USES OF POWER IN DESIGNING LONG-TERM ENVIRONMENTAL SURVEYS

Wageningen 2004 # 1

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 # 2

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 # 3

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 # 4

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 # 5

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 # 6

RESPONSES of INTERESTRESPONSES of INTEREST(continued II)(continued II)

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

Wageningen 2004 # 7

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 # 8

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 # 9

EXAMPLE OF STATUS,

SUMMARIZED BY A cdf

Wageningen 2004 # 10

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


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


POPULATION VARIANCE: POPULATION VARIANCE:

YEAR VARIANCE:YEAR VARIANCE:

RESIDUAL VARIANCE:RESIDUAL VARIANCE:

( ) LAKE

2

( ) YEAR2

IMPORTANT COMPONENTS OF VARIANCEIMPORTANT COMPONENTS OF VARIANCE

( ) RESIDUAL

2


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)


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)


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


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


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


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


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


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.


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


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


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


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


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.


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:


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


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


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


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


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


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.


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%


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


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


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



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



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


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


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


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


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





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



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



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



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


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



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


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


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


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


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.



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

USES OF POWER IN DESIGNING LONG-TERM ENVIRONMENTAL SURVEYS

Documents