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Long Sequence Time Series Evaluation Using Standardized LongSequence Time Series Evaluation UsingStandardized Principal Gomponents Abstract With UnstandardizedPCA, the transformationcoefficients are The potential of using Standardized Principal Components developedby computing the principal eigenvectorsof the variance/covariancematrix. In this way, bands with higher for the analysis of long time seriesof spatial envircnmental data is ossessedusing a sertesof 36 monthly AvHRR-derived variability contribute more to the developmentof the new componentimages. With StandardizedpcR (Singh and Harri- Nnvt imagesfor Africa for the years 7986-88as an illustra- 1985) are computedfrom the correla- tion. The first componentis found to represent the charac- son, the eigenvectors teristic NDw rcgardlessof the season.The second, third, and tion matrix. The effect is to force each band to have eoual weight the new componentimagei is fourth componentsrelate to seasonalchanges in Nnw. The in the derivation of and values fifth and sixth componentsuncover a sensor-relateddrift in identical to convertingall image to standardscores the Nnvt values due to successivelylater equatorial crossings (by subtractingthe mean and dividing by the standarddevia- of the NOAA-Isatellite. The seventh and eighth components tion) and computing the UnstandardizedPrincipal Compo- illustrate NDw anomalies related to significant El Ninol nents of the results. Southern Oscillation (nt'tso) events,primarily in southern Eastman(1992a) has shown that, when the imagedata Africa. The techniqueis shown to be a comprehensiveindi- set consistsof a single variable time seriesof environmental cator of change eventsin time seriesdata that is sensitive to data,the first standardizedcomponent indicates the charac- periodic and aperiodic events alike. teristic value of that variablewhile the secondand all re- maining standardizedcomponents represent change elements Introduction of successivelydecreasing magnitude. In addition, both East- Principal ComponentsAnalysis (pcA)using Unstandardized man (1992a)and Fung and LeDrew(1987) indicate that Stan- Componentshas long beenused in remotesensing as a data dardized PCAappears to be more effective than pca compressiontool. The first two componentsof Standardized Unstandardized in the analysisof changein multi-tem- pcA have also been used for land-coverclassification, but poral image data sets. with mixed results (Tucker ef o1.,19BE; Townshend et o1., 1987).However, a recent study has suggestedthe potential of LongSequence Time Series PCA using PCAand StandardizedComponents as a tool for the In this study, the PCAprocedure of the IDRISIsoftware system analysisof changein spatial time seriesdata (Eastman, (Eastman,1992b) was modified to allow the computation of 1992a).In that study, a PCAprocedure capable of analyzing- up to 62 componentsin order to examinethe utility of the up to 12 bands was used to study artificial data setsand approachfor the investigationof long time seriesdata. To fa- monthly AvHnn-derivedNormalized Difference Vegetation cilitate data entry, imagefile namesare enteredby meansof Index' (Novt) imagery for Africa over the course of a year a standardIDzuSI time seriesfile-a simple ASCttfile of imaee and for the samemonth over four years.The results showed namesthat is used in a variety of time ieries procedures that the techniqueis able to identify both cyclic seasonalele- such as image display sequencingand time profiles. Output ments of changeand isolatedchange events. In this study, a consistsof the componentimages and a set of data tables. modification of the PCAprocedure allowing a large number Full tablesof the variance/covarianceand correlationmatri- of bands to be analyzedis used to study tli'e pote'ntialof ces,eigenvalues and eigenvectors,and componentloadings StandardizedPrincipal Componentsfor the analysisof long are provided for the first 12 components.In addition, a data time seriesdata sets. file consistingof the eigenvaluesand the componentload- Principal ComponentsAnalysis undertakesa linear ings for all componentsis createdin a format suitablefor in- transformationof a set of imagebands to createa new band put into a spreadsheet. set with imagesthat are uncorrelatedand are orderedin To test the technique,a 36-month sequenceof avrinn-de- terms of the amount of varianceexplained in the orisinal rived wovI data was analyzedfor the continent of Africa. The data(Johnston, 1980, pp.127-1,5liMather, f SOZ,pplZOO- data were extractedfrom the NGDCMonthly Generalized 218).Most commonly,the techniquehas been used in re- Global VegetationIndex data set within the NOAA-EPAGlobal mote sensingas a procedurefor data compressionby dis- EcosystemsDatabase (NOAA-EPA, 1992). The dataset used carding minor componentswith little explanatoryvilue. consistedof 10-minuteresolution raster data setsof NDVIfor the monthsof lanuary 1986through December 1988, scaled 'The NDVIindex is derived by dividing the difference between the by NOAAto an B-bit integerrange. An oceanmask image infrared and red imagesby the sum of the infrared and red images, from the U.S. Navy Fleet Numerical OceanographicCenter i.e., NDvr = 0R - R/OR + R). Global Elevationdata set, also within the NOAA-EpAGlobal EcosystemsDatabase (NOAA-EPA, 1992), was used to mask water areas.Assigning the value zeto to all water areasas- PhotogrammetricEngineering & RemoteSensing, suresthat theseregions are forced to show up in the first Vol. 59, No. B, August 1993,pp. 1,302-13t2. Reprinted-from PhotogrammetricEngineering & Remote Sensing, Ronald Eastman Vol. 59, No. 6, pp. f. June1993, 991-996. Michele Fulk 0099-11 1 2/93/5908-1 307$03.00/0 The Clark Labs for CartographicTechnology and Geographic o1993 American Society for Photogrammetry Analysis, Clark University, Worcester,MA 01610. and RemoteSensing PE&RS Plate1' StandardizedPrincipal Component lmages 1 through8 derivedfrom monthly NDV; data, January 1986 to December 1988" component,thus removing them from all changecompo- and the componentbeing diagrammed.For example,if a nents, month shows a strongpositive correlationwith fspecific component,it indicates that thai month contains a latent The36-Month Africa Time Series Experiment (i,e.,to someextent hidden or unapparent)spatial pattern The interpretationof the results of using standardizedpCA that has strong sim',larityto the on-e-depiciedin the compo- on 36 monthly NDVIimages for Africa is basedon the exami- nent image.Similarly, a strongnegative correlation indicltes nation of the component images (Plate 1) and the graphs of that the monthly imagehas a Iatent pattern that is the in- the co-mponentloadings (Figure 1). The loading ctiarts illus- v-erseof that shown (i.e., with positive and negative anom- trate the correlation between each of the 36 monthly images alies reversed).To enhancethe visualization oTthe 1308 PE&RS LOADINGS LOADINGS COMPONENT 1 0.8 0.15 0.1 0.6 0,05 0.4 o 0.2 {.05 -0.1 -0.15 4.4 4.2 I t me m i j a s o n d I I m ! m I j a s o n d j I m a m I j a s o n d il mami jaBo nd ll m! ml lr. on d jt maml ir !on d 1986 1987 1088 1986 1987 1988 LOADINGS LOAOINGS LOADINGS LOADINGS 0.06 0-6 COMPONENT7 0.04 0.04 o.@ o.a2 0 0 "o.o2 -o.M {.04 {.G {.06 .0.m -0.08 -0.m jf mam jla Bo nd lf m.ml jaBo nd ll mam j ,.. ond 1986 1987 1988 1986 1987 1988 Figure1. Loadings(y-axis-) of the originalmonthly images (X-axis) on the first eightstandardized principal components. Loadings canequally be thoughtof as the correlationbetween the originalimages and the derivedcomponents, componentsin Plate 1, a linear contraststretch was applied MeanMonthly NDVI to the output imagesof the PcA softwareprogram. In the case of the first componentin Plate 1, the minimum and maxi- NDVI mum valueswere used as the bounds of the stretch.For all 109.90 other components,however, stretches were forced to be sym- 103.r6 metrical about the value 0 (the no changevalue) with a mild saturation(1 percentmaximum) in the tails," This no change s4.42 position has a yellow color while positive and negative 89.68 anomaliesshow up in increasinglevels of greenor red/ brown respectively,In all cases,water areaswere maskedto 82.94 have a black color. 74.20 The first chart in Figure 1 illustratesthe Ioadingsfrom the first two StandardizedPrincipal Components.Compo- 69.46 nent 1 (Plate1 and Figure 1) clearly representsthe character- 62.?3 istic NDVIintegrated over all seasons-the loadingsare high and very consistentover the entire period. In effect,this 55.99 componentindicates that the major elementof variabili.tyin 49.25 NDVIis that which occurs spatially, 42.51 Component2 illustratesthe first changecomponent - j f m amj j a s o nd i t m am j j a s o nd j I m am i i a s o nd the most prevalentelement of variability in tr,uvtthat is un- J986 1987 1988 correlatedwith the characteristicpattern in Component1, As can be seenby the loadingsin Figure1, this component Figure2. Timeseries profile of monthlyNDVI for a repre- shows an annual cycle indicating that this secondmajor ele- sentativesite in the Sahelaffected by the positiveanomaly ment of variability in wovt in Africa is that causedby the in Component3, January1986 to December1988. winter/summerdichotomy, Summer months correlatepos- itively with the componentwhile winter months correlate negatively.3The negativecorrelation thus indicatesthat the winter months tend to have an inverseoattern to the summer lengths would naturally lead to a larger NDVImeasurement pattern shown. than expected.Figure 2 illustratesa time seriesprofile over The secondchart in Figure 1 illustratesthe loadings the 36-month sequenceof Novt
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