Temporal signatures and harmonic analysis of Temporal signatures and harmonic analysis of natural and anthropogenic disturbances of natural and anthropogenic disturbances of

forested landscapes: a case study in the forested landscapes: a case study in the Yellowstone regionYellowstone region

L. Monika Moskal, PhDL. Monika Moskal, PhDAssistant ProfessorAssistant ProfessorActing Director - Remote Sensing and Geospatial Analysis LaboratoryActing Director - Remote Sensing and Geospatial Analysis Laboratoryhttp://ozarksgeography.smsu.edu/RSGAL/

Department of Geography Geology and PlanningDepartment of Geography Geology and PlanningSouthwest Missouri State UniversitySouthwest Missouri State Universityhttp://www.faculty.smsu.edu/l/lmm878f/

Ecological scale and hierarchy theoryEcological scale and hierarchy theory

• Ecosystems are open systems and Ecosystems are open systems and incorporate disturbances at multiple incorporate disturbances at multiple spatial and temporal scales; thus, spatial and temporal scales; thus, ecosystems must be understood within ecosystems must be understood within a larger spatial and temporal context. a larger spatial and temporal context.

Yellowstone NPYellowstone NPRemote sensing and temporal changeRemote sensing and temporal change

Remote sensing and temporal changeRemote sensing and temporal change

10 years temporal change10 years temporal change

Yellowstone NPYellowstone NP

Seasonal changeSeasonal change

Vegetation phenological metrics (Reed et al., 1994)Vegetation phenological metrics (Reed et al., 1994)

Duration of greennessDuration of greenness

Ran

ge

of

ND

VI

Ran

ge

of

ND

VI

MonthMonth

ND

VI

VA

LU

ES

ND

VI

VA

LU

ES

Maximum NDVI

Latent greenness

Onset ofOnset ofGreennessGreenness

End ofEnd ofGreennessGreenness

JanJan FebFeb JunJunMarMar AprApr MayMay SepSepAugAugJulJul OctOct NovNov DecDec

AccumulatedNDVI

AVHRR weekly composite imagesAVHRR weekly composite imagesW

eek 1

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Select pixel with maximum NDVI value

52 biweekly periods per year52 biweekly periods per year13 years13 years676 time ‘snapshots’ 676 time ‘snapshots’

Each weekly image is a Each weekly image is a composite of seven imagescomposite of seven images

1989 - 20011989 - 2001

Samples selected based Samples selected based on Landsat TM, GIS and on Landsat TM, GIS and

field datafield data

Why Harmonic Analysis? Why Harmonic Analysis?

• Do we know the length of the cycles?Do we know the length of the cycles?• When the cycle length is known, harmonic analysis When the cycle length is known, harmonic analysis

provides estimates of the sinusoid parameters (using provides estimates of the sinusoid parameters (using least square methods):least square methods):– MeanMean– PhasePhase– AmplitudeAmplitude

• When the cycle length is unknown exploratory When the cycle length is unknown exploratory methods can be used:methods can be used:– Periodogram analysisPeriodogram analysis– Spectral analysisSpectral analysis

AmplitudeAmplitude

PhasePhase

002π2π

Phase and amplitude of a periodic seriesPhase and amplitude of a periodic series

Am

pli

tud

e

Decomposition of a seasonal NDVI Decomposition of a seasonal NDVI series into component termsseries into component terms

Res

cale

d N

DV

I

0 + 10 + 1 + 20 + 1 + 2 + 3

Adding successive terms Adding successive terms to produce final curvesto produce final curves

Total variance and partial variance:Total variance and partial variance:

•Since a time series is the sum of many Since a time series is the sum of many sinusoidal functions (harmonics);sinusoidal functions (harmonics);

•The variance of a time series is the sum The variance of a time series is the sum of the variances of those harmonics, andof the variances of those harmonics, and

•The variance in a given harmonic can be The variance in a given harmonic can be calculated as a proportion of the total calculated as a proportion of the total variancevariance

Seasonal NDVI seriesSeasonal NDVI series

Davis, 1986Davis, 1986

Harmonic analysis:Harmonic analysis:Implications for changes in harmonic parametersImplications for changes in harmonic parameters

• Changes in AMPLITUDE (phase Changes in AMPLITUDE (phase unchanged) indicate:unchanged) indicate:

– Changes in vegetation conditionChanges in vegetation condition• Insect attack/DiseaseInsect attack/Disease• Thinning/Selective CuttingThinning/Selective Cutting• Flooding/DroughtFlooding/Drought

– Changes in vegetation typeChanges in vegetation type• Regeneration of vegetationRegeneration of vegetation• Loss of vegetationLoss of vegetation

– natural or anthropogenic natural or anthropogenic disturbancedisturbance

• Ecotonal shifts Ecotonal shifts • SuccessionSuccession

Variance of amplitudeVariance of amplitude

ND

VI

ND

VI

TimeTime

Stable amplitudeStable amplitude

ND

VI

ND

VI

TimeTime

Sudden loss in amplitudeSudden loss in amplitude

ND

VI

ND

VI

TimeTime

Progressive loss in amplitudeProgressive loss in amplitude

Harmonic analysis:Harmonic analysis:Implications for changes in harmonic parametersImplications for changes in harmonic parameters

• Changes in PHASE AND Changes in PHASE AND AMPLITUDE indicate:AMPLITUDE indicate:

– Significant changes in vegetationSignificant changes in vegetation• Changes in land management Changes in land management • Changes in regional climate?Changes in regional climate?

Variance of phaseVariance of phase

0

Low interannual variability in phaseLow interannual variability in phase

2π

0π

Circular varianceCircular variance

RR = 0.99 = 0.99

0

High interannual variability in phaseHigh interannual variability in phase

2π

Circular varianceCircular variance

RR = 0.10 = 0.10

0π

Research goal and objectivesResearch goal and objectives

How do natural forest vegetation communities differ from How do natural forest vegetation communities differ from human-managed forest vegetation in seasonal and human-managed forest vegetation in seasonal and interannual variability?interannual variability?

• Can interannual and seasonal patterns for the various Can interannual and seasonal patterns for the various disturbed and undisturbed forested landscapes be disturbed and undisturbed forested landscapes be discerned?discerned?

• How do the interannual and seasonal patterns vary for How do the interannual and seasonal patterns vary for undisturbed, naturally disturbed and human impacted undisturbed, naturally disturbed and human impacted forested landscapes?forested landscapes?

RESULTS: Implications of harmonic parameters:RESULTS: Implications of harmonic parameters:Amplitude and average NDVIAmplitude and average NDVI

AMPLITUDE AMPLITUDE - indicates the rate at which vegetation - indicates the rate at which vegetation 'green up' or onset of greenness occurs'green up' or onset of greenness occurs

AVERAGE NDVIAVERAGE NDVI - indicates the 13 year average NDVI - indicates the 13 year average NDVI or 'greenness' for a forest type or 'greenness' for a forest type

The amplitude of the harvested The amplitude of the harvested forest is substantially greater forest is substantially greater than the amplitude of the than the amplitude of the mature and burned forestsmature and burned forests

• Harvested forest are replanted Harvested forest are replanted with high wood yielding species with high wood yielding species selected for ‘optimal' annual selected for ‘optimal' annual growthgrowth

• Natural forest such as mature Natural forest such as mature and post fire regenerating forests and post fire regenerating forests 'green up' at a slower rate'green up' at a slower rate

00

55

1010

1515

2020

2525

3030

3535

4040

BurnedBurned HarvestedHarvested MatureMature

Am

plit

ud

e

Am

plit

ud

e

110110

115115

120120

125125

130130

135135

140140

ND

VI

ND

VI

Average NDVIAverage NDVI

RESULTS: Implications of harmonic parameters:RESULTS: Implications of harmonic parameters:PhasePhase

PHASEPHASE - indicates when the maximum - indicates when the maximum 'greenness' occurs, values range from 'greenness' occurs, values range from

0 to 20 to 2(January to December)(January to December)

Higher phase values for a mature Higher phase values for a mature and burned forests indicate that and burned forests indicate that the peak of the 'green up' occurs the peak of the 'green up' occurs later in the seasonlater in the season

• Phenological complexity of an Phenological complexity of an undisturbed forests ensures that the 'green undisturbed forests ensures that the 'green up' progresses slowly throughout the up' progresses slowly throughout the seasonseason

Low phase values for the Low phase values for the harvested forest indicate an early harvested forest indicate an early 'green up''green up'

•Harvested forest are often replanted with Harvested forest are often replanted with aggressive species selected for maximum aggressive species selected for maximum growth and yield & thus early 'green up'growth and yield & thus early 'green up'

3.53.5

3.63.6

3.73.7

3.83.8

3.93.9

44

4.14.1

BurnedBurned HarvestedHarvested MatureMature

P

ha

se

(0

to

2P

ha

se

(0

to

2

AugustAugust

SeptemberSeptember

Harvested:Harvested: Four harmonics for Four harmonics for 2001 NDVI explained 97.3% of 2001 NDVI explained 97.3% of the variability and thus were used the variability and thus were used in the modelin the model

Burned:Burned: Seven harmonics were Seven harmonics were needed to explain 97.1% of the needed to explain 97.1% of the variability for the 2001 NDVI modelvariability for the 2001 NDVI model

Significant results: Significant results: • Bi-modal peak in the Bi-modal peak in the

naturally regenerating naturally regenerating forests was consistently forests was consistently more difficult to models - more difficult to models - can this indicate greater can this indicate greater species diversity?species diversity?

9090

100100

110110

120120

130130

140140

150150

160160

170170

180180

WeeksWeeks

ND

VI

ND

VI Actual NDVIActual NDVI Predicted NDVIPredicted NDVI

HarvestedHarvested

00 1313 2626 3939 5252

9090

100100

110110

120120

130130

140140

150150

160160

170170

180180

00 1313 2626 3939 5252

WeeksWeeks

ND

VI

ND

VI

BurnedBurned

Actual NDVIActual NDVI Predicted NDVIPredicted NDVI

RESULTS: Modeling seasonal diversity of RESULTS: Modeling seasonal diversity of regenerating forest cover typesregenerating forest cover types

ConclusionsConclusions

Harmonic analysis of time-series data provide a replicable Harmonic analysis of time-series data provide a replicable method of quantifying and monitoring temporal diversity of method of quantifying and monitoring temporal diversity of various forested landscapes.various forested landscapes.

Significant findings:Significant findings:

• Naturally regenerating demonstrate highly diverse temporal Naturally regenerating demonstrate highly diverse temporal signatures and diverse, internannual/seasonal trends)signatures and diverse, internannual/seasonal trends)

•A dynamic directional A dynamic directional change in the phase change in the phase and amplitude of the and amplitude of the forest landscape was forest landscape was observed and needs to observed and needs to be supported with be supported with further analysis using further analysis using additional successional additional successional classesclasses

Progressive loss in amplitudeProgressive loss in amplitude

ND

VI

ND

VI

TimeTime

Progressive gain in amplitudeProgressive gain in amplitude

MatureMature

BurnedBurned

Field view Aerial digital camera view

Future directions in harmonic analysis...Future directions in harmonic analysis......possibilities for remote sensing research......possibilities for remote sensing research...

• Detrending of AVHRR data (sensor degradation shift)Detrending of AVHRR data (sensor degradation shift)• Classification of amplitude and phase images:Classification of amplitude and phase images:

• Advantages over raw NDVI temporal data?Advantages over raw NDVI temporal data?

• Analysis of residuals (Actual NDVI - harmonic curve):Analysis of residuals (Actual NDVI - harmonic curve):• Can we detect critical thresholds / other phenomena?Can we detect critical thresholds / other phenomena?

• Sensitivity analysis:Sensitivity analysis:• What's the minimum number of points required?What's the minimum number of points required?• Can we replace composites with a sparse daily set?Can we replace composites with a sparse daily set?

• Temporal endmembers:Temporal endmembers:• Can we estimate relative proportions of cover types? Can we estimate relative proportions of cover types?

(Data fusion with finer resolution sensors to get a more (Data fusion with finer resolution sensors to get a more detailed spatial information)detailed spatial information)

LandsatLandsat

QuickbirdQuickbird

Stem mapStem map

Hypertemporal image Hypertemporal image features (MODIS, AVHRR)features (MODIS, AVHRR)

19 stems19 stems

calib

ratio

n/d

ata

fu

sio

nca

libra

tion

/da

ta f

usi

on

Filed data for the research described here were funded by the National Aeronautics and Space Administration (NASA) Earth Science Enterprise Food and Fiber Applications of Remote Sensing (FFARS), Project NAG13-99019 (P.I. Dr. M. Jakubauskas).

This project was conducted at the Kansas Applied Remote Sensing (KARS) Program

Mr. Jude Kastens (code development)

AcknowledgmentsAcknowledgments

K ansas Appl ied R em ote S ensing P rogram