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Sensitivity of EVI-based harmonicregression to temporal resolution in thelower Okavango DeltaNiti B. Mishra a , Kelley A. Crews a & Amy L. Neuenschwander ba Department of Geography & the Environment , The University ofTexas , Austin , TX , 78712 , USAb Center for Space Research and Applied Research Laboratories,The University of Texas , Austin , TX , 78712 , USAPublished online: 04 Jul 2012.

To cite this article: Niti B. Mishra , Kelley A. Crews & Amy L. Neuenschwander (2012) Sensitivity ofEVI-based harmonic regression to temporal resolution in the lower Okavango Delta, InternationalJournal of Remote Sensing, 33:24, 7703-7726, DOI: 10.1080/01431161.2012.701348

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International Journal of Remote SensingVol. 33, No. 24, 20 December 2012, 7703–7726

Sensitivity of EVI-based harmonic regression to temporal resolutionin the lower Okavango Delta

NITI B. MISHRA*†, KELLEY A. CREWS†and AMY L. NEUENSCHWANDER‡

†Department of Geography & the Environment, The University of Texas, Austin, TX78712, USA

‡Center for Space Research and Applied Research Laboratories, The University of Texas,Austin, TX 78712, USA

(Received 2 May 2011; in final form 18 October 2011)

In this study, we examined how satellite time-series-based characterization of eco-logical cycles and trends is sensitive to the temporal depth and spacing of thetime series and whether the observed sensitivities were cover and/or cycle spe-cific. We fitted a harmonic regression (with annual, semi-annual and quasi-decadalcycles) to an 85-image Landsat time series (1989–2002) covering the lowerOkavango Delta, varying the temporal depth and spacing of time-series vectorsfollowing two different but comparable approaches (i.e. systematic vs random vari-ation). The results show that as the temporal depth decreases, the sensitivity toboth short- and long-term ecological cycles was lost in the seasonally dynamicenvironment. The degree to which characterization of ecological cycles and trendswas influenced by temporal depth and spacing was dependent on the functionaltype of vegetation and dynamics of the disturbance regime(s). Ecological cycleswere comparatively better characterized, even at reduced temporal depths, forwoodland-dominated areas, riparian vegetation and more frequently flooded areas(i.e. less dynamic systems) compared with less routinely and non-flooded grass-lands, mixed savannas and more frequently burned areas. Detection sensitivity wasalso found to be cycle specific, as, at reduced temporal depths, the semi-annualcycle was less easily detected than the annual cycle for the majority of the studyarea. Temporal spacing of time-series vectors was also found to be important:the chances of misinterpreting system variability as a change were much higherwhen vectors were randomly chosen. Interestingly, at a reduced temporal depth,the harmonic model unexpectedly produced a higher coefficient of determinationdue to model under-specification for both vector selection approaches. However,randomly selected vectors produced much larger artefacts. These results indicatethe need for caution in selecting a time series not only for its temporal depth butalso for its temporal spacing, particularly as related to the inherent environmentalperiodicity of the study area.

1. Introduction

Scientists and policymakers require an understanding of land-cover change andecosystem dynamics over increasingly large spatiotemporal extents for addressing theimpacts of global climate change on both biophysical and socio-economic systems

*Corresponding author. Email: niti@mail.utexas.edu

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online © 2012 Taylor & Francis

http://www.tandfonline.comhttp://dx.doi.org/10.1080/01431161.2012.701348

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7704 N. B. Mishra et al.

(Defries et al. 1999, Kerr and Ostrovsky 2003, Rindfuss et al. 2004). Remote-sensinginstruments operating at multiple spatial and temporal resolutions have long beenused for quantifying ecosystem dynamics because of their ability to provide synop-tic, consistent and repeatable measurements (Coppin et al. 2004, Lu et al. 2004). Themultiscale capability of these sensors makes them especially suitable for capturingchanges caused by both natural (fire, hurricane) and anthropogenic (deforestation,urbanization) disturbances over daily to decadal scales (Lunetta et al. 2004).

Ecosystems are complex and adaptive systems driven by both internal and exter-nal processes (Levin 1998, Pickett and Cadenasso 2002), with functionality affectedby climatic trends/oscillations and natural/anthropogenic disturbances operating ata variety of spatiotemporal scales (McCarthy et al. 2000, Hewitt et al. 2001, Foleyet al. 2002). Ecosystem dynamics can be temporally decomposed into trends, short-term seasonal cycles and inter-annual cycles operating at temporal scales of a fewyears to several decades. While intra-annual cycles are driven by annual temperatureand rainfall interactions impacting vegetation phenology, inter-annual cycles are moreoften related to climatic trends and oscillations. Characterizing such ecological trendsand cycles is often of interest to ecologists seeking to understand ecosystem dynamicsand health (Rasmusson 1991, Anyamba 1997, Anyamba et al. 2001). Recently, studiesfocusing on ecological trends and cycles have often been based on the analysis of time-series data derived from remote-sensing systems. These studies model ecological cyclesusing either Fourier analysis to segment the landscape based on identified periodici-ties (Andres et al. 1994, Moody and Johnson 2001, Canisius et al. 2007) or harmonicregression to assess how well landscape segments fit with periodicities reported in theclimatic change and vegetation ecology literatures (Jakubauskas et al. 2001, Immerzeelet al. 2005, Julien et al. 2006, Bradley et al. 2007, Eastman et al. 2009, Verbesseltet al. 2010). Most of these studies utilized low spatial resolution but temporally richtime-series data (e.g. Moderate Resolution Imaging Spectroradiometer (MODIS)) tominimize the risk of confounding system variability with change. In contrast, time-series analysis using higher spatial resolution (e.g. Landsat and Advanced SpaceborneThermal Emission and Reflection Radiometer (ASTER)) data sets has the capabil-ity to characterize landscape dynamics at much finer spatial scales and could detectecological trends and cycles that were either undetected or significantly different fromthe results produced using coarser resolution data sets (Turner et al. 2001, Wu et al.2002, Wu 2004). However, the effort of studies using high-resolution time-series datahas largely been impeded by lack of time-series data availability (Lunetta et al. 2004).Further, although the effect of upscaling or downscaling on landscape characteriza-tion has been extensively studied (Wickham and Riitters 1995, Marceau and Hay1999, Wu 2004, Wessman and Bateson 2006, Wu and Li 2006, Buyantuyev and Wu2007), there have been few examples that examine the effect of varying temporal reso-lution on characterizing landscape dynamism at low (Zhang et al. 2009) or high spatialresolution.

The objective of this research was to examine how the temporal depth and spacingof satellite time-series data affect the interpretation of ecological cycles and detectionof long-term ecological trends in seasonally dynamic environments. The availabilityof a deep, high temporal resolution time series (85 images ranging from April 1989 toOctober 2002) at a high spatial resolution (30 m, Landsat Thematic Mapper (TM) andEnhanced Thematic Mapper Plus (ETM+)) for the lower Okavango Delta offers anunusual opportunity to examine this methodology’s potential applicability to areasand situations where temporally rich data may be unavailable for practical reasons

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such as cloud cover (Asner 2001, Ju and Roy 2008), return intervals (Stathopoulou andCartalis 2009) or sensor failure (Markham et al. 2004). In particular, the high degreeof spatiotemporal variability in the study site’s vegetation combined with its stronglyseasonally driven environment made it a prime testing ground for the importance oftemporal depth and spacing in time-series assessments.

2. Background

2.1 Ecological theory for ecosystem dynamics

Monitoring ecosystem dynamics by characterizing the ecological trends and cycleshas often been based on equilibrium and non-equilibrium theory (Perry 2002,Pickett and Cadenasso 2002). Assumptions under classical equilibrium theory (i.e.ecosystems are closed, self-regulating systems) were found to be inadequate toaccount for the stochastic processes and non-linear dynamics depicted by ecosystems;non-equilibrium theory provided a more suitable theoretical basis for this purpose(Holling 1973, De Angelis and Waterhouse 1987, Wu and Loucks 1995, Perry2002). The theory of ecosystem resilience developed as a more pragmatic alternative,centring on the magnitude of disturbance an ecosystem can sustain without shiftinginto an alternate state (Gunderson 2000, Folke et al. 2004). However, monitoringresilience entails the development of resilience indicators and identification of criticalthresholds and therefore requires knowledge of feedbacks (Bennett et al. 2005,Groffman et al. 2006, Druce et al. 2008). Hence, monitoring the rate of change anddirection of key variables in complex systems has been suggested as both a practicaland relevant indicator of resilience and system dynamics (Bennett et al. 2005). Keyvariables utilized in long-term monitoring of ecosystem dynamics at landscape andregional scales have often included remotely derived vegetation indices (VIs) (e.g.normalized difference vegetation index (NDVI), enhanced vegetation index (EVI))that serve as proxies for the vigour of photosynthetic vegetation or other biophysicalvariables (e.g. leaf area index (LAI), fractional photosynthetically active radiation(FPAR)) (Cohen et al. 2003, Xie et al. 2008). This study utilized vegetation response,as represented by EVI, calculated from 14 years of Landsat TM and ETM+ images.EVI has been documented as a more robust vegetation index than NDVI in itsgreater responsiveness to vegetation structure, lowered sensitivity to atmospheric andsoil/litter variations and particularly suitable for assessing seasonality of ecologicalprocesses in a grassland–shrubland–woodland matrix (Huete et al. 2002, Ferreira andHuete 2004, Tatem et al. 2004, Hay et al. 2006).

2.2 Ecological time-series analysis

Landscape dynamics can result from any combination of long-term natural change,climatic variability, anthropogenic alteration and natural vegetation dynamics(Lambin et al. 2003). Thus, it becomes increasingly difficult to relate landscape changeto a specific process based on multitemporal remote sensing when the time betweenscenes becomes too long (Lunetta et al. 2004, Crews-Meyer 2006). The use of atime series overcomes these limitations. Further, ecological processes are describedto have trends, cycles and structural residuals (Rodríguez-Arias and Rodó 2004) thatare extractable via time-series decomposition. Coarse spatial resolution satellite timeseries have been utilized at regional and global spatial scales to derive related variables,monitor ecological processes and characterize phenological cycles (Moulin et al. 1997,Moody and Johnson 2001, Zhang et al. 2003, Stockli and Vidale 2004) for agricultural

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assessment (Jakubauskas et al. 2002, Hill and Donald 2003, Canisius et al. 2007), land-cover classification (Andres et al. 1994) and land-cover change detection (Lunetta et al.2006, Canisius et al. 2007).

The availability of high spatial resolution imagery (e.g. Landsat TM/ETM+,Système Pour l’Observation de la Terre (SPOT)) for the past few decades has facili-tated time-series studies at times at the expense of temporal resolution. To monitorlong-term wetland vegetation dynamics in the Great Lakes Basin, Leahy et al. (2005)applied multitemporal clustering on 23 years of Landsat imagery and found that largesections of the study area covered by shallow marshes experienced an increase in theemergent vegetation with decreasing water level. For investigating the interaction offlooding and fire with vegetation in the lower Okavango Delta, Neunschwander andCrews (2008) utilized a 14 year EVI time series to identify landscape clusters that weresimilar in spectral response over time. Analysis of long-term EVI trends of these clus-ters depicted the spatial association with the disturbance history. Besides long-termecological trend analysis, studies have also tried to exploit high resolution time seriesto estimate changes in vegetation cover and the rate of recovery following a distur-bance, e.g. volcanic eruption, human-induced deforestation or insect attack (Lawrenceand Ripple 1999, Schroeder et al. 2007, Goodwin et al. 2010).

In environmental remote sensing, it is generally agreed that with increasing temporalresolution, the accuracy of characterizing landscape dynamism increases and wouldbe best characterized with data more narrowly spaced in time (Zhang et al. 2003, Xieet al. 2008). In most cases, studies make use of the highest temporal resolution dataavailable at a given spatial resolution. Very few studies have considered examiningthe sensitivity of their results to the temporal composition (depth and spacing) of theinput time series. In a recent study investigating the sensitivity of phenology detec-tion to the temporal spacing of MODIS time-series EVI images, Zhang et al. (2009)found that the temporal resolution of a minimum 6- to 16-day spacing was required todetect phenology with considerable precision. Furthering this approach, in this studywe conducted sensitivity testing for ecological cycles and trends at a wetland–savannainterface in southern Africa by utilizing a much higher spatial resolution data set.

2.3 Harmonic regression for ecological time-series analysis

Harmonic regression is a mathematical technique used to decompose a complex, staticsignal into a series of individual sine or cosine waves, each characterized by a spe-cific amplitude and phase angle (Immerzeel et al. 2005). Rather than fitting the datato a linear polynomial function (Braswell et al. 1997, Lawrence and Ripple 1999),harmonic regression fits data to a described trend or cycle. This approach has gen-erally been utilized only when sufficiently rich time-series data are available, such aswith Advanced Very High Resolution Radiometer (AVHRR) archives. Several stud-ies have successfully applied harmonic regression in analysing time series of AVHRRNDVI (e.g. Jakubauskas et al. 2001, 2002, Moody and Johnson 2001, Canisius et al.2007), as well as MODIS time series for studying climate change and global vegetationcycles (Zhang et al. 2003, Bradley et al. 2007). However, this approach is not typicallyregarded as a methodology employed for detecting land-cover change using finer reso-lution imagery (Braswell et al. 1997, Zhang et al. 2003). Using SPOT VEGETATION-derived NDVI time series over Tibet, Immerzeel et al. (2005) showed how Fourier-transformed NDVI are better related to land-use and precipitation patterns than theoriginal NDVI influenced by atmospheric noise. An alternative to harmonic analysis

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for characterizing frequency variability is wavelet analysis, more powerful in that it islocalized in space and has an infinite set of possible basis functions that can detectinformation normally obscured by Fourier analysis (Kestin et al. 1998, Torrence andCompo 1998). Martinez and Gilabert (2009) used a wavelet transform method on anAVHRR-derived NDVI time series to extract vegetation dynamics parameters such asmean and minimum NDVI, amplitude of phenological change, timing of maximumNDVI and magnitude of land-cover change. Galford et al. (2008) applied waveletanalysis to five years of MODIS-derived EVI to detect the expansion of row-cropagriculture in Brazil. Wavelet decomposition of the residuals from harmonic analy-sis enabled Neuenschwander and Crews (2008) to detect a quasi-decadal signal in thetime series of the lower Okavango Delta, which has been included in this study.

3. Site and situation

The study was conducted in the southeastern part of the Okavango Delta, Botswana,an internationally recognized wetland of importance by the Ramsar Convention onWetlands (www.ramsar.org) (Kgathi et al. 2005, Mfundisi 2008). The Okavango Deltais a complex wetland–savanna ecosystem providing critical habitat and resources toboth humans and wildlife (Ringrose et al. 1988). The study area is located in a distalregion of the delta near the village of Maun at the wetland–savanna interface and isapproximately 2430 km2 in size. The source of water for the delta is the OkavangoRiver (formed by the confluence of the Kavango/Cubango and Cuito Rivers), whichdrains into the dry Kalahari sands, creating a vast wetland oasis (Ross 2003, Talukdar2003). The Okavango Delta is not truly a delta but an (inland) alluvial fan, charac-terized by relatively low gradients (1:5500 in the panhandle, 1:3300 in the fan itself),low energy and extremely low salinity (0.04 ppt). Although the area is typically con-sidered to be a wetland, over 60% of the delta is comprised of spatially heterogeneousgrassland, savanna and woodland (McCarthy et al. 2000). The study area receivesa mean annual rainfall of 453 mm (range about 444–472 mm) (Alemaw et al. 2003).Precipitation patterns over the Okavango Delta have been reported to follow a cyclicalpattern in response to both short- and long-term climatic oscillations. Several stud-ies have confirmed the precipitation pattern over the Okavango Delta to follow thedominant 18 year oscillation observed in the summer rainfall over southern Africa,resulting in alternating 9 year periods being, respectively, wetter than average and drierthan average (Rogers 1988, McCarthy et al. 2000, 2003, Wolski et al. 2003). Combininganalysis of long-term rainfall records of two stations (Maun and Shakawe) in thevicinity of the delta, McCarthy et al. (2000) also reported 3 and 8 year oscillationsin precipitation. Neuenschwander and Crews (2008) reported a quasi-decadal cycle(10.8 years) for the lower distal region of the delta. The rainfall over the area was alsoreported to be below the long-term average since the 1970s until the last few years, i.e.for the entire study period (Warne 2004).

The delta’s functioning is effected by a variety of driving forces that influence bothits vegetative composition and its overall function (Ringrose et al. 1988, McCarthyet al. 2000). The annual flooding in the Okavango Delta, fed by both local andupstream precipitation, sustains the wetland system (Kgathi et al. 2006). The non-localflooding source starts in the Angolan highlands, with the peak of the annual floodtypically reaching the northern portion of the delta’s panhandle between Januaryand March. The flood water reaches the distal portion of the delta between Mayand August, which is winter and the peak of the dry season (McCarthy et al. 1998,

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Neuenschwander and Crews 2008). The study area has shown variation in the spatio-temporal distribution of flooding frequencies. Mapping of flooding history using a14 year time series depicted that flooding frequency varied from permanent channelsto active floodplains (flooded every 1 to 2 years), less active floodplains (flooded every3 to 7 years) and rarely flooded areas (never flooded during the 14 years). Further,the extent and level of flooding also varied within and among these areas (Heinl et al.2006, Neuenschwander and Crews 2008). Besides flooding, fire is another major dis-turbance regime affecting the ecological dynamics of the Okavango Delta. Analysis offire dynamics over 14 years (1989–2002) found that the grasses in active floodplainswere most frequently burned with a fire return interval (FRI) of 2–3 years, transi-tioning to 4–5 years in areas adjacent to floodplains and increasing to 5–7 years indrylands. Additionally, the majority of drylands and woodland savannas did not burnmore than once during the study period (Neuenschwander and Crews 2008). Owingto its proximity to Maun, fire frequency in the southern part of the study area is alsoinfluenced by human-induced fires to facilitate extraction of natural resources andincrease grazing areas for domesticated animals (Mbaiwa 2003, Kgathi et al. 2006).

4. Data and methodology

4.1 Image preprocessing, disturbance mapping and temporal land-cover classification

This study utilized a time series of 85 TM/ETM+ images spanning April 1989 toOctober 2002, with images spaced roughly every 2 months. Preprocessing of datawas conducted and is described in both Heinl et al. (2006) and Neuenschwanderand Crews (2008). Briefly, the images were geometrically corrected and co-registeredwith a root mean square error (RMSE) value of less than half of the pixel size. Thedark object subtraction (DOS) method was applied after Chavez (1988) for atmo-spheric correction and apparent surface reflectance retrieval. EVI was calculated foreach scene individually, and then stacked into a time series where each pixel had an85-member trajectory of EVI. In order to group pixels that exhibited similar trajec-tories in EVI change through time, Iterative Self-Organizing Data Analysis Technique(ISODATA) clustering was performed on this stacked data set with a maximum of20 iterations, a minimum of 5000 pixels per cluster and a maximum class standarddeviation of 0.25. Based on both reduction and threshold in class separability aswell as information classes previously identified in land-cover mapping studies of thearea (McCarthy et al. 2003, Neuenschwander et al. 2005), 35 output clusters wereselected (figure 1). These clusters represented regions on the landscape that were tem-porally statistically similar, rather than spectrally similar as with standard ISODATAapplications (Crews-Meyer 2002).

Based on the value of each pixel’s trajectory, the mean EVI value was calculated,which resulted in 85 mean EVI vectors for each of these 35 clusters describing thebehaviour of the vegetation response from 1989 to 2002. Seasonal variation wasobserved as a general trend in the mean EVI time series, with highest EVI valuesoccurring during wet, summer months (November to March) and lowest EVI val-ues occurring during dry, winter months (May to August). As an illustration, thetemporal response of few selected clusters, as depicted by the 85-vector mean EVItime series, is plotted in figure 2. The clusters forming the lower envelope of the tem-poral trajectories (clusters 1–7) had the lowest mean EVI, representing water andwetland classes (vegetation in periodically flooded channel). Clusters with the high-est mean EVI forming the upper envelope of the mean EVI trajectory (e.g. cluster nos.

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Figure 1. Thirty-five EVI-based temporal clusters result of ISODATA classification for thelower Okavango Delta.

Figure 2. Plot of 85-vector mean EVI time series for six selected clusters out of total 35clusters. The number beside the class name in the legend represents their respective clusternumbers.

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34 and 35) were associated with riparian vegetation along channels. More descriptionof land cover associated with each cluster can be found in Neuenschwander (2008).The land-cover type associated with each cluster was defined based on fieldwork con-ducted in 2006 and 2007, interpretation of pan-sharpened Advanced Land Imager(ALI) imagery from September 2003, an earlier vegetation map and derived patternsof flooding and fire over the 14 year study period (Neuenschwander and Crews 2008).

4.2 Harmonic regression

Harmonic regression was applied on the mean EVI time series of each cluster. Theharmonic regression model used in this study was defined as follows:

Y = β0 + cT +n∑

i=1

Ai sin(

2π is

T)

+ φi, (1)

where Y is the EVI, β0 is an offset, c is the trend, Ai is the amplitude of the ithoscillation, φi is the phase component of the ith oscillation, s is the fundamentalfrequency and T is the time-dependent variable. Previous work established the com-bined harmonic wavelet processing protocol used here. The harmonic regression fitsthe EVI time series for each temporal cluster with trend, bias, annual, semi-annualand decadal cycles. While the annual cycle modelled the annual variability in the sig-nal, the semi-annual cycle was included to model the distinct dry and wet seasonalityof the region. The EVI time series was linearly interpolated into 15.5 day intervals (oneand a half month) for performing wavelet decomposition of the residuals from annualand semi-annual fit. Because previous results evidenced the importance of a 10.8 yearsignal, a quasi-decadal cycle was included along with annual, semi-annual cycles toattempt explain more variance in the time series. t-Tests and two-tailed significancelevels of each model coefficient for each EVI cluster were calculated.

4.3 Sensitivity analysis

Neuenschwander and Crews (2008) found statistically significant results between trendand pattern in land-cover trajectories and climatic oscillations and cycles in a seasonalenvironment also influenced by disturbance regimes. The study was able to utilize har-monic regression as a technique largely because of the extraordinary temporal depthand spacing of the input images. However, for most remote-sensing studies, it is verydifficult and even rare to find time series of high spatial resolution (∼30 m) data withmoderately high temporal resolution (approximately 2 to 3 months), especially fortropical areas where cloud cover is a major limitation. Therefore, it is important totest this methodology’s potential applicability to similar studies in other parts of theworld where the temporal depth and spacing of images are highly constrained. Thistesting was conducted in two ways: (a) by systematically varying the temporal depthand spacing of EVI vectors and (b) by randomly varying the temporal depth andspacing of EVI vectors. A schematic representation of this approach is illustrated infigure 3. When systematically varying the temporal depth, the spacing of EVI vec-tors was methodically controlled. The vector elements were selected at three levelsof temporal depth: a 43-element vector (selecting every second EVI vector, leavingone in between), a 29-element vector (selecting every third EVI vector, leaving twoin between) and a 17-element vector (selecting every fifth EVI vector, leaving four inbetween) (figures 3 and 4). The systematic selection of EVI vector elements is, however,

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Figure 3. Schematic representation of the methodology followed to systematically and ran-domly select EVI vectors at temporal depths of 43-, 29- and 17-element EVI vectors. Althoughthe original 85-element vector spacing suggests constant temporal spacing, yet the data wereonly approximately consistent in temporal spacing due to practical limitations.

Figure 4. Illustration of how the systematic versus random selection method followed in thisresearch selects vectors from EVI time series at different temporal depth and spacing. (a) Theoriginal 85-element vector time series for the lower distal portion of the Okavango Delta.Plots in the left panel (b)–(d) represent the vectors selected following the systematic selectionapproach at three temporal depths (i.e. 43-, 29- and 17-element vectors, respectively). Plots inthe right panel (e)–(g) show the vectors selected following the random selection approach butat the same three temporal depths. All of the plots represent vectors for cluster no. 35, whichrepresents riparian woodlands in the study area.

an idealistic case, since in reality temporal spacing of imagery may be less regularfor practical reasons, e.g. cloud cover or sensor failures (Asner 2001, Markham et al.2004, Stathopoulou 2009). Hence, a second approach of selecting EVI vectors was alsodeveloped wherein the EVI vector elements were generated randomly using a statisticalprogram (R) at the same three temporal depths (i.e. 43-, 29- and 17-element vectors)100 times each (to avoid artefacts associated with a small random sample). The secondapproach was expected to be a more robust test for examining this method’s potentialapplicability. Figure 4 provides an illustration of how the systematic versus randomselections generated differently spaced vectors at the same temporal depth.

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5. Results and discussion

5.1 Effect of time-series temporal depth/spacing on ecological cycles

5.1.1 Systematic variation. Sensitivity testing was first performed by systemati-cally reducing the number of EVI vectors to three temporal depths (i.e. 43-, 29- and17-element vectors). The results indicated that although in general the characterizedcycles were sensitive to the temporal positioning of the input time series, the pattern ofthis sensitivity was spatially heterogeneous across the landscape. Since clusters anal-ysed in this study represented parts of the landscape exhibiting similar vegetationspectral responses over the study period, it was important to examine whether theobserved sensitivities at different temporal depths were cycle specific (e.g. annual vssemi-annual) as well as cluster specific.

The results show that sensitivity was cycle specific. Among the three modelled cycles,the annual cycle was the least sensitive as it was found to be statistically significant forall 35 clusters at temporal depths of 43- and 29-element vectors and for all but threeclusters at the temporal depth of 17-element vectors (figure 5). These results could beinterpreted in light of the sampling theorem, which states that if a signal is sampledat an interval d, then frequencies less than 2d cannot be detected (Li et al. 2005).Therefore to detect an annual and semi-annual cycle, the temporal spacing betweenimages should be no greater than 6 months (two images per year) and 3 months (fourimages per year), respectively. This rule of thumb corresponds to the annual cyclebeing successfully detected for all of the EVI clusters at temporal depths of 43- and29-element vectors, due to the fact that two scenes per year were sufficient to capturethe annual cycle without any aliased effects. Theoretically, detecting the annual cycle ina 14 year time series would require a minimum of 28 EVI vectors and the 17-elementvector should not have been sufficient. However, the annual cycle was found to bestatistically insignificant for only three EVI clusters at a temporal depth of 17-elementvectors (figure 5). This result was later confirmed as a sampling artefact since theannual cycle in the harmonic regression with a different set of systematically selected17-element vectors was found to be statistically insignificant for five clusters.

It was also expected that the semi-annual cycle (requiring one scene every threemonths) would not be detectable for any of the EVI clusters at any of the threereduced temporal depths. Detection of the semi-annual cycle was also expected tobe poor because with reducing temporal depth, EVI vectors would lose sensitivityto account for vegetation phenology as well as influence of class-dependent vari-ability in lag time required to recover from disturbances (e.g. fire and flood). Usingsystematically selected 43-, 29- and 17-element vectors, the semi-annual cycle was sta-tistically insignificant for 9, 5 and 18 EVI clusters, respectively (figure 5). However,at the same temporal depths but with harmonic regression using an alternate set ofsystematically selected EVI vectors, the number of statistically insignificant clusterschanged to 5, 11 and 23, respectively. These results highlight the effect of samplingartefacts that could be misinterpreted as change in the strength of annual and semi-annual cycles if analysis lacks sufficiently rich as well as suitably spaced time-seriesdata.

Further analysis of the results revealed more cluster-specific sensitivity. Some clus-ters were more sensitive than others in that the modelled annual and semi-annualcycles became insignificant even with 50% of temporal depth (43-element vector).These clusters mainly represented grasses and sedges on both active and secondaryfloodplains (cluster nos. 2, 4 and 7) and shrub vegetation on islands (cluster no. 9) that

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Figure 5. Effect of reduced temporal depth and spacing of systematically and randomlyselected EVI vectors on the significance of cycles fitted to the harmonic regression model. Theresults for the randomly selected vectors represent the mean number of statistically insignificantclasses obtained from 100 iterations of harmonic regression. The results at a temporal depth of85-element vectors represent the findings from Neuenschwander and Crews (2008) and the restis from this study.

were regularly flooded and burned. Ecologically, these areas represent portions ofthe landscape that require high temporal depth of satellite time series for accuratelycharacterizing the processes and disturbances affecting them. In contrast, parts of thestudy area were comparatively less sensitive because the annual and semi-annual cycleswere found to be statistically significant even at 50% and 40% of the initial tempo-ral depth. These clusters were characterized as insignificant only when the temporaldepth was further reduced to 20%. These less sensitive landscapes were representedby riparian and mopane woodlands, scrub and mixed mopane (cluster nos. 24, 27,30, 34 and 35) with low levels of burning (1–2 burns) and flooding. It is very likelythat annual and semi-annual cycles of these areas will be confidently characterizedat comparatively low temporal resolution time-series spacing. Additionally, parts ofthe landscape represented by grasses/sedge in active floodplains that experienced reg-ular flooding (flooded every one to two years) and frequent burning (burned morethan eight times) were consistent in their response to decreasing temporal depth: i.e.modelled ecological cycles for these clusters were statistically insignificant across allthree levels of reduced temporal depths. Hence, it would be most difficult to correctlydetect ecological dynamics for these landscapes at decreased temporal resolution.Interestingly, other parts of the landscape were not so consistent in that their initial (at85-element vectors) statistically significant annual and semi-annual cycles were char-acterized as insignificant with 43-element vectors, but at more reduced temporal depth(i.e. 29-element vectors) these cycles were again found to be significant. Spatially, theseclusters represented mixed grass–woody or woody–shrub and shrub-dominated areasthat experienced intermediate level burning (3–7 burns) or flooding (cluster nos. 12,17, 18 and 21).

5.1.2 Random variation. Harmonic regression was performed for 100 iterationswith randomly selected vectors. The annual cycle was statistically significant for all100 iterations at temporal depths of 43- and 29-element vectors. However, at a tempo-ral depth of 17-element vectors, 10 out of 100 iterations yielded at least one statistically

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insignificant cluster for the annual cycle. The results of 100 iterations for the semi-annual and the quasi-decadal cycles more explicitly revealed the stochasticity. Forexample, at a temporal depth of 43-element vectors, the minimum and maximum num-bers of insignificant clusters for semi-annual and quasi-decadal cycles were between3–16 clusters and 8–26 clusters, respectively. Similarly for 17-element vectors, thesame value ranged between 0–28 insignificant clusters for the semi-annual cycle and0–33 insignificant clusters for the quasi-decadal cycle. Further, at a temporal depthof 43-element vectors, the average numbers of statistically insignificant EVI clusterswere higher for the quasi-decadal cycle than the semi-annual cycle (figure 5). However,as the EVI temporal depth was reduced to 29- and 17-element vectors, this differ-ence gradually became irresolvable. These results depict that when using randomlyselected vectors for ecological time-series analysis, it is very likely that both short- andlong-term ecological cycles will go undetected or be mischaracterized.

Since this study was conducted at a wetland–savanna interface, its structural andfunctional vegetation characteristics can be considered as representative of the vari-ety of tree–grass ratios observed in southern African savannas to a certain extent.Differential phenology (semi-annual cycle) of woody and herbaceous components is adefining characteristic of savanna system dynamics (Prince and Tucker 1986, Dougillet al. 1999, Chidumayo 2001, Scanlon et al. 2002, Furley 2004). Detecting this dif-ferential phenology to characterize the woody versus herbaceous component anddetermining the overall phenological characteristics of savannas have also been theobjectives of several studies (Dougill et al. 1999, Shackleton 1999, Chidumayo 2001,Scanlon et al. 2002, Archibald and Scholes 2007). The results of this study suggest thatin southern African savannas, the sensitivity of detecting ecological cycles is associatedwith a certain phenology and disturbance regimes. In general, phenological charac-teristics of the savanna landscape with a spatially dominant or co-dominant woodycomponent (i.e. acacia woodlands, mopane woodlands and riparian woodlands) thatare not subject to disturbances (e.g. flood, fire) could be characterized successfully,even if the high resolution images are available at a very low temporal resolutionbut at a regular temporal interval (depicted by systematically spaced 17-element vec-tors for 14 years). Additionally, woodland savannas with an understory herbaceouslayer (scrub/mixed mopane, acacia shrubbed woodland) that are subject to occasionalburning (once every three to five years) require comparatively higher temporal resolu-tion (depicted by systematically spaced 29-element vectors for 14 years). In contrast,the phenological characterization of grass-dominated savannas susceptible to frequentdisturbances such as flooding and fire and that green up for a comparatively shorterduration in response to seasonal rainfall can only be detected at a very high tem-poral resolution (i.e. >43 systematically spaced vectors over 14 years). Additionally,landscapes marked by co-dominance of grass–shrub and low scattered woody coverwith intermediate fire frequency (burning every three to four years) will require rela-tively high temporal resolution data (∼43 systematically spaced vectors over 14 years).However, if time-series images are not available at a constant interval, the phenologicalcycles of even the less dynamic parts of the landscape (e.g. riparian/mopane wood-lands not subject to disturbances) could not be confidently characterized even at arelatively high temporal resolution (∼43-element vectors) and our monitoring abilityis significantly challenged. Besides temporal dynamics, another characteristic associ-ated with many savanna systems is their fine-scale spatial heterogeneity. In this study,that heterogeneity is exacerbated by a highly interdigested fire history and extremelyhigh spatial and temporal localized variations in precipitation, and thus informs the

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uncertainty in the results of previous studies conducted in southern Africa savanna atmuch lower spatial resolution.

5.2 Effect of time-series temporal depth/spacing on ecological trends

5.2.1 Systematic variation results. The results of harmonic regression with system-atically selected vectors depict that as the temporal depth of EVI vectors in theharmonic regression model is reduced, fewer clusters were found to have a statisti-cally significant trend. The results discussed in this section are illustrated in table 1and figure 6. Compared to 18 clusters with a significant trend observed at a temporal

Table 1. Statistical significance of the trend detected for each EVI cluster at different temporaldepths of EVI vectors selected via the systematic approach.

Temporal depth of EVI vectors/trend value and significance

Cluster 85 43 29 17

1 1.01 × 10−5∗∗ 1.2 × 10−5∗∗ 1.23 × 10−5∗∗ 6.2 × 10−6

2 1.17 × 10−5∗∗ 1.2 × 10−5∗∗ 1.36 × 10−5∗ 7.49 × 10−6∗3 7.29 × 10−6∗∗ 7.9 × 10−6∗∗ 1.28 × 10−6 3.53 × 10−6∗∗4 1.11 × 10−5∗∗ 1.3 × 10−5∗∗ 1.35 × 10−5 1.63 × 10−5

5 6.12 × 10−6∗∗ 7.3 × 10−6∗∗ 7.42 × 10−6∗∗ 7.44 × 10−6

6 1.51 × 10−5∗∗ 1.6 × 10−5∗∗ 1.5 × 10−5∗ 1.87 × 10−5

7 8.44 × 10−6∗∗ 1 × 10−6∗∗ 1.08 × 10−∗∗6 6.01 × 10−6∗∗8 7.67 × 10−6∗∗ 8.9 × 10−6∗∗ 8.79 × 10−6 4.69 × 10−6

9 7.02 × 10−6∗∗ 8.5 × 10−6∗∗ 8.03 × 10−6∗ 1.9 × 10−6

10 2.24 × 10−6∗∗ 3.8 × 10−6∗∗ 3.36 × 10−6 −4 × 10−7

11 8.23 × 10−7 1.6 × 10−6 3.59 × 10−6 2.27 × 10−6

12 −3.31 × 10−6 −2 × 10−6 −1.1 × 10−6 −7 × 10−6

13 −2.53 × 10−6 −1 × 10−6 −1.6 × 10−6 −9.6 × 10−8∗∗14 −3.12 × 10−6∗∗ −3 × 10−6 1.94 × 10−6 −6.3 × 10−6

15 −3.58 × 10−6 −2 × 10−6 −1.5 × 10−6 −7.9 × 10−6

16 −3.77 × 10−6 −1 × 10−6 −4 × 10−7 −7.9 × 10−6

17 9.23 × 10−7 2.4 × 10−6 1.91 × 10−6 −1.7 × 10−6∗∗18 −3.93 × 10−6 −3 × 10−6 −2.4 × 10−6 −6.1 × 10−6

19 −3.49 × 10−6∗∗ −2 × 10−6 −1.9 × 10−6 −6 × 10−6

20 8.13 × 10−6 1 × 10−6 8.54 × 10−6 7.22 × 10−6

21 1.23 × 10−6∗∗ 2.5 × 10−6∗∗ 1.3 × 10−6∗ −2.8 × 10−7

22 −4.92 × 10−7 1 × 10−6 2.31 × 10−7 −3.1 × 10−6

23 1.25 × 10−6 1.9 × 10−6 3.57 × 10−7 −3.8 × 10−7

24 −1.66 × 10−6 4.8 × 10−7 −1.8 × 10−6 −3.8 × 10−6

25 −1.44 × 10−6 −7 × 10−7 −2.6 × 10−6 −2.8 × 10−6

26 2.43 × 10−6 3.3 × 10−6 1.57 × 10−6 6.39 × 10−7

27 −1.89 × 10−6∗ −6 × 10−7 −2.5 × 10−6 −5.3 × 10−6

28 5.66 × 10−6 7 × 10−6 5.8 × 10−6 4.85 × 10−6

29 −4.38 × 10−6∗∗ −2 × 10−6∗ −3 × 10−6∗ −8.2 × 10−6

30 2.32 × 10−6 −2 × 10−7 1.43 × 10−7 −6 × 10−6∗31 5.83 × 10−6 7.8 × 10−6 6.35 × 10−6 3.23 × 10−6

32 1.41 × 10−5∗∗ 1.6 × 10−5 1.37 × 10−5 1.76 × 10−5

33 2.39 × 10−6∗∗ 4.5 × 10−6∗∗ 3.03 × 10−6∗∗ 1.43 × 10−7

34 5.58 × 10−6 7 × 10−6 5.34 × 10−6 3.88 × 10−6

35 1.01 × 10−5∗∗ 1.2 × 10−5∗∗ 1.23 × 10−5∗∗ 6.2 × 10−6∗∗

Note: ∗∗p < 0.01; ∗p < 0.05.

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Figure 6. Magnitude and direction of change in the EVI trend at reduced temporal depthsof EVI vectors. For each EVI cluster, the four-bar plot represents the trend of that cluster attemporal depths of 85-, 43-, 29- and 17-systematically selected vectors, respectively. The barcolour for each cluster represents the interpreted overall direction of change in trend for eachcluster.

depth of full 85-element vector, at reduced temporal depths of 43-, 29- and 17-elementvectors, the number of clusters with a significant trend dropped to 14, 10 and 7 clusters,respectively. Further, only three out of 35 clusters (cluster nos. 2, 7 and 35) depicted asignificant trend at all four temporal depths. Spatially, these clusters represented flood-plain grasses, miscanthus/sedge and riparian woodlands, respectively. Additionally, atreduced temporal depths, few new clusters (i.e. cluster nos. 13, 17 and 30) showedsignificant trends that were depicted to be statistically insignificant initially at fulltemporal depth of 85-element vectors. These clusters were spatially represented bygrasses, acacia shrubbed savanna and riparian woodlands, respectively. It was alsointeresting to note that the trend of most of the riparian woodland-dominated clus-ters (cluster nos. 32, 34 and 35) was significant even at reduced temporal depths of 43-and 29-element vectors. Other clusters having significant trends at these two tempo-ral depths represented channel and floodplain grasses; sedge and hippo grasses; andacacia grassland and island shrub vegetation (cluster nos. 1, 2, 5, 8 and 9).

The effect of reduced temporal depth on the magnitude and the direction of trendwas also analysed. For this purpose, the changes in magnitude and direction of theEVI trends were compared with the changes in magnitude and direction of the trendsobserved with 85-element vectors. In general, with systematic variation in tempo-ral depth, the direction of change in the trend from full to reduced spacing couldbe generalized in five classes: no change, strong positive to positive, no trend topositive/negative trend, negative to strong negative and positive/negative to no trend(figure 6). Further analysis revealed more subtle patterns. Four clusters that displayedno trend with 85-element vectors showed either a negative or a positive trend withreduced temporal depth. Ten clusters that initially depicted either a positive or a neg-ative trend changed to no trend with at least one of the three temporal depths. Thetrend of two clusters changed from strong positive to positive for 29-element vectors,

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Figure 7. Spatial representation of direction of change in trend of EVI clusters. (a) The resultsfrom systematic variation and (b) random variation in temporal spacing of EVI vectors.

and for cluster number 15, the negative trend changed to positive with 29-element vec-tors. Thus, with a lesser number of temporal vectors, the long-term ecological trend ofdifferent portions of the landscape becomes increasingly harder to determine due toincreased data gaps. Since each EVI cluster represented a specific functional vegetationtype, spatial mapping of the five trend variation categories yields a better understand-ing of the ecological response of different vegetation communities (figure 7(a)). Whensystematically varying the temporal resolution of the EVI vectors, clusters spatiallyassociated with savannas (cluster nos. 4, 8, 15 and 31) showed the highest variation intrend followed by clusters co-dominated by woodland (cluster nos. 9, 10, 21 and 32).Clusters representing frequently flooded floodplains (cluster nos. 1, 6, 7 and 33) withstrong positive trends were comparatively stable at different temporal depths. Clustersinitially exhibiting no trend values (cluster nos. 13, 16, 17, 20 and 30) that were spa-tially in the proximity of settlements or were frequently burned or irregularly floodedwere mischaracterized as a negative trend at a reduced temporal depth (figure 7(a)).

5.2.2 Random variation results. To reduce the artefacts associated with randomselection of EVI element vectors, trend values of 100 iterations of harmonic regressionwere averaged at each of the three temporal depths of analysis (figure 8). Six broad

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2.00E-05

1.50E-05

1.00E-05

5.00E-06

0.00E+00

–5.00E-06

–1.00E-05

–1.50E-05

1 2 3 4 5 6 7 8 9 10 21 22 23 24 25 26 27 28 29 30 31 32 33 34 3515 16 17 18

EVI cluster number

No changePositive to strong positiveStrong positive to positiveNo trend to positive / negativeNegative to strong negativePositive to negative / negative to positive

EV

I tr

end

19 2011 12 13 14

Figure 8. Average magnitude and direction of change in EVI trend at reduced temporal depthsof EVI vectors. For each EVI cluster, the four-bar plot represents the average EVI trend of 100iterations calculated from randomly selected vectors at temporal depths of 85-, 43-, 29- and17-element vectors. The bar colour for each cluster represents the interpreted overall directionof change in trend.

categories were defined to summarize trend variations (as opposed to only five cat-egories for systematic variation case). These six categories are spatially representedin figure 7(b). All but two categories were comparable with categories of the sys-tematic variation results (i.e. positive trend to strong positive trend and positive tonegative/negative to positive trend).

Cross-comparison of the trend sensitivity results between systematic (figure 6) andrandom variations (figure 8) revealed important, if nuanced, differences. With system-atic variation, 21 out of 35 clusters depicted no significant changes in trend at all threetemporal depths, whereas with random variation they reduced to 14 clusters. With sys-tematic variation, 29 out of 35 clusters showed no significant changes in trend at both43- and 29-element vectors, whereas with random variation they reduced to 9 clusters.Besides changes in magnitude of the EVI trend, changes in direction of EVI trend werealso more variable for randomly selected vectors. With systematically selected vectors,three EVI clusters changed from no trend to either a positive or a negative trend; thesame increased to 11 EVI clusters when vectors were selected at random temporalspacing. More deviations of EVI trends were observed for many clusters at the 17-element vector level compared with temporal depths of 43- and 29-element vectors.Overall, using randomly selected vectors resulted in greater trend variations observedwithin EVI cluster and across the 35 EVI clusters. Further, the ecological trend estima-tion using randomly spaced time-series vectors at reduced temporal depths producedworse artefacts, where the estimated trend was opposite to that of the actual trend (e.g.EVI clusters 30 and 31 depicted opposite trends compared with those observed with85-element vectors). Thus, reduced temporal resolution of an ecological time serieschallenges the analyst’s ability to characterize landscape response to ecological cycles.Randomly spaced vectors further reduce this capability due to the stochasticity in

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spacing of vectors where more dynamic parts of the landscape (here, e.g. grasslands)are easily mischaracterized. For example, trend values at reduced temporal depthsfor cluster nos. 12, 13, 16 and 23 (that represent a variety of grasslands in the studyarea) deviated in the opposite direction from the initial trend observed using an 85-element vector. Chances of mischaracterizing trends of even more consistent parts ofthe landscape (e.g. woodlands) also cannot be ignored.

5.3 Sensitivity of R2 of harmonic regression to EVI temporal depth and spacing

In earlier research using harmonic regression on 85 EVI vectors, Neuenschwanderand Crews (2008) were able to explain 63–88% variance in 35 EVI temporal clusters.Here, we examined how the variations in EVI temporal depth and spacing affected thecoefficient of determination (R2) of the harmonic regression model. The calculated R2

values for the first iteration of harmonic regression using systematically selected vec-tors at three temporal depths (43, 29 and 17 vectors) are reported in figure 9(a). Withsystematically selected EVI vectors, as the temporal depth was gradually reduced,the R2 values for all clusters increased gradually with the maximum at a temporaldepth of 17 vectors. Spatially, the maximum increase in the R2 values was observed for

Figure 9. Effect of EVI temporal depth and spacing on coefficient of determination of har-monic regression (a) using systematic selection of vectors at four temporal depths and (b) meanof 100 iterations using randomly selected vectors at four temporal depths.

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clusters representing floodplain grasslands and acacia grasslands (cluster nos. 2 and8). Additionally, for portions of the landscape with initial moderate R2 values (rep-resented by shrubbed savanna, dry grasses and acacia thickets) and high R2 values(represented by hippo grass, shrubbed woodland and mopane woodland), the R2

increased further to reach (artificially) higher values (figure 9(a)). The range of R2

values also decreased with decreasing temporal depth. Similar analysis was performedusing EVI vectors selected at random temporal spacing. Given the artefacts associatedwith randomly selected vectors, the mean R2 values of 100 iterations were calculatedfor each EVI cluster at the same three temporal depths. These mean R2 values of the100 iterations (figure 9(b)) were then compared with the R2 values of systematicallyselected vectors (figure 9(a)). Again, the results indicated higher R2 values at reducedtemporal depths for all clusters with resultant R2 values for harmonic regression (using85- and 17-element vectors). Using randomly selected EVI vectors at temporal depthsof 43-and 29-element vectors, the R2 values of 100 iterations tended to lose variabil-ity due to averaging of values. The R2 value for the majority of these clusters wasclose to the R2 value attained using 85-element vectors. However, the difference is stillclearly perceptible for results using 17-element EVI vectors where all the EVI clustershave higher R2 values compared with 85-element vector results. Overall, statistically,at reduced temporal depths, the harmonic regression appeared to explain more vari-ance in the time-series data and appeared to be a more robust model, when in fact thewide temporal spacing eliminated observable cycles that were reduced to lower noisein the 17-element case. So, ironically, the apparent statistical significance increasesdespite the ecological significance (or accuracy/reliability) being greatly reduced forspatially heterogeneous and temporally fluctuating environment (e.g. floodplains andsavannas). It is imperative to make a note that statistical significance is not necessarilyecological significance, and results from inadequately spaced observations can greatlymischaracterize the landscape processes and dynamism.

6. Conclusions

This research furthers a relatively new dimension to the way high spatial resolutiontime-series data have been utilized in ecological research. These results have broadsignificance for studies involving time-series analysis and particularly serve as a refer-ence for future research seeking to characterize both short- and long-term ecologicalcycles. Overall, the results depict that as the time-series temporal depth decreases, sen-sitivity to both short- and long-term ecological cycles is lost in seasonally dynamicenvironments. Further with the same temporal depth but with randomly spaced time-series vectors, the results are significantly different because of the stochasticity inimage selection, mimicking the problem researchers’ face when anniversary or sea-sonal imagery is not available. Further, this sensitivity varies spatially depending onthe functional type of vegetation and dynamics of disturbance regime(s) on the land-scape. This study shows that in the southeastern distal region of the Okavango Delta,ecological cycles were comparatively better characterized, even at reduced temporaldepths, for woodland-dominated areas and more frequently flooded areas. However,less routinely and non-flooded grasslands, bush-dominated savannas and more fre-quently burned areas were very sensitive to the temporal depth of ecological timeseries. The reduced explanatory power for slightly and moderately reduced vectorswas anticipated; what was unexpected was that for the highly reduced element vectors,the R2 value was higher than the more accurate 85-element vector results.

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An important recommendation from this work is that when working in seasonallydynamic or temporally variable environments, annually or biannually comprised timeseries that appear highly statistically significant likely are not so but rather are simplyunderspecifying the model. Determination of a long-term ecological trend necessar-ily depends on the richness and depth of a time series. These results illustrate howreduced temporal depth and/or spacing causes the estimation of a long-term trendthat tends to drift away from the actual trend. The chances of mischaracterizing trendsare highest with reduced temporal depths and randomly selected vectors, where aninitial positive trend could be characterized as negative and vice versa. Further, forlong-term trend monitoring, time series of 14 years are likely insufficient as climaticcycles also operate at larger intervals (Turner et al. 2001), but remote-sensing sci-entists are limited by the historical availability of synoptic spaceborne or airborneinformation. Owing to practical limitations, perhaps the use of more high temporalresolution images (e.g. MODIS) will continue to be favoured by scientists for moni-toring long-term ecological cycles and trends. But the results of coarse-scale data sets(more suitable for regional-scale monitoring) should not be taken as surrogates of eco-logical characteristics at landscape level that is shaped by much finer-scale ecologicaldynamics. Even at coarser resolution, time-series data sets are often developed usinga standard compositing period that typically varies between 16 days and 3 months(Vancutsem et al. 2007, Hüttich et al. 2011). Hence, studies should select a data setdeveloped using a compositing period that suitably represents the temporal dynamicsof the landscape under study. Further studies assessing the relative impacts of tempo-ral spacing and depth using high spatial resolution data in seasonal environments areneeded in similarly dynamic systems to ascertain whether the results here are broadlyapplicable across such systems and to avoid misleading or even incorrect interpre-tations (Schafer 1993, Shaver 1993, Johnson 1999). However, we contend that theseresults necessarily obtained in a particular ecosystem in fact reach a more overarching,generalizable and ecologically informed standard: image time-series depth and spacingmust be assessed with regard to the inherent periodicities of processes at work in thelandscape.

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