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Probability Survey Design: An Overview Anthony (Tony) R. Olsen USEPA NHEERL Western Ecology Division Email: [email protected] Voice: 541 754-4790 Why Monitoring Programs Fail Objectives for monitoring are not clearly, precisely stated and understood

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Probability survey design an overview l.jpg

Probability Survey Design:An Overview

Anthony (Tony) R. Olsen

USEPA NHEERL

Western Ecology Division

Email: [email protected]

Voice: 541 754-4790

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Why Monitoring Programs Fail

  • Objectives for monitoring are not clearly, precisely stated and understood

  • Monitoring measurement protocols, survey design, and statistical analysis become scientifically out-of-date

  • Monitoring results are not directly tied to management decision making

  • Results are not timely nor communicated to key audiences

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Types of Statistical Designs

  • Experimental designs

    • Random allocation of treatments

  • Observational studies

    • Factor space designs

      • Gradient studies

    • Available sites

  • Survey designs

    • Census

    • Probability survey

  • Response designs needed in all

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Survey DesignResponse Design

  • Survey design is process of selecting sites at which a response will be determined

    • Probability model for inference is based on the randomized selection process

    • Has a spatial component and may have a time component

  • Response design is process of obtaining a response at a site:

    • A single index period during a year

    • Multiple periods during year: monthly, quarterly

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The Response Design:Index Period

  • Time period within year selected for measurement (ecologically based)

  • Measurements may be taken more than once during index period with response design giving protocol for obtaining single value for indicator

  • Indicator variability within index period contributes to non-survey sampling error

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Ecological Resource Typesfrom Survey Design Perspective

  • Finite population of discrete entities

    • 0-dimensional

    • All small lakes in the 48 conterminous states

    • All 8-digit USGS CU in the 48 conterminous states

  • Continuous areal population

    • 2-dimensional

    • All forest land

    • All coastal estuarine resources

  • Continuous linear network population

    • 1-dimensional embedded in 2-dimensions

    • All perennial wadable streams

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Basic Spatial Survey Designs

  • Simple Random Sample

  • Systematic Sample

    • Regular grid

    • Regular spacing on linear resource

  • Spatially Balanced Sample

    • Combination of simple random and systematic

    • Guarantees all possible samples are distributed across the resource (target population)

    • Generalized Random Tessellation Stratified (GRTS) design

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Why aren’t Basic Designs Sufficient?

  • Monitoring objectives may include requirements that basic designs can’t address efficiently

    • Estimates for particular subpopulations requires greater sampling effort

    • Administrative restrictions and operational costs

  • Ecological resource occurrence in study region makes basic designs inefficient

    • Resource is known to be restricted to particular habitats

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Stratification: Reasons to Use

  • Administrative or operational convenience

    • Regions or states need to be operationally independent

  • Particular portions of the target population require different survey designs

    • Design for extensive wetlands (Everglades) may be different from praire pothole wetlands

  • Increase precision by constructing strata that are homogeneous

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More complex Survey Designs

  • Spatial strata random sample

    • Don’t have a list frame

    • Alternative way to spatially balance sample

  • Unequal probability sample

    • Alternative to stratification

    • Requires auxiliary information

  • Cluster sample

    • Can decrease field operation

  • Multiple stage sample

    • Way to decrease cost of sample frame construction

  • Adaptive Sampling

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Survey Design Key Components

  • Objectives stated precisely and quantitatively

  • Target population explicitly, precisely defined

  • Sampling frame constructed that represents the target population

  • Decision on which survey design meets needs

  • Selection of sites using survey design

  • Statistical analysis match survey design

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Study Objectives

  • Study objectives determine the monitoring design

    • Usual to have multiple objectives

    • Objectives compete for samples

    • Precise statements are required

    • Objectives must be prioritized

  • Target population and subpopulations are determined by objectives

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What is a Target Population?

  • Target population denotes the ecological resource about which information is wanted.

  • Requires a clear, precise definition

    • Must be understandable to users

    • Field crews must be able to determine if a particular site is included

  • More difficult to define than most expect.

  • Includes definition of what the elements are that make up the target population

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Subpopulations and Domains

  • Subsets of the target population that are of particular interest

  • Examples for aquatic ecosystems

    • Ecoregions, biogeographic regions

    • All lentic resources in region with area < 100 ha

    • All lotic resources with with Strahler order < 4

    • Tidal creeks versus open water estuarine areas

    • All lotic resources with < 20% riparian canopy cover

    • All 5-th field HUCs with >10 NWI wetland polygons

    • All 6-th field HUCs with >25% Federal land ownership

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Subpopulations: Impact on Design

  • Objectives identify critical subpopulations with expected sample sizes: Domains

  • Survey design addresses domain sample size requirements

    • Explicitly using stratification, unequal weighting

    • Implicitly when other requirements provide sufficient sample sizes

  • Other subpopulations can not be defined prior to sample selection

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Generalized Random Tessellation Stratified Designs

  • Spatially balances sample across the resource (improved precision)

  • Overview of process for areal resource

    • Randomly place hierarchical grid over area

    • Randomly select point within each grid cell

    • Select grid such that expected number of sample points in cell < 1 & expect most random points in cells to be in resource

    • Hierarchically randomize points to place them on line, assigning each point unit length

    • Select a systematic sample from the points using a random start

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GRTS Survey Design Options

  • Multiple density categories to allocate samples: unequal probability

  • Nested subsamples for measuring additional indicators or duplicate samples

  • Panels for monitoring over time

  • Oversample selection to address non-target and inaccessible sites

  • Special study areas with study-wide base

  • Explicit stratification

  • Incorporate multiple stage sampling

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Panels and Oversample

  • Panel: a collection of sites that will have the same revisit schedule over time

    • Basic design is single panel

    • 5-year rotating panel: panel 1 visited in year 1, 6, 11,etc; panel 2 visited in year 2, 7, 12, etc; …

    • More complex possible to balance priority of status estimation versus trend estimation

  • Oversample: design adjustment for

    • expected non-target sites

    • landowner access denial sites

    • physically inaccessible sites

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Example Designs

  • Everglades marshes and canals

  • Streams and rivers in 12 western states

  • Headwater watersheds in coastal plains of Mid-Atlantic

  • Prairie pothole wetlands in North Dakota and South Dakota

  • 6-th field hydrologic units in Pacific Northwest

  • FIA and FHM monitoring of forests

  • Amphibians in Olympic National Park and Southeast Oregon

  • Riverine wetlands associated with the Great Lakes

  • All Lakes >1 ha for fish tissue contaminants

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Monitoring Design Information

  • WWW.EPA.GOV/WED click on EMAP Monitoring Design and Analysis

    • Overview of survey design

    • Bibliography

    • Design and analysis information

  • EMAP Design Team

    • Works with States, Tribal Nations, EPA Regions, Other Federal Agencies

    • Members from ORD ecology divisions, NERL, Office of Water

    • Contact: Web page above

27


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Multiple Density Nested Random Tessellation Stratified Survey Design

  • Enables design-based estimators and variance estimators

    • Precise control over inclusion probabilities

    • Element & region variable probability assignment

    • Joint inclusion probability can be determined

  • Controls sample and subsample spatial balance

  • Nested subsamples easily selected

  • Unified theory for 0-, 1-, and 2-dimensional resources such as lakes, streams, and coastal waters

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Spatially-Structured “List”

  • Finite resource: 0-dimensional

    • Assign each unit to grid cell using GIS

    • Randomly order units within a single cell

    • Apply hierarchical randomization to cells

  • Linear resource: 1-dimensional, can be network

    • Clip linear resource to cell boundaries using GIS

    • Divide into segments

    • Randomly order units within a single cell

    • Apply hierarchical randomization to cells

  • Extensive resource: 2-dimensional

    • Select one point at random within each cell

    • Apply hierarchical randomization to cells

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Expansion of hexagon hierarchy to three levels

200 500 600 100 300 400 000

140 150 120 130 100 110 160

121 126 122 120 125 123 124

  • Grid Cell Shape

  • hexagon

  • Square

  • Diamond

  • Grid Cell Address

  • General Balanced Ternary

  • Peano Key

  • Morton Key

Hierarchical Randomization based on Hexagons


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Systematic Sample with Random Start from Ordered “List”

Randomized List: 2 4 0 3 6 1 5 1 4 2 0 6 5 3 1 5 0 4 2 6 3 4 2 6 0 5 1 3

4 2 53

Assign weights:

2 4 0 3 6 1 5 1 4 2 0 6 5 3 1 5 0 4 2 6 3 4 2 6 0 5 1 3

4 2 53

Systematic

Sample

Random Start

2 4 0 3 6 1 5 1 4 2 0 6 5 3 1 5 0 4 2 6 3 4 2 6 0 5 1 3

4 2 5 3

Sample: 42 46 24 20 23 50 53 36 31

Translate location on line to lake identifier, lat/long location on stream, lat/long location of point


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Stratification and Unequal Probability Selection

  • Stratification: reasons

    • Improve precision of results

    • Operational/administrative efficiency

    • Different subpopulations require different survey designs

  • Unequal weighting

    • Allocate sample to subpopulations

    • Improve precision of results

    • Based on auxiliary information

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Status, Change, Trend

  • Status

    • How many stream km in Region III meet their designated use?

    • How many stream km have degraded riparian zones?

  • Change/Trends

    • Has the status of the streams in Region III changed between two time periods?

    • What is the trend over the last 10 years in the percent of stream km in Region III that meet their designated use?

    • What is the trend in nitrate concentration on the Santiam River at its confluence with the Willamette River.

34


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Highland Stream Conditions

Biological Quality

% of Stream Length

Ranking of Stressors


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Monitoring Design and Analysis: Key Steps

  • Specify objectives and scope

  • Select sites to sample

  • Gain site access

  • Measurement protocols

  • Determine indicator based on measurements

  • Inference from the sample to entire aquatic resource

  • Communication of results

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Target Population: Lakes

  • All lakes (and reservoirs) within the conterminous U.S. excluding the Laurentian Great Lakes and the Great Salt Lake with permanent fish population.

  • A lake is defined as a permanent body of water of at least one hectare in surface area with a minimum of 1,000 sq m of open (unvegetated) water, and a maximum depth of one meter or more.

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Aquatic/riparian Resource

  • Define geographic region of interest - e.g. a state or province.

  • Aquatic/riparian components

    • Stream channel: habitat and water column

    • Stream near-channel: riparian

    • Stream upland area: terrestrial influence

  • Raises question of what constitutes the elements of the target population

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Alternatives for Defining Elements of Stream Target Population

  • All watersheds defined by a point anywhere on stream network (Point)

  • All watersheds defined by dividing the landscape into hydrologic units at a specified scale (HUC)

  • All watersheds defined by stream segments of network (Segment)

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Implications of choice

  • How many (what proportion of) stream km support aquatic life use?

  • How many (what proportion of) watersheds in region have greater than 50% of stream length supporting aquatic life use?

  • How many (what proportion of) stream segments in region support aquatic life use?

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State-wide Monitoring:When Multiple Years Required

  • Rotating basins

    • Each year monitor subset of state

      • Census

      • Probability Survey

    • Complete all subsets in 5-years

  • State-wide

    • Each year sample over entire state

    • Complete all sites to be sampled in 5-years

      • Census: partition all sites into 5 subsets

      • Probability survey over time

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Sampling Frame: Streams

  • GIS coverage that includes all streams in the target population

  • River Reach File Version 3 (RF3); NHD

  • Quality of RF3 as sampling frame

    • Excludes some channels that appear on 1:24,000 USGS maps and not on maps

    • Includes some channels/features that are not streams

  • Impacts survey design

    • Limited information available in RF3 to help define design for domains

    • Other GIS coverages can add attributes required

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Sampling Frame: Lakes

  • GIS coverage of lakes and reservoirs

  • RF3; NHD; state lists/coverages

  • Lakes: two alternatives for elements

    • Each lake is element: lake viewed as a point

    • All points in all lakes are elements: area view

  • Quality of RF3 as sampling frame

    • Excludes some lakes and reservoirs

    • Includes features that are not a lake or reservoir

    • Target population may be more restrictive than all of RF3

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Sampling Frame: Coastal Waters

  • GIS coverage of coastal waters in study

    • Estuary open water

    • Tidal streams

    • Near-shore waters

  • Elements are all point locations within target population

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RF3 Sample Frame: Lakes


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Sample Selected: Lakes


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Delaware Reporting

Traditional 305(b) Report

Chemical Evidence

Aggregation of Existing Data

New Report

Chemical Evidence

Probability Survey

New Report

Biological Evidence

Probability Survey

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Survey DesignImproved Estimates of Population SizeOregon Coastal Coho Salmon

  • Historic long term monitoring of spawning suggests minimal problem

  • Historic survey biased

  • Salmon populations continue to decline

  • Survey results more accurately reflect populations

  • State program modified based on probability design

Estimated No. Fish per mile


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