0][1-0] XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX
[1-n][1-n] XX
XX
XX
XX
XX
XX
XX
XX
XX
XX
XX
XX
XX
XX
XX
XX
XX
XX
XX
XX
Wageningen 2004 # 36
FIRST TEMPORAL DESIGN FAMILYFIRST TEMPORAL DESIGN FAMILY
30 site visits per year30 site visits per year
[1-0][1-0] 3030 2020 1010 00
[1-n][1-n] 00 1010 2020 3030
ALWAYSALWAYS
REVISITREVISITNEVERNEVER
REVISITREVISIT
Wageningen 2004 # 37
POWER TO DETECT TRENDPOWER TO DETECT TREND
FIRST TEMPORAL DESIGN FAMILY FIRST TEMPORAL DESIGN FAMILY NO YEAR EFFECTNO YEAR EFFECT
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
30:020:1010:200:30
Always Revisit
Never Revisit
Wageningen 2004 # 38
POWER TO DETECT TRENDPOWER TO DETECT TREND
FIRST TEMPORAL DESIGN FAMILY, FIRST TEMPORAL DESIGN FAMILY, MODEST (= SOME) YEAR EFFECTMODEST (= SOME) YEAR EFFECT
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
30:020:1010:200:30
Wageningen 2004 # 39
POWER TO DETECT TRENDPOWER TO DETECT TREND
FIRST TEMPORAL DESIGN FAMILYFIRST TEMPORAL DESIGN FAMILYBIG (= LOTS) YEAR EFFECTBIG (= LOTS) YEAR EFFECT
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
30:020:1010:200:30
Wageningen 2004 # 40
SERIALLY ALTERNATING TEMPORAL SERIALLY ALTERNATING TEMPORAL DESIGN [(1-3)DESIGN [(1-3)4 4 ] SOMETIMES USED BY ] SOMETIMES USED BY
EMAPEMAP
YEARYEAR 11 22 33 44 55 66 77 88 99 1100
1111
1122
1133
1144
1155
1166
1177
1188
1199
2200
2211
FIAFIA XX XX XX
[(1-[(1-3)3)4 4 ]]
XX XX XX XX XX XX
XX XX XX XX XX
XX XX XX XX XX
XX XX XX XX XX
Wageningen 2004 # 41
SERIALLY ALTERNATING TEMPORAL SERIALLY ALTERNATING TEMPORAL DESIGN [(1-3)DESIGN [(1-3)4 4 ] SOMETIMES USED BY ] SOMETIMES USED BY
EMAPEMAP
YEARYEAR 11 22 33 44 55 66 77 88 99 1010 1111 ……
FIAFIA XX XX
[(1-[(1-3)3)4 4 ]]
XX XX XX ……
XX XX XX ……
XX XX XX ……
XX XX ……
Unconnected in an experimental design Unconnected in an experimental design sensesense Very weak design for estimating year effects, if
present
Wageningen 2004 # 42
SPLIT PANEL [(1-4)SPLIT PANEL [(1-4)5 5 , ---, --- ]]
YEARYEAR 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020 2121
FIAFIA XX XX XX
[(1-4)[(1-4)5 5 ]] XX XX XX XX XX
XX XX XX XX
XX XX XX XX
XX XX XX XX
XX XX XX XX
AGAIN, Unconnected in an AGAIN, Unconnected in an experimental design senseexperimental design sense Matches better with FIA Still a very weak design for estimating
year effects, if present
Wageningen 2004 # 43
SPLIT PANEL [(1-4)SPLIT PANEL [(1-4)5 5 ,(2-3),(2-3)5 5 ]]
This Temporal Design IS connectedThis Temporal Design IS connectedHas three panels which match up with FIAHas three panels which match up with FIA
YEARYEAR 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020 2121
FIAFIA XX XX XX
[(1-4)[(1-4)5 5 ]] XX XX XX XX XX
XX XX XX XX
XX XX XX XX
XX XX XX XX
XX XX XX XX
[(2-3)[(2-3)5 5 ]] XX XX XX XX XX XX XX XX XX
XX XX XX XX XX XX XX XX
XX XX XX XX XX XX XX XX
XX XX XX XX XX XX XX XX
XX XX XX XX XX XX XX XX
Wageningen 2004 # 44
SECOND TEMPORAL DESIGN FAMILYSECOND TEMPORAL DESIGN FAMILY
30 site visits per year30 site visits per year
[1-4][1-4] 3030 2020 1010 00
[2-3][2-3] 00 55 1010 1515
Wageningen 2004 # 45
POWER TO DETECT TRENDPOWER TO DETECT TREND
SECOND TEMPORAL DESIGN FAMILY SECOND TEMPORAL DESIGN FAMILY NO YEAR EFFECTNO YEAR EFFECT
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
30:020:5
10:10 0:15
Wageningen 2004 # 46
POWER TO DETECT TRENDPOWER TO DETECT TREND
SECOND TEMPORAL DESIGN FAMILYSECOND TEMPORAL DESIGN FAMILYSOME YEAR EFFECTSOME YEAR EFFECT
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
30:020:5
10:10 0:15
Wageningen 2004 # 47
POWER TO DETECT TRENDPOWER TO DETECT TREND
SECOND TEMPORAL DESIGN FAMILYSECOND TEMPORAL DESIGN FAMILYLOTS OF YEAR EFFECTLOTS OF YEAR EFFECT
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
30:020:5
10:10 0:15
Wageningen 2004 # 48
COMPARISON OF POWER TO DETECT TRENDCOMPARISON OF POWER TO DETECT TRENDDESIGN 1 & 2 = ROWSDESIGN 1 & 2 = ROWS
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
YEAR EFFECT
NONE SOME LOTS
Wageningen 2004 # 49
POWER TO DETECT TRENDPOWER TO DETECT TREND
VARYING VARYING YEAR EFFECTYEAR EFFECT AND TEMPORAL AND TEMPORAL DESIGNDESIGN
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
YEARS
PO
WE
R
TEMPORAL DESIGN 2
TEMPORAL DESIGN 1NONE
SOME
LOTS
Wageningen 2004 # 50
STANDARD ERROR OF STATUSSTANDARD ERROR OF STATUS
TEMPORAL DESIGN 1, NO YEAR EFFECTTEMPORAL DESIGN 1, NO YEAR EFFECT
0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20
YEARS
SE
ST
AT
US
30:0 20:10 10:20 0:30
TOTAL OF 30 SITES
110 SITES VISITED BY
YEAR 5 410 SITES VISITED BY
YEAR 20
Wageningen 2004 # 51
STANDARD ERROR OF STATUSSTANDARD ERROR OF STATUS
TEMPORAL DESIGN 2, NO YEAR EFFECTTEMPORAL DESIGN 2, NO YEAR EFFECT
0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20
YEARS
SE
ST
AT
US
30:020:5
10:10 0:15
TOTAL OF 150 SITES
TOTAL OF 75 SITES
Wageningen 2004 # 52
GENERALIZATIONSGENERALIZATIONS
Each site can have its own trendEach site can have its own trend These very likely differ
How should we approach this reality?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:YearsRiversSites within rivers
Wageningen 2004 # 53
ILLUSTRATIONILLUSTRATION
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.
Wageningen 2004 # 54
Wageningen 2004 # 55
This research is funded by
U.S.EPA – Science To AchieveResults (STAR) ProgramCooperativeAgreement
# CR - 829095
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.
FUNDING ACKNOWLEDGEMENT
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