Use of imputed tree lists for Use of imputed tree lists for FVS landscape projections:FVS landscape projections:

An overview of some An overview of some issues and opportunities.issues and opportunities.

Eric L. SmithEric L. SmithForest Health Technology Enterprise TeamForest Health Technology Enterprise Team

U.S. Forest ServiceU.S. Forest ServiceFort Collins, COFort Collins, CO

Problem: We would like to run FVS simulations Problem: We would like to run FVS simulations for large landscapes, but we only have plot data for large landscapes, but we only have plot data

for some of the standsfor some of the stands

One solution: For each uninventoried One solution: For each uninventoried stand, use imputation techniques to find stand, use imputation techniques to find plot data taken from a similar site and plot data taken from a similar site and use that data as if it were taken from use that data as if it were taken from

the un-inventoried stand. the un-inventoried stand.

Imputation Imputation

““Imputation” is a generic term for methods Imputation” is a generic term for methods which can be used to estimate missing which can be used to estimate missing data. There are many ways to do this. For data. There are many ways to do this. For example, in FVS, you can provide a tree example, in FVS, you can provide a tree height but, if you don’t, FVS can impute it: height but, if you don’t, FVS can impute it: estimate it from a height as fn(dbh) model. estimate it from a height as fn(dbh) model.

Nearest Neighbor Imputation Nearest Neighbor Imputation

““Nearest Neighbor” (NN) imputation is a Nearest Neighbor” (NN) imputation is a statistical technique which substitutes statistical technique which substitutes many values from another sample plot many values from another sample plot which is like the plot with the missing data, which is like the plot with the missing data, based on what information you do have based on what information you do have about the plot with the missing values. about the plot with the missing values.

The kind of information we do have (or can The kind of information we do have (or can get) includes the kind of mapped data in get) includes the kind of mapped data in GIS coverages and satellite data. GIS coverages and satellite data.

Why NN Imputation? Why NN Imputation?

• In general, use of an entire plot sample In general, use of an entire plot sample insures the group of data elements insures the group of data elements represents a realistic combination of represents a realistic combination of conditionsconditions

• For use in FVS, we need the whole tree list For use in FVS, we need the whole tree list and sometimes addition plot dataand sometimes addition plot data

Process exampleProcess example Gradient Nearest Neighbor Gradient Nearest Neighbor

from Ohmann and Gregory, 2002from Ohmann and Gregory, 2002

Example mapped data Example mapped data

LandsatLandsat Bands, transformations, textureBands, transformations, texture

ClimateClimate Means, seasonal variabilityMeans, seasonal variability

TopographyTopography Elevation, slope, aspect, solarElevation, slope, aspect, solar

Soil Soil Texture, drainage, mineral typeTexture, drainage, mineral type

DisturbanceDisturbance Past fires, harvest, &IDPast fires, harvest, &ID

LocationLocation Lat., Long.Lat., Long.

OwnershipOwnership Federal, state, forest industry, other privateFederal, state, forest industry, other private

Adapted from Ohmann and GregoryAdapted from Ohmann and Gregory

Mapped data informationMapped data information

• Physiographic variables relates to “potential Physiographic variables relates to “potential vegetation” or successional pathwayvegetation” or successional pathway

• Satellite data relates to current tree sizes Satellite data relates to current tree sizes and density (pathway state)and density (pathway state)

• If management (or fire) has created variation If management (or fire) has created variation in understory conditions which is hidden from in understory conditions which is hidden from the satellite by the overstory, this could be a the satellite by the overstory, this could be a problem.problem.

The status of NN for FVSThe status of NN for FVS

• The NN technique most associated with FVS, Most The NN technique most associated with FVS, Most Similar Neighbor (MSN), has been around for over Similar Neighbor (MSN), has been around for over 10 years, additional techniques are being added to 10 years, additional techniques are being added to the software by Crookston and others.the software by Crookston and others.

• There is a increased recognition for the need for There is a increased recognition for the need for landscape simulations for fire and other landscape simulations for fire and other applications.applications.

• FIA annual data increasing available for all forested FIA annual data increasing available for all forested lands, while recent stand exam data is decreasing.lands, while recent stand exam data is decreasing.

• Adequate computer storage, processing power, Adequate computer storage, processing power, software, and GIS-based mapped data are now software, and GIS-based mapped data are now widely available to perform large imputation widely available to perform large imputation projects. projects.

Some current Major NN EffortsSome current Major NN Efforts

• Crookston Crookston et alet al, RMRS, Moscow, RMRS, Moscow– MSN support, new YAImpute packageMSN support, new YAImpute package

• Ohmann Ohmann et alet al, PNWRS, Corvallis, PNWRS, Corvallis– Gradient NN (GNN), mapping in CA, OR, WAGradient NN (GNN), mapping in CA, OR, WA

• McRoberts & Finley, NRS, St. PaulMcRoberts & Finley, NRS, St. Paul– Faster processing (ANN), variance estimationFaster processing (ANN), variance estimation

• Twombly, NRIS, have Informs, will travelTwombly, NRIS, have Informs, will travel– MSN inside INFORMS, creates Nat’l Forest mapsMSN inside INFORMS, creates Nat’l Forest maps

• LeMay LeMay et alet al, UBC, Vancouver, UBC, Vancouver– Various application in CanadaVarious application in Canada

Large NN imputations are hereLarge NN imputations are here

PNW, OhmannPNW, OhmannMn, McRobertsMn, McRobertsPa, ListerPa, ListerNFs, TwomblyNFs, Twombly

Scale: Compartments to States Scale: Compartments to States

The application of NN imputation to fill in a The application of NN imputation to fill in a (small?) number of uninventoried stands in (small?) number of uninventoried stands in a small landscape takes place in a very a small landscape takes place in a very different information context than the NN different information context than the NN allocation of large scale inventory plots to allocation of large scale inventory plots to a large area (sub-states to multi-states). a large area (sub-states to multi-states).

Small area applicationSmall area application

• Can know conditions and historyCan know conditions and history• Can gather more ground informationCan gather more ground information• Can relate imputation results to the on the Can relate imputation results to the on the

ground realityground reality• Inventory often linked to purpose and Inventory often linked to purpose and

reasonably intensivereasonably intensive• Homogeneous areas (stands) can be Homogeneous areas (stands) can be

predefined and be a sampled unitpredefined and be a sampled unit• Data and relationships between data are Data and relationships between data are

likely to be consistentlikely to be consistent

Large area applicationLarge area application

• Too large to have direct knowledge aboutToo large to have direct knowledge about• Sampling intensity is generally lowSampling intensity is generally low• Homogeneous areas not pre-defined but can be Homogeneous areas not pre-defined but can be

done so (using image analysis and GIS tools)done so (using image analysis and GIS tools)• Data and relationships between data are often Data and relationships between data are often

inconsistent across areainconsistent across area• Can gather more information- but through existing Can gather more information- but through existing

sources of remote sensing and other mapped datasources of remote sensing and other mapped data• Inventories may not be linked to the desired Inventories may not be linked to the desired

applications of the usersapplications of the users• However, inventory design may provide However, inventory design may provide

statistically reliable population estimatesstatistically reliable population estimates

Scale shifts focus to map dataScale shifts focus to map data

Fine scale details are less reliable as sample intensity Fine scale details are less reliable as sample intensity decreases and the imputation geographic range decreases and the imputation geographic range increase;increase;

But,But, from the stand point of the inventory estimates, from the stand point of the inventory estimates, imputation allows:imputation allows:

(1) the more precise estimation of inventory data for (1) the more precise estimation of inventory data for small areas; small areas;

(2) the estimation of additional types of summary (2) the estimation of additional types of summary variables for post stratified conditions; variables for post stratified conditions;

(3) the FVS projection of inventory subpopulations (3) the FVS projection of inventory subpopulations using associated tree lists by area and adjusted for a using associated tree lists by area and adjusted for a range of site conditions.range of site conditions.

Error and VarianceError and Variance

• Need goodness of fit measures to evaluate Need goodness of fit measures to evaluate the relative quality of proceduresthe relative quality of procedures

• Understanding sources of errors which Understanding sources of errors which contribute to variance needed to know if contribute to variance needed to know if and how they can be reducedand how they can be reduced

• Variance estimates for NN results are Variance estimates for NN results are complex and difficult, and under active complex and difficult, and under active investigationinvestigation

• There are different approaches used by There are different approaches used by different disciplines different disciplines

FIA Plot DesignFIA Plot Design

Trees 5 inch and over Trees 5 inch and over are measured on 4 are measured on 4 subplots, each subplots, each 1/241/24thth acre acre

Trees 1 to 5 inch are Trees 1 to 5 inch are measured on 4 measured on 4 microplots, each microplots, each 1/3001/300thth acre acre

Eventually, there Eventually, there should be at least should be at least one plot per 6000 one plot per 6000 forested acres, forested acres, nationwide nationwide

30 m

30 mSpatial scale: FIA vs. Landsat Spatial scale: FIA vs. Landsat

• Landsat pixels are 30x30 Landsat pixels are 30x30 meters (900 mmeters (900 m22))

• Each FIA subplot (>5 in.) is 167 Each FIA subplot (>5 in.) is 167 mm22 (19% of the pixel) (19% of the pixel)

• Each FIA microplot (1 to 5 in.) Each FIA microplot (1 to 5 in.) is 13.7 mis 13.7 m22 (1.5% of the pixel) (1.5% of the pixel)

• This difference in scale may This difference in scale may result in an underestimate the result in an underestimate the accuracy of the imputation if accuracy of the imputation if the sample estimates are the sample estimates are assumed to be “true”assumed to be “true”

• In addition, there is positional In addition, there is positional error and other sampling and error and other sampling and measurement error associated measurement error associated with FIA plot data, Landsat with FIA plot data, Landsat data, and other map data data, and other map data

Image from McRoberts, 2006Image from McRoberts, 200630m x 30m pixel30m x 30m pixel

k Nearest Neighbork Nearest Neighbor

• k Nearest Neighbor technique allows the selection of k Nearest Neighbor technique allows the selection of more than one reference data set, usually averaged more than one reference data set, usually averaged to estimate target conditions. (using 3 closest to estimate target conditions. (using 3 closest neighbors would be “k=3”)neighbors would be “k=3”)

• In FVS, the kNN approach could treat the multiple In FVS, the kNN approach could treat the multiple near neighbors as imputed sub-plots.near neighbors as imputed sub-plots.

• This may be desirable in the case of a scale This may be desirable in the case of a scale mismatch between the intensive plot and the map mismatch between the intensive plot and the map data. It also creates more variation across the data. It also creates more variation across the landscape, perhaps better representing transitions landscape, perhaps better representing transitions between conditions. between conditions.

• kNN option is included in YAImpute kNN option is included in YAImpute

Questions:Questions:

• Would k > 1 be a good tradeoff between Would k > 1 be a good tradeoff between real mixes of plot conditions and the real mixes of plot conditions and the sample uncertainty of plots smaller than sample uncertainty of plots smaller than pixels?pixels?

• Could additional Could additional pixel-sized pixel-sized information be information be gathered at sample point locations (e.g. gathered at sample point locations (e.g. photo-interpreted crown cover or cover photo-interpreted crown cover or cover type) and included in the multivariate data type) and included in the multivariate data analysis?analysis?

How much does it matter?How much does it matter?

• The issues of goodness of the imputation The issues of goodness of the imputation need to be considered in the context of the need to be considered in the context of the simulation: the use of the results and the simulation: the use of the results and the models’ sensitivity to the lack of accuracy.models’ sensitivity to the lack of accuracy.

• Model applications have a range of Model applications have a range of sensitivitysensitivity

• Analysis projrcts have a range of sensitivityAnalysis projrcts have a range of sensitivity• Sensitivity tests can be performed Sensitivity tests can be performed

Envision project using imputed dataEnvision project using imputed data

This imputation application has a low sensitivity to errorThis imputation application has a low sensitivity to error

Crystal Lakes Fuel Trt ProjectCrystal Lakes Fuel Trt ProjectArapaho-Roosevelt NFArapaho-Roosevelt NF

as seen from road intersectionas seen from road intersection

A fire-beetle project using MSNA fire-beetle project using MSN

This FFE WWPB application has catastrophic and contagion behaviors, This FFE WWPB application has catastrophic and contagion behaviors, and may be sensitive to imputation errors and may be sensitive to imputation errors

Five Buttes Analysis Area Deschutes Nat’l ForestFive Buttes Analysis Area Deschutes Nat’l Forest

Imputation Sensitivity AnalysisImputation Sensitivity Analysis

2011 HIGH2011 HIGH 2011 LOW2011 LOW

In this analysis, two landscapes were imputed, high and a low pine beetle risk, based In this analysis, two landscapes were imputed, high and a low pine beetle risk, based on risked rating stands which fell in each of many stand classifications. These maps on risked rating stands which fell in each of many stand classifications. These maps represent the no action, “after beetle outbreak” BA for eachrepresent the no action, “after beetle outbreak” BA for each Red River pine beetle analysis, Nez Perce National ForestRed River pine beetle analysis, Nez Perce National Forest

Sensitivity: High minus LowSensitivity: High minus Low

2011 H-L2011 H-L

The difference in the two extremes show how much the results may have The difference in the two extremes show how much the results may have changed if better data were available, and where the uncertainty is changed if better data were available, and where the uncertainty is manifested on the landscape. This is the “no action” alternative; so a manifested on the landscape. This is the “no action” alternative; so a comparison can also be made as to the sensitivity of the action-no action comparison can also be made as to the sensitivity of the action-no action difference to these 2 extreme landscape ranges.difference to these 2 extreme landscape ranges.

1986 H-L1986 H-L

An additional challengeAn additional challenge

What is “most similar” depends on what aspects are What is “most similar” depends on what aspects are considered in the analysis.considered in the analysis.

If these products are used in decision making, we If these products are used in decision making, we face the challenge to produce understandable, face the challenge to produce understandable, useful products which can be integrated with other useful products which can be integrated with other corporate resource data systems and analyses.corporate resource data systems and analyses.

(Its not so good to have several, different estimates (Its not so good to have several, different estimates of where something important might be. It drives of where something important might be. It drives the boss crazy, but the appellants’ lawyers love it) the boss crazy, but the appellants’ lawyers love it)

AcknowledgementsAcknowledgements

• Nick CrookstonNick Crookston• Andrew McMahan Andrew McMahan • Ron McRobertsRon McRoberts• Ken PierceKen Pierce• Al StageAl Stage

• and to all of you from out of town, who are here on and to all of you from out of town, who are here on Valentine’s Day, away from those you hold dearValentine’s Day, away from those you hold dear