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

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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 measurementsfor a repre- from the third and fourth components.Component 3, like sentativearea in this region.As can be seen,the expeited Component2, also shows an annual cycle, but this time it sjnusoidal shapeof the annual NDVrpattern is broken by a indicatesareas that undergo strong changesin the late spring distinct shoulder in the periods from Novemberuntil March, and autumn periods.In Plate 1, Component3, quite promi- the period in which the Harmattanwinds are normally expe- nent positive and negativeanomalies are seenin the Guinea- rienced.The suggestionis that this shoulder results from an Congolic/Zambesianand Guinea-Congolic/Sudanicvegetative abnormallyhigh apparentNDVI as a result of atmospheric transitionzones (White, 1983), These areas are southand dust.In addition,the pronounceddrop in NDVIjusfbefore north of the central equatorialforest region,respectively. the late summer green-upperiod may relate to the cleansing Theseareas experience maximum vegetationpeaks in the of atmosphericdust by earlyrains. These rains would re- late fall and late spring, respectively,as a result of the coin- move dust from the air, but the vegetationwould not vet cidenceof the sun's latitudinal position and the rainy sea- have had time to respond.Thus, vie seea drop to the mini- son. In addition, the imageshows a quite intriguing positive mum NDVIlevel, followed by an increaseas the green-uppe- anomaly acrossthe Sahel and into the Ethiopian highlands. riod proceeds, The pattern in the Ethiopian highlands is easily explained- As can be seenin Figure 1, Component4 shows a pro- the areanormally experienceswet and dry periods at these nounced and consistentsemi-annual sequence. Examination times. However,the interpretationof the pattern in the Sahel of the componentimage (Plate1) clearlyshows that this il- is not so obvious.The late autumn (the time at which the Iustratesthe regionssubject to a double precipitation maxi- positive anomaly is strongest)is normally a time of signifi- mum due to the double crossinqof the Inter-Trooical cant decreasein biomass,yet the imagefor Component3 in- ConvergenceZone (compare,foi example,to Figure 1B in dicatesthat the vegetationindex is abnormallyhigh for this WMO(1984) that mapsthese areas). time of year. This is also the time of the Harmattanwinds, a Components5 and 6 are particularly interesting.The prevailing wind pattern out of the Saharathat leadsto signif- graph of loadingsfor Component5 (Figure tl showJ a pro- icant amounts of dust in the Sahel,Althoueh further data gressivetrend over the three-yearperiod. The imageof Com- would be neededto confirm this, the evideice in the data ponent 5 indicatesa high positive anomaly in desertareas suggeststhat atmosphericdust is leading to a greaterNDVI (notethe Sahara)and the lakesof EastAfrica, Clearlvthis is measurementthan anticipated,The greaterattenuation of the illogical becauseit suggeststhat desertand water shorterred wavelengthscompared to the infrared wave- increasingin wovt over time. A time seriesprofile ".6", for repre- "r. sentativelocations within theseregions (Figure 3), however, confirms this trend in the data.Aiindicated in Tateishi and ,A 1 percentsaturation forcesthe highest 1 percentof data cells to Kajiwara(1992), the NOAA-ssatellite experienced progres- take on the brightestcolor and the lowest percent a 1 to becomethe sive delayin the time of darkestcolor, regardlessof actual value. Beciuse the stretch equatorialcrossing (from 14:20in was December1984 forced to be symmetricalabout 0 (no change),the stretchwas under- to 16:10in November19BB), Ieading to suc- taken using end points such that a maximum of 1 percentwould be cessivelyshallower solar anglesand, hence,longer atmos- saturatedin any tail. phericpaths. Tateishi and Kajiwara(1992) state that the 3BecauseAfrica spansthe equator,seasonal terms (winter, sum- effect of this is to diminish, through scattering,the shorter mer, etc.) for the northern hemispherehave been arbitrarily adopted red wavelengthreflectances more than the lJnger infrared throughout this article. wavelengthreflectances. As a result, the NDVIiarould ap-

1310 PE&RS Late 1986and 1987experienced a pronouncedENSO Maximum Monthly NDVI riod. warm phase,followed in 19BBby a sharp transition to an NDVI eruSocold phase(WMO, 19Bg).ENSO warm phasesare typi- 62.00 cally associatedwith drought in southernAfrica and en- 56.50 t\ hancedprecipitation in equatorialEast Africa (WMO, 1984; t. ,^' ,'a ENSopattern is clearlyvisi- I 1987;19Sg). The southernAfrica 51.00 \, /- ble in the imagesof Components7 and B in Plate1. Simi- Central Sahara Desert 45.50 larly, the loading charts for thesecomponents showpositive negativecorrelations with 1986 40.00 correlationswith 1987 and and 1988.It would appearthat the two componentsshow 34.50 the spatial progressionof the drought. For example,in Com- 29.00 ponent 7, with a peak correlationin early 1987,the area most strongly affectedin southernAfrica is Botswana'How- 23.50 peak in late 1987, Lake Vicloria ever,in ComponentB, with a correlation 18.00 the areamost strongly affectedhas moved towards the east in (1989),the patternfor equatorial 12.50 coast.As noted WMO eastAfrica did not show a typical ENSopattern during this 7.OO particular ENSoepisode. We seethis in the more typical moist pattern for eastAfrica in Component7, giving way to a 1986 1987 1988 drier pattern in ComponentB. Figure3. Timeseries proflles of monthlyNDVI for sites in The proceduredeveloped for this analysisis capableof the centralSahara Desert and LakeVictoria, January 1986 producing as many componentimages as there are original to Decernber1988. bands in the data.However, examination of Components9 through 12 did not show any significant regional effects. Rather,more localized changesappear to be brought out. As a result, the analysiswas stoppedafter the eighth compo- nent. It is worth noting, however,that no clear guidelinesex- pear to increasein theseareas. Component 5 has thus de- ist for when to stop an analysis.In PCA,the strengthof a tected a known and significant false trend in the NDVI component(as reflected both in the eigenvalueand in the data.a rangeof loadingson that component)will be determinedby In addition to the systematictrend in Component 5, both the magnitudeof the variability it explains and the area the loadingsalso show a somewhatirregular semi-annual over which that variability occurs.Thus, changeelements in cycle such as that found in Component4. Examinationof time seriesanalysis will be areaweighted. Small magnitude the time profilesin Figure 3, however,clearly illustrate changesmay come out in early componentsif they affect that the loading pattern is a compositeof the cyclesassoci- large areas.Conversely, large effectsmay come out in later ated with an annual cvcle in the Saharaand the semi-an- componentsif they occupy only a small portion of the area nual cycle associatediryittr the precipitation maximum of analyzed.Thus, it would not be unreasonableto examinemi- the lakesof equatorialAfrica. Component6 would also ap- nor components(such as thosebeyond componentB in this pearto relateto this sensoreffect, As indicatedby Tateishi analysis)if very localized effectswere of interest. (personalcommunication, 1992) this progressivedrift in the NDVIoutput has the effect of decreasingthe range of NDVIin forestedregions. This is illustratedby the decreas- Conclusions ing amplitude of the cyclic pattern of loadingson Compo- It would appearfrom the aboveillustration that the ability of nent 6. The semi-annualcycle is typical of that associated StandardizedPrincipal Componentsto uncover significant with the double precipitation maximum of equatorial forest changeevents over long time seriesis very strong.The ENSo- areas(such as we seein Component4), and fhe amplitude relatedprecipitation patternsrepresent the most significant is clearly decreasing,Similarly, the componentimage anomaliesto take place over Africa during the 1986-88pe- (Plate1) shows a strongnegative anomaly in heavily for- riod. Not surprisingly,these were lower in magnitudethan ested regions of the continent. the effectsattributable to seasonalchanges. It is also interest- The analysisthus shows that, after the generalgeograph- ing that the procedurepicked up significant anomaliesin the ical and major seasonaleffects, the next major agentof varia- output of the sensorsystem itself, and that thesewere also bility in the vovt data over the three-yearperiod was system- seento be of greatermagnitude than the ENsoevents. How- relatedvariability in the output of the AvHRR-derivedindex ever, as noted above,components are effectivelyarea itself. It should be noted that, once a changecomponent has weighted.The sensordrift effect is in fact quite small but af- been created,the effectsof that componentare then held fectsbroad areasof the image (particularly the Sahara).The constantas subsequentcomponents-are calculated (Johnston, ENSOeffects occupy substantiallyless areabut have a dra- 1980,pp. 739-747),To the extent that ComponentsE and 6 matic effect on natural ecosystems, are able to describethese sensor system effects, later compo- StandardizedPrincipal ComponentsAnalysis would nents would thus be free of their influence. thus appearto be a remarkablycomprehensive tool for the Components7 and 8 (Plate1 and Figure 1) are also of analysisof anomaliesand trends in Iong time seriesdata. It considerableinterest, Both would appearto relate to El-Niflo/ is clearly very effectivein isolating periodic seasonaleffects, SouthernOscillation (rNsO)events spanning the 1986-88pe- However,it is equally effectivein isolating trends in value and variability (aswith the sensordrift problem) and iso- {It is interestingto note the drop at the end of the sequenceback Iated anomalousevents. Given our generallack of techniques to approximatelythe zero correlationlevel. The majority of the No- for the abstractionof significant changeevents in Iong time vember1988 data and all of the December1988 data were actualiv seriesimage data, the technique should prove to be a major derivedfrom NoAA-rr,not NoAA-e. tool in the areasof remote sensingand cts. WMO, 1984, The Global Climate Sysfem:A Critical Review of the References Climate SystemDuring 1982-1984,World MeteorologicalOrgan- Eastman,|. Ronald, 1992a.Time SeriesMap Analysis Using Stan- ization, Geneva. dardized Principal Components.ASPRSIACSMI RT I 2 Technical L987, The GhobalClimate System:Autumn 1984 - Spring Papers,Volume l: Global Change and Education, 3-8 August, 1986.World MeteorologicalOrganization, Geneva. Washington,D.C., pp. 795-204. 1989. fie Global Climate System:Climate SystemMonitor- Analysis System. 1992b.IDRISI: A Grid-BasedGeographic ing, June1986-November 19B8. World MeteorologicalOrganiza- Version 4.0. Clark University,Worcester, Massachusetts. tion, Geneva. Fung, T., and LeDrew,E. 1987.Application of Principal Components Analysis to ChangeDetection, PhotogrammetricEngineering & (Received26 November1992; accepted 21 January1993) RemoteSensrng, Vol.53, No. 12, pp. 1649-1658. Johnston, R.J.,1980. Multivariate StatisticalAnalysis in Geography. Longman,New York. |. Ronald Eastman Mather, P,M,, 1987,Computer Processing of Remotely-SensedIm- J. Ronald Eastmanis Director of the Clark Labs for Carto- oges.John Wiley and sons,New York. graphic Technologyand GeographicAnalysis and Associate NOAA-EPA, 7992. Global EcosystemsDatabase Project CD-ROM.Na- Professorof Geographyin the GraduateSchool of Geography tional Oceanic and Atmospheric Administration, National Geo- at Clark University. He is also the author of the IDRISIGeo- physical Data Center,Bouider, Colorado. graphic Information Systemwhich is distributed on a non- Singh,A., and A. Harrison,1985. Standardized Principal Compo- profit basisby the Clark Labs.His recent researchinterests nents. Internatjonal lournal of RemoteSensrng, Vol. 6, No. 6, include changeand time seriesanalysis with remotely pp. 883-896. sensedimages, error and uncertainty, and decision support Tateishi, R., and K. Kajiwara, 7992. Global Land Cover Monitoring tools for GIS. by AWRII NDW Data. Earth Environmenf, Vol. 7, pp. 4-14. Townshend,I., C. Iustice, and B. Kalb, 1987.Characterization and Michele Fulk Classificationof South American Land CoverTypes Using Satel- Michele A, Fulk is Public Re- Iite Data.International lournal of RemoteSensing, VoI. 8, No. 8, OutreachRepresentative and pp.1189-1207. searchAssociate at The IDRISIProiect, Clark University Grad- uate School Tucker, C., l, Townshend,and T. Gofl 1985.African Land-Cover of Geography,where she has worked since ClassificationUsing SatelliteData. Science, YoL 227, No. 4685, Januaryof 1991, She is also pursuing a master'sdegree in In- pp.369-375. ternationalDevelopment at Clark University. Her researchin- White, F., 1983. Tfte Vegetationof Africa: A DescriptiveMemoir to terestsinclude changeand time seriesanalysis and Accompany the UNESCOIAETFATIUNSOVegetation Map of Af- applicationsof cIs and imageprocessing to problemsof de- rico. UNESCO, Paris. velopment and resourcemanagement.

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t3',2 PE&RS