Earth Trends Modeler

J. Ronald Eastman

• Remotely Sensed Image Series• NOAA AVHRR• Terra/Aqua MODIS

• Multisystem Grids• GPCP• ISCCP

• Interpolated Grids• Tyndall/CRU

• Hybrid Grids• SST OI• TOPEX/Poseidon

• Modeled Grids• NCEP/NCAR• NCEP/DOE

• Remotely Sensed Image Series• NOAA AVHRR• Terra/Aqua MODIS

• Multisystem Grids• GPCP• ISCCP

• Interpolated Grids• Tyndall/CRU

• Hybrid Grids• SST OI• TOPEX/Poseidon

• Modeled Grids• NCEP/NCAR• NCEP/DOE

Earth Trends ModelerDesigned for the analysis of earth system observational time series

Designed for the analysis of earth system observational time series

Vertical Application / Project StructureVertical Application / Project Structure

Exploration / Visualization ToolsExploration / Visualization Tools

Temporal profilingTemporal profiling

Trend AnalysisTrend Analysis

•• tau = tau = p(concordancep(concordance) ) –– p(discordancep(discordance))•• tau = (16/21) tau = (16/21) –– (5/21) = 0.52(5/21) = 0.52

discordancediscordance

concordanceconcordance

MonotonicityMonotonicity: Kendall: Kendall’’s Taus Tau

•• TheilTheil--SenSen = median of = median of pairwisepairwise slopesslopes•• robust (resistant to outliers)robust (resistant to outliers)•• has a has a breakdown boundbreakdown bound (a measure of (a measure of

how many wild values there can be how many wild values there can be before it is affected) = 0.29 of the length before it is affected) = 0.29 of the length of the seriesof the series

Median TrendMedian Trend

Seasonal Trend AnalysisSeasonal Trend Analysis

•• using remotely sensed data, problem using remotely sensed data, problem in identifying phenological events in in identifying phenological events in the context of noise, short term the context of noise, short term climate variability and climate climate variability and climate teleconnections that can significantly teleconnections that can significantly disrupt the normal cycledisrupt the normal cycle

0

50

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Jan-

86

Mar

-86

May

-86

Jul-8

6

Sep

-86

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-86

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87

Mar

-87

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-87

Jul-8

7

Sep

-87

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-87

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88

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89

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-89

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-89

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-90

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0

Sep

-90

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-90

Date

NDVI

•• alternative perspective alternative perspective –– focus on focus on the continuous annual cycle of the continuous annual cycle of vegetation productivity vegetation productivity –– i.e., the i.e., the phenological curve.phenological curve.

•• Phenology: the scientific study of Phenology: the scientific study of recurrent biological events (e.g., recurrent biological events (e.g., bud burst, flowering, leaf drop, bud burst, flowering, leaf drop, breeding, migration, etc.) breeding, migration, etc.)

8282 8383 848486868585

8787 88888989 9090 9191 9292

9393 9494 9595 9696 9797 98989999 0000 0101 0202 0303

General Approach: Two Stage Time Series AnalysisGeneral Approach: Two Stage Time Series Analysis

Stage 1: Harmonic analysis of each yearStage 1: Harmonic analysis of each yearto establish a set of shape parameters for to establish a set of shape parameters for the seasonal curvethe seasonal curve

∑=

=

++=2/

10 )2sin()(

Tn

nnn T

nxaaxf ϕπStage 2: Analyze and map trends in the Stage 2: Analyze and map trends in the shape parametersshape parameters

Stage 1: Harmonic Analysis of the Annual CurveStage 1: Harmonic Analysis of the Annual Curve

)2cos()2sin(2/

10 T

ntbTntaay n

Tn

nn

ππ++= ∑

=

=

∑=

=

++=2/

10 )2sin(

Tn

nnn T

ntaay ϕπ

wherewhere n = harmonicn = harmonica = amplitudea = amplitudej j = phase angle (in degrees from 0= phase angle (in degrees from 0--360)360)tt = time= timeT =T = period (total length of time in the series)period (total length of time in the series)

Harmonic Regression with two harmonics (annual and semiHarmonic Regression with two harmonics (annual and semi--annual) is used to create a best fit seasonal curveannual) is used to create a best fit seasonal curve

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-0.6

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0 30 60 90 120 150 180 210 240 270 300 330 360

degrees

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-0.8

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0 30 60 90 120 150 180 210 240 270 300 330 360

degrees

•• These two harmonics can produce a very These two harmonics can produce a very broad family of generalized seasonal curves, broad family of generalized seasonal curves, including curves with single or double peaks.including curves with single or double peaks.

•• Account globally for 82% of the variance in Account globally for 82% of the variance in NDVI (90% in N. Hemisphere NDVI (90% in N. Hemisphere extratropicsextratropics))

•• Discarding the higher frequencies removes Discarding the higher frequencies removes the 30the 30--50 day Madden50 day Madden--Julian oscillation and Julian oscillation and isolated shortisolated short--term events and noiseterm events and noise

•• The resulting curve is thus an abstraction in The resulting curve is thus an abstraction in the same sense that a regression line the same sense that a regression line describes a linear relationshipdescribes a linear relationship

Focus on Harmonics 1 and 2Focus on Harmonics 1 and 2

Harmonic 0 = mean annual value Harmonic 0 = mean annual value Harmonic 1 = annual cycleHarmonic 1 = annual cycleHarmonic 2 = semiHarmonic 2 = semi--annual cycleannual cycle

The result of the first stage analysis is thus a set of five shaThe result of the first stage analysis is thus a set of five shape pe parameters for each year in the seriesparameters for each year in the series

Stage 2: Trend Analysis of the Shape Parameters Stage 2: Trend Analysis of the Shape Parameters

TheilTheil--SenSen median slope trend analysis of the five shape parametersmedian slope trend analysis of the five shape parameters

•• TheilTheil--SenSen = median of = median of pairwisepairwise slopesslopes•• robust (resistant to outliers)robust (resistant to outliers)•• has a has a breakdown boundbreakdown bound (a measure of how many (a measure of how many

wild values there can be before it is affected) = 0.29 wild values there can be before it is affected) = 0.29 of the length of the seriesof the length of the series

•• therefore shorttherefore short--term term interannualinterannual variability (such as variability (such as ENSO) is eliminated.ENSO) is eliminated.

The result of the second stage analysis is thus a set of five trThe result of the second stage analysis is thus a set of five trend end maps related to the shape parametersmaps related to the shape parameters

Harmonic 0 = mean annual value Harmonic 0 = mean annual value Harmonic 1 = annual cycleHarmonic 1 = annual cycleHarmonic 2 = semiHarmonic 2 = semi--annual cycleannual cycle

Seasonal Trend MapsSeasonal Trend Maps

Trend maps can then be used to create STA color compositesTrend maps can then be used to create STA color composites

Visualization of the Five Parameter TrendsVisualization of the Five Parameter Trends

AmplitudesAmplitudesR = Amp0 / G = Amp1 / B=Amp2R = Amp0 / G = Amp1 / B=Amp2

PhasesPhasesR = Amp0 / G = Phase1 / B=Phase2R = Amp0 / G = Phase1 / B=Phase2

Seasonal Trend AnalysisSeasonal Trend Analysis

Principal Components / EOF AnalysisPrincipal Components / EOF Analysis

Empirical Orthogonal Teleconnection AnalysisEmpirical Orthogonal Teleconnection Analysis

CrossCross--EOTEOT

SpatialSpatial--Temporal Fourier/PCATemporal Fourier/PCA

Wavelet AnalysisWavelet Analysis

Linear ModelingLinear Modeling

Preprocessing ToolsPreprocessing Tools