Seasonal variation of the vegetated land surface across tropical South America was evaluated using Trajectory Analysis (TA) on the Pathfinder AVHRR Land (PAL) NDVI data. These 8 km 10-day maximum-value composite images of the Normalized Difference Vegetation Index (NDVI) span nearly two decades (7/81–12/99) that include several ENSO warm/cold phases. The derived trajectory established a baseline to assess the effect of climatic events related to the El Niño/Southern Oscillation (ENSO) on the temporal development of the spatial dependence structure of the NDVI image time series. Results indicate that ENSO phases have significant effects on the spatial dependence structure of the land surface in Tropical South America that would be undetected, if the spatial domain of remotely sensed data were neglected. As such, TA provides an important technique for the assessment of the effects of global change and long-term land use/land cover transformations on phenologies of the vegetated land surface.
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 Tropical terrestrial ecosystems are subjected to substantial inter-annual climatic variability owing to El Niño Southern Oscillation (ENSO) cycles, particularly due to frequent El Niño episodes [Tian et al., 1998]. An ENSO cycle is composed of (1) a warm phase (El Niño) characterized by a significant warming of the sea surface temperature (SST) in the Tropical Pacific Ocean and a breakdown of the easterly trade winds, (2) a cold phase (La Niña), characterized by a significant cooling of the SST and a strengthening of the easterly trade winds, and (3) an interphase between these extremes [Trenberth, 1997]. Several indices to measure the onset, duration and termination of ENSO cycles have been proposed and are operational. One of such indices is the SST anomaly for a region in the eastern Tropical Pacific designated Niño 3.4 region (5°N–5°S and 120°W–170°W). This index has been proven to be a suitable quantitative estimation of ENSO phases, detecting the onset of El Niño or La Niña, if anomalies beyond ±0.4°C are maintained during more than six consecutive months [Trenberth, 1997] (Figure 1).
 The dynamics of the vegetated land surface can be related to climatic variations induced by ENSO extremes [Myneni et al., 1996; Anyamba and Eastman, 1996; Liu and Juarez, 2001; Mennis, 2001; Seiler and Kogan, 2002], because vegetation integrates the recent conditions in the atmospheric boundary layer [Peters et al., 2002]. Therefore, synoptic monitoring of vegetation dynamics, now enabled by the constellation of satellite remote sensing systems, provides a way to analyze spatio-temporal effects of ENSO extremes. One such system is the series of Advanced Very High Resolution Radiometer (AVHRR) sensors on-board the National Oceanic and Atmospheric Administration (NOAA) Polar-orbiting Operational Environmental Satellites (POES). The temporally composited observations of the Normalized Difference Vegetation Index (NDVI)—defined as the difference between the reflectance in the near-infrared and red channels normalized by their sum—are available from the AVHRR at 8km spatial resolution since mid-1981. The AVHRR NDVI has been widely used to evaluate the variability of surface vegetation at regional and global scales across a range of temporal resolutions [Tucker, 1979; Holben, 1986; Prince and Tucker, 1986; Los et al., 2000].
 AVHRR NDVI has been associated with SST anomalies with some success [Anyamba and Eastman, 1996; Myneni et al., 1996; Batista et al., 1997; Liu and Juarez, 2001], although problems arise due to short time periods of analysis, non-constancy of atmospheric conditions, and thus inter-image calibration issues [Simoniello et al., 2004], non-linear influences of ENSO cycles on vegetation condition [Mennis, 2001; Peters et al., 2003], and loss of sensitivity of NDVI at intermediate to high vegetation cover density [Gitelson et al., 1996; Gitelson, 2004; Viña et al., 2004]. Since climatic modes have regional effects on the vegetation [Kogan, 2000], both the per-pixel NDVI values and the relationships among pixels—their spatial dependence—may be affected. Therefore, the magnitude and direction of the deviations from baseline NDVI and spatial dependence values may be used to evaluate the extent of the impact of particular climatic episodes, such as strong ENSO phases, on the vegetation and its seasonality.
 Metrics that describe relationships among pixel values are more resistant to the effects of changing illumination, atmospheric conditions, and other sources of ephemeral noise than the direct comparison of pixel values through time [Henebry, 1993; Henebry and Su, 1993]. Trajectory Analysis (TA) offers an alternative approach to enhance signal amidst these competing sources of noise through a process of characterization of spatial pattern through time and application of an accumulative anomaly filter. The technique consists of first decomposing an image into two complementary aspects of spatial structure: spatial dependence (SD) and spatial heterogeneity (SH). SD pertains to the degree of spatial autocorrelation among the elements of the spatial data (e.g., pixels in raster data sets), while SH pertains to the dynamic range available to allocate the values among the elements of the spatial data. Second, a time series of images portraying the same geographic area is transformed into a trajectory by plotting the SD-SH decomposition of each image as time-ordered coordinates in an SD-SH metric space [Henebry and Su, 1993]. Third, anomalies in the trajectory are identified and summed within a moving temporal window. The main goal of this study was to evaluate the interannual variability of vegetation in Tropical South America using TA on a long NDVI image time series (1981–1999) to identify anomalies within the data record that can be related to ENSO cycles.
2.1. Study Area
 The selected area for this study was Tropical South America, the land area falling within 20° North and South of the Equator, including all or some part of ten countries (Colombia, Ecuador, French Guiana, Guyana, Peru, Suriname, Venezuela, and portions of Bolivia, Brazil and Paraguay). The dominant vegetation types are (1) lowland broadleaf moist forests (several types) of the Amazon basin, (2) seasonal woodland and grassland savannas of the Orinoco basin (Colombia and Venezuela), southern Brazil, northeastern Paraguay and eastern Bolivia, and (3) agricultural areas scattered throughout the region. Seasonality of precipitation over Tropical South America is driven primarily by the dynamics of the Inter-Tropical Convergence Zone, although it is also affected by climate modes, principally ENSO [Nimer, 1979].
2.2. AVHRR NDVI Data
 The study used the NASA Pathfinder AVHRR Land (PAL) dataset, a 10-day AVHRR NDVI Global Area Coverage (GAC) Maximum Value Composite (MVC) image time series, with a resolution of 8 km by 8 km(=316,470 pixels per image) for the period between July 1981 and December 1999. Although this dataset has recognized calibration problems induced mainly by satellite orbital drift and lack of correction for atmospheric scattering and water vapor absorption, it is still very useful for analysis given its global extent, high temporal frequency, long temporal record, and free availability. A total of 654 images were analyzed, three for each month of the period studied, with the exception of the months of September–December of 1994, due to the failure of the AVHRR sensor onboard the NOAA 11 satellite.
2.3. Spatial Dependence Metric
 To characterize spatial dependence in the image time series, we used a scale of fluctuation (SOF) technique [Vanmarcke, 1983] modified by Henebry  to estimate spatial correlation length. A key advantage of SOF is intensive resampling, which results in a distribution of estimates of spatial dependence. The distribution gives a more robust description of spatial structure than a single estimate.
 The SOF algorithm has six steps. First, a single transect is built up from a random walk within the image and the variance along this transect is calculated. Second, this transect is smoothed with a moving-average of nearest neighbors, the variance of the smoothed transect is calculated and normalized (divided) by the variance of the original transect, and the normalized variance is then weighted (multiplied) by the size of the moving-average window, which puts the metric into the units of the data's spatial resolution. Third, the neighborhood of the moving-average window is successively enlarged and the variance of each successively smoothed transect is calculated and normalized. Fourth, the weighted normalized variances are plotted as a function of the moving-average window size. Fifth, if the data exhibit a stationary pattern of spatial dependence, then the plot will approach a plateau, which is the SOF or correlation length. Patchiness within the image usually produces a plot with an initial peak in the SOF value and a subsequent decay. Some approximation to the peak or plateau can be used as an estimate of the predominant SOF (Figure 2). Sixth, the image is resampled by many random walk transects to generate a sampling distribution of SOF values to characterize the image's spatial dependence.
 In this study, the SOF was estimated for 1,000 random-walk transects for each NDVI image. Each random-walk transect covered an area corresponding to 10% of the total study area. An average trajectory was obtained by plotting the mean SOF and NDVI values of each image as time-ordered coordinates in a SOF-NDVI metric space. The outliers of this average trajectory were identified as greater or lesser than two standard errors from the mean (2 SEM) and then integrated (summed) within moving windows of 3 months (9 consecutive images) or 12 months (36 consecutive images). Outlier trajectories were visualized by plotting the time-integrated outliers in the SOF domain against those in the NDVI domain, thereby revealing the cumulative effects of unusual occurrences in the spatial structure of the image time series.
3. Results and Discussion
 The baseline trajectory of the study area exhibited seasonality in both NDVI and SOF: higher average NDVI values occurred between May and July and lower NDVI values between August and March. In contrast, monthly average SOF values were higher between July and September and lower between February and May (Figure 3).
 Three-month accumulated anomaly trajectories for the study period capture two unique periods in the image time series. First, a significant persistent deviation that began with the first 10-day composite in August 1991 following the eruption of Mt. Pinatubo in June 1991 (Figure 4, black triangles). This event induced a persistent reduction in NDVI values together with an increase in SOF values. Second, the decay and failure of the AVHRR sensor on NOAA-11 in 1994, which induced a persistent increase in NDVI values and a reduction in SOF values (Figure 4, white squares). Ignoring these extreme event periods (8/91–8/92 and 4/94–9/94), the remaining trajectories revealed significant persistent deviations across the study area that correspond to the strong Warm Phase (El Niño) of 1982–83 and the strong Cold Phase (La Niña) of 1989. On the one hand, the effects of El Niño of 1982–83 across the study area decreased the NDVI values and slightly increased the SOF values (Figure 4, gray circles), as a response to the drought conditions caused by the inhibition of the convective activity associated to ITCZ in most of the north-northeast of South America [De Souza and Ambrizzi, 2002]. On the other hand, La Niña of 1989 is associated with near normal NDVI values, but a decrease in SOF values (Figure 4, gray diamonds).
 Long-term accumulation of anomalies can be used to establish the persistent effects of climatic variability on vegetation. Twelve-month accumulated anomalies show the persistent effect of ENSO cycles on the vegetation of tropical South America (Figure 5). El Niño (La Niña) years tend to exhibit persistent positive (negative) anomalies in the SOF, which are associated with increases (reductions) in spatial dependence. These patterns could be explained by the extensive reduction in precipitation during El Niño years, associated with a reduction in cloud cover, and normal to higher precipitation values during La Niña years [Trenberth and Hoar, 1997; Poveda et al., 2005]. Previous studies [e.g., Kogan, 2000] reported that the vegetation of northern South America experience severe moisture and thermal stress in boreal winter during El Niño years, but no distinct differences were observed for La Niña years. This study shows that years under La Niña conditions exhibit opposite trends to those of El Niño years, with persistent negative outliers in SOF, characteristic of lower spatial dependence (Figure 5). The strong positive SOF anomaly observed during the 1991–1992 period is likely associated with an interaction of Pinatubo's atmospheric effects and the dry conditions induced by El Niño of 1991–1992.
 The incorporation of the spatial domain into the analysis provides insights into the climate-vegetation dynamic not evident when viewing NDVI aspatially. Average trajectories plotted in an SOF-NDVI metric space show a seasonal variability that cannot be seen with NDVI data alone. An average trajectory describes an appropriate baseline for change analysis. Deviations from the study area's average trajectory suggest that ENSO phases have significant effects on SOF variation and, thus, on the spatial dependence of the vegetation in Tropical South America. Trajectories in metric spaces constitute valuable monitoring tools for detecting changes in the vegetated land surface that are entangled with variations of climatic conditions, and which might go undetected if analyses of the data's spatial domain were neglected.
 TA enables the identification of an average spatio-temporal structure in image time series that could be used to assess significant deviations from this expectation. In this study, deviations in the spatio-temporal structure of the AVHRR NDVI time series of tropical South America were found to be associated with ENSO cycles. TA holds promise as a powerful algorithm for ecological forecasting [Clark et al., 2001].
 In addition to providing information on the impact of climatic variability on the vegetation of Tropical South America, this study illustrated the value of tracking the changing spatial structure within an image time series. To harness observational datastreams for effective change analysis, additional research is needed into theory about information content in image time series and practical techniques to implement spatio-temporal analyses.
 We thank the anonymous reviewers for prodding us to increase the manuscript's clarity. We acknowledge support from NSF Biodiversity and Ecosystem Informatics (BDEI) grant # EIA 0131937. The image data used were produced through funding from the EOS Pathfinder Program of NASA's Mission to Planet Earth in cooperation with NOAA. Data were obtained from EOSDIS DAAC at Goddard Space Flight Center. A contribution of the University of Nebraska Agricultural Research Division, Lincoln, NE, Journal Series No. 14531.