Gradients or hierarchies? Which assumptions make a better map? Emilie B. Grossmann Janet L. Ohmann Matthew J. Gregory Heather K. May.

Gradients or hierarchies? Which assumptions make a better map?

Emilie B. GrossmannJanet L. Ohmann

Matthew J. GregoryHeather K. May

How does the world work?

• The World is a Gradient– Curtis 1957

• The Vegetation of Wisconsin

• The World is a Hierarchy– Delcourt et al. 1983

• The World is Shaped by Many Different Things– Wimberly and Spies 2001 Influences of environment and

disturbance on forest patterns in coastal Oregon watersheds

– “No single theoretical framework was sufficient to explain the vegetation patterns observed in these forested watersheds.”

Regional-Scale Vegetation in Western Oregon:a (very) simple conceptual model.

Tree Species Distributions

Rainfall-Temperature GradientCool/Wet Hot/Dry

Loca

l Sca

le

Reg

iona

l Sca

le

Short-term Long-term

Forest Structure

Can

opy

Clo

sure

Time Since Disturbance

Spatial Data Covering Regional Scales in Western Oregon

Tree Species Distributions

Rainfall-Temperature GradientCool/Wet Hot/Dry

Loca

l Sca

le

Reg

iona

l Sca

le

Short-term Long-term

Forest Structure

Can

opy

Clo

sure

Time Since Disturbance

ElevationClimate (PRISM)Soil Parent Material

Local TopographyLANDSAT (bands and transformations)

Our Quest

• Make a highly accurate regional-scale vegetation map, that simultaneously represents detailed forest composition and structure.

• Peril #1:– The world is a complex place.

• Solution #1:– Use statistical models to sort out the complexity, and make a

prediction.

• Peril #2:– Statistical models often come with ASSUMPTIONS that cause

problems when violated.

• Solution #2:– Try to find a model with reasonable assumptions.– See whether it works any better than other methods.

Perils

You Are Here

Methods– Maps built from:

– 1677 plots (FIA annual plots)

– 19 possible mapped explanatory variables.

Landsat Bands 3,4,5, Tassled Cap

Climate PRISM: Means, seasonal variability

Topography Elevation, slope, aspect, solar

Location X, Y

studyarea

(2) Place new pixel

withinfeature space

(3) find nearest-neighbor plot within feature

space

(4) impute nearest

neighbor’s value to

pixel

Methods: k-NN

feature space geographic space

Elevation

Rainfall

(1)Place plots

within feature space

(2) calculate

axis scores of pixel from

mapped data layersstudyarea

(3) find nearest-

neighbor plot in

gradient space

(4) impute nearest

neighbor’s value to

pixel

Methods: GNNgradient space geographic space

CCAAxis 2

(e.g., Temperature, Elevation)

CCAAxis 1

(e.g., Rainfall, local

topography)

(1)conductgradient

analysis ofplot data

ASSUMPTION: Species exhibit unimodal responses to environmental variables.

studyarea

Methods: Random Forest Nearest Neighbor Imputation

Random Forest space geographic space

Methods: Classification Tree

|Elevation < 1244

August Maximum < 23.24 Temp

August Maximum < 25.60 Temp

Summer Mean < 12.79 Temp

Aug. to Dec. Temperature < 12.79 Differential

Elevation < 1625LANDSAT Band 5 < 24

PSME TSHEPSME THPL

ABAM TSMEPSME PIPO

High Elevation ( > 1244)High August Temp (> 23.24°C)High reflectance in Band 5 (> 24)

Methods: Random Forest

• A “Forest” of classification trees.

• Each tree is built from a random subset of plots and variables.

|ANNHDD < 4271.43

SMRPRE < 5535.09

X < 8808.88ANNHDD < 3950.45

SMRPRE < 5576.65

SMRTP < 2088.19

MR4300 < 166.968

ANNHDD < 4779.98

4215 4222 4224 4224

4228

4267 42154272 4228

|ANNTMP < 665.874

ANNVP < 591.82

ANNHDD < 4710.98X < 7248.68

STRATUS < 3.7435

X < 7762.43 X < 6340.86

ANNHDD < 3901.34215 42284215 4272

4215 4205

4224

4226 4224

|ANNGDD < 2578.11

ANNVP < 591.82

ANNGDD < 2190.48

ANNPRE < 740.947

STRATUS < 40.8768

R5400 < 117.208

ANNGDD < 3028.96

4228 4215

4272

4215 42154224

4224 4224

|ANNFROST < 1693.8

ANNFROST < 1271.82

CONTPRE < 788.967IDSURVEY < 456

ANNFROST < 2051.42

IDSURVEY < 423ADR5700 < 70.8343

4224 4224 4224 4224

4215 4272 4267 4228

|SMRTMP < 1206.3

ANNVP < 608.87

R5400 < 158.673

SMRTMP < 1105.53

ANNVP < 660.51

ANNVP < 610.822

TC200 < 134.347

SMRTMP < 1444.82

CONTPRE < 785.7484228 42154267

4272

4267 42154215

4224

4214 4224

|ANNHDD < 4204.74

DIFTMP < 2847.06

ANNHDD < 3669.42

CVPRE < 8079.84

DIFTMP < 3022.3

DIFTMP < 2854.2

SMRTMP < 1123.01SMRTMP < 1184.12

4226 42144224 4224 4215

4228 4272 4228 4215

|

Methods: Random Forest Imputation

|

157915

23610

81413

11181925

242317

1620

302726

2829

26162028

Accuracy Assessment

• Species Kappa

• RMSD

• Bray-Curtis Distance

Results

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k.NNGNNRFNN

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Species Presence-Absence(Kappa statistics)

Forest Structure

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Forest Structure: Basal Areak-NN GNN RFNN

PERIL!

COMPUTING TIME! Random forest took over a week to run.

Just finished last Friday morning.

If you are in a rush to prepare for a

conference, don’t take this route!!!

Crater Lake Closeup

Forest Structure: Basal Areak-NN

Forest Structure: Basal AreaGNN

Forest Structure: Basal AreaRFNN

Community Structure

euclidean gnn randomForest

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acc

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0.1

0.2

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Summary

• Species Kappas– Each model had strengths and weaknesses.– All did well with the dominants.

• Structure– RFNN consistently just a little bit better.

• Maps– Broad-scale: Indistinguishable– Local-scale: GNN noisiest

• Overall Community Structure– RFNN best.

Conclusion

• Random forest did the best all around. broad-scale (species composition)

AND

local-scale (structure)

But, there’s still room for improvement.

Acknowledgements