Temporal signatures and harmonic analysis of natural and anthropogenic disturbances of forested landscapes: a case study in the Yellowstone region L. Monika Moskal, PhD Assistant Professor Acting Director - Remote Sensing and Geospatial Analysis Laboratory Department of Geography Geology and Planning Southwest Missouri State University

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

Remote sensing and temporal change

10 years temporal change

Seasonal change

Vegetation phenological metrics (Reed et al., 1994) Duration of greenness Range of NDVI Month NDVI VALUES Maximum NDVI Latent greenness Onset of Greenness End of Greenness JanFebJunMarAprMaySepAugJulOctNovDec Accumulated NDVI

AVHRR weekly composite images Week 1 Day 1Day 2Day 3Day 4Day 5Day 6Day 7 Select pixel with maximum NDVI value 52 biweekly periods per year 13 years 676 time snapshots Each weekly image is a composite of seven images Samples selected based on Landsat TM, GIS and field data

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 provides estimates of the sinusoid parameters (using least square methods):When the cycle length is known, harmonic analysis provides estimates of the sinusoid parameters (using least square methods): –Mean –Phase –Amplitude When the cycle length is unknown exploratory methods can be used:When the cycle length is unknown exploratory methods can be used: –Periodogram analysis –Spectral analysis

AmplitudePhase0 2π Phase and amplitude of a periodic series Decomposition of a seasonal NDVI series into component terms Adding successive terms to produce final curves Total variance and partial variance: Since a time series is the sum of many sinusoidal functions (harmonics);Since a time series is the sum of many sinusoidal functions (harmonics); The variance of a time series is the sum of the variances of those harmonics, andThe variance of a time series is the sum of the variances of those harmonics, and The variance in a given harmonic can be calculated as a proportion of the total varianceThe variance in a given harmonic can be calculated as a proportion of the total variance Seasonal NDVI series Davis, 1986

Harmonic analysis: Implications for changes in harmonic parameters Changes in AMPLITUDE (phase unchanged) indicate:Changes in AMPLITUDE (phase unchanged) indicate: –Changes in vegetation condition Insect attack/Disease Insect attack/Disease Thinning/Selective Cutting Thinning/Selective Cutting Flooding/Drought Flooding/Drought –Changes in vegetation type Regeneration of vegetation Regeneration of vegetation Loss of vegetation Loss of vegetation –natural or anthropogenic disturbance Ecotonal shifts Ecotonal shifts Succession Succession Variance of amplitude NDVI Time Stable amplitude NDVI Time Sudden loss in amplitude NDVI Time Progressive loss in amplitude

Harmonic analysis: Implications for changes in harmonic parameters Changes in PHASE AND AMPLITUDE indicate:Changes in PHASE AND AMPLITUDE indicate: –Significant changes in vegetation Changes in land managementChanges in land management Changes in regional climate?Changes in regional climate? Variance of phase 0 Low interannual variability in phase 2π 0 π Circular variance R = High interannual variability in phase 2π Circular variance R = π

Research goal and objectives How do natural forest vegetation communities differ from human-managed forest vegetation in seasonal and interannual variability? Can interannual and seasonal patterns for the various disturbed and undisturbed forested landscapes be discerned?Can interannual and seasonal patterns for the various disturbed and undisturbed forested landscapes be discerned? How do the interannual and seasonal patterns vary for undisturbed, naturally disturbed and human impacted forested landscapes?How do the interannual and seasonal patterns vary for undisturbed, naturally disturbed and human impacted forested landscapes?

RESULTS: Implications of harmonic parameters: Amplitude and average NDVI AMPLITUDE - indicates the rate at which vegetation 'green up' or onset of greenness occurs AVERAGE NDVI - indicates the 13 year average NDVI or 'greenness' for a forest type The amplitude of the harvested forest is substantially greater than the amplitude of the mature and burned forests Harvested forest are replanted with high wood yielding species selected for optimal' annual growth Harvested forest are replanted with high wood yielding species selected for optimal' annual growth Natural forest such as mature and post fire regenerating forests 'green up' at a slower rate Natural forest such as mature and post fire regenerating forests 'green up' at a slower rate BurnedHarvestedMature Amplitude NDVI NDVI Average NDVI

RESULTS: Implications of harmonic parameters: Phase PHASE - indicates when the maximum 'greenness' occurs, values range from 0 to 2 (January to December) Higher phase values for a mature and burned forests indicate that the peak of the 'green up' occurs later in the season Phenological complexity of an undisturbed forests ensures that the 'green up' progresses slowly throughout the season Phenological complexity of an undisturbed forests ensures that the 'green up' progresses slowly throughout the season Low phase values for the harvested forest indicate an early 'green up' Harvested forest are often replanted with aggressive species selected for maximum growth and yield & thus early 'green up'Harvested forest are often replanted with aggressive species selected for maximum growth and yield & thus early 'green up' BurnedHarvestedMature Phase (0 to 2 Phase (0 to 2 August September

Harvested: Four harmonics for 2001 NDVI explained 97.3% of the variability and thus were used in the model Burned: Seven harmonics were needed to explain 97.1% of the variability for the 2001 NDVI model Significant results: Bi-modal peak in the naturally regenerating forests was consistently more difficult to models - can this indicate greater species diversity?Bi-modal peak in the naturally regenerating forests was consistently more difficult to models - can this indicate greater species diversity? RESULTS: Modeling seasonal diversity of regenerating forest cover types

Conclusions Harmonic analysis of time-series data provide a replicable method of quantifying and monitoring temporal diversity of various forested landscapes. Significant findings: Naturally regenerating demonstrate highly diverse temporal signatures and diverse, internannual/seasonal trends)Naturally regenerating demonstrate highly diverse temporal signatures and diverse, internannual/seasonal trends) A dynamic directional change in the phase and amplitude of the forest landscape was observed and needs to be supported with further analysis using additional successional classesA dynamic directional change in the phase and amplitude of the forest landscape was observed and needs to be supported with further analysis using additional successional classes Progressive loss in amplitude NDVI Time Progressive gain in amplitude Mature Burned

Field view Aerial digital camera view

Future directions in harmonic analysis......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? (Data fusion with finer resolution sensors to get a more detailed spatial information)Can we estimate relative proportions of cover types? (Data fusion with finer resolution sensors to get a more detailed spatial information) Landsat Quickbird Stem map Hypertemporal image features (MODIS, AVHRR) 19 stems calibration/data fusion

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 NAG (P.I. Dr. M. Jakubauskas). This project was conducted at the Kansas Applied Remote Sensing (KARS) Program Mr. Jude Kastens (code development) Acknowledgments